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Vibrational imaging and microspectroscopies based on coherent anti-Stokes Raman

scattering microscopy

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2005 J. Phys. D: Appl. Phys. 38 R59

(http://iopscience.iop.org/0022-3727/38/5/R01)

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 38 (2005) R59–R81 doi:10.1088/0022-3727/38/5/R01

TOPICAL REVIEW

Vibrational imaging andmicrospectroscopies based on coherentanti-Stokes Raman scattering microscopyAndreas Volkmer

3 Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

E-mail: a.volkmer@physik.uni-stuttgart.de

Received 4 November 2003, in final form 21 November 2004Published 18 February 2005Online at stacks.iop.org/JPhysD/38/R59

AbstractFor noninvasive characterization of chemical species or biologicalcomponents within a complex heterogeneous system, their intrinsicmolecular vibrational properties can be used in contrast mechanisms inoptical microscopy. A series of recent advances have made coherentanti-Stokes Raman scattering (CARS) microscopy a powerful technique thatallows vibrational imaging with high sensitivity, high spectral resolution andthree-dimensional sectioning capability. In this review, we discusstheoretical and experimental aspects of CARS microscopy in a collinearexcitation beam geometry. Particular attention is given to the underlyingphysical principles behind the new features of CARS signal generationunder tight focusing conditions. We provide a brief overview of theinstrumentation of CARS microscopy and its experimental characterizationby means of imaging of model systems and live unstained cells. CARSmicroscopy offers the possibility of spatially resolved vibrationalspectroscopy, providing chemical and physical structure information ofmolecular specimens on the sub-micrometre length scale. We reviewmultiplex CARS microspectroscopy allowing fast acquisition offrequency-resolved CARS spectra, time-resolved CARS microspectroscopyrecording ultrafast Raman free induction decays and CARS correlationspectroscopy probing dynamical processes with chemical selectivity.

1. Introduction

A subject of great interest in the physical and life sciencesis the noninvasive characterization of mesoscopic objectswithin a complex heterogeneous system through opticalmicroscopy. In recent years, the emphasis has been onthe development of microscopy techniques with the goalof achieving three-dimensional imaging with high spatialresolution, high sensitivity and high chemical selectivity. Inparticular, fluorescence microscopy with three-dimensionalsectioning capability by means of confocal detection [1] ormulti-photon excitation [2, 3] has become a powerful tool inbiological research [4, 5]. Chemical selectivity is providedby labelling with natural or artificial fluorescent probes [6, 7].

For chemical species or biological components that eitherdo not fluoresce or cannot tolerate the toxicity associatedwith staining and the photo-bleaching of fluorophores [8],their intrinsic molecular vibrational properties can be used ascontrast mechanisms. Infrared imaging [9] and spontaneousRaman imaging [10] are two prevalent methods in vibrationalmicroscopy. The former is limited to low spatial resolutionsdue to the longer wavelength involved and the vibrationalabsorption of the common solvent, water. Spontaneous Ramanscattering microscopy with laser excitation in the visible andnear-infrared avoids this problem. However, it is often limitedby the weak Raman scattering cross section, which necessitateshigh laser powers, and by the presence of an auto-fluorescencebackground.

0022-3727/05/050059+23$30.00 © 2005 IOP Publishing Ltd Printed in the UK R59

Topical Review

The signal-to-background limitations inherent to spon-taneous Raman detection schemes can be circumvented bythe use of a nonlinear process that significantly enhances theRaman scattering signal. As such, surface-enhanced Ramanscattering has been demonstrated to provide single-moleculedetection sensitivity [11, 12], but requires the addition of col-loidal metal particles to the system and lacks the reproducibilityof enhancement efficiency. In an alternative attempt, coherentanti-Stokes Raman scattering (CARS) has been combined withoptical microscopy. Because of its coherent nature, in whichthe molecular bonds oscillate in phase and interfere construc-tively, and its active pumping of the vibrational states, theCARS signal is at least five orders of magnitude more sensitivethan spontaneous Raman scattering. Although it is not possibleto detect a single vibrational mode at room temperature, it isfeasible to detect a macromolecule with thousands of identicalvibrational modes that interfere coherently.

CARS was first reported in 1965 by Maker and Terhune[13] and has been used extensively as a spectroscopic toolfor chemical analysis in the condensed and gas phases[14–17]. Other nonlinear coherent optical processes, such assecond-harmonic generation (SHG) [18–20], sum-frequencygeneration [21], third-harmonic generation [22–24] and theoptical Kerr effect [25], have also been combined withscanning microscopy. Among them sum-frequency generationprovides vibrational contrast, but this technique is surface-sensitive instead of bulk-sensitive. For all techniques,ultrashort pulses of high peak powers and moderate averagepower are required for efficient signal generation. Theseare readily available using state-of-the-art Ti : sapphire lasertechnology.

In 1982, Duncan et al [26, 27] first reported CARSmicroscopy using a noncollinear pump and Stokes visibledye laser beams and a two-dimensional detector to recordthe anti-Stokes beam in the phase matching direction. Theuse of visible light resulted in a large two-photon enhancednonresonant background signal. Zumbusch et al [28] revivedCARS microscopy in 1999 by using tightly focused collinearlypropagating a pump and Stokes near-infrared laser beams anddetecting CARS in the forward direction. CARS microscopyhas been demonstrated to provide the following advantages:(i) It does not require fluorescent probes. (ii) Since there isno population of electronic excited molecular states, photo-bleaching and damage to biological samples are suppressed.(iii) It is much more sensitive than spontaneous Ramanmicroscopy, requiring only a moderate average power forexcitation. (iv) Being a nonlinear microscopy with signalgeneration confined to the focal volume, it exhibits a three-dimensional sectioning capability similar to that of multi-photon-induced fluorescence microscopy. (v) The use ofnear-infrared excitation minimizes sample heating due tothe lack of water absorption, significantly reduces two-photon enhancement of the nonresonant background third-order susceptibility and provides a deep penetration depth forimaging through thick tissues or cells.

However, it is important to realize that, unlike influorescence detection, CARS detection is not background-free. Electronic contributions to the third-order susceptibilityfrom the sample and the solvent cause a nonresonantbackground signal, which provides no vibrational contrast.

In addition, the solvent water has strong resonant signalsof broad spectral width. Both background signals oftenoverwhelm the CARS signal from small objects and limit thesensitivity.

During recent years, various methods have been developedthat permit efficient suppression of nonresonant backgroundsignals in CARS microscopy. These include epi-detection[29, 30], counter-propagating CARS [31], polarization-sensitive detection [32], pulse-sequenced detection [33] andthe implementation of coherent control techniques [34].Another significant advance in not only increasing the sen-sitivity but also in providing high spectral resolution of CARSmicroscopy involved the use of narrow-bandwidth excita-tion pulses from two synchronized picosecond Ti : sapphirelasers instead of femtosecond broad-bandwidth excitation[30, 35, 36]. Progress has been made to develop less complexand more cost-efficient single-laser narrow-bandwidth excita-tion schemes, including the use of nonlinear fibres [37, 38] andpulse-shaping schemes [34]. Furthermore, implementation oflaser beam scanning with CARS microscopy has been demon-strated to provide high image acquisition rates, allowing thevisualization of fast dynamical processes [39, 40].

Unlike in fluorescence or incoherent Raman microscopy,the contrast mechanism in CARS microscopy is governed bythe coherent sum of both the resonant and nonresonant CARSradiations of the sample and/or the solvent. An amount oftheoretical work that takes the distinct coherent features ofsignal generation in CARS microscopy into account has beenpublished [29, 31, 41–44].

Based on the above advances, CARS microscopy hasemerged as a highly sensitive analytical tool for vibrationalimaging of C–H stretch vibrations [28, 39, 40, 45–49] andC–C skeletal vibrations in lipids [50, 51], of O–H stretchvibrations in water [48, 49, 52, 53] and of Raman modes withinthe spectral fingerprint region of proteins [30, 32, 54]. CARSimaging has been used in chemical mapping of live unstainedcells [28–30, 32, 39, 40, 45, 52, 54, 55], of lipid membranemodel systems [46–51], of silica nanoparticle suspensions [53]and of patterned polymeric photoresist film [56].

Beyond imaging, the combination of CARS microscopywith spectroscopic techniques has been used for investigationof the chemical and physical structure of sub-micrometresized samples. As such, multiplex CARS microspectroscopywith high spectral resolution was applied to monitoringthe thermodynamic state of phospholipid bilayer systemsvia their characteristic CARS spectra [46, 50, 51, 57]. Inthe time domain, the ability to record the ultrafast Ramanfree induction decay (RFID) of a microscopic samplewas demonstrated with high temporal resolution [33].Furthermore, CARS correlation spectroscopy was developed,which can probe three-dimensional diffusion dynamics withchemical selectivity [58, 59].

By taking advantage of optical heterodyne detection(OHD) in CARS microscopy, the detection sensitivity ofa single lipid monolayer [57] and a bilayer [47] has beenaccomplished using the CARS contrast from the C–D and C–Hstretch modes, respectively. The number of CH2 groups in theexcitation volume was estimated to be ∼4.4 × 106 [47].

Variants of collinear CARS microscopy also havereported, including the BOXCARS geometry [41], wide-field

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(nonconfocal) CARS microscopy [60] and near-field scanningoptical microscopy using a fibre probe [61] and a metal tip [63].

Because a comprehensive feature article devoted to theabove advances in instrumentation, theory and predominantlybiological applications of CARS microscopy is readilyavailable [64], most of this review is dedicated to theunderlying physical principles behind both CARS imagingand CARS microspectroscopy, with chosen examples takenfrom recent literature. This paper is organized as follows:sections 2 and 3 start out with a brief review of the fundamentaltheory of CARS in general and of the signal generation incollinear CARS microscopy in particular. This identifiesthe analogies between conventional CARS spectroscopy andCARS microscopy, while concurrently indicating the distinctnew features of CARS under tight focusing conditions.Section 4 gives an overview of the instrumentation inCARS microscopy and its experimental characterization bymeans of imaging of model systems. Sections 5 and 6are dedicated to the principles behind and applications ofCARS microspectroscopies in the frequency domain and timedomain, respectively, while CARS correlation spectroscopyis discussed in section 7. A summary and a brief outlookconclude this review.

2. Fundamentals of coherent anti-Stokes Ramanscattering

2.1. Basic theory

CARS is a four-wave mixing process involving three laserpulses, i.e. the pump, probe and Stokes pulses with centrefrequencies at ωp, ωp′ and ωS (ωp > ωp′ > ωS), respectively.The respective electromagnetic fields with amplitudes Ep, Ep′ ,ES and wave vectors kp, kp′ , kS interact with the sampleand induce a third-order nonlinear polarization, which is mostgenerally described by [14, 65]

P(3) = P(3)nr +∑

r

P(3)r =(

χ(3)nr +∑

r

χ(3)r

)EpEp′E∗

S.

(1)

P(3) is a source of coherent radiation at the CARS frequencyωAS = ωp + ωp′ − ωS, being higher than the input frequencies,provided phase-matching is fulfilled.

χ(3)r is a complex quantity, χ(3)r = χ(3)r ′+ iχ(3)r ′′

,and represents the Raman response of the molecules. Theinduced polarization, P(3)r , is resonantly enhanced when theRaman shift, ωp − ωS, coincides with the frequency, r ,of the rth Raman-active molecular vibration (figure 1(a)).Therefore, χ(3)r provides the intrinsic vibrational contrastmechanism in CARS microscopy. The sum extends over allr molecular Raman transitions that are coherently preparedby the pair of pump and Stokes pulses. The nonresonantterm χ(3)nr represents the electronic response of both the one-photon (figure 1(a)) and two-photon (figure 1(b)) electronictransitions [16]. With input laser pulse frequencies awayfrom one- and two-photon electronic resonances, χ(3)nr isessentially independent of frequency and is a real quantity. Itis important to realize that in contrast to P(3)r , the concurrentnonresonant polarization, P(3)nr , is simply a source for an

Figure 1. Energy level diagrams for (a) the Raman-resonant andnonresonant one-photon electronic contributions and (b) for thenonresonant two-photon enhanced electronic contributions to theCARS process. v denotes the vibrational state of a Raman modewith resonance frequency r . g and e indicate the electronic groundand excited states, respectively. (c) Polarization vector geometry forthe pump field (Ep), Stokes field (ES), nonresonant CARSpolarization (P(3)nr ), CARS polarization of the rth Ramanresonance (P(3)r ) and the unit vector indicating the direction ofanalyser transmission (eA).

unspecific background signal limiting the sensitivity of CARSdetection.

More explicitly, if monochromatic and linearly polarizedinput fields that collinearly propagate in the z direction areconsidered, the induced polarization of equation (1) can beexpressed by its ith Cartesian components,

P(3)i (ωAS) = 6

m!

