enhanced nonlinearity by h-bonded polymer complex in liquid...

Enhanced nonlinearity by H-bonded polymer–dyecomplex in liquid crystal for holographic gratings

Elena Ouskova,1,2,3,* Andrii Pshenychnyi,1 Antoni Sánchez-Ferrer,4

Dariia Lysenko,1,3 Jaana Vapaavuori,1,5 and Matti Kaivola1

1Department of Applied Physics, Aalto University School of Science, P.O. Box 13500, FI-00076 Aalto, Finland2BeamEngineering for AdvancedMeasurements Company, 809 S. OrlandoAve., Suite I, Winter Park, Florida 32789, USA

3Institute of Physics, National Academy of Sciences of Ukraine, Pr. Nauki 46, Kyiv 03028, Ukraine4ETH Zurich, Department of Health Sciences and Technology, Schmelzbergstrasse 9, LFO, CH-8092 Zürich, Switzerland

5Department of Chemistry, Université de Montréal, P.O. Box 6128, Downtown Station,Montréal, Québec, H3C 3J7, Canada

*Corresponding author: [email protected]

Received March 24, 2014; revised May 2, 2014; accepted May 3, 2014;posted May 6, 2014 (Doc. ID 208752); published June 5, 2014

We have studied a new heterogeneous liquid-crystalline material where H-bonded polymer–azo-dye complexesare used as dopants to the liquid crystal (LC) bulk at a very low concentration. Double enhancement of theholographic gratings’ diffraction efficiency occurred in the complex-doped LC compared to dye-doped LC.The grating formation/relaxation processes in complex-doped LC showed anomalies that were explained bythe presence of polymer with H bonds. The gratings appeared to be formed due to a change of both the absorptioncoefficient and refractive index. Using such complexes as dopants gives perspectives for tuning and control of theLC properties, and for possible optical applications. © 2014 Optical Society of America

OCIS codes: (160.3710) Liquid crystals; (160.5335) Photosensitive materials; (160.5470) Polymers;(190.4400) Nonlinear optics, materials; (190.4710) Optical nonlinearities in organic materials.http://dx.doi.org/10.1364/JOSAB.31.001456

1. INTRODUCTIONAzo dyes are popular as dopants to liquid crystals (LCs). Theycan modify the unique LC properties due to light-inducedconformational changes in the azo dye molecules that induceeither reorientation of the nematic director or a change in theorder parameter. These two parameter changes allow for tun-ing the LC optical properties in the visible spectrum range andcontrol of light beam propagation. Both conformational [1],supra [2], dye-assisted orientational [3,4], and colossal [5,6]optical nonlinearities have been reported at low light powerin comparison with pure LC.

Most of the numerous publications about light-inducedeffects in azo-doped LCs relate to studies of low-molecular-weight dopants, and extensive experimental data are col-lected for such systems. Much less work is devoted to studiesof LCs doped with azo-containing macromolecular additives[7–10]. Nevertheless, replacement of low-molecular-weightazo dyes with compounds having more complex structures(such as azo polymers or even comb-shaped polymers, carbo-silane dendrimers) promises new interesting nonlinear opticaleffects and potential applications. The studies of nonlinearoptical properties of LC with high-molecular-weight dopantshave demonstrated their increased optical nonlinearity andpeculiarities in their optical response [3,4,7].

Of particular interest are systems based on hydrogen-bonded polymer–azo-dye complexes. Such complexes havethe advantage of simple and easy preparation without heavychemical synthesis, and their components are commerciallyavailable. Moreover, H bonding allows modular tunability

of the complexes. In our recent studies, we have found thatintroducing a H-bonded polymer–azo-dye complex into anematic LC matrix at low concentration results in a self-orientation of the LC in a cell and a spontaneous anchoringtransition from planar to homeotropic alignment on a rubbedpolyimide surface [8]. Moreover, the unique self-orienting azocompositions showed a strong nonlinear response at very lowlight powers of cw laser irradiation [9,10]. Self-phase modula-tion was observed and studied, showing nonthreshold fastformation of aberration rings (on the order of milliseconds)with a change of the refractive index of up to 0.04 andhigh nonlinear parameter (up to 10−3 cm2∕W) at an unusualirradiation geometry: normal incidence of light onto a homeo-tropically aligned LC. The optical nonlinearity in the complex-doped LC was 1.5 times higher than in an azo-dye-doped LC,and the thermal and conformational mechanisms causing thelight-induced order parameter change were suggested [9].It should be noted that the comparison was made betweencomplex-doped LC and the LC doped with the same azodye, which was in the complex.

