Dynamics and efficiency of all-optical poling in polymers

17 April 1998

Chemical Physics Letters 286 Ž1998. 415–420

Dynamics and efficiency of all-optical poling in polymers Celine Fiorini, Jean-Michel Nunzi ´ LETI (CEA — Technologies AÕancees ´ ), DEIN–SPE, Groupe Composants Organiques, CEA r Saclay, 91191 Gif-sur-YÕette Cedex, France Received 28 July 1997; in final form 30 December 1997

Abstract A phenomenological model for photoinduced orientation mechanism in dyed polymers was recently proposed. Based on essential observable parameters, we develop here a simplified resolution which permits the derivation of an analytical dependence for the photoinduced second-order susceptibility. It shows that optimization of the all-optical poling efficiency must be treated not only in terms of nonlinear optics but also in terms of chemical physics and dynamics. Optimization of the poling dynamics involves key seeding parameters such as writing beam energies and matrix rigidity. Experiments performed in polymethylmethacrylate grafted or doped with Disperse Red 1 are used to verify the model. The two key parameters are the competing spontaneous and photoinduced orientation diffusion rates. q 1998 Elsevier Science B.V.

1. Introduction After the first evidence of a photoinduced second-harmonic ŽSH. generation in glass optical fibers w1x, all-optical poling has become an efficient orientation technique in the case of polymer materials. The major breakthrough with such a technique is the possibility of full control over the material polar molecular order, which opens new prospects in the field of devices for frequency conversion. Indeed, one important feature of such a technique is that molecules are self-organized in a periodic structure with a spatial period satisfying the phase-matching condition for frequency doubling. The physical origin of the process was identified as an efficient quasi-permanent orientation of the molecules following the selective polar excitation resulting from the coherent superposition of two beams at fundamental v and second-harmonic 2 v frequencies w2,3x. Recently, a simple model accounting for the essential phenomenology derived from experimental observations was proposed w4x. Experiments have been carried out in order to study in more detail the influence of the dual-frequency interference pattern on the all-optical poling efficiency. For this purpose, experiments were performed using different relative phase or energies for the writing beams at v and 2 v frequencies. In the stationary regime, the good agreement between numerical simulation and experiment confirmed the validity of the hypothesis concerning the molecular orientation mechanisms inside the polymeric matrix in the stationary regime w4x. In this Letter, we develop a further simplified implementation of the model in order to obtain insight into the transient all-optical poling regime. Understanding of the poling behavior and dynamics is of practical interest in view of materials optimization. The key parameters for optimization of both poling efficiency and dynamics are then identified. We show that optimization of the all-optical poling efficiency must be treated not only in terms 0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 0 0 8 - 6