∑jkl

χ(3)ijkl(−ωAS; ωp, ωp′ , −ωS)

×Ej(ωp)Ek(ωp′)El(ωS)∗. (2)

m is equal to the number of identical input frequencies iffrequency degeneracy applies. The indices of the total CARSsusceptibility tensor components, χ

(3)ijkl = χ

(3)nrijkl +

∑r χ

(3)rijkl ,

refer in their order of appearance to the Cartesian polarizationcomponents of the CARS, pump, probe and Stokes fields. Formedia with isotropic symmetry, such as liquids, only threeresonant tensor elements are independent, from which the othercomponents can be derived [66],

χ(3)1111 = χ

(3)1122 + χ

(3)1212 + χ

(3)1221. (3)

In transparent and optically inactive media, where theinput frequencies are away from any electronic transitionfrequencies, and only the molecular ground state is populated,the selection rules of both resonant CARS and spontaneousRaman scattering are identical [67, 68]. Accordingly, fora given Raman-active resonance r , the amplitudes of χ

(3)rijkl

can be expressed in terms of the isotropy and symmetricanisotropy invariants of the corresponding spontaneous Ramanscattering tensor, α2 and γ 2

s , respectively [67–69]. In thecase of frequency-degenerate CARS (ωp = ωp′ and m = 2,see below), permutation of Cartesian indices results inχ

(3)1122 = χ

(3)1212, and the two independent tensor components

assume the following form [67, 68]:

χ(3)r1111 = Ar,1111

δr − ir

= CNr

α2 + (4/45)γ 2s

δr − ir

, (4)

χ(3)r1221 = Ar,1221

δr − ir

= CNr

(1/15)γ 2s

δr − ir

. (5)

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δr = r − (ωp − ωS) is the detuning from the rth Ramanresonance at frequency r with a half-width at half maximum(hwhm) of r . N is the number density of Raman-activescatterers, and C is a proportionality constant.

The ratio between the susceptibility components,χ

(3)1221/χ

(3)1111, defines the resonant and nonresonant depolariza-

tion ratios,

ρr = χ(3)r1221

χ(3)r1111

= 3γ 2s

45α2 + 4γ 2s

and ρnr = χ(3)nr1221

χ(3)nr1111

,

(6)

respectively. ρr is the direct CARS analogue for thespontaneous Raman depolarization ratio of the rth Ramanmode, with values ranging between zero for an isotropicvibrational mode symmetry and 0.75 for an anisotropic one.In contrast, ρnr has no spontaneous Raman analogue. Forthe nonresonant background susceptibility tensor components,Kleinman’s symmetry conjecture holds [70],

χ(3)nr1111

3= χ

(3)nr1122 = χ

(3)nr1212 = χ

(3)nr1221 , (7)

and ρnr in equation (6) assumes the value 13 .

CARS involving three independently tunable laser beamswas first demonstrated by Bloembergen and co-workers[65, 71], and was subsequently combined with polarization-sensitive detection by Koroteev and co-workers [69, 72].Three-colour CARS was demonstrated to be advantageous intime-domain CARS experiments using a collinear input beamgeometry [73, 74]. The latter has been implemented in time-resolved CARS microspectroscopy [33] and will be discussedin more detail in section 6.

2.2. Frequency-degenerate polarization CARS

For ease of experimental implementation, pump and probefrequency-degenerate (i.e. ωp = ωp′ ) polarization CARSrequiring only two laser beams at different frequencies ismost commonly applied. The corresponding theory has beenreported elsewhere [75, 76]. Briefly, the polarization geometryshown in figure 1(c) is considered. The pump field, Ep, islinearly polarized along the x axis and forms an angle φ

with the linearly polarized Stokes field, ES. Both fieldsare propagating along the z axis. As a result, P(3)nr andP(3)r are linearly polarized at an angle α = tan−1(ρnr tan φ)

and βr = tan−1(ρr tan φ) relative to the x axis, respectively.According to equations (1)–(7), the vector components of thetotal induced polarization, P(3), can then be written as [75, 76]

P (3)x = 3

(χ

(3)nr1111 +

∑r

χ(3)r1111

)E2

pE∗S cos φ, (8)

P (3)y = 3

(ρnrχ

(3)nr1111 +

∑r

ρrχ(3)r1111

)E2

pE∗S sin φ. (9)

Regarding the following discussion of nonresonantbackground suppression, it is convenient to project the CARSpolarization components of equations (8) and (9) onto the

directions parallel and perpendicular to P(3)nr , i.e.

P(3)|| = 3 cos φE2

pE∗S

cos α

(χ

(3)nr1111 +

∑r

(cos2 α +

ρr

ρnr

sin2 α

)χ

(3)r1111

),

(10)

P(3)⊥ = −3 sin α cos φE2

pE∗S

∑r

(1 − ρr

ρnr

)χ

(3)r1111. (11)

The detected signal intensity of the polarization-sensitiveCARS radiation passing an analysing polarizer set at an angle ε

relative to P(3)nr is thus given by

ICARS(α, φ, ε) ∝ |P(3) · eA|2 = |P(3)|| cos ε − P(3)

⊥ sin ε|2.(12)

The unit vector eA = (cos ε, − sin ε) denotes the directionof transmission of the analyser. Finally, substitutingequations (10) and (11) into (12) yields [75, 76]

ICARS ∝(

3 cos φE2pE

∗S

cos α

)2

X(α, ε, χr, χnr), (13)

where

X(α, ε, χr, χnr) =[(χnr)2 cos2 ε +

∑r

f 2r |χr |2

+2χnr cos ε∑

r

frχr ′

+ 2∑r =s

frfs(χr ′χs ′

+ χr ′′χs ′′

)

]

(14)

is the modulus square of the coherent sum of susceptibilitycomponents χ

(3)r1111 and χ

(3)nr1111 . To simplify the notation, all

subscripted indices (1111) and the superscripts indicating thethird-order process in the susceptibilities have been droppedand will be omitted. The coefficient

fr = cos ε

(cos2 α +

ρr

ρnr

sin2 α

)+

sin 2α sin ε

2

(1 − ρr

ρnr

)(15)

accounts for the polarization control of the experiment and forthe depolarization properties of the rth Raman mode of thesample.

With regard to the analysis of experimental data, it isuseful to eliminate the proportionality constants and laseramplitudes involved in the absolute intensity of equation (13)by normalization with a nonresonant reference intensitymeasured under identical experimental conditions,

I refCARS ∝

(3 cos φE2

pE∗S

cos α

)2

(χnrref)

2. (16)

The normalized CARS signal is given by

ICARS

I refCARS

=(

χnr

χnrref

)2 [cos2 ε +

∑r

f 2r

∣∣∣∣ χr

χnr

∣∣∣∣2

+ 2 cos ε∑

r

fr

χr ′

χnr

+2∑r =s

frfs(χr ′

χs ′+ χr ′′

χs ′′)

(χnr)2

]. (17)

As a consequence, the amplitudes in the nonlinearsusceptibilities of equation (4) are scaled by the constant(χnr)−1 of the sample, i.e. Ar/χ

nr .

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Ωr–(ωp–ωS)

––

(χnr)2 + |χr|2 + 2χnrχr

–1

Figure 2. Typical CARS spectral profile modelled for an isolatedLorentzian Raman band assuming equation (4) (r = 4.6 cm−1,Ar = 4 cm−1) and parallel-polarized input and CARS fields(φ = α = 0). According to equation (14), the total CARS spectrum(——) is composed of a constant nonresonant background (χnr )2, aresonant contribution |χr |2 and a heterodyne term of dispersivecharacter, 2χnrχr ′

.

It is instructive to discuss equations (13)–(17) in moredetail. In their order of appearance the terms involved inexpressions (14) and (17) describe the nonresonant backgroundsignal, the purely resonant Raman contributions, the mixingof nonresonant background and Raman modes and theinterferences among different Raman resonances, respectively.Figure 2 displays the spectral characteristics of each intensityterm for a spectrally isolated Raman resonance in the presenceof a nonresonant background. Their sum yields the well-known CARS dispersive line shape.

In comparison, the spontaneous Raman spectrum isdescribed by the sum of the imaginary parts of the complexresonant susceptibility,

IRaman(ω) ∝∑

r

χr ′′. (18)

Accordingly, the measured spontaneous Raman intensity islinearly dependent on the number density of Raman-activescatterers.

In condensed-phase CARS, the effect of the nonresonantcontribution, χnr , is most profound when a sample withweak Raman modes is embedded in a nonlinear medium.The nonresonant background of the latter can be easilycomparable with or larger than the resonant contributionfrom the sample of interest. This is a situation commonlyencountered in CARS microscopy. Depending on theexperimental situation, the CARS detection sensitivity to weakresonances can then be restricted either by the nonresonantbackground or by photon shot noise [77]. To maximizeeither the relative or the absolute CARS intensity, polarization-sensitive CARS detection schemes and OHD techniques havebeen developed.

2.3. Background suppression in polarization CARS

Since the relative contribution of each term to the totalCARS signal in equations (14) and (17) depends on theadjustment of the angles φ and ε, polarization-sensitiveCARS detection allows both extracting the polarization

properties of the vibrational resonances and suppressingthe nonresonant background. For detection of intenseRaman resonant amplitudes, i.e. |χr | χnr , the frequency-independent nonresonant background limits the CARSsensitivity. Maximum suppression of nonresonant backgroundin polarization-sensitive CARS is accomplished if the analyserdirection is perpendicular to P(3)nr , i.e. for ε = 90˚ in figure 1.Consequently, the first and third summands in equations (14)and (17) vanish, and the only contributions that can be detectedthrough the analyser arise from the projection of P(3)r onto theanalyser direction [75, 76, 78]. As a result, the absolute CARSsignal shows a square dependence on the number density ofRaman-resonant scatterers. Note that there is no advantagein applying background-suppressed polarization CARS ifρr ≈ ρnr = 1

3 , where P(3)r and P(3)nr are about parallel. Inan actual experiment, complete background cancellation isprevented due to imperfections of the optics, denoted by aneffective extinction ratio κ . The fraction of nonresonantsignal that leaks through at ε = 90˚ is |P (3)nr

|| |2/κ .Consequently, the background-suppressed CARS detectioncontrast is given by the signal-to-background ratio, S/B =κICARS(α, φ, ε = 90˚)/|P (3)nr

|| |2. From equations (10), (13)–(15), it follows that at ε = 90˚ the contrast is maximizedfor α = 45˚. With tan φ = 3 tan α, the optimal valuefor the angle φ formed by the pump and Stokes field isdetermined to be 71.6˚ [75, 76]. This polarization geometryhas been used for nonresonant background suppressionin collinear two-beam CARS microscopy by Cheng et al[32, 46]. Examples for polarization CARS imaging andmicrospectroscopy will be presented in sections 4 and 5,respectively.

2.4. Optical heterodyne detected CARS

Suppression of nonresonant background using polarization-sensitive detection at ε = 90˚ or, alternatively, by use ofpulsed-sequenced CARS detection, which will be introducedin section 6, is accompanied by a significant reduction inthe absolute strength of the Raman-resonant CARS signal,resulting in modest detection sensitivity for very weakresonances and/or low sample concentrations. Background-free CARS spectroscopy without any loss of resonant signalstrength can be achieved through phase-controlled OHDschemes. In OHD–CARS, the measured signal is theinterference of a weak resonance CARS with an intensenonresonant CARS radiation, which acts as a local oscillatorfield. As Oudar et al [75] have pointed out, OHD–CARSallows the recovery of both the real and imaginary parts ofthe Raman-resonant susceptibility. Furthermore, it allows asignificant enhancement of the CARS detection sensitivitythrough amplification of the Raman-resonant signal. For weakresonances, i.e. |χr | χnr , the second and fourth summandsin equation (14) become negligible, and the nonresonantbackground and the heterodyne mixing term then dominate thetotal CARS intensity. As a result, the amplified CARS signalis proportional to the real part of the resonant susceptibilityand falls off linearly with the number density of the Ramanscatterers.

In methods based on nonlinear interferometry, originallyproposed by Chang et al [79], the CARS field generated by

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the sample is heterodyne mixed with a local oscillator fieldprovided by a second nonresonant CARS source. Becauseboth anti-Stokes fields, typically generated in each arm of aMach–Zehnder interferometer, are coherent with each other,their phase difference can be controlled via variation of theoptical delay between the two CARS sources. Nonresonantbackground suppression is then achieved by addition of thesample field with a local oscillator field with a phase ofopposite sign [80, 81]. The potential of CARS interferometryfor nonresonant background suppression in CARS microscopyhas been recently reported using detection in the time domain[82, 83] as well as in the frequency domain [84].

Recently, Silberberg and co-workers [34, 85–87] haveintroduced a different approach for active phase control inCARS based on coherent control techniques. By tailoringthe spectral phase of a single ultrashort laser pulse, theinterference between quantum paths induced in the sampleby various spectral components of the pulse is controlled.As such, phase-sensitive detection of the resonant signalhas been demonstrated, where the strong nonresonant CARSbackground of the same species is used as the localoscillator [85]. Background-free CARS spectroscopy has beenachieved by use of both spectral phase and polarization pulseshaping [86].

Even without active phase-control schemes, weak Ramansignal amplitudes can be amplified by interference with theintense nonresonant signal from the same sample. Thisis the case when a fraction of the nonresonant backgroundcontribution, which acts as a local oscillator, is allowed topass the analyser. Since the nonresonant background signalscales with cos2 ε (equation (14)), the analyser setting, ε,controls the strength of the local oscillator. In the limit ofparallel-polarized excitation fields (φ = α = 0), equation (15)reduces to fr = cos ε, and the total CARS signal is maximizedwhen the analyser is set parallel to the input field polarizations(ε = 0). In contrast, the signal is maximally suppressed ifthe analyser is set to ε = 90˚ relative to the parallel-polarizedinput fields. OHD with parallel-polarized pump and Stokesfields has been used in CARS microscopy for imaging [47] andmicrospectroscopy [57], where shot-noise limited detectionsensitivity has been achieved (see sections 4 and 5).

