snell law 1

Chemical and spatial resolution with a SNOM

introduction to near field optics aperture SNOMSNOM tipsapertureless SNOM applications in solid state phisicssome examples in biology

Snell law 1Total reflection in a prismClassically Snell law:

No light is classically trasmitted in a medium of lower refractive index when a critical angle is reached:

n1

2211 sinsin nn

n2

n1

n22

1

c2

1sin nn

c

Snell law 2E

k

yx

z

n2 = n

n1 = 1

III E sin,0,cosE

IIT nnE sin,0,sin1 22E

IIT nniE sin,0,1sin 22 E

1sin,0,sin 22 IIT ninc k

• The transmitted polarization is along z

• The wave vector along z is immaginary: exponential decay• The wave vector along x is higher than /c• Notice that high k means small : higher spatial resolution

TM = linear polarization in the plane Oxz

Angular spectrum• Decomposition of the field in plane waves at z constant

dudvezvuFzyx vyuxi ,,,,E

ê

02

2

EEc

• The field should satisfy the Helmholtz equation

• Fourier component can be written as:

iwziwz evuBevuAzvuF ),(),(,,

dudvevuAyx vyuxi ,0,,E

• The evolution along z can be deduced by the field at z=0

2222 cvuw

Angular spectrum 2ê

dudvevuFzyx wzvyuxi 0,,,,E

Where from Helmholtz equation:

2

2222

cwvu

2

222

cvu

w is

imaginary!

This expression of the electric field is general: no approximations have been used until nowu and v are spatial frequenciesw introduces a decaying exponential in the

expression of the Field vs z


duevuFzyx wzvyuxi 0,,,,E

Example 1: 1D periodic grating

y

xz

We measure the field intensity far away form O along the z axis

In y direction there is no modulation so the only spatial frequency allowed is v=0; in x direction u assumes discrete values n/d n=1,2,…n.

The only wave vector allowed are etc.

Those values represent the nth diffraction order of the grating

If d< w becomes imaginary and the only propagating wave vector is (0,0,0) and the grating is no longer diffracted.

The spatial information is retained only in the near field

22 1,0,1 dcd

22 2,0,2 dcd


dxdyevuEyxF vyuxi

a

0,,0,,

Example 2: propagation through a small squared aperture

y

xz

2sin

2sin

1)0,,(

vaua

uvvuF

F 0 slowly at high spatial frequency: sharp edges.F has a maximum for u,v (0, /a) but, when a<

wiwcvu 22222222 48

And the part or all the light that maximizes F cannot propagateAgain, The spatial information is retained only in the near field

How to detect the near filed if it not propagating?

Theorem of reciprocity[Time reversibility of the Maxwell equation]

If a plane wave is diffracted into an evanescent wave by a subwavelenght scatterer,

A subwavelenght scatterer should be diffracted into a propagating wave by the same object

Near field detection

• The light is collected near the sample by a tapered optical fiber with a subwavelenght aperture

• Low light throughput• Resolution limited to /10

Physical mechanism SPATIAL FILTERING

• True spectroscopic information (including PL, EL, etc)• Dependence only on the tip geometrical properties• No dependance on the tip physical properties• No wavelenght dependence

Aperture SNOM

Illumination

Sample surface


• The near field decays exponentially with distance

• The tip should be kept at a controllede distance from the sample surface

• Feed back mechanism: shear force (similar to AFM tapping mode)

• Feedback detection: quartz oscillator (STM current is not suitable for biological samples; optical methods are disturbing the optical response).

