Analyses of the Diffraction Efficiencies, Birefringence, and Surface

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2654

J. Phys. Chem. B 1998, 102, 2654-2662

Analyses of the Diffraction Efficiencies, Birefringence, and Surface Relief Gratings on Azobenzene-Containing Polymer Films F. Lagugne´ Labarthet, T. Buffeteau, and C. Sourisseau* Laboratoire de Physicochimie Mole´ culaire (UMR 5803-CNRS), UniVersite´ Bordeaux I, 351 Cours de la Libe´ ration, 33405 Talence, France ReceiVed: NoVember 3, 1997; In Final Form: January 20, 1998

Dynamical experimental studies on the diffraction efficiencies and the formation of birefringence grating and surface relief grating on doped and/or covalently bonded azobenzene derivatives containing polymer films were carried out using laser beams with different polarizations. From polarization analyses of the first-order ((1) diffracted beams, the contributions to the diffraction efficiency are separated into an anisotropic (or birefringence) part and a surface relief part. During the growth of the gratings the dynamical responses of both contributions appear to be quite distinct, and estimates of the time variations of the anisotropic phase shift, ∆φ, due to the induced birefringence and of the surface relief height, 2∆d, due to the polymer mass transport are obtained. Calculations and simulations of the theoretical expressions allow us to confirm the experimental findings and to reproduce all the observed polarized first-order diffraction curves with good agreement, even when the surface relief is important in the covalently bonded azobenzene polymer films. In these functionalized systems we thus conclude that very efficient permanent surface relief gratings are formed using right-circular and left-circular interfering laser beams.

Introduction Azo-dye-containing polymer systems have received much attention in the last few years because of their potential uses in various optical applications, i.e. photon mode optical memories,1,2 information storage,3 optical switching,4 and nonlinear optics.5 Many recent studies have shown that the main interest of amorphous polymers containing azobenzene derivatives is due to their dichroic and birefringent properties when they are illuminated by a polarized light;6-12 this is the consequence of a reversible “trans T cis” photoisomerization with respect to the NdN double bond, which causes a redistribution in the orientation of the photochromic entities. Therefore, amorphous polymers containing side-chain azobenzene groups have been demonstrated to be good candidates for reversible optical storage,4-8 and several groups have already found that diffraction gratings with efficiencies up to 70% can be created in such thin films by using two interfering polarized laser beams.8,13-20 In fact, the feasibility of recording phase polarization holograms with mutually orthogonal polarizations in materials having photoinduced anisotropy was first demonstrated by Kakichashvili21 and later by Todorov et al.22,23 More recently, the formation of a large surface modulation on such polymer films, as checked by Atomic force microscopy (AFM),13-16,24 has been assigned to a polymer chain migration, and during recordings, two distinct processes, i.e., the formations of birefringence grating and surface relief grating, were observed. Also, the observation of strong surface relief features has been reported, even when the two writing beams had parallel polarizations, thus ruling out the possibility of thermal effects.18,24 Finally, Holme et al.18 have shown that it is possible to extract information about the magnitudes and the time variations of the anisotropy resulting from the reorientation of the dye * Author to whom correspondence should be addressed. E-mail: csouri@ morgane.lsmc.u-bordeaux.fr.

molecules and of the phase changes caused by the induced surface relief grating through polarization measurements of the diffracted beams in the first order. However, their recent and elegant experiments were performed on a low Tg (20-30 °C) side-chain liquid crystalline polyester film in which the anisotropic phase grating contribution was by far dominant and severe approximations were made to interpret the results. In the present study we have made use of a quite general Jones’ matrix formalism for birefringent materials presenting a surface modulation and thus tried to develop more precise expressions for the intensities of the diffracted beams. In this approach we have considered that orientation effects taking place in these photosensible systems are governed by the “holeburning” mechanism. Therefore, we have derived the various expressions of the polarization contents for a circularly as well as a linearly polarized probe beam. Finally, we have compared experimental results obtained on dye-doped and covalently bonded polymer systems in order to show how far the amplitude of the surface relief grating is different in both systems and can be followed or monitored from such polarization analyses. Experimental Part We have followed dynamical grating formations either on doped polymer systems (Disperse Red 1/ PMMA; 10% w/w) or on functionalized polymer films (pDR1M-co-MMA; 12% DR1M). Thin films were made by dissolving the polymer/ dye system in chloroform; solutions were filtered with 0.6 µm micropore and spun cast onto glass substrates. Films were baked for 1 h at 90 °C in order to remove any remaining solvent. Film thicknesses were checked by profilometry measurements and typically ranged from 0.9 to 1.1 µm. The experimental setup for grating inscription (Figure 1) was similar to that first proposed by Rochon et al.13 A 514.5 nm beam from an linearly polarized laser line (ILT 5490) was used

