Fluid Mechanics Model and Analysis for the Photofabrication of Surface Relief Grating on Azo Polymers
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regarding on the film thickness and the irradiating light intensity [13]. Moreover, the photoinduced surface deformation with a Gaussian laser beam was recently investigated by Bian et al [14]. In the literature, strong polarization and light intensity dependence of the surface deformation process has been reported, and analyzed by their optical field gradient force model. In this paper, in order to obtain a better understanding of the photoinduced SRG formation process, its dynamics has been examined on a quantitative basis. A systematic study of the SRG photofabrication process has been performed regarding the influence of experimental and geometrical parameters such as the film thickness and the spacing of the interference light pattern. The photoinduced surface deformation with one-dimensional Gaussian laser beam has also performed and discussed within the framework of our fluid mechanics model. EXPERIMENTAL An azobenzene polymer (PMD) was obtained by copolymerization of 4-(N-(2methacryloyloxyethyl)-N-ethylamino)-4’-nitroazobenzene and methyl methacrylate. Detailes of this synthesis will be reported in the literature [6]. The number averaged molecular weight (Mn) and the glass transition temperature (Tg) of the polymer were 5.9 × 103 and 128 °C, respectively. Amorphous thin films with good optical quality were prepared on glass substrates by spin coating. The absorption coefficient α of the azobenzene polymer film at 488 nm was 12.3 µm-1. The thickness of the films was measured by using a mechanical stylus profiler. The surface structure was measured by AFM (Nanoscope IIIa, Digital Instruments Co. ) in the tapping mode under ambient condition. The 488-nm line from an Ar+ laser was employed for the light irradiation. The sinusoidal light pattern for recording SRGs was produced by interference of two beams with right- and left-circular polarized light. The one-dimensional Gaussian beam was produced by focusing of single laser beam using a cylindrical lens and the azobenzene film was put at the focal plane. The width of the focused Gaussian beam σ was measured by laser beam profiler. Experimental parameters for each experiment were summarized in table 1. More details of the optical setup can be refered to the previous literature [2,6,14]. Table 1 Experimental conditions for photoinduced surface deformation (a) Irradiated total photon energy [J/cm2] Irradiated light intensity [mW/cm2] Film thickness [µm] Spacing of the interference light pattern (a, b) Width of the Gaussian beam (c) [µm]
(b)
(c)
14.1
7.1
40.0
30.0
1.14 × 103 158
0.025 ~ 0.83 1.0
0.79
0.69
0.76 ~ 3.6
2.3
(a) : for the film thickness h dependence measurement(b) : for the grating spacing Λ dependence measurement (c) : for one-dimensional Gaussian beam irradiation ANALYTICAL BACKGROUND Recently, Barrett et al. proposed the model based on fluid mechanics to describe the dynamics of the SRG photofabrication [10]. Although their model was based on simplified Navier-Stokes equation with no distribution in force field, they succeeded to expla
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