3. Theoretical depiction of collinear CARSmicroscopy

Frequency-degenerate CARS microscopy using both acollinear geometry [28] and a folded BOXCARS [41] beamgeometry has been demonstrated. The rationale for theBOXCARS geometry in conventional CARS spectroscopy isto fulfil the phase matching condition, | k|l π , wherethe wave vector mismatch, k = kAS − (2kP − kS), isminimized while the interaction length, l, is maximized. Underthe tight focusing conditions in collinear CARS microscopy,however, a small dimension of the excitation volume and alarge cone angle of wave vectors compensate the wave vectormismatch induced by the spectral dispersion of the refractiveindex of the sample, and the phase matching condition canbe fulfilled [42, 88]. Therefore, the collinear beam geometry,schematically shown in figure 3(a), became the configurationof choice in CARS microscopy, exhibiting superior spatialresolution and image quality.

Figure 3. Schematic configurations for three wave vectorgeometries in collinear CARS microscopy. (a) F-CARS andE-CARS microscopy with co-propagating incident beams, forwardand backward signal collection, respectively, andpolarization-sensitive detection of the forward-scattered CARS(P-CARS). (b) C-CARS microscopy with counter-propagatingincident beams and forward signal collection along the direction ofthe pump beam propagation. The corresponding wave vectordiagrams along the optical axis z are indicated. (P, polarizer;HWP/QWP, half-/quarter-wave plate; BC/BS, dichroic beamcombiner/splitter; Obj, objective lens; F, filter; L, lens; A, analyser).

3.1. Theoretical concept

In order to theoretically describe the signal generation incollinear CARS microscopy, it is necessary to considerits distinct features: (i) Under tight focusing conditions,the excitation field distribution is no longer that of aGaussian beam because of the breakdown of the paraxialapproximation. (ii) The actual extent of wave vector mismatchis controlled by the microscope’s geometry for the propagationdirections of both the incident beams and the CARS radiation.(iii) CARS microscopy deals with a heterogeneous sample ofRaman scatterers of arbitrary shape and size embedded in anonlinear medium, i.e. the solvent. In order to elucidate theconsequences for image contrast and detection sensitivity inCARS microscopy, these points will be discussed in moredetail as follows.

3.1.1. Tightly focused excitation fields. It is assumed thatthe incident pump and Stokes beams are of Gaussian intensityprofile, propagate along the z-axis and are focused onto thesample by a high numerical aperture (NA) objective lens. Thefocal field at any point within the focal volume, E(r), canthen be calculated according to the theoretical description ofa tightly focused Gaussian beam [89, 90]. Figure 4(a) showsa simulated intensity distribution near the focus. Unlike influorescence or spontaneous Raman microscopy, where theemission is solely governed by the local intensity of the focalexcitation field, CARS microscopy also relies on the localphase affecting the coherent summation of anti-Stokes fieldsfrom individual Raman scatterers. The corresponding phasedistribution is shown in figure 4(b), where the plane-wave partexp(ikz) has been subtracted. The Gouy effect, that is the axial

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E(0, z)2 (a.u.)

E(ρ

, 0)2

(a.u

.)

(φ–kz) / π

––

–– –

Figure 4. (a) Calculated intensity distribution, |E(ρ, z)|2, withρ =

√x2 + y2 and (b) phase distribution, φ(ρ, z), of the focal field

for a Gaussian beam focused by an objective lens of NA = 1.4 at anindex of refraction of the medium 1.5. The waist of the input beamis assumed to match the back aperture of the objective lens. Thelateral and longitudinal intensity profiles exhibit fwhm of ∼0.4λ and∼1.0λ, respectively.

phase transition of −π along the optical axis in the region fromz = −λ to z = λ, is evident. Because of the interaction of thepump and the conjugate Stokes fields in CARS microscopy,the additional phase mismatch associated with the Gouy effecton each beam is negligible [31]. Note that this is in contrast tothe situation in third-harmonic generation under tight focusingconditions, where the induced Gouy phase shift dominates thephase mismatch [44, 91].

3.1.2. The wave vector mismatch for various collineargeometries. Another way of phrasing the phase matchingcondition in CARS microscopy is to say that the coherencelength defined by π/ k has to exceed the effective interactionlength, l, which is determined by the axial dimension of thenonlinear sample. Consequently, the actual value of k actsas a size filter for a scatterer of the dimensions for which anefficient CARS signal is generated. As schematically shown infigure 3, three geometries of both the input beams and CARScollection can be defined in collinear CARS microscopy thatdetermine the wave vector mismatch. In figure 3(a), both thepump and Stokes beams are collinearly co-propagating along z,and the anti-Stokes radiation is assumed to propagate in boththe forward (kAS along z) and backward (kAS along −z)directions. The phase matching condition along z is alwaysfulfilled for forward-detected CARS (F-CARS) (| k| = 0),whereas in the case of backward-detected CARS (or epi-detected CARS (E-CARS)) a large wave vector mismatch of| k| = 2|kAS| = 4nπ/λAS is introduced [29]. As with

E-CARS, a large wave vector mismatch is established in thegeometry with collinearly counter-propagating input beamsand CARS detection in the forward direction with respect tothe axial propagation direction of the incident pump beam. Inthis configuration depicted in figure 3(b), and denoted counter-propagating CARS (C-CARS), the wave vector mismatchalong z amounts to | k| = 2|kS| = 4nπ/λS. Here, therefractive index of medium n is assumed to be independentof frequency.

3.1.3. CARS signal generation. The above plane waveapproximation is strict only for the CARS radiation along theoptical axis z. The generation of the F-CARS signal withtightly focused excitation beams was theoretically depictedin the thick-sample limit by Potma et al [42]. Hashimotoand Araki [43] derived the optical transfer function of CARSmicroscopy. Volkmer et al [29] provided a more appropriatedescription of the total CARS field generated by an ensembleof coherently induced Hertzian dipoles that constitute thescattering object, while taking into account the wave vectormismatches for F-CARS and E-CARS signals. This workhas been further generalized by Cheng et al [31] by useof the Green’s function method to calculate the CARSsignal generated with tightly focused Gaussian beams forsamples of arbitrary shape and size. The theoretical conceptemployed is generally applicable to any nonlinear coherentmicroscopy [44].

In brief, assuming that the incident fields are unperturbedby the presence of the heterogeneous sample, and the refractiveindex mismatch between the object of interest and thesurrounding medium is negligible, the generated CARS fieldis obtained by solving the nonlinear wave equation in theslowly varying amplitude approximation. As illustrated infigure 5, the solution of the wave equation for a point sourceof P (3)(r) = χ(r)E2

P(r)E∗S(r) at position r yields the far-field

CARS radiation per unit volume, εAS(R, r, χ(r)), at positionR (|R| |r|). χ(r) denotes the total susceptibility of eithera point inside the object of arbitrary shape and size, χobj(r),or inside the surrounding solvent, χsolv(r). Ep(r) and ES(r)represent the spatially overlapped and tightly focused pumpand Stokes fields, with the intensity and phase distributionsshown in figures 4(a) and (b), respectively. The total transverseCARS field at R, denoted EAS(R), is then the coherentsummation of the CARS radiation field generated within theused space occupied by the object and the solvent Vobj andVsolv, respectively:

EAS(R) =∫

Vobj

εAS(R, r, χobj(r))dVobj

+∫

Vsolv

εAS(R, r, χsolv(r))dVsolv. (19)

By introducing the total sample volume, V = Vsolv + Vobj, thatis limited to the focal excitation volume, equation (19) can berecast as

EAS(R) =∫

Vobj

εAS(R, r, (χobj − χsolv))dVobj

+∫

V

εAS(R, r, χsolv)dV. (20)

In this representation of the total field, the CARS radiation fieldgenerated at any point inside the object space is proportional to

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an effective susceptibility given by the difference χobj − χsolv.Finally, the collected CARS intensity is proportional to theintegrated Poynting vector over the cone angle along thespherical surface of constant R,

ICARS ∝∫ 2

1

d

∫ 2π

0d|EAS(R)|2R2 sin , (21)

εAS(R, r, χχobj (r))

Figure 5. Definition of parameters for the calculation of the far-fieldCARS radiation, εAS(R, r, χobj(r)), from a point source within anobject with χobj embedded in an isotropic nonlinear solvent mediumwith χsolv, by excitation with tightly focused pump and Stokes laserbeams. Incident Gaussian beams, Einc, with beam waists of w0 arefocused by a high NA objective (NA = n sin γmax) of focal length f . and are the spherical coordinates specified by the vectorR(R, , ).

–

–

–

–

–

–

Figure 6. CARS signal dependence on the size of an object placed in vacuum at the origin of tightly focused excitation beams for differentexperimental geometries. Upper panels: calculated F- and E-CARS intensities as a function of (a) a sphere and (b) a hemisphere of diameterD. (c) Calculated forward- and backward-detected C-CARS intensities as a function of sphere diameter, D. (n = 1.52, NA = 1.4 andλp = 0.9λS = 1.1λAS are assumed.) Lower panels: schematics of the corresponding geometries used for the calculations. Filled and whitearrows denote the total CARS radiation fields from a sub-micrometre sized object with χobj and the surrounding solvent/substrate with χsolv,respectively (not drawn to scale).

where the integration range [1, 2] is [0, γmax] for forwarddetection (F-CARS and C-CARS) and [π − γmax, π ] forbackward detection (E-CARS).

Using the above theoretical model, the signal generationin the different geometries has been numerically calculated[29, 31]. The upper panel of figure 6(a) displays the theoreticalsize dependence of F-CARS and E-CARS signals from anobject sphere of diameter D in vacuum (i.e. χsolv = 0) placedat the origin of the overlapped foci of the co-propagatingpump and Stokes beams. The F-CARS signal increases quasi-quadratically with D because of constructive interference inthe forward direction, and saturates when the sphere diameterexceeds the longitudinal dimension of the focal excitationvolume, i.e. for >1.0 µm for near infrared excitation. TheE-CARS signal has the same amplitude as the forward signalwhen D is smaller than the pump wavelength, λp, and reachesa maximum at ∼0.3λp. With increasing sphere diameter,the E-CARS amplitude decreases rapidly and exhibits anoscillating behaviour with a periodicity of ∼λAS/2n, beingthe result of the interference effect associated with the largewave-vector mismatch in E-CARS. For large D, whichresembles the case of focusing into an isotropic bulk medium,the E-CARS intensity is negligible, i.e. >105 times smallerthan the corresponding forward signal at D = 8λp. Thisis a consequence of destructive interference in the backwarddirection. Figure 6(b) displays the simulated CARS signalfrom a hemisphere located in the z > 0 region with its centreat the focus. The F-CARS signal displays the same behaviouras that for a spherical sample. The E-CARS signal, however,reaches a maximum when D is equal to ∼0.5λp and convergesto a constant value that is ∼1.2% of the F-CARS signal. Thisinefficient cancellation of the E-CARS signal is in contrast tothe above result found for a sphere and is explained by thesymmetry break of the focal plane caused by the boundaryin χ of the semi-infinite object. Figure 6(c) shows boththe calculated forward-detected C-CARS signal dependenceand the backward-detected one on the diameter of a spherefor the configuration depicted in figure 3(b). Both curves

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evolve like the E-CARS signal in the co-propagating geometry(figure 6(a)). The oscillating behaviour in the forward-detected C-CARS signal exhibits a maximum at ∼0.4λp anda periodicity of ∼λS/2n, in accordance with the interferenceeffect associated with the large wave vector mismatch for thisconfiguration. For large D, which resembles once more thecase of focusing into an isotropic bulk medium, the C-CARSsignals are negligible.

3.2. Contrast mechanisms in F-, E- and C-CARS

In order to obtain a qualitative picture for the CARS contrastmechanism in each wave vector geometry, a sub-micrometreobject with χobj embedded in an isotropic nonresonantmedium, i.e. χsolv = χnr

solv = 0, is considered next. Thepropagation of the pump and Stokes fields is assumed tobe parallel to z. The anti-Stokes emission can then beapproximated to propagate parallel to z. This is schematicallyshown for the different geometries in the lower parts offigure 6, where the total CARS radiation fields generated bythe object and the solvent, i.e. the first and second integralsin equation (19), are symbolized by filled and white arrows,respectively.

Based on the above signal dependences on the object size,the F-CARS geometry is predicted to provide only a poorimaging contrast when the object volume is much smaller thanthe focal excitation volume (Vobj V ). From equation (20)it follows that a weak F-CARS signal from an object is eithersuperimposed on a large bulk solvent F-CARS backgroundwhen χobj > χnr

solv or that it can cause a negative imagecontrast by depleting the background signal when χobj < χnr

solv.The coherent sum of the resonant susceptibility component ofthe object (χr

obj) and the nonresonant background componentdominated by the solvent and/or the glass substrate (χnr

solv)

results in an expression for the total F-CARS intensity thatis similar to equation (14). As discussed in section 2.4, in thecommon case where |χr

obj| χnrsolv, the intense nonresonant

signal can act as a local oscillator in such a heterodyne detectionscheme and can be used for resonant signal enhancement [57].