S1089-5647(98)00050-9 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/21/1998

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Figure 1. Experimental setup for grating inscription. We have used the following configurations: rotator V + polarizer V (IVV), rotator V + polarizer H (IVH), rotator H + polarizer H (IHH), rotator H + polarizer V (IHV), λ/4 + polarizer V (I⊥), λ/4 + polarizer H (I|), and λ/4 without polarizer (I∩). The terms 0, (1 indicate the 0th-order transmitted and the (1-order diffracted beams, respectively.

for writing. The beam was expanded to a diameter of 10 mm, and the irradiance on the sample was approximately 100 mW/ cm2. A quarter wave plate was used to set a circular polarization of the pump beam. This beam was incident onto the sample holder, which consisted of a sample set at right angle to a front surface mirror. The mirror reflected half of the incident pump beam with an orthogonal polarization, which interfered with the direct beam onto the sample. The sample holder was set on a goniometer in order to control the incidence angle (θ) of the pump beam, which defines the pattern spacing (Λ) according to Bragg’s law: Λ ) λ/(2 sin θ). A scanning electronic microscope was used to check the grating spacing, and a typical photograph of a 1 µm pattern is presented in Figure 2a; also a surprising surface relief was obtained by superimposing two orthogonally photoinduced gratings, as shown in Figure 2b: this method provides us high optical quality and homogeneous surface gratings. The time evolution of the optically induced grating was monitored using a linearly polarized He-Ne (TEM00, 632.8 nm, 5 mW) laser beam and a silicon diode as detector. The probe beam was modulated at a sampling rate of 1 kHz and demodulated with a lock-in amplifier to improve the signal/ noise ratio. According to the detector position, we can follow the time variation of the zero order transmitted and the first ((1)-order diffracted beams. As shown in Figure 1, different configurations of polarization can be set by adding a λ/4 plate on the incident beam and/or a Polaroid on the diffracted beam. In typical experiments, analyses were performed on 1 µm spacing gratings (i.e., θ ≈ 15°), with a time resolution of 1 point/s, during a 1500 s exposure (pump on) followed by a 1000 s relaxation period (pump off). Theoretical Treatment Under the “angular hole-burning” model as reported by Sekkat et al.9 and considering a very small angle of incidence (θ e 15°), the transmission Jones’ matrix describing the polarization grating on a phase hologram created by two circularly polarized orthogonal recording beams is given by circular

[Jphase]

(

eiφ0

)

)

cos ∆φ + i sin ∆φ cos δ i sin ∆φ sin δ i sin ∆φ sin δ cos ∆φ - i sin ∆φ cos δ (1)

Figure 2. Scanning electronic microscopy photographies of (a) a single grating pattern and (b) two orthogonally superimposed gratings (×15000). The time exposure and pump irradiance were 1 h and 100 mW/cm2, respectively.

where φ0 ) (-2πd/λ)((n| + n⊥)/2) and ∆φ ) (-2πd/λ)((n| n⊥)/2) ) -πd∆n/λ is the anisotropic phase shift due to the induced birefringence ∆n, d is the film thickness, and λ is the probe wavelength; the term δ is the phase difference between the two writing waves. The complete transmittance matrix may be developed into the zero-order and the (1 first-order beams:

{

( )

[Tanis] ) eiφ0 cos ∆φ

( ) ( )}

1 0 eiδ i 1 + sin ∆φ + 0 1 2 1 -i -1 e-iδ i sin ∆φ 2 -1 -i

(2)

Similarly, it is well-known that a surface relief grating also appears during the polarization holographic recording process, giving rise to a surface modulation, d + ∆d cos(δ + φ0), the amplitude transmittance of which is given by

( )

[Trelief] ) ei∆ψ cos(δ+φ0)

1 0 0 1

(3)

where ∆ψ ) (πneff∆d)/λ. neff is the effective refractive index associated with an inhomogeneous layer (polymer + air), 2∆d is the surface relief height, and the constant φ0 accounts for the possible phase shift

2656 J. Phys. Chem. B, Vol. 102, No. 15, 1998

Lagugne´ Labarthet et al. functions according to

SCHEME 1: Illustration of the Phase and Surface Relief Gratings, as Well as the Related Parameters ∆φ, ∆ψ, and O0