Polymer–azo-dye complex-doped LC looks very promising,as it combines the unique anisotropic properties of LCs withthe stability of polymers and the light sensitivity and collectivemolecular response of azo dyes. The unique properties of LCsdoped with hydrogen-bonded polymer–azo-dye complex aredetermined by a combination of relatively high orientationmobility of the azo fragments and a strong depression of theirtranslation diffusion due to the H bonds. These propertiesallow us to expect an effective holographic grating recording

1456 J. Opt. Soc. Am. B / Vol. 31, No. 7 / July 2014 Ouskova et al.

0740-3224/14/071456-09$15.00/0 © 2014 Optical Society of America

http://dx.doi.org/10.1364/JOSAB.31.001456

to be possible in the LCs doped with hydrogen-bondedcomplexes. Here, we report on the first observations ofdynamic diffraction gratings in such systems.

2. MATERIALSA classic LC, 4-pentyl-40-cyanobiphenyl [5CB from PI Chemi-cals Co., Ltd., Fig. 1(a)], was selected as a nematic matrix for apolymer additive poly(4-vynilpyridine) [P4VP from PolymerSource Inc.; Mn, 1000 g∕mol; Mw, 1200 g∕mol; Fig. 1(b)].An azo dye, 4-dimethylamino-40-hydroxyazobenzene [HAB–DMA from TCI, Fig. 1(c)] formed H bonds with side pyridinefragments of the polymer. The HAB–DMA dye molecule is anazobenzene-type molecule, which absorbs in visible range. Asan azo dye, HAB–DMA can undergo trans-to-cis isomerizationthat makes it a suitable dopant to trigger light-induced effectsin a LC matrix in the visible.

To make the composition, the polymer–azo-dye complexP4VP�HAB–DMA�0.5 was prepared by simple mixing of thecomponents in a solvent, as described in detail in [8]. Duringthe formation of the complex, the azo dye statistically con-nects to every second side fragment of the polymer viaH bond, as confirmed with FTIR measurements [11]. Weintroduced 0.5 wt. % of the complex in 5CB, and the solventwas evaporated. Since the used polymer can be consideredoligomeric, the polymer–azo-dye complex is essentially amacromolecular dopant in an LC matrix, and thus it doesnot disturb LC orientation.

The resulting mixture, 5CB� 0.5%P4VP�HAB–DMA�0.5,was studied in a symmetrical cell of 20 μm thickness withplanar boundary conditions provided by rubbed polyimide.The doping with the complex led to a slight decrease ofthe clearing temperature, Tc. The Tc value measured with0.01°C accuracy in the oriented samples was 35.6°C–35.8°Cin pure 5CB and 35.1°C–35.7°C for complex-doped LC.

The polarization absorption spectra of complex-doped5CB showed two main absorption bands with maxima atλn−π� � 456 nm and λn−π� � 412 nm (Fig. 2), which appearedto be almost the same as those in azo-dye-doped LC(5CB� 0.25%HAB–DMA) with the same concentration ofthe dye (0.25 wt. %), with a small shift of the maximum ofa few nanometers.

3. EXPERIMENTSA. Experimental SetupThe nonlinear optical properties of the complex-doped LCwere studied by recording the dynamic holographic gratingsand comparing the results with LC doped only with the sameazo dye at the corresponding concentration. The sinusoidalintensity gratings were recorded by irradiating the cell withtwo equal linearly polarized beams with a total power P0 �P1 � P2 � 2P1 from an Ar-ion laser (λpump � 457 nm) thatintersected at a small angle in the cell’s plane (Fig. 3). Theincident light wavelength was near the maximum of oneof the absorption bands of the mixture λn−π� (see Fig. 2).

Fig. 1. Chemical structures of (a) the LC 5CB, (b) polymer P4VP,and (c) azo dye (HAB–DMA). (d) 3D sketch of the polymer–azo-dye complex.

Fig. 2. Polarization absorption spectra of 5CB� 0.5% P4VP�HAB–DMA�0.5 before (A∥ and A⊥) and at irradiation (A∥;irr. andA⊥;irr.) with e-wave of 457 nm laser of 300 mW∕cm2. The thicknessof the cells was 20 μm.