In contrast, a way of imaging small objects embeddedin a nonresonant solvent with high contrast is provided bythe epi-detection geometry [29, 30]. Because the E-CARSsignal intensity from an isotropic bulk medium is negligible,the second term in equation (20) vanishes, and the signalfrom the microscopic object with an effective susceptibilityof χobj − χsolv provides the first contrast mechanism inE-CARS microscopy. Note that because of the modulussquare dependence of the signal, the E-CARS image contrastis determined by |χobj − χsolv|2. As a result, objects withχobj < χsolv provide positive image contrast. As depictedin figure 6(b), the second contrast mechanism in E-CARSmicroscopy is provided by the symmetry break of the focalplane induced by objects with an interface perpendicular tothe optical axis [31]. It should be noted that the refractiveindex mismatch between the object and the solvent, which isnot considered in the calculation, could cause back-reflectionof intense F-CARS from the solvent and/or glass substrate. Inpractice, if the input beams are not focused on the interfaceperpendicular to the optical axis, the back-reflected signal isdefocused on the detector and can be minimized by the use

of confocal detection. For small scatterers, the back-reflectedsolvent signal is negligible compared with the epi-scatteringsignal from the object. If back-reflection of strong nonresonantforward-scattered signals from the bulk solvent and/or glasssubstrate occurs, it can amplify the weak resonant signal fromthe object propagating in the epi-direction via heterodynemixing [47].

One way of avoiding a back-reflected signal from the bulksolvent at an interface is to employ a counter-propagatingbeam geometry according to the C-CARS configurationdepicted in figure 3(b), which provides an image contrastmechanism that resembles that in E-CARS microscopy. Sinceany bulk contribution to the C-CARS signal is significantlysuppressed, back-reflection of the nonresonant backgroundsignal is negligible.

Note that both E- and C-CARS microscopy cannotdiscriminate the intrinsic nonresonant background of an objectitself since both wave vector geometries act effectively as asize filter for the scattering object of a dimension smaller thanπ/ k. Consequently, the spectral selectivity is poor when thenonresonant signal exceeds the resonant signal from the object,i.e. χnr

obj − χnrsolv χr

obj.

4. Instrumentation and experimentalcharacterization of collinear CARS microscopy

4.1. Laser light sources

Almost all CARS microscopes implemented to date are basedon the frequency-degenerate CARS process that requires twosynchronized laser pulse trains at different frequencies, i.e.ωp and ωS, with one of them being tunable for adjusting thedesired Raman shift, ωp − ωS. Near-infrared laser beamsare used to prevent two-photon electronic resonances. Assuch, Zumbusch et al [28] used transform-limited femtosecondpulses generated by a regeneratively amplified Ti : sapphirelaser pumped optical parametric amplifier system (Coherent,RegA/OPA). A fraction of the fundamental amplifier output istypically used as the pump beam in CARS, while the remainderis used to generate a train of inherently synchronized pulsesat the second colour, e.g. the Stokes wavelength, by meansof optical parametric amplification (OPA). The wavelengthtunability of the OPA output yields an accessible range ofRaman shifts of 700–3500 cm−1 [28, 29, 31, 58].

CARS with transform-limited femtosecond excitationpulses results in poor spectral selectivity because theirbandwidths are broader than the Raman line widths. Therefore,numerous efforts have been made in order to increasethe spectral resolution in CARS microscopes based on afemtosecond amplified laser system. The simplest way isto introduce a slit in the spectrally dispersed femtosecondpump and Stokes pulses to reduce their bandwidths, effectivelyconverting them into picosecond pulses [28, 55]. A moreefficient use of the disposable pulse energies is provided whena linear chirp is introduced to the femtosecond pulses. Knutsenet al [92] have recently reported on a multiplex CARSmicroscope where the achieved spectral resolution (∼5 cm−1)is defined by the temporal overlap of a transform-limitedStokes pulse (∼90 fs) with a linearly chirped pulse stretched toseveral picoseconds (∼10 ps). In a different approach, Hellerer

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et al [93] have demonstrated femtosecond CARS microscopyusing both linearly chirped pump and Stokes pulses with thesame amount of chirp. This way, the entire bandwidth of bothpulses is focused into a narrow spectral region, resulting in ahigher spectral resolution (∼3 cm−1).

A significant improvement of not only the spectralresolution but also the sensitivity in CARS microscopyhas been achieved by implementing a laser light sourcethat directly generates narrow-bandwidth and transform-limited pump and Stokes pulses of which the spectral widthmatches the Raman resonance line width to be probed[30]. This has been achieved with high-repetition ratepicosecond laser systems that consist of two electronicallysynchronized mode-locked Ti : sapphire oscillators operat-ing at 80 MHz (Spectra-Physics, Tsunami/Lock-to-Clock)[30, 32, 39, 40, 45, 46, 48, 50, 51, 57, 59, 63, 94] or at 76 MHz(Coherent, Mira/Synchro-LockAP) [35, 36, 47, 56]. The pumpand Stokes pulse widths are typically about 5 ps, correspond-ing to a spectral width of ∼2.9 cm−1. The wavelength of eachlaser beam can be independently tuned, which results in anadjustable Raman shift covering the entire spectrum of molecu-lar vibrations from 100 to 3400 cm−1. Compared with a CARSmicroscope based on a piscosecond regeneratively ampli-fied Ti : sapphire laser pumped OPA system (Spectra Physics,Spitfire/OPA) operating at pulse repetition rates of 1 kHz [54],a mode-locked oscillator-based setup operating at a muchhigher repetition rate (∼100 MHz) has the advantage of an im-proved signal-to-noise ratio and image scan rate. Furthermore,changing the mode of operation of one of the two oscilla-tors from picosecond to femtosecond enables the realizationof multiplex CARS microspectroscopy [46, 50, 51, 57]. Anintrinsic limitation of the electronic synchronization scheme,however, can be the residual electronic timing jitter betweenpump and Stokes pulses and its sensitivity to external perturba-tions. Typically, a jitter of ∼700 fs is achieved by locking thefundamental repetition rates of the oscillators onto each other[30]. Tighter synchronization using high-harmonic lockingtechniques with a temporal jitter as small as ∼20 fs has beendemonstrated to considerably increase the signal-to-noise ratioin CARS microscopy [35, 36, 47].

Recently, Xie and co-workers [95] have implementedhigh frame rate CARS imaging based on a high repetitionrate mode-locked picosecond laser pumped optical parametricoscillator (OPO) system. Since the wavelength-tunable OPOoutput pulse is deterministically related to the phase of therepetition frequency of the pump laser output pulse, sucha laser system provides inherently synchronized pump andStokes pulses, obviating the need for complex electronicsynchronization schemes, and is thus much less vulnerableto external perturbations.

In recent years, appreciable efforts have been made todevelop less complex and more cost-efficient laser light sourcesfor CARS microscopy. As such, CARS microscopy based ona single mode-locked femtosecond Ti : sapphire laser, whichis readily available in two-photon fluorescence microscopyapplication facilities, has been reported. In a scheme setup by Paulsen et al [37], the low-power nonlinear responseof a photonic crystal fibre is used to generate a frequency-shifted soliton output as the pump beam in the CARS process.A part of the fundamental 795 nm beam from the oscillator

operating at 76 MHz (50 fs pulses) is used as the Stokes beam.Another demonstration of single-laser CARS microscopyusing a nonlinear fibre has been reported by Kee andCicerone [38]. Here, a narrow-band slice (∼13 cm−1) ofthe spectrally dispersed femtosecond pulse and the long-wavelength part of a broadband continuum generated in atapered nonlinear fibre by the remainder of the pulse are usedas the pump and Stokes pulses, respectively. This way, abroadband multiplex CARS microscope that allows spectralimaging over a range of Raman shifts of 2500 cm−1 witha spectral resolution of ∼13 cm−1 has been developed. Adifferent concept for single-laser CARS microscopy with highspectral resolution, as introduced by Silberberg and co-workers[34, 85, 86], is based on coherent control techniques. Incontrast to standard two-beam CARS, the CARS signal isproduced by an intrapulse four-wave mixing process of allthe frequency components within the bandwidth of a singleultrashort laser pulse (∼20 fs). By tailoring the spectralphase of the pulse via Fourier-transform pulse shaping usinga programmable liquid-crystal spatial light modulator (SLM),the interference of all quantum paths in the sample inducedby various spectral components of the pulse is controlled.A periodic modulation of the spectral phase yields a selectiveexcitation at a given Raman shift [34], while a phase gateapplied to a narrow spectral band provides single-pulsemultiplex CARS [85, 87]. The spectral resolution of thegenerated CARS signal, reported to be about 5 cm−1, isdetermined by the pixel size of the SLM [87].

4.2. The CARS microscope

In conventional two-beam CARS microscopy, both linearlypolarized pump and Stokes beams are temporally overlappedand collinearly sent into an optical microscope resembling oneof the geometries schematically shown in figure 3. Tightfocusing is accomplished with a high NA objective lens(e.g. an oil immersion lens with NA = 1.4). The CARSsignal is collected in the backward direction by the sameobjective lens (E-CARS [29]) or parfocally in the forwarddirection using a second lens (F-CARS [28] and C-CARS[31]). Because of the high directionality of the F-CARSradiation, the collection with a condenser lens as a secondlens has been demonstrated to be sufficient [39, 55]. Forpolarization-sensitive CARS detection (P-CARS [32]), the F-CARS geometry is combined with polarization control of theinput beams (see figure 3(a)), where the angle formed by thepump and Stokes beam polarization is adjusted to φ = 71.6˚with a half-wave plate. An additional quarter-wave plate isused in the pump beam to compensate for the birefringence,induced mainly by the dichroic mirrors. A rotatable polarizeris used as an analyser before the detectors (see also multiplexCARS set up in figure 11). From the practical point of view,E-CARS obviates the need for a second microscope objectivelens and thus leaves the above space for sample manipulation.E-CARS detection can be readily implemented with a standardepi-fluorescence microscope setup.

The collected CARS radiation is then spectrally filteredand confocally detected by use of either single-photon countingor analogue detection techniques. For the former an avalanchephotodiode with an active area of about 150 × 150 µm2

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(SPCM-APD, EG&G Canada) is typically used [28].For applications where the emphasis is on fast imageacquisition rates rather than detection sensitivity, an analoguephotomultiplier detector module is employed [39, 55]. Inmultiplex CARS microspectroscopy, detection is typicallyperformed by use of an imaging spectrometer equipped witha detector array (e.g. a CCD camera) for capturing a CARSspectrum over a wide range of Raman shifts in a single-shotmeasurement [46, 51] (see section 5).

To obtain images, either the sample is scanned withrespect to the fixed laser beams or the laser beamsare scanned with respect to the fixed sample. Bothsample-scanning [28–30, 32, 33, 45, 47, 48, 52, 54–56] with athree-dimensional closed-loop piezo-driven stage and laser-scanning [39, 40] with an x–y galvanometer beam scannerhave been implemented. In laser scanning, the highpulse repetition rate, of the order of ∼100 MHz, providedby picosecond Ti : sapphire oscillators in conjunction withanalogue detection, allows fast image acquisition rates oftypically a few seconds for a 512 × 512 pixel image [39].In sample-scanning, however, the image acquisition rate is forthe most part limited by the piezo-scanner. In order to avoidphotodamage to the sample while still maintaining a high peakpower, it is therefore beneficial to reduce the pump and Stokeslaser pulse repetition rate to several hundred kilohertz usingPockel [30] or Bragg cells [47]. The acquisition rate is typically∼10 min for a 512 × 512 pixel image. For applications wherethe highest detection sensitivity is required, sample-scanningin combination with single-photon detection is the method ofchoice [47, 57].

4.3. Characterization of imaging properties of model systems

Typically, polystyrene beads of well-defined size spin-coatedon a glass cover slip and covered with water are used tocharacterize the imaging properties in CARS microscopy.Figure 7 shows images of individual 0.5 µm beads recordedunder identical experimental conditions when tuned into aRaman shift centred at ∼1595 cm−1 where C=C stretchvibrations of polystyrene reside. The F-CARS image of thebead in figure 7(a) exhibits a poor contrast because bulk watergives rise to a large background signal. In addition, two dipsabout the bead are observed in the lateral F-CARS intensityprofile. This phenomenon is attributed to the coherent mixingbetween the F-CARS of the object and that of the surroundingwater, similar to the coherent effect observed in SHG imaging[96]. Comparison of this F-CARS image with the E-CARSand C-CARS images in figures 7(b) and (c), respectively,clearly demonstrates the efficient rejection of the bulk solventsignal, a concomitant lack of coherent imaging effects andan increase in sensitivity for sub-micrometre sized objects inE-CARS and C-CARS microscopy. It was found that theE-CARS of pure water is more than 100 times smaller than itssimultaneously measured F-CARS, which is consistent withthe calculation in figure 6(a) [29]. For the tight-focusingconditions specified above, a fwhm of <400 nm is typicallyobserved in the lateral intensity profiles across the beads[28, 30, 50, 54], which is smaller than the bead diameter. Thisis in contrast to fluorescence microscopy, where the lateralintensity fwhm of a fluorescent bead is determined by the

0.0 0.5 1.0 1.5 2.0 2.5 3.00

50100150200

x (µm)

sign

al (

cts)

0.0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

sign

al (

cts)

x (µm)

(c) C-CARS xy- image

(a) F-CARS xy-image

FWHM0.34 µm

0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20

sign

al (

cts)

x (µm)

FWHM0.34 µm

FWHM0.36 µm

(b) E-CARS xy- image

(d) F-CARS xz- image

0 500 1000

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0.0

z (µ

m)

signal (cts)

FWHM1.18 µm

Figure 7. (a) F-CARS, (b) E-CARS and (c) C-CARS xy-images of0.5 µm polystyrene beads embedded in water. Parallel polarizedpump and Stokes beams were 110 fs pulse trains with a repetitionrate of 250 kHz at 800 nm and 917 nm (Raman shift centred at∼1595 cm−1), respectively. The average pump and Stokes powerswere 100 µW and 50 µW, respectively. The image size measures(a) 207 × 84, (b) 207 × 68 and (c) 207 × 138 pixels with a pixeldwell time of 4.88 ms. The lateral intensity profiles along the linesindicated by the arrows are shown below each image. (d) F-CARSxz-image of an interface between a coverglass and immersion oil.Parallel-polarized 5 ps pump and 110 fs Stokes pulses at a repetitionrate of 76 MHz and centred at 717 nm and 900 nm (Raman shift∼2840 cm−1) were used, respectively. The average pump andStokes powers were 4 mW and 2 mW, respectively. The imagemeasures 40 × 132 pixels with a pixel dwell time of 4 ms. The axialedge profile along z, together with its smoothed first derivative(solid line), is shown next to the image.

convolution of its diameter with the point spread functionof the excitation/detection profile. In CARS microscopy,the convolution method cannot be used due to the modulussquare dependence of the signal on the coherent sum ofCARS radiations from a number of vibrational modes (seeequations (12)–(15)). Figure 7(d ) shows the F-CARS imagein the x–z plane from an interface between a coverglass andrefractive index matched immersion oil. Plotting the CARSsignal along z yields an axial edge function, which exhibits aweak nonresonant background in glass and an intense CARSsignal originating from the symmetric CH2 stretch vibrations at∼2840 cm−1 in oil. The axial resolution is measured from thesmoothed first derivative of the longitudinal intensity profile,resulting in a typical fwhm of 1.2 µm.

