Second harmonic generation of ultrashort laser pulses in nonlinear photonic crystals is investigated by numerical methods based on the approximation of slowly varying amplitudes and a unidirectional approximation, applicable to simplify the wave equation with nonlinear polarization in a dispersive medium. Under the same experimental conditions, the results of these approximations are compared. Comparative analysis shows that up to 10 fs of the main pulse duration, both approximate methods describe this process of frequency conversion in almost the same way, but below 10 fs, there is a discrepancy between their results. Mainly, the formation of the temporal profile of the second harmonic pulse and its efficiency are compared. A method for obtaining time profiles of the second harmonic pulse using a unidirectional approximation where the incident field is used entirely in both the spectral and time domains of the calculation is also shown. The effect of dispersion up to the third order of smallness is taken into account, during the use of the approximation of slowly varying amplitudes.
Рузиев З.Дж., Собиров О.И., Корабоев К.А., Сапаев У.К. Численное моделирование генерации второй гармоники ультракоротких лазерных импульсов в нелинейных фотонных кристаллах. Математическое моделирование и численные методы, 2022, № 1, с. 3–14.