Fig. 3. (a) Experimental setup for grating recording: Mf, flip mirror;M, mirror; BS, beam splitters; P, polarizers; F, filter to cut recordingbeams; D1, D2, photodiodes for measuring diffracted beam intensities;D3, photodiode for measuring test beam incident intensity; α, anglebetween recording beams and (b) experimental setup for detectingof light-induced changes of the total and on-axis transmittances withone recording beam of Ar-ion laser: Mf is absent; D4, photodiode formeasuring total intensity; D5, photodiode for measuring total trans-mittance just after the cell; D6, photodiode for measuring on-axistransmittance at a distance of 75 cm from the cell.

Ouskova et al. Vol. 31, No. 7 / July 2014 / J. Opt. Soc. Am. B 1457

The cell’s plane and the LC director were perpendicular to theincidence plane. The interference pattern in a cell’s plane

I � I0�1� 2

��I1I2

p

�I1 � I2�cos�2πx∕Λ�

�� I0�1� cos�2πx∕Λ��;

(1)

with a period of Λ � λpump∕2 sin�α∕2� (where x is the coordi-nate along the pattern and α is the angle between the record-ing beams), resulted in the recording of thin Raman–Nath typeoptical gratings. The Raman–Nath diffraction behavior wasverified [12] via the Klein–Cook parameter [13] defined asQ � 2πλL∕nΛ2, where λ is the vacuum wavelength, L is thethickness of the cell, n is the mean refractive index, and Λis the grating period. Since Q was < 1 (0.5 for 10 μm gratingperiod, 0.05 for 30 μm grating period, and 0.02 for 50 μm gra-ting period), the recorded gratings were of the Raman–Nathtype [12]. Both the intensities of the first self-diffraction ordersof the pump Ar-ion laser beams I�1d and intensities of the firstdiffraction orders of the test beam of the He–Ne laser(λtest � 633 nm), I�1d;test, were measured as a function of theintensity, polarization, period of the interference pattern,and the exposure time. In the Raman–Nath regime, in a caseof a very small amplitude and phase modulation, the diffrac-tion efficiency η of the grating is connected with a change ofthe refractive index Δn by the formula

η � I�1d;test∕Itest � J21�2πLΔn�I0�∕λtest� ≈ jπLΔn�I0�∕λtestj2;(2)

where J1 is the first-order Bessel function, L is the cell’s thick-ness, and λtest is the wavelength of the test beam.

B. Holographic Grating RecordingAfter switching on the recording beams, the diffracted beamsappeared, and the diffraction efficiency η achieved a station-ary value ηsat within several seconds. After switching off therecording beams, the gratings fully relaxed. The recordedgratings were fully reversible, and no residual diffractionwas observed in the irradiated areas after numerousrecording–relaxing cycles.

The stationary saturated value of the diffraction efficiencyηsat strongly depended on the polarization of the recording andtest beams to the orientation of the LC director. The maximalself-diffraction and the diffraction of the test beam were ob-served when the polarization of the pump and test beamscoincided with the LC director, which meant that an extraor-dinary wave (e-wave) was propagating in the LC (see Table 1;

the angle α between the two recording beams was 0.87°,which corresponds to a grating period of Λ � 30 μm). Suchpolarization dependence is typical for LC systems with alight-induced isomerization of own or dopant molecules[14]. In these systems, the light-induced changes of the refrac-tive index Δn are proportional to the concentration of thelight-induced isomers, c, which is most effective for theextraordinary wave because of the positive absorption dichro-ism of the LC molecules and dopants. Thus, all the followingmeasurements were done in the ee-e configuration, where thefirst indices denote the recording beams and the third index isfor the test beam polarization.

Figure 4 shows the diffraction efficiency of the first-orderdiffraction of the test beam as a function of the intensity of therecording beams and grating period. The complex-doped LCappeared to be twice as effective as LC doped only with azodye. The intensity dependence of the saturated stationarydiffraction efficiency ηsat was not monotonic [Fig. 4(a)], butit had a maximum of nearly 0.25% for a range of intensitiesof 30–100 mW∕cm2. For larger intensities, the efficiencydecreased and showed a tendency to saturation. As fordye-doped LC, the intensity dependence of diffraction effi-ciency was almost monotonic, contrary to the complex-dopedLC, and saturates with intensity. Using the formula in Eq. (2)for the case of maximum diffraction efficiency, the refractiveindex change Δn and nonlinear parameter n2 � Δn∕I0 ofcomplex-doped LC can be obtained: Δn ≈ 5 × 10−4, and n2is up to 10−2 cm2∕W.