By use of picosecond excitation, Cheng et al [39] havedemonstrated high-sensitivity E-CARS imaging of a 0.2 µmpolystyrene bead based on the more intense aromatic C–Hstretch vibration at 3045 cm−1. With measured fwhm valuesof ∼280 nm and ∼0.75 µm for the lateral and axial intensityprofiles, respectively, this experiment represents the most aptcharacterization of the CARS excitation volume in CARSmicroscopy with a detection sensitivity that is adequate forimaging a single 0.1 µm bead with a high contrast.

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E-CARS xz-image

F-CARS xy-image

Figure 8. CARS imaging of the symmetric CH2 vibration at aRaman shift of ∼2847 cm−1 in phospholipid bilayer membranes.(a) E-CARS xz-image (224 × 120 pixels) of a GUV close to asupported bilayer with an intermembrane separation of ∼3 µm.The average power of pump and Stokes beams was 20 mW and15 mW, respectively. The pixel dwell time was 2 ms. (b) F-CARSxy-image (256 × 256 pixels) of an erythrocyte ghost vesicle witha diameter of ∼7 µm taken in the equatorial plane. The averagepower of the pump and Stokes beams was 0.3 mW and 0.1 mW,respectively, at a pulse repetition rate of 250 kHz. The pixel dwelltime was 1 ms. The orientation of the parallel-polarized pump andStokes laser polarization is indicated by the double arrow.The lengths of the coordinate axes are 2 µm (Adapted from Potmaand Xie [47]).

A more biologically relevant model system thatdemonstrates the distinct characteristics of F-CARS andE-CARS signal detection and at the same time explores thesensitivity of CARS microscopy was reported by Potma andXie [47]. Using 3 ps pump and Stokes pulses at a repetitionrate of 76 MHz tuned to a Raman shift of 2849 cm−1, they havevisualized the νs(CH2) modes in unilamellar phospholipidmembranes. Figure 8(a) shows the E-CARS xz-image ofthe lower part of a single spherical giant unilamellar lipidvesicle (GUV) above a planar lipid bilayer supported on acoverglass in the xy-plane. The E-CARS signal from theGUV is most intense when its lipid bilayer tangent plane iseffectively parallel to the horizontal xy-plane and graduallydecreases as the bilayer becomes more aligned with the opticalaxis z. This observation is in accordance with the picturegiven in section 3.2, where an increasing effective axialinteraction length l of the membrane increases the wave vectormismatch in the E-CARS configuration (see figure 6(a)).A demonstration of the second contrast mechanism in E-CARSmicroscopy is provided by the signal from the supportedbilayer membrane spanning the xy-plane. This samplegeometry resembles the situation schematically depicted infigure 6(b). Here, heterodyne mixing of the relatively weak

E-CARS field of the membrane with the intense back-reflectednonresonant F-CARS field from the glass substrate at theglass/membrane interface results in a threefold amplificationof the bilayer signal. Figure 8(b) shows an F-CARS xy-imageof a single spherical erythrocyte vesicle taken in the equatorialplane where the effective longitudinal interaction length, l,of the membrane is maximized (see figure 6(a)). Becauseof constructive interference of CARS radiation from a largenumber of νs(CH2) modes, the F-CARS signal from thelipid bilayer visibly exceeds the nonresonant F-CARS signalfrom the surrounding water. In addition, efficient excitationin the direction parallel to the orientation of the parallel-polarized pump and Stokes laser polarization is observed,whereas regions perpendicular to the excitation polarizationshow weak CARS contrast. This photoselection effect revealsthe expected preferential alignment of the symmetry axis ofthe CH2 groups parallel to the bilayer tangent plane (comparefigure 8(b)) [47]. In a similar study, Cheng et al [48]have visualized ordering of water molecules confined betweenconcentric phospholipid bilayers. The mutual orientationbetween the νs(CH2) stretch mode of lipid hydrocarbon chainsprobed at 2845 cm−1 and the O–H stretch mode of interlamellarwater molecules probed at 3445 cm−1 has been determined viatheir respective photoselection effects.

4.4. Contrast in live cell imaging

One of the key applications of CARS microscopy with greatpotential for the life sciences is the noninvasive chemical map-ping of live unstained cells [27–30, 32, 39, 40, 45, 52, 54, 55].No cellular damage was observed at the average power levelstypically used for imaging [39, 40]. It is therefore worthwhileto compare the contrast mechanisms in live cell imaging basedon F-CARS, E-CARS and P-CARS detection.

Figures 9(a) and (b) compare the F-CARS and E-CARSimages of epithelial cells with ωp −ωS tuned to the fingerprintregion of the Raman spectra of proteins and nucleic acids.Both the pump and Stokes beams were parallel polarized andno polarization sensitive detection was used. The acquisitionof the F-CARS image in figure 9(a) necessitated a lowerexcitation power. However, as seen from the intensity profilebelow the image, the large water background overwhelms theF-CARS signals from the cellular components, resulting in apoor image contrast. F-CARS detection is, therefore, suitablefor imaging based on vibrational modes with large resonantCARS signals, i.e. χr

obj χnrsolv, such as for example lipid

membranes with a high density of the C–H stretch vibrations.In contrast, as shown in figure 9(b), E-CARS imaging

dramatically increases the sensitivity of CARS detection forscatterers smaller than the wavelength of light by meansof efficient rejection of the bulk water background [29].The nucleus and other intracellular components are clearlyobserved. The smallest feature in the intensity profileacross the line indicated by the arrows is 375 nm, whichis smaller than the diffraction limit [30]. However, asexamined above, E-CARS imaging alone cannot discriminatethe intrinsic nonresonant background of a small object itself.Thus, E-CARS is advantageous for vibrational imaging ofsub-wavelength objects with strong resonant CARS signals.This is the case in imaging of live cells based on the

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F-CARS xy-image E-CARS xy-image P-CARS xy-image

Figure 9. Comparison of contrast in F-CARS, E-CARS and P-CARS images of unstained live (a, b) epithelial and (c) NIH3T3 cells takenwith 5 ps pulse trains at a repetition rate of 400 kHz. (a) F-CARS image recorded with parallel-polarized pump and Stokes beams withaverage powers of 0.4 mW and 0.2 mW, respectively, at a Raman shift of 1579 cm−1. (b) E-CARS image recorded with average pump andStokes powers of 2.0 mW and 1.0 mW, respectively, at a Raman shift of 1570 cm−1. (c) P-CARS image taken with background-suppressedpolarization detection. The pump and Stokes beams were tuned to the aliphatic C–H stretch vibration at a Raman shift of ∼2860 cm−1, withaverage powers of 2.0 mW and 1.0 mW, respectively. Shown below each image is the intensity profile along the line indicated by the arrows.The acquisition time was 12 min for each image.

C–H stretch vibrations where the resonant signal exceeds theeffective nonresonant background, χr

obj > (χnrobj − χnr

solv).E-CARS imaging could be complicated by back-reflection ofthe forward CARS signal at an interface (see discussion insection 3.2).

P-CARS microscopy allows suppressing nonresonantbackground contributions from both the object and solvent.Figure 9(c) shows the P-CARS image of NIH3T3 cells, wherethe background suppressed polarization CARS introduced insection 2.3 has been applied [45]. In contrast to the F-CARSimage in figure 9(a), taken with parallel polarized pump andStokes beams, small features arising from the aliphatic C–Hstretch vibrations at 2860 cm−1 were clearly detected withhigh signal-to-background ratios. The remaining backgroundobserved in the intensity profile of figure 9(c) arises fromleakage of the excitation beams and of the residual nonresonantsignal. In conclusion, P-CARS provides a method of high-contrast vibrational imaging for objects with a strong resonantCARS signal, e.g. imaging based on C–H stretch vibrations inmembranes and amide bands in proteins. A modest detectionsensitivity is prevalent for a weak resonant CARS signal due tothe reduction of its absolute signal strength upon backgroundsuppression. P-CARS is insensitive to imaging based onRaman bands with a depolarization ratio of ∼ 1

3 .

5. CARS microscopy in the frequency domain

In the limit of monochromatic pump and Stokes beams,the frequency dependence of the real and imaginary partsof the nonlinear susceptibility χ

(3)r1111 (equation (4)) and a

constant nonresonant background give rise to the typical CARSdispersive line shape, as shown in figure 2. In order to providea more appropriate description of the measured CARS signal inthe frequency domain, the finite spectral width of the excitationpulses has to be taken into account. Accordingly, the induced

third-order polarization of equation (1) is recast as [97],

P (3)(ωAS) =∫ +∞

−∞dωp

∫ +∞

−∞dωS

∫ +∞

−∞dωp′

×χ(3)(−ωAS; ωp, ωp′ , −ωS)Ep(ωp)E∗S(ωS)Ep′(ωp′)

×δ(ωp + ωp′ − ωS − ωAS). (22)

The frequency-resolved CARS spectrum is then given by

ICARS(ωAS) ∝ |P (3)(ωAS)|2. (23)

5.1. Signal dependence on the spectral width of excitationpulses

Because of the multi-photon character of the CARS process,one would assume that a high peak power of femtosecondinput pulses provides a high signal to background ratio, asin the signal generation in two-photon induced fluorescencemicroscopy. However, this conventional wisdom does nothold for vibrational imaging with CARS microscopy. Toillustrate this point, the dependence of CARS signals onthe equal Gaussian spectral width of the pump and Stokespulses of constant energies is simulated for an isolated Ramanband. Figure 10(a) depicts the normalized CARS spectralline shapes calculated for two 29 cm−1 and two 7.5 cm−1

pump and Stokes pulses using equations (22) and (17). Thesame line shape parameters as for the simulation shown infigure 2 are used. While a broad CARS spectral profilewith poor contrast is obtained with two 29 cm−1 (0.5 ps)pulses, both the CARS spectral resolution and contrast areconsiderably improved upon excitation with two 7.5 cm−1

(2 ps) pulses. Figure 10(b) shows the calculated dependenceof spectrally integrated CARS intensities of both the purelyresonant and nonresonant contributions on the spectral width.While the resonant CARS signal is saturated when the pulsebandwidth exceeds the Raman line width, the nonresonantsignal has a quadratic dependence. Consequently, the ratioof the resonant signal to nonresonant background decays with

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-100 -50 0 50 1000.0

0.5

1.0

1.5

2.0 7.5 cm-1 (2.0 ps) 29 cm-1 (0.5 ps)

Raman profile

Ωr-(ω

p-ω

S) / cm-1

(a)

I CA

RS/ I

CA

RS

ref

(b)

50 100 1500.0

0.2

0.4

0.6

0.8

1.0

3

resonant

nonresonant (x 0.01)

Ir/I

nr

Pulse temporal width / fs

1001503005000

sign

al /

back

grou

nd

CA

RS

inte

nsity

(a.

u.)

Pulse spectral width /cm-1

Figure 10. Simulated CARS signal dependence on the equal Gaussian spectral width of transform-limited pump and Stokes pulses ofconstant energies. Based on the C==C mode of polystyrene, an isolated Raman band with r = 1601 cm−1, r = 4.6 cm−1 andAr/χ

nr = 4.0 cm−1 is assumed. (a) Calculated normalized CARS spectral line profiles for 29 and 7.5 cm−1 input pulses. (b) Spectrallyintegrated CARS intensities of the resonant and nonresonant background signals as a function of the pulse bandwidth. Their ratio is shownto be higher for picosecond excitation pulses than femtosecond excitation pulses [30].

increasing spectral pulse width. It is therefore desirable touse narrow-bandwidth excitation schemes to achieve not onlyhigher spectral resolution but also higher sensitivity in CARSmicroscopy [30].

