Third-order nonlinear and linear time-dependent dynamical diffraction of X-rays in crystals

For the first time the third-order nonlinear time-dependent Takagi's equations of X-rays in crystals are obtained and investigated. The third-order nonlinear and linear time-dependent dynamical diffraction of X-rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third-order nonlinear time-dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.