Table 1. Number of Orders Observed in theDiffraction of the Test Beam and in theSelf-Diffraction in Different IrradiationGeometries of the Complex-Doped LC

Geometry (RecordingBeams–Test BeamPolarization)

Pump I0,mW∕cm2

No. of Orders ofSelf-Diffraction

No. ofOrders ofTest Beam

oo-e 110 0 2ee-e 110 3 3ee-o 110 3 2oo-o 110 0 1

Fig. 4. (a) Dependence of the saturated stationary diffractionefficiency ηsat of the first-order diffraction of the test beam in the com-plex-doped and azo-dye-doped LC on intensity (the grating period isΛ � 30 μm). (b) Dependence of the stationary diffraction efficiencyon the grating period (the total intensity I0 � 30 mW∕cm2) in the com-plex-doped LC. The recording and test beams were parallel to the LCdirector (e-waves).


The dependence of the diffraction efficiency on the periodof the grating is presented in Fig. 4(b). In the measured range,ηsat increased with the period Λwith a changing rate: faster upto Λ � 30 μm, and then slower beyond that.

The dynamics of the grating recording are unusual andstrongly depend on the intensity of the recording beams(Fig. 5). The dependence η�t� is monotonic at low intensities(< 20 mW∕cm2), and has an extremum at the high intensities.This maximum shifts to the shorter exposure times andbecomes more pronounced with the increase of the intensity.We cannot claim that this extremum is caused by overmodu-lation, as even at high intensities, the observed maximal val-ues of diffraction efficiency are far below the theoreticallyexpected value of 33.8% for a thin phase grating, 6.25% fora sinusoidal transmittance grating [15,16], or 4.8% for a gratingof modulation of absorbance [17].

1. Optical Bleaching and DefocusingTo understand the unusual dynamics of the gratings formationin the complex-doped LC (Fig. 5), we measured the depend-ence of the light-induced changes of the total (Fig. 6) andon-axis transmittances (Fig. 7) on the laser intensity at457 nm using a method which is a modification of the spatialprofile analysis technique [18]. Only one pump laser beam wasused to irradiate the sample [Fig. 3(b)]. Since, during the gra-ting recording, the intensity modulation in the cell’s plane isI � I0�1� cos�2πx∕Λ��, i.e., the intensity at the maximum is2I0, we applied a one-beam intensity of Ipump � 2I0 to havethe same effect on the sample. The laser beam was notconvergent/divergent, and the beam waist at the sample planewas about 1 mm. The spot was stable over the time of theexperiment. A set of photodiodes [Fig. 3(b)] measured inci-dent laser power (before the sample), the total transmittedpower through the sample (close after the sample), and theon-axis transmittance through a pinhole (30 μm) in the farfield, visualizing the light-induced convergence/divergenceof the beam, if any. All dependences were normalized tothe spectral transmittance at 457 nm before the irradiationin order to distinguish the nonlinear optical response.

The experiments showed an increase of the sample’s trans-mittance by a factor of more than two, and the dependence onthe intensity [Fig. 6(a)]. This is assumed to be due to opticalbleaching, i.e., light-induced change of the absorption coeffi-cient, which strongly depends on the intensity [Fig. 6(b)].

The dynamics of the on-axis transmittance of the samplemeasured through a pinhole in the far field [Fig. 7(a)] showeddefocusing, i.e., light-induced refractive index changeoccurred. Light-induced defocusing depended on intensity[Fig. 7(b)]. The defocusing is quite strong (up to 45% at highintensities), and can be clearly seen when the refractive non-linear response is separated from the absorptive one by nor-malizing of the on-axis transmittance to total transmittance[Fig. 7(c)]. At low intensities, the defocusing effect diminishesand disappeared at intensities < 100 mW∕cm2. In the dye-doped LC, the light-induced defocusing is lower comparedwith complex-doped LC, and does not exceed 9%. To provethe appearance of defocusing effect, we measured the Gaus-sian profile of the laser beam without and with the cell usingthe knife-edge technique [19] at distances right after the celland in the far field. The measured profiles showed that, in thefar field after the cell, the Gaussian beam waist increased withdistance. These results confirmed light-induced defocusing.