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of nonlinear optics but also in terms of chemical physics and thus dynamics. The influence of parameters such as poling temperature and laser energy is studied experimentally, and it confirms the theoretical dependence. 2. Photoinduced orientation dynamics The all-optical poling technique is a seeding type process consisting of the simultaneous irradiation of a material by two fields at fundamental and second-harmonic frequencies. The photoinduced polar order results from the redistribution of molecules following their repeated selective polar excitation w4x. Polar excitation involves simultaneous one- and two-photon absorption processes on highly coherent electronic excited states w5x. In fact, the excitation probability can be written as the sum of three terms w3x: two axial terms related to oneand two-photon absorption, respectively and the polar term corresponding to the interference between one- and two-photon absorption. Practically, in addition to molecular orientational diffusion, polar ordering also results from the competition between polar and axial excitations. For the sake of simplicity, we restrict ourselves to the uniaxial problem in which polar order only depends on the polar Euler angle u . Practically, it corresponds to an all-optical poling process using linear polarizations of writing beams and uniaxial nonlinear molecules. As discussed previously, variation of the orientational distribution of molecules N Ž V 0 . initially oriented in the solid angle V 0 Ž u 0 , w 0 . is obtained after adding all the contributions to the photoinduced polar ordering w4x: d NŽ V0 . s yj Ž A cos 2 u 0 q B cos 4 u 0 q C cos 3 u 0 . N Ž V 0 . dt qjHH Ž A cos 2 u 1 q B cos 4 u 1 q C cos 3 u 1 . N Ž V 1 . P Ž V 1 ™ V 0 . d V 1 q D= 2 N Ž V 0 . . Ž 1. The first line in Eq. Ž1. corresponds to orientation hole-burning terms, the second line corresponds to the reorientation following non-radiative relaxation and the third line corresponds to orientational diffusion. j is the quantum efficiency for molecular reorientation: it accounts for parameters such as resonant excitation, non-radiative relaxation, transient photochromism, laser rate and matrix rigidity, etc. P Ž V 1 ™ V 0 . is the normalized probability for an excited molecule to leave its initial direction V 1Ž u 1 , w 1 . and change to the direction V 0 Ž u 0 , w 0 .. We have no direct access to the reorientation process, so that practically we consider the case of an isotropic angular redistribution: each molecule may rotate by any arbitrary angle with the same probability. As a consequence, the reorientation probability is a constant: P Ž V 1 ™ V 0 . s 1r4p. D is the orientational diffusion constant. A, B and C are the excitation rates due to the one-photon absorption at frequency 2 v , the two-photon absorption at frequency v and the interference term, respectively. The latter term is at the origin of the photoinduced second-order susceptibility x Ž2.. The phase dependence in cosŽ DF q D k P z . due to propagation along the z direction is contained in C. DF is the phase difference between writing beams measured on the front side of the sample Ž z s 0.. Excitation rates A, B and C are related to the field amplitudes at fundamental and SH frequencies Ev Ž z . and E2 v Ž z .. In the case of two-level molecules ŽFig. 1. with transition dipole moment m 01 and permanent dipole moment difference D m , we have w3,4x:

°A A m

~

BA

¢C A

2 5 2 5 2 01 E2 v s Bg

m201 D m2

Ž2" v . m201 D m

Ž "v.

2

,

5 Ev4 5 ,

Ž 2.

5 Ev2 E2)v 5 cos Ž DF q D k P z . s 2 Bg cos Ž DF q D k P z . ,

where g is a purely nonlinear optical parameter describing the relative weight between one- and two-photon

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Fig. 1. Amplitude of the second-harmonic generation signal in the case of two different Disperse Red 1rPMMA systems. Squares and triangles correspond to PMMA grafted with DR1 in a 35r65 molar ratio copolymer ŽDRG. and PMMA doped with DR1 in a 4 wt% guest–host system ŽDRD., respectively. The optical density at 532 nm is about unity in both samples. Determination of the photoinduced growth time t and of the second-order susceptibility x Ž2., sat induced at saturation is fitted from x Ž2. s x Ž2., sat w1yexpŽy trt .x, derived Ž2., sat Ž2., sat from Eq. Ž3.. We get t DR G f 3t DRD and x DRG f 2.5 x DRD .

absorption contributions. A ratio g s 1 corresponds to equal one- and two-photon excitation probabilities. g s 1 is conditioned by D m w4x. Owing to absorption at 2 v , g varies with propagation inside the sample:

g s g 0 exp Ž y a2 z . A

E2 v Ev2

.

With the present uniaxial restriction, the angular distribution N Ž V 0 . can be expanded in a Legendre polynomial series: 1 NŽ V0 . s NŽ u0 . s Ý 2 jq A j Pj Ž cos Ž u 0 . . , 2

j

where A j are the order parameters. Resolution of Eq. Ž1. leaves a linear set of coupled differential equations that describes the evolution of the order parameters A j w4x, from which photoinduced anisotropy and non-centrosymmetry can be determined. The second-order susceptibility x Ž2. depends indeed on the material order parameters A j :

x XŽ2.X X s Ne00b Ž 35 A1 q 25 A 3 . , where N0 is the number of molecules per unit volume and b is the hyperpolarizability of the molecule. An analytical solution permits easy identification of the relevant parameters for an efficient poling. Importantly, the basic physics of the photoinduced poling dynamics is already contained into the first-order Legendre polynomial A1. Though first-order truncation is a raw approximation, experimental results show its relevance to the prediction of all-optical poling features. Additionally, experimental analysis of the second-order susceptibility tensor x Ž2. photoinduced using linear writing beam polarizations yields w4x, x XŽ2.Y Y x XŽ2.X X