∞

Ij(i∆ψ) cos[j(δ + φ0)] ∑ j)1

ei∆ψ cos(δ+φ0) ) I0(i∆ψ) + 2

(4)

and, as described by Olver,25 the modified Bessel function of the jth order, Ij(i∆ψ), is related to the normal Bessel function Jj(∆ψ) by the relation between the phase and relief gratings, as shown in Scheme 1. The exponential term must be developed into modified Bessel

Ij(i∆ψ) ) ei(π/2)jJj(∆ψ)

(5)

As the probe beam passes first through the relief grating and then through the polarization grating, the total Jones’ matrix of the system is (∞

T ) TanisTrelief ) e {T0 + iφ0

e(kiδT(k} ∑ k)(1

(6)

where T0, Tk are the transmission Jones matrices of the zero-order transmitted beam and of the kth-order diffracted beams. Carrying out the above calculations, one gets

T0 )

(

cos ∆φ J0(∆ψ) - sin ∆φ J1(∆ψ) cos φ0 sin ∆φ J1(∆ψ) sin φ0

sin ∆φ J1(∆ψ) sin φ0 cos ∆φ J0(∆ψ) + sin ∆φ J1(∆ψ) cos φ0

)

(7)

and

T(k )

(

a+b c

c a-b

)

(8)

where

a ) ik cos ∆φ Jke(kiφ0 ik b ) sin ∆φ[Jk-1e((k-1)iφ0 - Jk+1e((k+1)iφ0] 2 ik-1 c ) ( sin ∆φ[Jk-1e((k-1)iφ0 + Jk+1e((k+1)iφ0] 2 in which, for simplicity, J0, J1, and Jk stand for J0(∆ψ), J1(∆ψ), and Jk(∆ψ), respectively. If the probe He-Ne laser is right circularly polarized (∩), i.e.

()

E0 1 x2 i

then under polarization analyses the zero-order transmitted wave and the higher-order diffracted ones take the following intensity expressions:

{

E02 or S-k) ) [cos2 ∆φ Jk2 + sin2 ∆φ Jk+12 - sin 2∆φ JkJk+1 cos φ0] 2 E02 I∩⊥(S0 or S-k) ) [cos2 ∆φ Jk2 + sin2 ∆φ Jk+12 + sin 2∆φ JkJk+1 cos φ0] 2

I∩| (S0

and

{

E02 [cos2 ∆φ Jk2 + sin2 ∆φ Jk-12 + sin 2∆φ JkJk-1 cos φ0] ) 2 E02 [cos2 ∆φ Jk2 + sin2 ∆φ Jk-12 - sin 2∆φ JkJk-1 cos φ0] I∩⊥(S+k*0) ) 2

I∩| (S+k*0)

(9a) (9b)

(10a) (10b)

Here, the notations I∩| and I∩⊥ stand for polarization analyses along the parallel and perpendicular direction with respect to the incident plane, as shown in Figure 1, i.e., strictly parallel and perpendicular to the grating vector for the zero-order transmitted wave.

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J. Phys. Chem. B, Vol. 102, No. 15, 1998 2657

Similarly, if the probe He-Ne beam is horizontally or vertically polarized, i.e., with the electric field matrix

()

E0

1 0

()

or E0

0 1

under polarization analyses the corresponding intensities are given by

{

IHH(S0) ) E02[cos2 ∆φ J02 + sin2 ∆φ J12 cos2 φ0 - sin 2∆φ J0J1 cos φ0] IVV(S0) ) E02[cos2 ∆φ J02 + sin2 ∆φ J12 cos2 φ0 + sin 2∆φ J0J1 cos φ0] IHV(S0) ) IVH(S0) ) E02[sin2 ∆φ J12 sin2 φ0]

{

and

[ [

(11a) (11b) (11c)

] ]

1 cos2 ∆φ Jk2 + sin2 ∆φ(Jk-12 + Jk+12 - 2Jk-1Jk+1 cos 2φ0) 4 IHH(S(k) ) 1 + sin 2∆φ Jk(Jk-1 - Jk+1) cos φ0 2 1 cos2 ∆φ Jk2 + sin2 ∆φ(Jk-12 + Jk+12 - 2Jk-1Jk+1 cos 2φ0) 4 IVV(S(k) ) E02 1 - sin 2∆φ Jk(Jk-1 - Jk+1) cos φ0 2 1 1 IHV(S(k) ) IVH(S(k) ) E02 sin2 ∆φ(Jk-12 + Jk+12) + sin2 ∆φ Jk-1Jk+1 cos 2φ0 4 2 E02