At irradiation of the complex-doped LC, there are thusobserved both a light-induced change of the absorption coef-ficient, causing optical bleaching, and a light-induced changeof the refractive index causing beam defocusing. Obviously,the same processes occur at the grating recording. The holo-graphic gratings appeared to be formed by a light-inducedchange of both the absorption coefficient and the refractiveindex. These processes depend on intensity.

C. Holographic Grating RelaxationThe relaxation of the gratings is also unusual. The relaxationprocess was measured by tracking the intensity of a test beam

Fig. 5. Dynamics of the first-order diffraction efficiency at gratingrecording in the complex-doped LC. The grating period is Λ � 30 μm.

Fig. 6. (a) Dynamics of the normalized total transmittance T total ofthe complex-doped LC irradiated with e and o waves and (b) depend-ence of the saturated value Tsat;total on intensity at e-wave irradiation.The transmittances were normalized to the spectral transmittance at457 nm before irradiation.


using a photodiode connected to an oscilloscope as therecording beams were switched off. It appeared that the relax-ation process could not be fitted with a single exponentialfunction, but that was well described with two exponentialsA1e−t∕τ1 � A2e−t∕τ2 , giving two characteristic relaxation timesτ1 and τ2 (Fig. 8). Moreover, both relaxation times dependedon the intensity of the recording beams [Fig. 8(b)]. The ampli-tudes were A1∕A2 > 1 and also depended on the intensity.Both relaxation times for the complex-doped LC were almosttwice longer than those for the LC doped with the same azodye only.

To understand the origin of the grating relaxation, we mea-sured the thermal relaxation rate of the cis isomer of the azodye in the complex-doped LC using the method of Barrett et al.[20]. Exciting the chromophores with a circularly polarized

pump beam (λ � 457 nm, 30 mW∕cm2, Xenon-arc lamp fil-tered with a bandpass filter at 470 nm) for 4 s and detectingwith an Ocean Optics HR4000CG-UV-NIR spectrometer thesubsequent transmittance caused by cis-trans isomerizationgave the half-lifetime τcis for the HAB–DMA cis isomer inthe complex in LC (530 ms). The half-lifetime obtained herecorrelates well with one of the grating relaxation times τ1[Fig. 8(b)], thus indicating that one of the relaxation mecha-nisms is the thermal cis-to-trans isomerization of the azoben-zene molecules. The half-lifetime of the dye cis isomer withoutH bonding was shorter. The hydrogen bonding between thehydroxyl group from the azo dye and the pyridine nitrogenfrom the polymer seems to stabilize the cis form of the azodye, making the thermal relaxation slower.

4. DISCUSSIONAs we expected, the optical nonlinearity in the complex-doped LC was enhanced (the nonlinear parameter was upto 10−2 cm2∕W), and thus recording of the holographic gra-tings appeared to be more effective than in LC doped withthe same azo dye only. The presence of the polymer andits connection with the azo dye molecules via H bonds defi-nitely makes a difference; it results in a change of the opticalproperties, which improves the efficiency of the holographicgrating by a factor of two. This improvement has several rea-sons. First, the complex unit is much heavier than a separateazo dye molecule, making the diffusion process slower, thus,the light impact at grating recording is more effective. Second,

Fig. 7. (a) Dynamics of the normalized on-axis transmittance Ton-axisof the complex-doped LC irradiated with e and o waves (Ton-axis nor-malized to the spectral transmittance at 457 nm before irradiation).(b) Value of the normalized on-axis transmittance after saturationTsat;on-axis versus pump intensity. (c) Dynamics of the normalizedon-axis to total transmittance of the complex-doped and azo-dye-doped LCs.

Fig. 8. Dependence of the grating relaxation in the complex-dopedLC: (a) on the period (the total intensity I0 � 30 mW∕cm2) and (b) onthe total intensity of the recording beams (grating period isΛ � 30 μm). The recording and test beam polarizations were parallelto the LC director (e-waves).


the cis form of the azo dye in a complex lives longer, makingthe system more stable. Third, the polymer–azo-dye complexin the LC provides structural changes in the nematic matrixcompared to the azo-dye-doped LC: the LC molecules nowhave a different symmetry in their arrangement with respectto the azo dye, which is bound to the polymer chain. In a dye-doped LC, the azo dye molecules are “free” and surrounded byLC molecules from all around; in the case of the complex,the azo dye molecules are only partially surrounded by LCmolecules due to the presence of polymer chain. In [21],the authors suggest that in the nonlinearity mechanism, thisdifference in molecule arrangement plays an important role:during orientation-selective excitation of molecules (whichare dichroic) by polarized light, there is a torque due tochanges in intermolecular forces before and at irradiation.This torque is different for “free” dye molecules and H-bondedones. Thus at irradiation, the interaction of H-bonded azo dyemolecules and LC matrix is different from the interaction of“free” molecules and LC ones, and the influence on orderparameter change or dye-assisted LC reorientation will be dif-ferent in dye-doped and complex-doped LCs.

