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.