[

The above general expressions are in agreement with those already published by Holme et al.,18 which correspond to a limit case. Indeed, they have assumed that the phase shift of the surface relief was small and included only first-order terms with the crude simplifications J0(∆ψ) ) 1 and J2(∆ψ) ) 0. Thus, by using the zero-order transmitted beam before the grating formation for normalization (I0 ) E02 ) 1) and taking account of the transmission factors of the Polaroid elements, one can measure independently the polarized relative intensities I∩| (S+1), I∩⊥(S+1), I∩| (S-1), and I∩⊥(S-1) the total relative intensities without polarization analyses I∩(S+1) and I∩(S-1) when the probe He-Ne laser is right circularly polarized. Similarly, one can measure the polarized relative intensities IHH(S+1), IHV(S+1) or IVH(S+1), IVV(S+1) and the total relative intensities without analyses IH(S+1), IV(S+1) when the probe beam is linearly polarized. From measurements of the time variations of these relative intensities, we shall thus extract estimates of the ∆φ(t), ∆ψ(t), and φ0(t) parameters. It may be underlined that the above results were derived using the assumption of an effective “angular hole-burning” mechanism under low pump intensities, i.e., when considering a population of absorbing trans chromophores nT(cos θ) ) N(1 - τ cos2 θ)/4π, where θ is the angle of the polarization direction of the pump with respect to the long axis director of the cylindrical dye molecules and τ ) (Ipump/Isaturation) is assumed weaker than 1.0. Nevertheless, these results can be generalized to any photooriented system provided that it remains uniaxial and that the orientation effects are described in terms of the two first even-parity Legendre’ polynomials. Under these conditions the population is given by

nT(〈cos θ〉) )

∑(2l + 1)TlPl(cos θ) )

1 4π

1 (T P (cos θ) + 5T2P2(cos θ)) (13) 4π 0 0 Considering that 〈P0(cos θ)〉 ) 1 and 〈P2(cos θ)〉 )

1/ (3 2

(12a)

(12b)

]

(12c)

cos2 θ - 1) eq 13 becomes

nT(〈cos θ〉) )

1 5 15 T - T + T2 cos2 θ ) 4π 0 2 2 2 N (A + B cos2 θ) (14) 4π

((

)

)

so that the mean polarization susceptibility χ0 is now equal to NRuA/3 and the susceptibility variation ∆χ, related to the anisotropy ∆φ, equal to -NRuB/15 ) -RuT2/2 is substituted for NRuτ/15 (it is noteworthy that τ and B have positive and negative signs, respectively). This means that, according to our previous real-time UV-visible absorption spectroscopic results in these systems,12 one can make predictions about the time variations of the formation at short time of the birefringence grating provided there are no strong interferences with the surface relief mechanism. Thus, this paper is organized as follows: in the next section we present the main experimental results, and in the following discussion section we will discuss comparatively in the doped and the functionalized systems the time dependences of the relevant ∆φ, ∆ψ, and φ0 parameters. Experimental Results The experimental curves of I∩(t), I∩| (t), and I∩⊥(t) for the ( first-order diffracted beams in a doped polymer system are shown in Figure 3a,b. When the pump laser is turned on (after 60 s), the relative intensity of the +1 diffracted beam I∩(S+1), which corresponds usually to the diffraction efficiency, increases up to 1.5% in approximately 1000 s and then remains constant. The curves for the polarized relative intensities I∩| (S+1) and I∩⊥(S+1) have nearly the same shape in the first hundred seconds, but they are significantly different after 500 s. When the pump is turned off, all the curves decrease drastically, indicating that the grating is not permanent in this system; this comes from the relaxation in the orientation of the chromophores in the PMMA matrix. The diffraction efficiency of the -1order diffracted beam I∩(S-1) is very small after 1500 s (about 0.1%) but not zero, indicating that a surface relief grating is

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Lagugne´ Labarthet et al.

Figure 3. Experimental curves obtained on a doped polymer film as a function of time (a) for a +1-order diffracted beam using a circularly polarized He-Ne laser beam, (b) for -1-order diffracted beam using a circularly polarized He-Ne laser beam, and (c) for a +1-order diffracted beam using a linearly polarized He-Ne laser beam.

