Research Of The Phase-matched Third Harmonic Generation In Kerr Photonic Crystals

In recent years,with the development of high power laser technology,nonlinear optical frequency conversion has become one of the main technical ways to obtain coherent light,especially the frequency range where laser output can not obtain.However,in order to obtain high efficiency nonlinear optical frequency conversion,phase mismatch is the first problem to be solved.The phase mismatch originates from the inherent dispersion effect of the material,where the velocity of the interacting waves propagating in the material is different.We can easily control the dispersion characteristics of the artificial microstructure through artificial atom and artificial lattice,and that provides a new technical way to realize phase matching.The omnidirectional phase matching in a zero-index medium,the backward phase matching harmonic generation in the medium with a negative index and other anomalous nonlinear optical frequency conversion phenomena have been experimentally proved.Therefore,the phase matching of artificial microstructures becomes a new research hotspot.In this paper,the phase matching of the third harmonic generation in photonic crystals containing Kerr medium has been researched,which is a typical representative of the artificial microstructure.This paper reviews the metamaterials,photonic crystals and the third harmonic generation.Then,the research background and significance are presented.Finally,the traditional phase matching method,the current situation of domestic foreign development and the related theory are discussed in detail.The main work and contributions of this paper are as follows:Firstly,we study the influence of pulse shape and width on the third harmonic generation conversion efficiency by using the nonlinear finite-difference time-domain method.Although the analytical expression of the third harmonic of the continuous wave can be resolved with the small signal approximation,it is almost impossible to calculate the third harmonic generation conversion efficiency theoretically when the input is a pulse.Therefore,the third harmonic generation conversion efficiency of the pulse is estimated by introducing the correction factor related to the pulse shape and width.It can be found that the correction factor is a constant independent of the pulse width for the Gaussian pulse and the super-Gaussian pulse while the correction factor is related to the pulse width for the flat-top pulse by using the time-domain finite difference method to simulate the third harmonic generation of the Gaussian pulse,the flat-top pulse and the super-Gaussian pulse at the small signal approximation.Secondly,we design and simulate the phase-matched third harmonic generation in the photonic crystal made of aluminum nitride.Taking two-dimensional photonic crystal made of aluminum nitride as an example,equal effective refractive indices of the fundamental frequency and the triple frequency are achieved by adjusting the lattice constant and the dielectric column diameter of the photonic crystal,which satisfies the third harmonic phase matching condition.The nonlinear finite-difference time-domain method is used to simulate a Gaussian pulse propagating inside the pure aluminum nitride slab and the photonic crystal made of aluminum nitride respectively.The simulation results show that the third harmonic generation efficiency in the aluminum nitride slab varies with the transmission distance in the form of a sine function,indicating a phase mismatched THG,while the THG conversion efficiency in the PhC increases with the propagation length like a parabola,indicating a quasi-perfect phase matching.