Research Of Third Harmonic Generation And Its Enhancement In Nonlinear Photonic Crystals

In recent decades,nonlinear optical effects have been playing a more and more important role in many modern optical applications such as laser frequency conversion,all-optical switching,all-optical signal processing,laser communication and optical filter.For the conventional media,the nonlinearities are determined by their inherent properties and not subject to artificial control,thus result in their disability to meet the strict requirements in practical applications.For this reason,it is urgent to develop nonlinear optical materials with large nonlinear coefficient and tunable optical properties in practical applications.Studies have shown that the linear and nonlinear optical properties of artificial microstructures such as photonic crystals,metamaterials and et al can be regulated flexibly from their microstructure as well as material properties,which raise the possibility of providing a new technical approach to improve and expand the application of nonlinear optical effects.This paper focuses on two-dimensional photonic crystals which containing Kerr nonlinear medium,studies the basic principles of their ability to regulate and control nonlinear effects from the angle of effective nonlinear refractive index coefficient,and explores the enhancement of third harmonic generation.Specifically,based on a detailed summary of the research background,significance and current situation of domestic and foreign development and the related theory,the main work and innovations in this paper are as follows:Firstly,we studied the effective nonlinear refractive index coefficient of two-dimensional square lattice photonic crystals under the condition of TE waves from theoretical estimation as well as electromagnetic simulation.We revised the traditional effective medium theory by introducing field localization factors from the aspects of electric and magnetic field spatial average in an unit cell of photonic crystals respectively:the effective linear refractive index coefficients obtained by electric field spatial average agree well with the ones calculated by using PWEM.In addition,the electric field of TE waves is mainly concentrated in the low refractive index medium,which is different from the effect induced by TM waves.Then,the effective nonlinear refractive index coefficient is obtained by introducing the slow light enhancement factor.The theoretical results are in good agreement with the simulation results obtained by the finite difference time domain method.Secondly,we derived the expressions for computing the third harmonic generation of plane waves in matematerials,analyzed the change of third harmonic intensity induced by transmission distance variation for the phase matched and mismatched cases respectively,and proposed a method to quantitatively estimate the phase mismatch in artificial microstructures by considering the relationship(i.e.,a sine/cosine function or a parabola)between third harmonic intensity and the transmission distance.By using the finite difference time domain method to simulate the third harmonic generation in homogeneous isotropic Kerr medium,the results were obtained and proved consistent with the theoretical estimation.