xyz piezo

Feedback

Impedance detector

ElectrodesPiezo actuator

Aperture SNOM

• Operational modes

Aperture SNOM

Illumination CollectionIlluminationcollection

Reflectioncollection

Transmissionillumination

Transmission collection

• Typical set up

Aperture SNOM

LaserPol. controlfeedbackcontrol

xyzScanner

Detector

Topographic image

nf optical imageInverted

optical microscope

Optical fiber

Monochromator

• SNOM tips

Aperture SNOM

pulling

breaking

heatingHeating and pulling

method

Turner etching method

Hydrofluoric acidChemical etching

Aluminum vapor

Glass

Al coating

Optical fiber

• SNOM tips• Calculation of the

distribution of electric field as a function of the tip geometry

Aperture SNOM

Source: InAs QdotPoint like source /40 below the surface

• SNOM tips - pulling

Aperture SNOM

CoreCore Light propagation

CladdingCladding

Metal Metal coatingcoating

• SNOM tips - etching

Aperture SNOM

CoreCore Light propagation

CladdingCladding

Metal Metal coatingcoating

Holes are dug by various methods:The best results are obtained by FIB

• SNOM tips - polymerization

Aperture SNOM

Core Light propagation

Cladding

Metal coating

• Photopolimerization

90% wt Pentaerythritol triacrylate (monomer)

8% wt methyldiethanolamine (cosynergist)

2% wt eosin (dye)

High sensitivity to the argon laser light (514 nm)

• SNOM “japanese” etching

Aperture SNOM

Three different etching stepsSolution NH4F:HF:H2O

X : 1 : 1X=10 angle 20o

X=2.7 angle 50o

The selectivity between core and cladding comes from different quartz doping with Ge

• Application1: blood cell with malaria disease

Aperture SNOM

Study of blood cells infected by malaria’s plasmodium falciparium.(PF)Pf expresses several proteins in particular PfHRP1 and MESA that arefixed on the cell membrane.Proteins on cell membrane are colored with specific antibody marked with a red and a green fluorophorHere PfHRP1 is marked red


Aperture SNOM

Comparison between SNOM and confocal microscope images in the sdame blood cell:

SNOM is sensitive to cell surface

CM images a plane section at the focal plane

Cellular structure is resolved on the SNOM image but not in CF image


Aperture SNOM

Colocalization of host membrane and PF proteins

a) Control experiment: PfHRP1 is bound with antibodies marked either with green or red. The perfect overlap excludes any instrumental effect

b) Colocalization of host protein (green) and MESA protein (red)good colocalization Mesa and host proteins interact oin the cell surface

c) Colocalization of host protein (green) and PfHRP1 protein (red)No interaction at the cell membrane

NB the three ijmages refers to different blood cells groups

• Application2: single molecule detection and FRET mechanism

Aperture SNOM

• Application2: single molecule detection and FRET mechanism

Aperture SNOM

Green and red spot are due to not hybridized ssDNA (red can also arise from complete FRET effect)Yellow spot arise from hybridized dsDNA with competing green and red emission

• Application3: optical quantum corral

Aperture SNOM

The experiment:

Testing the subwavelkenght modulation induced on the local density of states of the optical modes by the fabrication of nanometric opticla corrals

Substrate ITOModulators 100nm100nm50nm gold particles deposited by e-beam lithography

To test the real LDOS the tip should act as a perfetct dipole at a nanometric distance from the surface.Real tips always pertirb the LDOS and what is measured is the combined LDOS of the sample and the tip!


Aperture SNOM

Light Polarization control

Elliptical mirros that selects only the near field radiation (propagating radiation is not allowed in the “forbidden light region with >c

The signal is 0 only closo to the sample


Aperture SNOM

Teorical optical LDOS in x, y and z direction


Aperture SNOM

Near field results in trasmission.Best results obtained with a gold coated tip without apertures(the tip

At the tip the polarization is tilted along z

The Snom data are fitted with a 1:4 mixing of the zx,y) polarization

• Application4: excitonic wave function of a quantum dot

Aperture SNOM

Low temperature operationIllumination collection mode


Aperture SNOM

Different emission spectra at increasing power (LEFT) and on different dots (Right)The far field spectra average the different contribution and the structure is lost


Aperture SNOM

Excitonic wave function mapping of different dots showing that bi-exciton is more confined A weak alignment along (1-10) crystallographic direction can be noticed


• Scattering SNOM

Unlimited resolutionChemical sensitive

Physical mechanism: TIP-SAMPLE INTERACTIONStrong wavelenght dependenceStrong dependance on the tip physical properties