All previously mentioned changes in the complex-dopedLCs result in double effective grating. In the following section,we qualitatively discuss the grating formation/relaxation andits anomalies in the complex-doped LC in detail.

A. Light-Induced Changes in the Complex-Doped LCIn general, to explain the behavior of the complex-doped LCunder irradiation with resonant light, one should refer to thecharacteristics of the azo dye in the composite. Many azoben-zene compounds undergo the trans-to-cis photoisomerizationprocess either in solution [22] or in liquid-crystalline solidmatrices [23]. Azobenzene molecules have two stable configu-rations or isomers: the trans isomer, with a planar conforma-tion of the aromatic rings together with the azo group (rod-likeshape), and the cis isomer, with an out-of-plane configurationof the aromatic rings (bend-like shape). The trans-to-cis iso-merization process will take place when irradiating the transisomer with resonant light, while the cis isomer can be isomer-ized either by means of light or heat. The trans isomer usuallyhas two main absorption bands which correspond to then − π� electronic transition (S1←S0) and the π − π� electronictransition (S2←S0), while the cis isomer has the same transi-tions shifted to shorter wavelengths [24].

The HAB–DMA dye molecule is an aminoazobenzene-typederivative with an amino electron donor group in the paraposition (dimethylamino) with a π − π� electronic transitionband shifted to longer wavelengths. The π − π� band overlapswith the n − π� electronic transition band and aids the photo-isomerization process. The absorption of a photon at λpump �457 nm by the trans isomer promotes an excitation of oneelectron from the occupied π bonding (π) or the nonbonding(n) molecular orbital to the empty π antibonding molecularorbital (π�) in time scales of the order of 1–10 ps [25]. Then,the excited trans isomer undergoes a transformation into anexcited cis isomer state in the π antibonding molecular orbital(π�), which relaxes to its corresponding ground state throughan adiabatic photoreaction [26]. The final ground cis isomerstate evolves upon time to the corresponding ground transisomer state due to the low activation energy barrier, closingthe cycle in less than a second.

Figure 9 shows two main absorption bands of the complex-doped LC S1 and S2 at λn−π� � 456 nm and at λπ−π� � 412 nmfor the trans isomer. After conversion to the cis isomer, theabsorption bands shift to λn−π� � 448 nm and λπ−π� � 367 nm.The analysis of the spectrum at irradiation shows the absorp-tion bands due to the presence of a residual amount of thetrans isomers, and allows for the estimation of a concentra-tion of the cis isomers of approximately 70%.

When the azo dye molecule isomerizes, it changes the trans-mittance of the system and induces reorientation of either theLC director [3,4] or a local disorder of the liquid–crystallinematrix [1], that leads to a change in the intrinsic refractive/absorption parameters of the whole system. We have calcu-lated order parameter change [8] based on the polarizationspectra of the complex-doped LC without and with irradiationusing the formula

SLC ≈ Sdye � �Amax;jj − Amax;⊥�∕�Amax;jj � 2Amax;⊥�; (3)

where Amax;jj and Amax;⊥ are the absorption maxima for lightpolarized parallel and perpendicular to the LC director, re-spectively (Fig. 2). We observed a decrease of the orderparameter from S � 0.43 to 0.26 at irradiation with an e-waveof intensity 300 mW∕cm2 at 457 nm. Based on the polarizationspectra (Fig. 2) and the fact that the grating recording in thecomplex-doped LC is the most effective in the ee-e irradiationconfiguration, the dye-assisted reorientation mechanism canbe neglected. Thus, light-induced order parameter changedue to the trans-to-cis photoisomerization process of the

Fig. 9. UV–Vis deconvoluted spectra of the complexP4VP�HAB–DMA�0.5 in the 5CB matrix (a) before irradiation and(b) at irradiation with e-wave of 457 nm laser of 300 mW∕cm2. Thethickness of the cells was 20 μm.


azo dye molecules in the complex is responsible for thegrating formation in the complex-doped LC.