Figure 4. Experimental curves obtained on a functionalized polymer film as a function of time (a) for a +1-order diffracted beam using a circularly polarized He-Ne laser beam, (b) for a -1-order diffracted beam using a circularly polarized He-Ne laser beam, and (c) for a +1-order diffracted beam using a linearly polarized He-Ne laser beam.

formed during the irradiation of the polymer film. The polarized relative intensities I∩| (S-1) and I∩⊥(S-1) are quite similar, and no significant differences are observed during the irradiation period. All these observations are in agreement with eqs 9a, 9b and 10a, 10b considering that the phase shift of the surface relief is small (i.e., J2(∆ψ) , J1(∆ψ) and J0(∆ψ) ≈ 1) and that cos φ0 is positive (i.e., φ0[0,π/2]). Similarly, for the same doped polymer film the experimental curves IHH(t), IHV(t), IVH(t), and IVV(t) of the +1-order diffracted beam are shown in Figure 3c. These curves are sensitive to polarization analyses as expected from eqs 12a, 12b, and 12c. It is noteworthy that IHV(t) is approximately equal to IVH(t) and that IHH(t) is larger than IVV(t), indicating again that cos φ0 is positive. In addition, the relative intensities obtained now for a functionalized polymer film are presented in Figure 4a (circularly polarized probe laser, +1-order diffracted beam), 4b (circularly polarized probe laser, -1-order diffracted beam), and 4c (linearly polarized probe laser, +1-order diffracted beam).

All the experimental curves reveal a more important diffraction efficiency than observed previously. For instance, the diffraction efficiency on the +1-order diffracted beam is 8% at 1500 s and reaches 15% after 1 h of irradiation (even better efficiencies can be achieved using a higher laser power), while it did not exceed 1.5% for the doped polymer film. Moreover, when the pump laser is turned off, the decreases in the diffraction efficiencies are very small, confirming that the diffraction grating is quasi-permanent. Nevertheless, the behavior of the time dependences of the I∩(S+1), I∩| (S+1), and I∩⊥(S+1) curves is not straightforward to understand: in the first hundred seconds their shapes are similar to those observed with a doped polymer, whereas after a few hundred seconds the diffraction efficiencies appear to be very dependent on the polarization of the probe laser. In particular, as shown in Figure 4a, both the I∩| (S+1) and I∩⊥(S+1) curves exhibit an initial and rapid growth (on the order of seconds) of the efficiency up to 2% and 1%, respectively, corresponding to formation of the reversible volume birefringence grating; then

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a slower increase process is noted on the I∩| (S+1) curve, while the I∩⊥(S+1) one displays firstly a drastic decrease (on the order of 600 s) and secondly a monotonic increase. This provides evidence of interfering contributions in the formation mechanisms of the phase and surface relief gratings. Finally, and in contrast with the above behavior, it is remarkable that the diffraction efficiencies of the -1-order diffracted beam increase quasi-continuously and their dependences on the polarization are weak. Discussion The determination of the phase shifts due to the anisotropy ∆φ (phase grating) and surface relief ∆ψ (surface grating) as well as the phase shift φ0 between the two gratings can now be carried out from the experimental curves. However, depending on the values expected for ∆ψ in the doped or functionalized polymer films, a different strategy has been used. Doped Polymer System. The diffraction efficiency of the -1-order diffracted beam I∩(S-1) allows the direct estimation of the phase shift of the surface relief grating. Indeed, considering the sum of eqs 9a and 9b, we obtain

I∩(S-1) ) cos2 ∆φ J12(∆ψ) + sin2 ∆φ J22(∆ψ) (15) If we assume that both phase shifts due to the anisotropy and the surface relief are small in this system, so that cos2 ∆φ . sin2 ∆φ and J12(∆ψ) . J22(∆ψ), respectively, the intensity in the I∩(S-1) response must be governed by J12(∆ψ) and is only dependent on the surface relief. Under these conditions one can determine ∆ψ, and its time variations ∆ψ(t) are reported in Figure 5a. Then, the phase shift of the phase grating ∆φ can be obtained from the diffraction efficiency of the +1-order diffracted beam I∩(S+1) by using the relation

(x

∆φ ) arccos

I∩(S+1) - J02(∆ψ)

)

J12(∆ψ) - J02(∆ψ)

(16)

where J0(∆ψ) and J1(∆ψ) are calculated from the values of ∆ψ reported above. The time variations of ∆φ(t) are shown in Figure 5a. We thus come to the conclusion that the phase grating and the surface relief grating are appearing simultaneously, but their time dependences are markedly different during the irradiation process as well as during the relaxation when the pump is turned off. Now the phase shift between the phase grating and the surface relief grating, φ0, can be determined from the polarized relative intensities of the +1-order beam by using the relation

