Research On Several New Effects Of Microstructured Optical Materials

Micro structured optical materials play an important role in the study of modern optics.Our work mainly focused on microstructured optical materials such as optical superlattices and cylindrical gratings.We will study the properties of these microstructured optical materials and make theoretical investigation on several related new effects.Some meaningful results are obtained.The main research parts are summarized as follows:1.We take a theoretical investigation on the reciprocal property of a general class of 2D nonlinear photonic quasicrystal with the rectangular projection method.The 2D quasicrystal structure can be constructed with the projection from 3D cubic lattice to a 2D plane.Connecting the projection parameters and the structural parameters,we obtain the analytical expression for the Fourier spectrum of the quasicrystal structure explicitly.The results are verified by numerical calculations.Besides,it is interesting to find that the result has a similar form to the corresponding expression of the well-known ID Fibonacci lattice.Thus,we predict a further extension of the result to higher dimensions.2.The backward Cerenkov-type second-harmonic generation in bulk optical superlattices has been studied theoretically.We use the non-paraxial wave equations to avoid the paraxial approximation.Under proper boundary conditions,the analytical expression for second-harmonic field distribution and the corresponding phase-matching condition are obtained strictly by solving the non-paraxial wave equations.We mainly focus on the backward Cerenkov-type second-harmonic generation.Further research is taken on its mathematical model the physical requirement of this condition is clarified.Besides,the way to realize the backward Cerenkov-type second-harmonic generation in optical superlattices is pointed out.3.Deep research is taken on the Talbot self-imaging effect.Based on the self-imaging of 1D and 2D periodic grating,we discuss the requirement for the self-imaging of quasi-periodic grating,and a corresponding condition is deduced under proper approximation.Furthermore,we build the imaging theory for cylindrical gratings.We obtain the analytical expression of the amplitude,and the corresponding intensity distribution has been calculated numerically.We make further discussion about the self-imaging condition of cylindrical gratings.4.We deduce the radial paraxial wave equation and develop a numerical simulation method based on it.We extern the paraxial wave equations from rectangular coordinate system to polar coordinate system.A radial paraxial wave equation is obtained from the Helmholtz equation in cylindrical coordinates with the slowly varying amplitude approximation.This extension provides an efficient way to solve radial problems such as the self-imaging of cylindrical gratings.