Time dependent analysis of the formation of a half-period surface relief grating on amorphous azopolymer films

The formation of a surface relief grating (SRG) on amorphous copolymer films containing azobenzene chromophores in side chain positions is conducted using two linearly polarized interfering beams with orthogonal polarization directions (p+s). Time dependent analyses of the diffraction efficiency were carried out by measuring simultaneously the transmitted zero order (I(0)) as well as the first (I(±1)) and second (I(±2)) diffracted orders. Two main contributions to the diffraction efficiency are evidenced: an anisotropic (birefringence) part coming from the normal period grating plus another anisotropic and surface relief part (SRG) due to the half-period grating. The origin of the weak amplitude SRG stems from the interference of particular I(±1) diffracted orders, whose resulting polarization and angular Bragg’s conditions are in accordance with the existence of a double frequency modulation. Using the matricial products of Jones, theoretical expressions of transmitted and diffracted orders are thus derived. Extracted values of the phase shifts and, therefore, of the birefringence (Δn,Δn′) and surface relief amplitude (2Δd) are then compared to data from optical and topographic atomic force microscopy measurements. Time dependent calculations of these relevant parameters as well as analyses of the polarization states of transmitted and diffracted orders are in good agreement with the proposed model.