5.2. Narrow-bandwidth CARS microspectroscopy

Both high spectral resolution and sensitivity in CARSmicroscopy have been demonstrated by use of twoelectronically synchronized Ti : sapphire oscillators providingtransform-limited picosecond pump and Stokes pulses [30].A frequency-resolved CARS spectrum (equation (23)) isrecorded by tuning the wavelength of one laser beam[30, 32, 47, 48, 54]. In an alternative approach, both pumpand Stokes pulses originally derived from a femtosecondamplifier/OPA laser system have been linearly chirped bythe same amount in order to obtain a narrow instantaneousfrequency difference in the CARS process at a given timedelay between the pulses [93]. By scanning the time delay,the CARS spectrum is acquired. High spectral resolutionhas also been achieved in single-pulse CARS microscopybased on coherent control techniques that involve the selectiveexcitation of a given Raman mode by periodic modulationof the spectral phase within the bandwidth of a femtosecondpulse from a Ti : sapphire oscillator [34]. Here, the modulationperiod determines the Raman shift to be probed. A spectrumis obtained by scanning the phase modulation periodicity.Common to all narrow-bandwidth excitation schemes issequential scanning of an experimental parameter in order toobtain a CARS spectrum. This is not only time consuming butalso prone to sources of noise induced by fluctuations in laserpulse parameters. As a consequence, dynamical changes in aCARS spectrum are difficult to follow.

5.3. Principles of multiplex CARS microspectroscopy

This problem can be circumvented by use of multiplex CARSspectroscopy, which was first demonstrated by Akhmanovet al [98], the concept of which is illustrated in figure 11(a).A narrow-bandwidth pump pulse and a broad-bandwidthStokes pulse are used to simultaneously excite multiple Ramanresonance frequencies. Thus, a CARS spectrum over a

Figure 11. (a) Principle of multiplex CARS microspectroscopy:a narrow-bandwidth pump pulse determines the inherent spectralresolution, while a broad-bandwidth Stokes pulse allowssimultaneous detection over a wide range of Raman shifts. Themultiplex CARS spectra shown originate from a single 0.5 µmpolystyrene bead (——) and from the nonresonant background ofthe coverglass (- - - -) at a Raman shift centred at 1600 cm−1.(b) Energy level diagram for a multiplex CARS process. (c)Schematic of the multiplex CARS microscope (P, polarizer;HWP/QWP, half-/quarter-wave plate; BC, dichroic beam combiner;Obj, objective lens; F, filter; A, analyser; FM, flip mirror; L, lens; D,detector; S, sample).

wide range of Raman shifts is captured in a single-shotmeasurement that is insensitive to fluctuations in the excitation.The bandwidth of the pump pulse determines the inherentspectral resolution of the measurement, while that of the Stokespulse determines the spectral width of the CARS spectrumgenerated. Assuming that the integration over the spectralprofile of the pump pulse in equation (22) can be neglectedbecause its spectral fwhm is much smaller than the typicalRaman line width, the observed multiplex CARS spectrum isapproximated by the product of the dispersive CARS spectral

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profile and the Stokes pulse intensity spectrum. This is shownin figure 11(a) for a CARS spectrum of a 0.5 µm polystyrenebead in the region of the quadrant stretch vibrations at 1582 and1600 cm−1 of the monosubstituted benzene rings. The energylevel diagram of the multiplex CARS scheme is schematicallyshown in figure 11(b).

The combination of multiplex CARS spectroscopy withmicroscopy was first reported by Otto et al [99]. Incontrast to previous work of multiplex CARS spectroscopy[14, 15, 100, 101], where a narrow-bandwidth picoseconddye laser and a broad-bandwidth picosecond laser usingmultiple dyes were employed as the pump and the Stokesbeam, respectively, multiplex CARS microspectroscopyhas been typically implemented with two electronicallysynchronized Ti : sapphire oscillators providing transform-limited picosecond pump and femtosecond Stokes pulses[46, 50, 51, 57]. Recently, broadband multiplex CARSmicroscopy based on a single femtosecond pulse source andbroadband continuum generation in a tapered nonlinear fibrehas been demonstrated [38]. Alternative excitation schemes,as introduced in section 4.1, have been proposed for multiplexCARS microscopy [85, 87, 92].

Figure 11(c) shows a schematic of a standard two-beam multiplex CARS microscope that uses the P-CARSgeometry depicted in figure 3(a). The temporally overlappedpump and Stokes pulse trains are collinearly combined andtightly focused into a sample mounted on a three-dimensionalscanning stage. Under the tight focusing condition, the phase-matching condition is insensitive to the laser wavelength ina collinear beam geometry, which allows spectral recordingover a wide spectral range without changing the alignment.Detection of the parfocally collected CARS signal is performedeither by use of a point detector for recording the spectrallyintegrated CARS signal in imaging applications or by useof an imaging spectrometer equipped with a liquid nitrogencooled CCD detector array for recording the multiplex CARSspectrum at a chosen position in the sample.

The spectral analysis is carried out on the normalizedCARS spectrum as defined by equation (17). Here, thereference CARS spectrum is conveniently obtained fromthe nonresonant background signal of the coverglass underidentical laser power and pulse chirp conditions. Whilethe chirp of the picosecond pump pulse is negligible, thefemtosecond Stokes pulse is significantly chirped due to groupvelocity dispersion induced by the microscope’s optics, inparticular by the microscope objective lens [102]. Simulationshave shown that the chirp in the femtosecond Stokes pulseslightly reduces the bandwidth of the nonresonant multiplexCARS spectral profile [46]. Least-squares fitting to thenormalized CARS spectrum allows concurrent determinationof the Lorentzian line parameters (Ar/χ

nr , r and r ) ofthe individual Raman modes and of the magnitude of thenonresonant background that is independent of the inputlaser pulse parameters [14, 15, 101, 103]. Furthermore, theimplementation of polarization-sensitive detection allows usto suppress the nonresonant background [100], to determinethe depolarization ratios (ρr) of Raman bands [104] and toresolve composite and overlapping Raman bands on the basisof variations in vibrational symmetry [68] (see section 2).

–1

–1

–1–

–

Figure 12. (a) Spontaneous Raman spectrum of a multilamellarDSPC vesicle in the C–H stretch vibration region. (b) Multiplexpolarization-resolved CARS spectra of the DSPC vesicle indicatedby an arrow in the inset image in (c) (48 × 24 µm2 acquired into512 × 256 pixels with a pixel dwell time of 0.5 ms). The angleformed by the pump and Stokes field was optimized forbackground-suppressed polarization CARS (φ = 71.6˚ andα = 45˚), and the analyser angle was adjusted parallel andperpendicular to the pump beam polarization, ε = 135˚ and ε = 45˚,respectively. (c) Corresponding multiplex CARS spectrum with theanalyser angle adjusted perpendicular to the nonresonantbackground polarization, ε = 90˚. The average pump and Stokespowers were 1.2 mW and 0.6 mW, respectively. The spectrumacquisition was 2 s.

5.4. Multiplex CARS microspectroscopy of lipids

The Raman spectrum of lipid membranes consists of alarge number of overlapping peaks, whose relative intensitieschange notably with changes in hydration state, packing andconformational order. To utilize this spectral sensitivity tothe lipid environment, multiplex CARS microspectroscopyhas been applied to monitoring the thermodynamic state ofphospholipid bilayer model systems in the C–C skeletal region[50, 51] as well as in the C–H stretch vibration region [46, 57].Two examples will be presented in more detail as follows.

5.4.1. Multiplex P-CARS microspectroscopy. The additionalfeatures offered by the combination of polarization-sensitivedetection with multiplex CARS microscopy have been usedby Cheng et al [46] in the study of micrometre-sized multi-lamellar lipid vesicles formed by 1, 2-distearoyl-sn-glycero-3-phosphocholine (DSPC). Figure 12(a) shows the spontaneousRaman spectrum of this gel-phase lipid at room temperature inthe C–H stretch vibration region. Its spectral decompositioninto seven Lorentzian bands yields two prominent bandsat 2847 and 2882 cm−1 that are assigned to νs(CH2) andνa(CH2), the symmetric and asymmetric methylene stretch

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vibrations, respectively [105]. The polarization properties ofthe individual Raman bands of the DSPC vesicle indicatedby the arrow in the inset image are revealed in a seriesof multiplex CARS spectra taken at different polarizationdirections of the analyser. Here, the angle formed by the pumpand Stokes fields was optimized for background-suppressedpolarization CARS (φ = 71.6˚ and α = 45˚). As shown infigure 12(b), with the analyser polarization perpendicular tothe pump field polarization, i.e. ε = 45˚ (see figure 1(c) forpolarization geometry), the νa(CH2) band becomes prominentwhile the νs(CH2) band disappears. On the other hand,with the analyser polarization parallel to the pump fieldpolarization (ε = 135˚), the νs(CH2) band is clearly detected.Figure 12(c) shows the corresponding CARS spectrum, wherethe analyser polarization was set to ε = 90˚. Consequently, thenonresonant background is effectively suppressed. Moreover,the νa(CH2) band at 2882 cm−1does not show up, indicatingthat its depolarization ratio is close to that of the nonresonantCARS signal. Figure 12(c) implies that the νs(CH2) band at2847 cm−1 provides the highest contrast in CARS imaging oflipids. The recorded multiplex CARS spectra have been usedfor vibrational imaging of lipids in live cells with polarization-sensitive detection [39, 45, 46].

5.4.2. Multiplex OHD–CARS microspectroscopy. Wurpelet al [57] have demonstrated that the increased sensitivityprovided by a heterodyne-detected multiplex CARS spectrumallows study of the chemical and physical structure ofa planar supported phospholipid mono- and bilayer on aglass/water interface in the C–D stretch vibration region.Here, the intense nonresonant F-CARS from a glass substrateacts as the local oscillator field. The authors investigatedboth a deuterated bilayer formed by 1, 2-dipalmitoyl-D62-sn-glycero-3-phosphocholine (d62-DPPC) and an asymmetricbilayer where one leaflet is replaced by a monolayer of 1, 2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). Figure 13shows the corresponding normalized multiplex CARS spectratogether with the spontaneous Raman spectrum of thedeuterated lipid d62-DPPC in the C–D stretch vibrationregion (2000–2300 cm−1). Since the spectral signature ofC–D stretch vibrations is in a distinct window of the Ramanspectrum, the deuterated leaflet of the asymmetric bilayercan be imaged despite the insufficient axial resolution ofthe microscope. Under the dilute-sample approximation, i.e.χsolv = χnr

solv χrobj, the analysis of the CARS spectra in

figure 13(b) using the peak positions and line widths obtainedfrom the spectral decomposition of the spontaneous Ramanspectrum of d62-DPPC into a sum of Lorentzian lines, shownin figure 13(a) and equations (4), (15) and (17), yields a twofoldincrease of the peak intensity for the νs(CD2) signal of thebilayer when compared with that of the monolayer. Thisresult directly confirms the linear signal dependence on soluteconcentration, as is expected in heterodyne-detected multiplexCARS microscopy. It demonstrates that even at the level ofa single lipid monolayer the main Raman features can readilybe detected with a sufficient signal-to-noise ratio. The relativestandard deviation of the noise was shown to be equal to n−1/2,where n is the number of detected photons, indicating a shot-noise limited detection sensitivity [57].

– – – –

–

Figure 13. (a) Spontaneous Raman spectrum of d62-DPPC lipidsand its decomposition into Lorentzian line profiles. (b) Normalizedmultiplex CARS spectra (dots) of a planar supported bilayer andmonolayer formed by d62-DPPC on a glass–water interface forparallel-polarized input beams (φ = α = ε = 0), together with thefit to equations (4), (15) and (17) using the centre frequency and linewidth parameters extracted from the decomposition analysis in (a)(——). The spectrum exposure time was 0.64 s. Error bars indicatethe shot-noise standard deviation (from [57]).

6. Time-domain CARS microspectroscopy

All of the preceding discussion has dealt with the two-colourCARS process in the frequency domain. Accordingly, all thespectroscopic information regarding vibrational frequenciesand relaxation processes has been obtained from the positionsand widths of the Raman resonances, respectively. This sectiondeals with time-domain CARS microspectroscopy, wheremolecular vibrational frequencies and relaxation processes areanalysed through coherent oscillations and the decay of thetime-dependent signal, respectively. In principle, time-domainexperiments are related to frequency-domain experiments byFourier transform and carry the same information. However,in contrast to the driven motion of molecular vibrations inthe multiplex CARS method, time-resolved CARS allows therecording of the RFID, i.e. the free evolution of the molecularsystem is observed. This was first reported by Laubereauand Kaiser [106], who measured vibrational dephasing ratesin various liquids. Furthermore, the temporal responsesof the nonresonant and resonant contributions to the third-order susceptibility are markedly different [107]. Whilethe nonresonant contribution dephases instantaneously, theresonant contribution of RFID decays within hundreds offemtoseconds in the condensed phase. Time-domain CARSwith femtosecond excitation, therefore, allows the separationof nonresonant and vibrationally resonant signals [108].

6.1. Principles of time-resolved CARS microspectroscopy

The time-resolved CARS experiment involves three incidentelectric fields that are pulses much shorter than the relevantmaterial timescale. As illustrated in figure 14(a), typicallythe pump, Ep(t), and Stokes, ES(t), pulses are temporallyoverlapped. This pair of pulses impulsively polarizes themolecular vibrations in the sample. The relaxation of the

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Ep (t)2 Es (t)

2 Ep (t)2

,

P(3) (τ,t)

2

Figure 14. (a) Illustration of the pulse-sequenced detection schemetogether with the RFID in a typical time-resolved CARSexperiment. (b) Schematic of the three-colour time-resolved CARSmicroscope (P, polarizer; BC, dichroic beam combiner; FD, fixeddelay; VD, variable delay; Obj, objective lens; F, filter; A, analyser;L, lens; D, detector; S, sample).

induced third-order nonlinear polarization, P(3)(t), at ωAS =ωp + ωp′ −ωS is probed by scattering of the third pulse, Ep′(t),at a certain delay time, τ . A measurement of the RFID consistsof the anti-Stokes signal collected at a series of delay times.