(

φ0 ) arccos

I∩| (S+1)

-

I∩⊥(S+1)

)

sin(2∆φ) J0(∆ψ) J1(∆ψ)

(17)

The time variations of φ0(t) are shown in Figure 5b. Values of φ0 decrease rapidly in the first hundred seconds from probably the 90° value and, afterthat, reach a plateau equal to 80° during the irradiation. In fact, the divergence noted in the first few seconds is due to a difference in the kinetics (fast processes) of the two experimental curves I∩| (S+1) and I∩⊥(S+1). When the pump is turned off, the values of φ0 decrease again and reach a plateau value equal to roughly 60°: this behavior is certainly due to distinct relaxation mechanisms in the phase grating and in the erasing of the surface relief grating. As a complementary check of the above results, the set of parameters ∆φ(t), ∆ψ(t), and φ0(t) presented in Figure 5a,b were

Figure 5. Relevant parameters in a doped polymer sytem. (a) Time evolution of the phase shifts due to the anisotropy ∆φ(t) and to the surface relief ∆ψ(t) and (b) time evolution of the phase shift φ0 between the phase and surface gratings.

injected in the intensity eqs 9-12, and very good agreements between the experimental and simulated curves were obtained in all cases for both the circular and linear polarization configurations. Functionalized Polymer System. As shown by Rochon et al.8 from AFM experiments, the surface relief grating optically inscribed onto a functionalized polymer film displays a grating depth of few hundred nanometers. Thus, the phase shift of the surface relief presents higher values than that observed for the doped polymer system, and no assumption can be made on the Bessel functions. Consequently, a direct determination of ∆ψ(t) from the experimental curve I∩(S-1) is rendered impossible. The determination of ∆ψ(t) is now carried out by resolving numerically the following equality extracted from eqs 9 and 10:

cos ∆φ ) 2

I∩(S+1) - J02(∆ψ) J12(∆ψ) - J02(∆ψ)

)

I∩(S-1) - J22(∆ψ) J12(∆ψ) - J22(∆ψ)

(18)

The procedure consists in varying ∆ψ until the second equality of eq 18 is verified. At this stage the phase shift of the phase grating, ∆φ, can be determined by using the first equality of the same equation. This numerical method requires paying particular attention to the incrementation of ∆ψ in order to have good accuracy in the estimations of ∆ψ and ∆φ. The time variations of ∆ψ(t) and ∆φ(t) thus obtained are reported in Figure 6a. It is noteworthy that the phase shift of the surface relief increases rapidly in the first seconds and quasi-linearly after 100 s. The maximum value reached after 1500 s of irradiation is 10 times higher than that observed for the doped polymer system. Also, the phase shift of the phase grating increases rapidly in the first seconds, but it decreases significantly after 100 s; finally, it reaches a plateau value equal to

2660 J. Phys. Chem. B, Vol. 102, No. 15, 1998

Figure 6. Relevant parameters in a functionalized polymer sytem. (a) Time evolution of the phase shifts due to the anisotropy ∆φ(t) and to the surface relief ∆ψ(t) and (b) time evolution of the phase shift φ0 between the phase and surface gratings.

0.1 after 1000 s, whenever the laser is turned on (up to 1500 s) or off (between 1500 and 2500 s). To estimate the phase shift between the phase and the surface gratings, φ0, we may use the same method as previously described for the doped system (eq 17). The time variations of φ0(t) are thus reported in Figure 6b. Values of φ0 are close to 90° at the beginning of the irradiation and then decrease rapidly down to 0° after 500 s and remain constant; when the pump laser is turned off, in contrast to the phase shifts ∆ψ(t) and ∆φ(t), which are only very slightly decreasing, φ0 values increase quickly up to 60°; this could be due to the existence of a hysteresis effect in the thermal and mechanical stabilizations of the polymer mass transport and/or to the erasing of a very small fraction of the surface relief since, surprisingly, a similar final value was also observed in the doped system (Figure 5b). Comparison of Doped and Functionalized Polymer Systems. First, as indicated in the theoretical part we have calculated the amplitude of the surface relief grating, 2∆d, and the anisotropy of the phase grating, ∆n, by using the following expressions:

2∆d )

2λ∆ψ λ∆φ with neff ) 1.25 and ∆n ) eff πd πn

Since we know from polarimetric experiments that a polarized light induces negative birefringence in this material, it is noteworthy in the above definition that ∆φ remains positive. Therefore, the time variations 2∆d(t) and ∆n(t) are reported and compared in Figures 7a and 7b for the doped and functionalized systems. On the one hand, it is remarkable that in the doped system the amplitude of the surface relief increases rapidly in the first hundred seconds but, finally, remains relatively small and equal to about 20 nm. This shows that the used optical method is

Lagugne´ Labarthet et al.

