Multiwave mixing in Bi<sub>12</sub>SiO<sub>20</sub> causes the formation of multiple grating because of the photorefractive effect. These primary gratings interact and cause the formation of additional gratings at frequencies that are combinations of the primary grating frequencies. The nonlinear combinations of gratings stem from the nonlinear response of the space-charge field to the incident optical interference pattern through the generation of electrons into the conduction band. We investigate drift-dominated recording. The effects of nonlinear combinations of gratings are investigated quantitatively in a three-wave mixing configuration, in which one reference beam and two closely situated object beams induce three primary gratings. Using a sinusoidal phase modulation on one of the object beams provides absolute control of the primary grating strengths. Specifically, two of the primary gratings may be completely erased, and the nonlinear effect may be obtained as the relative change in the diffraction efficiency from the remaining grating. For drift-dominated recording an expression for the total space-charge field is derived, including multiple spatial frequencies. The derivation is based on the band-transport model. A numerical model is presented in which the relative change in diffraction efficiency is calculated from the corresponding change in the grating strengths. The grating strengths are found from the corresponding frequency components of the total space-charge field. The model is valid in the limit of low diffraction efficiencies and small coupling constants. The investigation is carried out with different values of the intensity ratio between the reference beam and the sum of the two object beams, the applied field to the crystal, and the separation angle between the two object beams. It is shown that relative changes of 200% in the diffraction efficiency occur. Thus the magnitude of the additional grating strengths may be substantial and even comparable with those of the primary grating. Comparing the predictions of the numerical model with the experimental data shows excellent agreement.
© 1995 Optical Society of America
P. E. Andersen, P. M. Petersen, and P. Buchhave, "Nonlinear combinations of gratings in drift-dominated recording in Bi12SiO20," J. Opt. Soc. Am. B 12, 2453-2462 (1995)