Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n1ef, n2ef, and n3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n1ef, n2ef, and n3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n1, n2 and n3 are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n1, n2 and n3 of the holographic gratings generated in the photopolymer material.