When electronic dephasing is much faster than either thenuclear dynamics of the molecular system or the optical pulses,the time-resolved CARS signal can be written as [109]

ICARS(τ ) ∝∫ ∞

−∞dt |P(3)(τ, t)|2, (24)

where the induced third-order polarization of equation (1) isrecast in the time domain as

P(3)(τ, t, ωAS) = −EP′(t)

∫ ∞

0dt2EP(t + τ − t2)

×E∗S(t + τ − t2) exp[i(ωP − ωS)t2]α(t2). (25)

The time-resolved CARS experiment probes the correlationfunction of the linear polarizability response of the sample,α(t2), which in the case of parallel polarization of the threeincident fields and the anti-Stokes field takes the followingform [110–112]:

α(t2) = Anrδ(t2) +∑

r

Aanisor exp(−irt2)

×[ (

ρ−1r − 4

3

)exp

(−t2

T2,r

)+

4

3exp(−t2(T

−12,r + T −1

or,r ))

].

(26)

The delta function (scaled by Anr) represents the instantaneousnonresonant (electronic) response of the system, whilethe rth Raman-active vibration is modelled as dampedexponentials of amplitude Aaniso

r , centre frequency r ,vibrational dephasing time T2,r , rotational correlation timeTor,r and depolarization ratio ρr . The response functionin equation (26) is connected by Fourier transformation

with the complex nonlinear susceptibilities of equations (4)and (5). Accordingly, all resonance parameters areindependently obtained by frequency-domain measurementsof the corresponding spontaneous Raman spectra detected withparallel and perpendicular analyser orientations with respectto the incident linear polarized excitation field, I

||Raman(ω) and

I⊥Raman(ω), respectively. The decomposition of their computed

isotropic and anisotropic Raman spectra into a series of r

Lorentzian line profiles,

I isoRaman(ω) = I

||Raman(ω) − 4

3I⊥

Raman(ω)

= 1

π

∑r

[Aaniso

r isor (ρ−1

r − 4/3)

(δr)2 + (isor )2

](27)

and

I anisoRaman(ω) = I⊥

Raman(ω) = 1

π

∑r

[Aaniso

r anisor

(δr )2 + (anisor )2

], (28)

respectively, is proportional to the Fourier transform of thecorresponding terms within the sum in equations (26) [113].Here, δr = ω−r represents the detuning from the rth Ramanresonance with iso

r = 1/T2,r and anisor = (T −1

2,r + T −1or,r ) being

the isotropic and anisotropic half-width values, respectively.In time-resolved CARS microscopy, the spatial width

of the input pulses (30 µm for a 100 fs pulse) exceeds thelongitudinal focal length (typically ∼1.2 µm). Thus, the time-dependent field envelopes of the input pulses and the coherentanti-Stokes field are assumed to be identical for each pointwithin the focal volume. This approximation allows usingthe above theoretical formalism to quantitatively describe thesignal transients under tight focusing conditions.

The implementation of time-resolved CARS formicrospectroscopy and its application in vibrational imagingbased on RFID has been demonstrated by Volkmer et al [33].The experimental layout of the RFID microscope is schemat-ically depicted in figure 14(b). A high repetition rate regener-atively amplified Ti : sapphire laser pumped OPA system wasused to provide inherently synchronized femtosecond pulsetrains at three different wavelengths. In a standard pumpand probe frequency-degenerate CARS scheme, the collineargeometry of the present experiment would result in an inter-ferometric signal time trace because of common frequencydegeneracy between the anti-Stokes probe scattering of interestand the undesirable anti-Stokes generation of the pump andStokes pulses. The use of three-colour CARS where the probefield is at a different frequency avoids this problem [73, 74].All three pulse trains were independently pre-compensatedfor group velocity dispersion by the microscope’s optics (notshown). The fields were independently expanded to a beamdiameter that matches the back aperture of the objective lens,linearly polarized along the x axis, collinearly overlappedand focused with a high NA objective lens into the sample.Optical delay lines were used to control the temporal overlapand delay between the different pulse trains. The anti-Stokessignal was parfocally collected with an identical objective lensin the forward direction, spectrally isolated and detected byan avalanche photodiode. Images were collected by rasterscanning the sample.

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0 1 2 3 4 5 60123

x / µm

-500 0 500 1000 1500102

103

104

105

water bead

CA

RS

sig

nal /

cps

τ / fs

3000 3040 3080

inte

nsity

(a.

u.)

Raman shift / cm-1

(a)

(b)

0 1 2 3 4 5 60.00.10.2

x / µm

int.

x10-4

/ cp

s

τ = 370 fsτ = 0 fs

Figure 15. Temporally and spatially resolved CARS signals from a1 µm polystyrene sphere embedded in water that corresponds to aRaman shift centred at 3054 cm−1. (a) Measured and simulated(line) decay curves when focused on the bead () and into bulkwater ( ). Inset: the parallel component of the spontaneous Ramanspectra with its decomposition into Lorentzian line profiles.(b) RFID images and the lateral intensity profiles along the linesindicated by the arrows at time zero and τ ≈ 370 fs, demonstratingthe complete removal of nonresonant background contributionsfrom both the object and solvent to the image contrast at τ ≈ 370 fs.The image size amounts to 230 × 118 pixels. The pixel dwell timewas 4.88 ms. The average power of each beam was ∼50 µW. Thefwhm parameters of the Gaussian input pulses were 185 fs, 85 fs and115 fs for the pump, probe and Stokes pulses with centrewavelengths at 715 nm, 798 nm and 914 nm, respectively.

6.2. Imaging based on the RFID

The ability to record the RFID of a microscopic sampleusing a time-resolved CARS microscope was demonstratedby imaging a 1 µm polystyrene bead embedded in water.Figure 15(a) displays the RFID measurement when focusedinto the bead and tuned to a Raman shift centred at 3054 cm−1.Due to the broad spectral width of the pump, probe andStokes fields, all the vibrational modes that make up thespontaneous Raman spectrum shown in the inset of figure 15(a)were coherently excited and contribute to the measured RFID.As shown in the inset, the parallel-polarized spontaneousRaman spectrum can be decomposed into three Lorentzianline profiles, which are assigned to the aromatic CH stretchvibrations of the benzene ring at 3035, 3051 and 3061 cm−1

[114]. The measured RFID curve exhibits an initial fastdecay of the instrumental response function (IRF), followedby a single exponential decay with a time constant of about∼390 fs, which is superimposed on a coherent oscillation(quantum beat) that recurs at τ ≈ 1280 fs. The fastestfeature in the time domain, i.e. the decay constant of 390 fs,corresponds to the broadest feature in the frequency domain,i.e. the line width of 15.4 cm−1 (fwhm) of the 3035 cm−1

resonance, which gives T2/2 ≈ 345 fs. The preparationof a coherent superposition of the 3035 and 3061 cm−1

modes with a difference frequency of 26 cm−1 accounts

for the observed quantum beat period of ∼1280 fs. Morequantitatively, the numerical simulation of RFID according toequations (24)–(28) satisfactorily reproduces the experimentaldata (solid lines in figure 15(a)). Here, the Lorentzian lineparameters extracted from the Raman spectrum and a Gaussianmodel for the measured time-dependent field envelopes of theinput laser pulses were used. The 3035 cm−1 resonance bandappears to be the dominant contribution to the observed RFIDcurve. The temporal resolution of the time-resolved CARSmicroscope was given by the IRF that was independentlymeasured by detecting the pure nonresonant coherent radiationoriginating from the glass substrate. The fwhm of the IRFamounts to 200 fs.

Figure 15(b) displays ultrafast vibrational images of thesame polystyrene bead at zero-time delay and at τ = 370 fs.Comparison of the two images clearly reveals that the time-delayed detection is capable of completely removing thenonresonant background contributions of both the object andthe solvent. As such, the solvent background signal issuppressed by a factor of∼130, with the remaining backgroundsignal in the time-delayed image being limited by the darkcount level of the detection system only. In contrast, themaximum signal from the polystyrene bead at time zero isreduced by only a factor of ∼12. Consequently, the signal-to-background ratio, S/B, increases from S/B(τ = 0) ≈ 4.2 toS/B(τ = 370 fs) ≈ 45. In this way, the vibrational contrastin the time-delayed image arises exclusively from the Raman-resonant modes. While this particular example of a polystyrenebead demonstrates an improvement in vibrational imagingsensitivity by more than one order of magnitude, the gain invibrational contrast can be even higher when Raman-activemodes with longer vibrational dephasing times are imagedand/or shorter excitation pulses are used.

7. CARS correlation spectroscopy

In fluctuation correlation spectroscopy, temporal signalfluctuations are monitored, which are caused by dynamicprocesses in the sample at low concentrations. Since thesample is at thermodynamic equilibrium, processes occurringon a broad time range from sub-microseconds to hours can,in principle, be investigated without the imposition of atransient disturbance. The most prominent optical fluctuationspectroscopy techniques are dynamic light scattering (DLS)[115, 116], which measures the fluctuation of quasi-elasticscattering intensity, and fluorescence correlation spectroscopy(FCS) [117–119], which measures concentration fluctuationsof specific fluorescent molecules and photophysical processesof the fluorophore itself [120]. The combination of chemicalcontrast provided by Raman scattering with the structural anddynamical information offered by correlation spectroscopywas reported by Schrof et al [121] using confocal spontaneousRaman microscopy and by Eggeling et al [122] usingsurface-enhanced resonance Raman scattering microscopy.As discussed in section 1, the restrictions inherent to thesemethods can be circumvented by use of coherent Raman signalenhancement via CARS [58, 59].

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Time / s

Figure 16. (a) Schematic of the two-colour excitation configurationin CARS correlation spectroscopy (CARS-CS) with collinear pumpand Stokes beams at frequencies ωp and ωS, respectively. The solidline represents the 1/e2 contour of the Gaussian excitation fieldamplitude profile defined by equation (30). (b) Photon numbertrajectory revealing the spontaneous number fluctuations about anequilibrium (〈N〉 ≈ 0.01) of 110 nm polystyrene spheres in waterdue to Brownian diffusion dynamics. The epi-detected CARScontrast arises from the breathing vibration of the benzene rings at∼999 cm−1.

7.1. Principles of CARS-CS

CARS correlation spectroscopy (CARS-CS) represents a noveltype of CARS spectroscopy that is a direct consequence of thespatial compartmentation provided by CARS microscopy. Thetight focusing of the excitation beams with a high NA objectiveand the inherent restriction of nonlinear signal generationto a focal volume of the order of femtolitres results in aprobe volume that can be much smaller than the averagevolume of particle occupancy given by the reciprocal particleconcentration.

Every dynamic process that leads to statistical fluctuationsin the CARS signal will induce a characteristic decay timein the autocorrelation curve. The intramolecular vibrationaldynamics that are accompanied by CARS intensity fluctuationsoccur on a femtosecond and picosecond timescale (seesection 6), which is too fast to be experimentally resolvedwith photon counting techniques. Therefore, CARS-CSpredominantly relies on particle number fluctuations causedby translational diffusion of scatterers through the openobservation volume occurring on the micro- and millisecondtimescale. This is in contrast to FCS, which is also sensitiveto photophysical processes of the fluorophore occurring onthe nanosecond and microsecond timescale. Figure 16illustrates the basic approach in two-colour CARS-CS. Thecollinear pump and Stokes pulses are spatially and temporallyoverlapped, and focused onto a sample to a diffractionlimited focal volume element. The radiated F-CARS orE-CARS is detected as a continuous function of time.It is vital to suppress any nonresonant CARS from thesurrounding solvent and/or autofluorescence background, e.g.in intracellular cell applications. Since both backgroundsignals are stationary and show no vibrational selectivity,they merely degrade the fluctuation contrast. For thatreason, CARS-CS is experimentally implemented usingpolarization-controlled F-CARS, time-delayed F-CARS orE-CARS detection schemes that allow efficient nonresonantCARS background rejection. Typically, the CARS signalis investigated by means of photon counting that registersdistinct photon arrival times, and is analysed in terms of its

photon number trajectory. As an example, figure 16(b) showsspontaneous stochastic fluctuations about an equilibrium dueto the translational diffusion dynamics of 110 nm polystyrenespheres in water. The average pump and Stokes laser intensitiesare kept constant, but the CARS intensity changes as particlesmove in and out of the fixed focal volume element, changing thenumber and distribution of particles in the illuminated regionabout its average. Such a photon number trajectory is analysedin the time domain by computing the normalized second-orderautocorrelation function (ACF) using a hardware correlator:

g(2)(τ ) = 〈I (t)I (t + τ)〉〈I (t)〉2

= 1 +〈δI (t)δI (t + τ)〉

〈I (t)〉2. (29)

Here, the temporal dependence of the signal, I (t) = 〈I (t)〉 +δI (t), is described by the signal fluctuation, δI (t), about itsmean, 〈I (t)〉 (see figure 16(b)). τ is the correlation time.Angular brackets denote time averaging over real time, t .

