Analysis of nonlinear optical propagation in a longitudinal deuterated potassium dihydrogen phosphate Pockels cell

Nonlinear optical propagation in a longitudinal deuterated potassium dihydrogen phosphate (DKDP) Pockels cell (PC) is studied analytically and with numerical simulations. Propagation equations are developed taking into account the nonlinear susceptibility tensor and the modification of the polarization state because of the voltage-induced birefringence of the Pockels cell. The analytical predictions are in good agreement with split-step simulations. The nonlinear polarization in the PC's crystalline medium leads to nonlinear phase shifts and crossed-wave generation. For the small nonlinearities consistent with typical operation in a laser system, a quarter-wave PC induces a nonlinear phase equal to the average of the nonlinear phase accumulated by a linearly and circularly polarized field of the same intensity propagating in the inactive PC. The contrast of a half-wave PC between crossed polarizers is not decreased by the nonlinear propagation because there is no generated cross wave in this configuration.