B. Anomalies in Holographic Grating Formation/RelaxationThe following peculiarities in the behavior of the holographicgratings in the complex-doped LC were observed:

• the grating relaxation process, which is describedwith the sum of exponentials with two characteristic times[Figs. 8(a) and 8(b)];

• intensity dependence of two grating relaxation times[Fig. 8(b)];

• nonmonotonic dependence of the saturated stationarydiffraction efficiency ηsat on the total intensity of the recordingbeams [Fig. 4(a)];

• dependence of the dynamic behavior of the diffractionefficiency η�t� on the total intensity of the recordingbeams (Fig. 5);

• light-induced change of both refractive index andabsorption coefficient, which depend on time and intensitydifferently (Figs. 6 and 7).

All these pecularities cannot be explained by the conven-tional model usually used in a case of grating recordingin dye-doped LCs [1,14]. This model assumes that gratingrecording is caused by an isomerization of the photosensitivemolecules, and the light-induced change in the refractiveindex Δn is proportional to the isomer concentration, namely,number of phototransformed molecules [1,14]. The isomerconcentration, in its turn, is proportional to the total intensityof the recording beams I0 [14]. From Eq. (2) η ∼ Δn2, thediffraction efficiency is proportional to the isomer concentra-tion, and thus to the total intensity. In the framework of thismodel, η�I0� should be quadratic at small intensities and sat-urate when reaching the photostationary equilibrium or maxi-mum cis isomer concentration at high intensities. On thecontrary, the experimentally obtained dependence η�I0� isnot monotonic [Fig. 4(a)], but has an extremum.

The dynamics of the grating formation/relaxation also can-not be explained by a simple model of the photoisomerizationof the dopants, in which these processes are described by asingle exponential function with the characteristic time deter-mined by the diffusion of the isomers and their lifetime. Thus,the multiple relaxation model should be suggested.

1. Two Relaxation TimesDespite the fact that it has not been seen on all azo dyes[1,9,11], multiple relaxation pathways [24] of cis isomers fol-lowing S1←S0 excitation have been predicted by simulations[27]. Similar to what we observed in the complex-doped LC, ithas been seen that direct S1←S0 excitation can relax not onlymonomodally, but bimodally or even stretched exponentially[28,29], depending on the solvent viscosity [30] and excitationwavelength [31,32]. Using a three-state model for photoisome-rization and assuming the optical transition rate from thetrans-to-trans� state and the thermal relaxation rate fromcis-to-trans states to have a form of the stretched exponential(or biexponential, as in our case), the authors of Ref. [29] wereable to analyze and explain the nonmonotonic behavior of thediffraction efficiency and the photoinduced birefringence. Inthis analysis, the concentration of the isomers depended on

the relaxation time and the degree of its dispersion throughthe expression [29]

c ∼S�x�

1� S�x�

�1 − exp

�−�1� S�x��

�tτ

�β��

: (4)

Here, S�x� � I�x�∕Isat is a saturation parameter, where Isat ∼τ−1 is the saturation intensity for the holographic grating, τ isthe azo molecules’ characteristic time, and I�x�, given byEq. (1), is the intensity interference pattern. The parameterβ (0 < β < 1) is a stretched exponent which quantifies theextent of the deviation from pure exponential, meaning thatthere is a dispersion of relaxation times [28]. In other words,the process of relaxation can be described with a set ofexponents.

Assuming that the relaxation of the cis isomers occursthrough different pathways (rotation, inversion, etc. [24]),one can get two (at least) characteristic times describing re-laxation of the gratings. The slower component of the gratingrelaxation process in the complex-doped LC with τ1 is morepronounced while the amplitude of the fast relaxation compo-nent with τ2 is smaller. The reason why the fast componenthas not been seen at half-lifetime measurements of cis isomeris still under discussion.

2. Grating Relaxation versus IntensityThe dependence of the grating relaxation times on intensitycan be explained as follows. As was shown in [33], the orderparameter S of the LC doped with an additive, which canundergo conformational changes, depends on the concentra-tion of the transformed molecules of the dopant. With theincrease of the pump intensity, the amount of the cis isomermolecules grows, reducing order parameter [see calculationwith Eq. (3) in Section 4.A] and inducing the LC matrix statecloser to the isotropic phase [33]. Since the matrix environ-ment changes with intensity, the half-lifetime of the cis-formmolecules τcis also changes depending on the order parameterof the LC [34]. As the relaxation time of the grating τ is deter-mined by the half-lifetime of the cis-form molecules τcis (seeSection 3.C), the higher the intensity, the lower the orderparameter, and consequently the faster the relaxation timeof the grating, which was experimentally observed.