Figure 7. (a) Grating depth as a function of time for the doped and functionalized polymers. (b) Birefringence as a function of time for the doped and functionalized polymers.

very sensitive and allows us to follow with good accuracy such a weak amplitude modulation. In contrast, for the functionalized system the surface relief amplitude increases more monotonically, except during the first few seconds, and leads to a significant surface modulation as large as 200 nm after a 1500 s period of irradiation. Even larger amplitudes (up to 900 nm) can be obtained during a longer period or by using a higher laser irradiance, and such results were easily confirmed by AFM profile measurements.8,14 On the other hand, it must be pointed out that quite distinct phase grating behaviors are effective in the doped and functionalized systems. In the former case, the birefringence increases very quickly up to ∆n ) -0.020 in the first hundred seconds and then reaches a plateau roughly equal to -0.023, whereas in the latter case a larger birefringence variation up to ∆n ) -0.032 is observed in the first few seconds and then a monotonic decrease down to -0.020 is noted in the following 1000 s period; finally, even though the surface relief is still increasing, the phase grating seems to be stabilized at the last value, which is similar to that obtained in the doped system. This shows that at long time the surface grating is dominant and the increase of its modulation is mainly due to a mass transport of the polymer without any significant modification in the average chomophore orientations. Furthermore, it is worthwhile to note that the phase and surface relief grating effects are rapidly erased in the doped polymer system at any time, when the pump laser is turned off; meanwhile they can be similarly erased in the functionalized system only during the first 500 s period of the phase grating formation, as shown in Figure 8. At a longer time of irradiation, if we turn off the pump laser, the diffraction efficiency does not display any variation or, at long time, even slightly increases: this could lead to some interesting applications in optical switching.

Azobenzene-Containing Polymer Films

Figure 8. Multiple laser on (v)-laser off (V) sequences during the grating inscriptions on a functionalized polymer film.

In conclusion, the photochromic effects appear comparable in both systems, and for the volume phase grating we obtain a birefringence of ∆n ) -0.02, a typical value for the optically induced birefringence already observed on these materials.4-8 Note that from the above developed optical method we are able to reveal with good accuracy birefringence variations as low as 10-3 on such complex molecular systems. Nevertheless, concerning the true orientation of the photochromic entities in the depths and on the tops of the surface relief, it is clear that additional space-resolved optical measurements are necessary. In fact, according to the above discussed ∆d and ∆n variations in the opposite direction at long time (Figure 7), one can suggest that the viscoelastic flow of the polymer involved in the surface relief formation is also responsible for partly erasing the birefringence effects; this could lead to some final broadenings in the dye molecular orientation distribution functions as compared to those expected from considering only the electric field amplitudes of the pump interfering beams in the grating pattern. Indeed, we have quite recently succeeded in recording well-defined and distinct polarized resonance Raman images by using a modern Raman spectrometer in conjunction with a confocal microscope; these results confirm that at the micrometer scale there exist broad and distinct distributions of the chromophore orientations in the various regions of the grating.26 Finally, variations of the phase shifts φ0(t) between the phase and the surface relief gratings in both systems were already presented above. At a very short time one may recall that the surface grating may be compared to the absorption grating in photorefractive materials27,28 and must be in phase with the intensity distribution, so that the phase shift is equal to 90°. However, as soon as the phase grating is formed, the φ0 values decrease to 80° in the doped system, implying that the diffraction due to ∆n contribution is neither purely diffusion nor drift limited absorption; also, φ0 values decrease to 0° in the functionalized system, indicating that it is now induced purely by the predominant polymer viscoelastic flows and mass transport effects. In this respect, it may be mentioned that Holme et al.18 have recently concluded on a quite different phase shift, surprisingly constant and equal to 180°, for a side-chain liquid crystalline azobenzene polyester system in which the surface modulation was less important. In fact, using our theoretical approach, one can estimate intermediate values of the phase shift φ0 varying from 90° to 18° from their experimental results obtained under a similar irradiance condition (140 mW/cm2), confirming the above observations. Conclusions Efficient photoinduced holographic diffraction gratings have been written on doped and functionalized azobenzene polymer