y A3 1 s 3 AA11 q 2 A3 f 3 ,

showing that the third-order contribution A 3 in x Ž2. is negligible. Truncation of the model to first order yields

x Ž2. f

3 Nb 5 e0

A1 A

g cos Ž DF q D k P z . 2

15 q 21g q 70 D

ž

1 y exp y

jB 35

Ž 15 q 21g 2 q 70 D . t

/

,

Ž 3.

where D s DrŽ j B . is a parameter describing the ratio between the spontaneous orientation and photoinduced reorientation diffusion rates. We see that ignoring the axial order parameter A 2 does not change the basic

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C. Fiorini, J.-M. Nunzir Chemical Physics Letters 286 (1998) 415–420

physics of the problem which is that a non-optimized intensity ratio g reduces the polar order expressed by Eq. Ž3.. Optimum poling efficiency is achieved with a writing beam intensity ratio corresponding to: g opt s Ž 15 q 70 D . r21 . Under low diffusion conditions, optimum intensity ratio is achieved for equal one and two-photon absorptions: g opt f 1. When both the relative phase w6x and relative intensity of the writing beams are optimized Žg f 1. w4x, the maximum photoinduced susceptibility x Ž2., sat that can be achieved after saturation depends only on the ratio D between spontaneous and photoinduced reorientation diffusion rates. 1 sat x XŽ2., . Ž 4. XX A 36 q 70 D This is evidence for the trade-off between matrix rigidity and photoinduced reorientation efficiency. As deduced from Eq. Ž3., growth time t of the photoinduced polar order:

(

x Ž2. s x Ž2., sat 1 y exp Ž ytrt . shows comparable dependence: 35rj B ts . Ž 5. 36 q 70 D Finally, we see that the microscopic all-optical orientation process is exclusively governed by two competing parameters which are the spontaneous and photoinduced orientation diffusion rates. 3. Experimental verification Confirmation of the model is given by all-optical poling experiments performed on thin polymeric films of polymethylmethacrylate ŽPMMA. grafted or doped with Disperse Red 1 Ž4-ŽN-Ž2-hydroxyethyl.-N-ethyl.amino-4X x-nitroazobenzene, DR1.. The glass transition temperature was determined by differential scanning calorimetry. It is Tg s 1308C in the grafted copolymer. In our apparatus w3,4x, writing and probing periods are alternated. Writing periods correspond to the simultaneous irradiation of the sample by the coherent superposition of the 1064 nm fundamental and the 532 nm second-harmonic light derived from a picosecond-pulsed Nd:YAG laser. Writing beam polarizations are set parallel and their relative intensities and phase are optimized Žg f 1 and cosŽ DF q D k P z . f 1, for samples thinner than one coherence length.. The photoinduced secondorder susceptibility x Ž2. is probed using SH generation inside the sample.

Fig. 2. Experimental growth Žnegative times. and decay Žpositive times. of the photoinduced x Ž2. under different sample temperatures. Sample is a spin-coated 0.1 mm thin film of PMMA grafted with DR1 Ž35r65 molecular ratio., its optical density is ; 0.3 at 0.532 mm. X The orientational diffusion constant D is fitted for each temperature from the dark decay at positive times using x Ž2. A expŽy trt . with X t s1r2 D.

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Fig. 3. Influence of the orientational diffusion constant D on the photoinduced x Ž2., sat measured at saturation. Sample is a spin-coated 0.1 mm thin film of PMMA grafted with DR1, its optical density is ; 0.3 at 0.532 mm. Each data point is obtained under optimized intensities and phase of the writing beams. Variation of the orientational diffusion constant D in the insert was achieved by varying the seeding X X temperature and analyzing the photoinduced x Ž2. decay t Žsee Fig. 2.. It fits with the functional behavior t ŽT . A expwy K rŽT0 yT .x, where T0 fTg q50. Fitting of the saturated x Ž2., sat dependence with D is achieved using Eq. Ž4.. For each data point, corresponding to a X X different seeding temperature, t was deduced from the functional behavior t ŽT . A expwy K rŽT0 yT .x shown in insert.