Apertureless SNOM

s-SNOMWe model the tip as a metallic sphereAssuming that >>a and using a quasi-electrostatic

theory

)2()1(4 3

tta

Ep

Tip polarization far away from the sample in an external electric field E

)1()1(

'

ss

pp

Dipole induced on the sample surface

33 22

'

r

p

r

pEind

Dipole induced on the sample surface

s-SNOM

316 r

pEEEp ind

Eza

p

3)(161

In a first order iterative process the dipole induced on the tip becomes

3)(161

)1(

zaeff

The total dipole (tip + sample) is that is having an effective polarizability

Eza

p

3)(161

1

In the case of field parallel to the surface the induced dipole is opposite to the field and the effective polarizability is

3)(321

)1(

zaeff

In a metal 1 and eff is

nearly 0

s-SNOM

3

3

3

)(16

41

)(4

za

a

a

tip

tiptipeff

)2()1(

4 3

tttip

tipa

3322

3

33141

1

8

azazaz

aeff

It is evident that eff is increased by the interaction only for z<<a,In other words when the tip very close to the surface

s-SNOM

Im;6

24

kCk

C abssca

The measurable quantities are the scattered and the absorbed light that is proportional to the cross section.Applying Mie theory of light scattering

Scatteing and absorption cross section for a gold sphere on gold and silicon substrates for normal and parallel polarization

If I’m able to scan a gold sphere close to the sample surface I can observe a contrast in scattered intensity and, therefore, a can obtain a chemical map of the surface

s-SNOM• Typical experimental set-up

• The main problem is that the light scattered by the tip that carries the information on tip-sample interaction is overwhelmed by background light by several orders of magnitude

s-SNOMThe dependence of (z) is not linear.

Oscillating the tip in a non contact mode (harmonic) fashion, a non-harmonic response is obtained.

The non-harmonicity increases with the oscillation amplitude.

By collecting the nth armonic signal (n>3) the near field signal can be obtained

s-SNOM•It works!

On the left the 1st harmonic signal is collected at fixed amplitude while changing the tip-sample distance. Even for tip-sample distance > 200nm ther is a huge signal, arising from cantilever scattering and independent of tip-sample interactionOn the right the 2nd harmonic is collected, the background is suppressed and the near field signal is restricted to a 20nm distance from the surface.

=633nm

s-SNOMLateral resolution and chemical contrast

Pattern of Au on silicon obtained by evaporation through a polystyrene lattice.The chemical contrast arise from differences in the dielectric constant value at 633nm.BUTTopographic effects are not excluded:It is true chemical contrast?(This is a big issue in SNOM and the major source of SNOM artifacts)

=633nm

s-SNOMTrue chemical contrast

Silicon surface with a laterally modulated p-n doping structure.The topogarphic contrast is just 0.1nm: the surface can be told to be flat, so the contrast is purely otpical/chemical

The optical-spatial resolution is about 50 nm is 10mSo the resolution approaches /200

800nm


• Tip-enhanced SNOM

Unlimited resolutionPhysical mechanism: FIELD ENHANCEMENT

Suitable only for particular light-matter interaction process (e.g. Raman scattering, second harmonic generation, etcWhere the light detected has a different wavelenght from the

excitation light.)

Strong analogy to SERS and SPR

Apertureless SNOM

Near field detection•Field enhancement on a tip apex•Antenna effect

te-SNOM• Set-up for tip-enhanced SNOM

te-SNOM

• Raman scattering from a single CNT

Here the excitation is localized, while the light scattered by the nanotube is then collected in far field through the optical microscope.

a) Confocal microscopeb) SNOM raman image taken at the G’ band wavelenght

With metal tipwithout

te-SNOM

• Raman scattering from a single CNT

Localization of radial breathin mode raman scattering along the nanotubea and b arc-discharge growth b and d CVD growth

Structural defects along the structure can be identified by raman snom experiment

te-SNOMConfocal vs SNOM microscopy

AND SNOM WINS!!!!!!!!AND SNOM WINS!!!!!!!!

+

snell law 1

Documents

field decays

field intensity

z constantthe field

distribution of electric

wave vector

field vs zangular spectrum

propagating wave

spatial frequenciesw