J. Phys. Chem. B, Vol. 102, No. 15, 1998 2661 films by interfering two circularly polarized pump laser beams. From dynamical polarization analyses of the transmitted (1order diffraction beams of another probe beam we have provided evidence for the formation of both a phase grating and a surface relief grating. Furthermore within the Jones’ matrix formalism we have developed a theoretical approach for the calculation of the various transmitted relative intensities, which are in good agreement with the observed experimental results. This allows us to determine the time-dependent variations of the birefringence (∆n) and of the surface modulation (2∆d) with a high sensitivity equal to (10-3 in ∆n and to (10 nm in ∆d, respectively. In a DR1-doped PMMA system and a DR1functionalized polymer system we conclude on a similar birefringence effect (∆n ) -2 × 10-2) but a very weak surface modulation (2∆d ) 20 nm) in the former case and a 10 times larger one (2∆d ) 200 nm) in the latter case; moreover, the phase and surface grating effects are permanent only in the functionalized system. Such values for the extracted ∆n and ∆d parameters are in good agreement with previous birefringence and AFM profile investigations. Finally, it is noteworthy that similar holographic gratings with high diffraction efficiencies can also be written on these materials under the other (p,p) laser polarization pump condition; the (s,-s) configuration is by far less efficient (p and s stand for polarization in the incident plane and perpendicular to the incident plane, respectively). Such studies are in progress, and the results will be reported in a forthcoming publication. Acknowledgment. The authors are indebted to the CNRS (Chemistry Department) and to the Re´gion Aquitaine for financial support. They are also thankful to A. Natansohn for providing the functionalized polymer and to P. Rochon and M. Pe´zolet for several fruitful discussions. References and Notes (1) Bach, H.; Anderle, K.; Fuhrmann, Th.; Wendorff, J. H. J. Phys. Chem. 1996, 100, 4135. (2) Maak, J.; Ahuja, R. C.; Tachibana, H. J. J. Phys. Chem. 1995, 99, 9219. (3) Tachibana, H.; Nakamura, T.; Matsumoto, M.; Komizu, H.; Mannda, E.; Niino, H.; Yabe, A. J. Am. Chem. Soc. 1989, 11, 3080. (4) Xie, S.; Natansohn, A.; Rochon, P. Chem. Mater. 1993, 5, 403. (5) Dumont, M.; Froc, G.; Hosotte, S. Nonlinear Opt. 1995, 9, 327. (6) Seki, T.; Sakuragi, M.; Kawaniski, Y.; Suzuki, Y.; Tanaki, T.; Fukuda, R.; Ichimura, K. Langmuir 1993, 9, 212. (7) Natansohn, A.; Xie, S.; Rochon, P. Macromolecules 1994, 27, 4781. (8) Barret, C. J.; Natansohn, A.; Rochon, P. J. Phys. Chem. 1996, 100, 8836. (9) Sekkat, Z.; Dumont, M. Synth. Met. 1993, 54, 373. (10) Buffeteau, T.; Pe´zolet, M. Appl. Spectrosc. 1996, 50, 7. (11) Lagugne´ Labarthet, F.; Sourisseau, C. J. Raman Spectrosc. 1996, 27, 491. (12) Lagugne´ Labarthet, F.; Sourisseau, C. New J. Chem. 1997, 21, 879. (13) Rochon, P.; Batalla, E.; Natansohn, A. Appl. Phys. Lett. 1995, 66, 136. (14) Ho, M. S.; Barrett, C.; Paterson, J.; Esteghamatian, M.; Natansohn, A.; Rochon, P. Macromolecules 1996, 29, 4613. (15) Kim, D. Y.; Li, L.; Jiang, X. L.; Shivshankar, V.; Kumar, J.; Tripathy, S. K. Macromolecules 1995, 28, 8835. (16) Kim, D. Y.; Li, L.; Kumar, J.; Tripathy, S. K. Appl. Phys. Lett. 1995, 66, 1166. (17) Jiang, X. L.; Li, L.; Kumar, J.; Kim, D. Y.; Shivshankar, V.; Tripathy, S. K. Appl. Phys. Lett. 1996, 68, 2618. (18) Holme, N. C. R.; Nikolova, L.; Ramanujam, P. S.; Hvilsted, S. Appl. Phys. Lett. 1997, 70, 1518. (19) Pham, V. P.; Galstyan, T.; Granger, A.; Lessard, R. A. Jpn. J. Appl. Phys. 1997, 36, 429.

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