The typical x Ž2. growth, recorded in two similar materials exhibiting different orientational diffusion constants D, is presented in Fig. 1. The large diffusion constant material is PMMA doped with DR1 and the low one is PMMA grafted with DR1. As can be deduced from the fit using x Ž2. s x Ž2., sat w1 y expŽytrt .x, the photoinduced polar order growth-rate 1rt is 3 times larger in the case of the guest–host system and the second-order susceptibility x Ž2., sat achieved at saturation is ; 3 times lower. This confirms the theoretical dependence in Eqs. Ž4. and Ž5., showing that both the all-optical poling growth time t and saturation x Ž2., sat vary in the same way, i.e. inversely with the diffusion constant D.

Fig. 4. Influence of the fundamental writing beam intensity Iv on the photoinduced x Ž2., sat measured at saturation. Sample is a spin-coated 0.1 mm thin film of PMMA grafted with DR1, its optical density is ; 0.3 at 0.532 mm. Each data point is obtained under optimized intensities and phase of the writing beams. Fundamental writing beam intensity Iv is practically tuned by variation of the laser energy. Since the second-harmonic writing beam is obtained by frequency doubling, the writing beams intensity ratio g f1 remains identical for all experimental points. The insert shows the intensity dependence of the photoinduced x Ž2. growth time t . Simultaneous fitting of x Ž2., sat and t is achieved according to Eqs. Ž4. and Ž5. using the same two parameters. Note that the last value of x Ž2., sat corresponding to 1r Iv2 s 0.028 is given only as a tendency. It was determined from a mono-exponential fit of the signal growth. However, the signal growth is so slow that a seeding time limited to ; 2 h was not enough to observe saturation of the growth.

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Typical x Ž2. growth and decay dynamics recorded in the film of PMMA grafted with DR1 are presented in Fig. 2. The diffusion constant D is controlled with the applied sample temperature. It is experimentally fitted from x Ž2. lifetime measurements in the dark, using a mono-exponential behavior deduced from the model:

x Ž2. Ž t . s x Ž2., sat exp Ž y2 Dt . . Figs. 3 and 4 show the influence of the ratio between spontaneous and photoinduced reorientation diffusion rates: D s DrŽ j B .. The writing beam energies in Fig. 4 were constant. The orientational diffusion constant D was varied using different sample temperatures. The insert in Fig. 4 shows the temperature dependence of the photoinduced x Ž2. lifetime t X s 1r2 D. It follows the usual Williams–Landel–Ferry or Vogel–Fulcher functional behavior w7,8x:

t X Ž T . A exp yKr Ž T0 y T . , in which K is a constant and T0 is related to the glass transition temperature Tg as T0 f Tg q 50. Experiments in Fig. 4 were performed at ambient temperature using different writing beam energies. As is shown by fitting with the theoretical dependencies derived from Eq. Ž5., in Figs. 3 and 4, the photoinduced x Ž2., sat measured at saturation is described by the model. This confirms that such self-consistent model provides a good prediction of the all-optical poling dynamics in polymers, using only two key competing parameters.

4. Conclusions New results concerning the dynamics of all-optical poling of polymers has been presented. A simplified resolution of a self-consistent model based on observable parameters, permits the identification of the key parameters for an optimized poling efficiency. After showing the influence of the relative phase and intensities of the writing beams w4x, we show here another important seeding condition which is the control of the relative weight between molecular mobility inside the matrix and photoinduced reorientation. Experimental results are in good agreement with the theoretical ones, confirming the relevance of such a phenomenological description. Interestingly, such a description may describe successfully all-optical poling beyond the axial restriction, in the case of octupolar molecules or fields w9,10x for instance. This opens interesting perspectives towards the macroscopic all-optical engineering of stable and transparent phase-matched materials for frequency conversion.

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