In order to theoretically describe the measured ACF inCARS-CS, a suitable model for both stochastic particle numberfluctuations and CARS signal generation has to be taken intoaccount. Xie and co-workers [59] have developed a theory forCARS-CS, which is based on a simplified description of thespatial excitation profile, as is commonly used in FCS theory.This allows a direct comparison of the ACF in CARS-CS withthat in FCS despite their distinct nature of signal generation.Briefly, in contrast to the tightly focused field description ofthe collinear excitation fields (see figure 4), the authors use anapproximation for the three-dimensional Gaussian excitationfield,

A(r) = E2p(r)Es(r) = A0 exp

[−2(x2 + y2)

w20

− 2z2

z20

]. (30)

w0 and z0 represent the lateral and axial 1/e2 half-widths,as defined in figure 16(a). Taking into account the wavevector mismatch along the z axis for the different geometriesdiscussed in section 3.1.2, the F-CARS and E-CARS signalintensities of an ensemble of independent point scatterers atconcentration c(r, t) are then given by equations (31) and (32),respectively:

IF-CARS(t) =∣∣∣∣∫

χ(3)A(r)c(r, t)dV

∣∣∣∣2

, (31)

IE-CARS(t) =∣∣∣∣∫

χ(3)A(r) exp(−ikASz)c(r, t)dV

∣∣∣∣2

. (32)

In analogy with the theoretical description of a Poisson-distributed concentration fluctuation, c(r, t) = 〈c〉 + δc(r, t),developed for FCS [123, 124], the autocorrelation modelfunction for F- and E-CARS-CS of sub-wavelength particlesundergoing free three-dimensional diffusion in the limit of verysmall number densities, 〈N〉 1, is given by [59]

g(2)F-CARS(τ )|〈N〉1 = g

(2)E-CARS(τ )|〈N〉1

= 1 +1

〈N〉(

1 +τ

τD

)−1 (1 +

τ

s2τD

)−1/2

, (33)

where s = z0/w0 and 〈N〉 = 〈c〉Veff is the averagenumber of particles in the effective excitation volume Veff =π3/2(w0/

√2)2(z0/

√2). The average lateral diffusion time

is defined as τD = (w0/√

2)2(4D)−1, with diffusion

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coefficient D. The identity of the ACFs in F-CARS andE-CARS detection simply reflects the symmetry in the forwardand backward directions of the CARS radiation field froma single scatterer of sub-wavelength dimension (see alsofigure 6(a)). In this case, the emission pattern approachesthat of isotropic fluorescence, and equation (33) has thesame mathematical form as describes the ACF in FCS forthree-dimensional translational diffusion [125–127]. The onlydifferences in the conventional (linear) FCS definitions ofVeff = π3/2w2

0z0 and τD = w20(4D)−1 result from the

introduction of the squared excitation Gaussian amplitudeprofile [128].

The ACF in CARS-CS no longer resembles the corres-ponding form of FCS when the number densities are com-parable with or larger than unity, i.e. 〈N〉 1. As Cheng et al[59] have theoretically and experimentally demonstrated, thecoherent sum of anti-Stokes fields from individual scattererscauses additional contributions, and the expression becomesdependent on the CARS detection geometry. Whereas in theforward detection scheme the time-zero amplitude of the ACF,g

(2)F-CARS(τ = 0), will vanish at large 〈N〉 (similar to FCS), the

epi-detected ACF takes the form

g(2)E-CARS(τ )|〈N〉1 = g

(2)E-CARS(τ )|〈N〉1

+ exp

(− k2

ASw20τ/τD

1 + τ/2s2τD

) (1 +

τ

2τD

)−2 (1 +

τ

2s2τD

)−1

.

(34)

The additional term in equation (34) reflects the large wavevector mismatch in the epi-detected CARS signal. Note thatfor a high concentration of particles, 〈N〉 1, equation (34)predicts a large initial amplitude that is exponentially decayingand independent of the average number density of scatterers.This inherent sensitivity of epi-detected CARS-CS for thedetection of scatterers at high concentrations is in markedcontrast with FCS, which relies on very low concentrations.Epi-detected CARS-CS may therefore be advantageous in thestudy of cluster and aggregate dynamics.

Figure 17. (a) Measured CARS-CS ACFs for an aqueous suspension of differently sized polystyrene spheres at a Raman shift of 3050 cm−1

(diameter: 110 nm, ; 202 nm, ; and 528 nm, ) and of PMMA spheres at 2900 cm−1 (diameter: 281 nm, ). The residuals of the fit to theACF for 202 nm beads (——) are displayed in the upper panel, revealing a steeper decay than predicted by equation (33). (b) Lateraldiffusion times, τD, extracted from fits of the ACFs to equation (33) plotted versus sphere diameter, d. The solid line represents the fit to theStokes–Einstein relation that yields the microscopic solvent viscosity (from [58]).

7.2. Application to microscopic determination of viscosities

The experimental characterization of CARS-CS has beenperformed on freely diffusing sub-micrometre sized polymerbeads of different chemical compositions by employingboth the E-CARS [58, 59] and the P-CARS [59] geometriesas depicted in figure 3(a). Experiments in the low-concentration limit (〈N〉 1), thus testing equation (33),have unambiguously demonstrated the information contentoffered by CARS-CS, i.e. the spectral selectivity based onthe vibrational contrast, the dependence of the initial ACFamplitude on the particle concentration, the dependence oflateral diffusion parameters on the bead size, and the influenceof viscosity on the Brownian motion.

As an example, figure 17(a) shows the dependenceof measured CARS-CS ACF curves on the diameter ofpolystyrene and PMMA spheres in an aqueous solution atRaman shifts of 3050 cm−1 and 2900 cm−1 corresponding tothe aromatic C–H stretch and aliphatic C–H stretch vibrations,respectively [58]. In order to better visualize the prolongationof lateral diffusion times with the increase in bead size, theACF curves have been normalized. With the focal dimensions,w0 and z0, deduced from the lateral and axial fwhm of theCARS intensity profiles in an independent experiment (see,e.g., figure 7), the lateral diffusion time, τD, can be extracted byfitting the experimental curves to equation (33). Figure 17(b)depicts the fit results, τD, versus sphere diameter, d. A lineardependence was found, which is in accordance with theStokes–Einstein relation, D = kBT /(3πηd), where kB, T andη are Boltzmann’s constant, temperature and solvent viscosity,respectively. A value for the microscopic solvent viscosity ofη = 0.001 Pa s was obtained from the slope of the linear fitin figure 17(b), which is in good agreement with the value forbulk water at room temperature [116]. As apparent from theresiduals of the fit to the ACF for 202 nm beads in figure 17(a),a steeper decay than predicted by equation (33) was observed.In fact, approximating the spheres of finite dimensions aspoint sources oversimplifies the experimental situation. Sucha size effect has been previously observed in FCS studiesof fluorescent spheres with diameters comparable with the

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dimensions of the excitation volume and has been accountedfor in a refined diffusion model [129].

7.3. Limitations and prospects

A major drawback of CARS-CS when compared with FCSis the limited detection sensitivity of CARS microscopy.While FCS exhibits single-molecule sensitivity, CARS-CSrelies on the coherent enhancement of thousands of Ramanmodes contributing to a detectable signal. Furthermore,the requirement for mode-locked pulsed excitation sourcesintroduces an additional modulation of the measured ACF atthe reciprocal pulse repetition rate of the laser. In order toseparate the amplitude of this modulation from the time regionof interest (microseconds to milliseconds) and to increase thenumber of excitation events in a given time interval, it isbeneficial to use excitation at high pulse repetition rates in themegahertz range. However, caution should be taken to avoidoptical trapping effects, directly affecting the translationaldynamics of the scattering objects of interest.

The additional advantage of CARS-CS over DLS and FCSis the spectral selectivity for individual chemical componentsin their native state, where fluorescent labelling is notdesired. This may not only allow mapping of three-dimensional diffusion coefficients, for example inside livecells, but also may offer a method of monitoring the specificinteraction of individual components within complex systems,e.g. aggregation processes of different chemical species.Furthermore, the extension of the CARS-CS technique tothe simultaneous recording of different time traces and theiranalysis by means of the cross-correlation function may allowinvestigation of correlated fluctuations between two differentspecies. These could be two distinct Raman spectral features ofone and the same compound or a specific intrinsic Raman bandand the emission of a more sensitive fluorescence label [121].

8. Conclusions

This contribution reviews the recent advances in collinearCARS microscopy. Its theoretical and experimental principlesand examples of its application to vibrational imagingand microspectroscopy of unstained mesoscopic objectsare surveyed. The utilization of new features of CARSsignal generation under tight focusing conditions based onthe wave vector mismatch in certain geometries and theimplementation of well-established methods in conventionalCARS spectroscopy with optical microscopy have allowedefficient suppression of a nonresonant background fromthe sample and/or surrounding solvent. As such, theuse of picosecond excitation sources, polarization-sensitivedetection, pulse-sequenced detection and epi-detectionschemes has significantly improved the detection sensitivityand image contrast in CARS microscopy. Based on theseadvances, CARS microscopy has been used to acquire a point-by-point chemical map of C–H stretch vibrations in lipids, ofO–H stretch vibrations in water and of Raman modes within thespectral fingerprint region of proteins. Additional specificityhas been achieved by targeted isotope labelling of a sample. Inaddition to the chemical specificity, the wave vector mismatchintroduced via the epi-detection geometry in E-CARS

microscopy provides a second contrast mechanism throughefficient CARS signal generation at interfaces in nonlinearsusceptibilities. This makes E-CARS microscopy a powerfultool for morphology characterization studies with concurrentchemical contrast, e.g. for the study of biological tissues [95].CARS microscopy has been applied for vibrational imagingof live unstained cells, of lipid membrane model systems andof composite materials. Recent instrumental developments inhigh repetition rate picosecond laser sources in conjunctionwith laser-scanning microscopy have provided high imageacquisition rates, allowing the visualization of fast dynamicalprocesses with three-dimensional spatial resolution and highchemical specificity.

Unlike in fluorescence and spontaneous Ramanmicroscopy, the quantitative interpretation of CARS images ismore complex due to the coherent image contrast induced fromdifferent specimens within the focal excitation volume and/ora single specimen with spectrally overlapping contributions tothe nonlinear susceptibility. Consequently, the efficient sup-pression of a nonresonant background signal from the sampleand solvent have significantly simplified image interpretation.A different approach to quantifying the CARS image contrastis based on the separation of individual susceptibility compo-nents by means of CARS microspectroscopy. For example, aquantitative assignment of the number distribution of Ramanmodes in a CARS image is obtained by monitoring the CARSspectra for each image pixel and subsequent spectral analysis.

The possibility of CARS microscopy for spatially resolvedspectroscopic measurements provides a wealth of informationin both the frequency domain and the time domain. Inthe frequency domain, multiplex CARS microspectroscopyallows chemical identification of molecules on the basis oftheir characteristic Raman spectra and the extraction of theirphysical properties, e.g. their molecular structures. Effortsin the development of broadband multiplex CARS schemesare currently under way, which will allow the identificationof specific specimens within a complex system consistingof a large number of different molecules (e.g. a biologicalcell) on the basis of the full CARS spectrum. In the timedomain, the ability to record the localized RFID occurring onthe femtosecond and picosecond timescales using three-colourtime-resolved CARS microscopes has been demonstrated.Dynamic processes, e.g. Brownian motion, occurring on themicrosecond and millisecond timescales, have been probedusing CARS correlation spectroscopy, which represents a newtype of vibrational spectroscopy.

The detection sensitivity of a single lipid bilayerhas been accomplished in CARS microscopy by takingadvantage of OHD. A promising approach for further improve-ment of the sensitivity is based on the realization of CARSunder electronic resonance conditions, which has not beenreported yet. In analogy to surface-enhanced resonance Ramanscattering (SERRS) [130], where single-molecule detectionsensitivity has previously been achieved [11], an additionalenhancement factor of at least three orders of magnitude isexpected for coherent anti-Stokes resonance Raman scattering(CARRS) microscopy. In addition, its applicability to nativebiological chromophores introduces an intrinsic CARS ‘label’,thus introducing additional chemical specificity. However,the concomitant enhancement of a nonresonant background

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signal may offset the resonance enhancement effect, and needsto be investigated.

In summary, CARS microscopy represents a noveland highly sensitive tool for vibrational imaging andmicrospectroscopy for tackling compelling problems inbiology and materials sciences. In particular, studiesof complex systems where fluorescent labelling of smallmolecules represents a severe perturbation of the system andapplications where morphological material information withchemical contrast is required will benefit from the use of CARSmicroscopy. Its wide proliferation would certainly profitfrom the availability of cost-efficient laser excitation sourcesoptimized for CARS microscopy. Recently, various promisingnarrow-bandwidth excitation schemes have been proposed.Further instrumental developments can be anticipated in thefuture.

Acknowledgments

I wish to thank Sunney Xie for the interesting and moststimulating time in his laboratory, where the work describedin this review had its origin. I also wish to acknowledge myformer co-workers Ji-xin Cheng and Lewis D Book for theircontributions to the work. The Faculty of Arts and Sciencesof Harvard University supported this work. I also wish tothank Eric O Potma, Michiel Muller and Andreas Zumbuschfor providing figures 8, 13 and 17, respectively. I acknowledgefinancial support from the Emmy-Noether programme of theDeutsche Forschungsgemeinschaft (DFG).

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