3. Grating Diffraction EfficiencyHaving two relaxation times, the nonmonotonic behaviorof the saturated stationary ηsat�I� [Fig. 4(a)] can easily beexplained. Since diffraction efficiency is proportional to cisisomer concentration, η also depends on two characteristictimes and on the saturation parameter S�x� [Eq. (4)], whichin turn depends on these characteristic times, thus makingthe dependence nonmonotonic.

4. Nonlinear Absorptive/Refractive ResponseThe optical bleaching caused by light-induced change of theabsorption coefficient and the light-induced beam defocusingcaused by light-induced change in the order parameter, andthus in the effective refractive index, are the two mechanismssuggested to be responsible for the dynamics of the holo-graphic gratings in the complex-doped LC. In contrast tothe conventional gratings in azo-dye-doped LCs [1,2], whereusually only a phase grating is recorded due to a change of


the refractive index, in our complex-doped LC, both absorp-tion coefficient and refractive index changes are involved, i.e.,both amplitude and phase gratings are recorded. Both absorp-tion coefficient and refractive index changes are causedby photoisomerization, but the change in the absorptioncoefficient is connected with the dye while the change ofthe refractive index is determined with the LC matrix pertur-bation due to dye form change. These two mechanisms domi-nate at different time and intensity ranges. In the beginning,the light-induced absorption dominates, but with time, thelight-induced refractive nonlinear response starts to gain atintensities >100 mW∕cm2. Both processes depend on theintensity, so that the grating development will show a nonmo-notonic behavior (Fig. 5).

To summarize, all the observed anomalies of the opticalproperties of the studied system can be explained by differentsymmetry in the arrangement of the LC molecules withrespect to the azo dye bounded to the polymer side fragment,dispersion of the relaxations of the cis isomers in the presenceof the polymer with H bonds, and modulation of both theabsorption coefficient and the refractive index of the system.The doping of LC with polymer–azo-dye complex leads to theenhancement of optical nonlinearity of LC: at the same exper-imental conditions, there is no grating formation in LC orpolymer-doped LC, but the holographic grating in complex-doped LC is twice as efficient as in LC doped with the sameamount of free azo dye.

5. CONCLUSIONSWe observed the enhancement of optical nonlinearity withhigh nonlinear parameter (up to 10−2 cm2∕W) in a new hetero-geneous liquid-crystalline material where a H-bondedpolymer–azo-dye complex was used as a dopant in a LC bulkmatrix at low concentration. The effective dynamic holo-graphic gratings were recorded in the complex-doped LC.Double enhancement of the diffraction efficiency of holo-graphic gratings recorded in the complex-doped LC, com-pared to a plain azo-dye-doped LC with the same dye, wasobserved at very low intensities (of an order of tensof mW∕cm2). Moreover, the grating formation/relaxationprocesses in complex-doped LC showed anomalies: nonmo-notonic intensity dependence of the stationary and dynamicdiffraction efficiency of the first-order diffraction, and twocharacteristic times describing the grating relaxation processdepending on intensity. The observed peculiarities in the op-tical properties of the complex-doped LC were explained bydifferent symmetry in the arrangement of the LC moleculeswith respect to the azo dye bounded to the polymer, temporaldispersion of the relaxations of the cis isomers in the presenceof the polymer with H bonds that provides limited mobility ofthe azo dye molecules, and modulation of both the absorptioncoefficient and the refractive index due to trans-to-cis photo-isomerization. The observed enhancement of nonlinearityby H-bonded polymer–dye complexes as dopants in LC givesperspectives for new ways of control and tuning of the LCproperties and novel optical applications.

ACKNOWLEDGMENTSThis research was supported by the Academy of Finland(PHORMAT project no. 135106). We are grateful toProf. Yu. Reznikov (Institute of Physics, NAS of Ukraine),

Dr. V. Gaivoronsky (Institute of Physics, NAS of Ukraine),and Dr. A. Shevchenko (Aalto University, Finland) for usefuldiscussions.

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