TRANSVERSE MODES IN PHASE-CONJUGATION RESONATOR(PCR) WITH FINITE APERTUREA(Ⅰ)——MATRIX EIGEN-EQUATION OF SELF-CONSISTENT FIELD  

作　　者：李先枢 徐家进 高燕球 

机构地区：[1]Department of Physics, Zhongshan University, Guangzhou 510275, PRC [2]Department of Physics, Guangzhou Teacher's College, Guangzhou 510400, PRC

出　　处：《Science China Mathematics》1990年第8期982-995,共14页中国科学：数学（英文版）

摘　　要：Based on 'the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens (cylindrical coordinates)' proposed by one of the authors (1981), the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes (including high-order modes, whose l≥2, p≥1) are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics (as the diffraction loss, the field distribution on the surface of spherical mirror) of all transverse modes in a PCR are just the same as those in some of the other PCR with different g_1.Some examples of calculation results are also given. They show that (ⅰ) the convengence of the above-mentioned equation is very good, (ⅱ) the calculation results with very high precision can be obtained practically, and the characteristics of TEM with very small or large losses can also be calculated precisly and (ⅲ) the choice of the reference light field does not affect correctness of the theory but affects the amount of calculation.Only the PCR with only one PCM being one of the two endreflectors of resonators is discussed, and the effect of response time of the PCM is ignored in this paper.Based on "the matrix theory for the propagation of a scalar light wave in a system consisting of plane screens （cylindrical coordinates）" proposed by one of the authors （1981）, the propagation of the self-consistent field in PCR is analyzed, and a matrix eigen-equation of the self-consistent field is presented. By solving the eigen-equation, the axisymmetrical PCR with finite aperture is calculated, and the diffraction losses, phase shifts, relative amplitude and phase distributions on each mirror surface of various order transverse modes （including high-order modes, whose l≥2, p≥1） are introduced.A quasi-equivalence relation of PCR is also given. According to this relation, some characteristics （as the diffraction loss, the field distribution on the surface of spherical mirror） of all transverse modes in a PCR are just the same as those in some of the other PCR with different g₁.Some examples of calculation results are also given. They show that （ⅰ） the convengence of the above-mentioned equation

关 键 词：phase CONJUGATION RESONATOR transverse mode MATRIX eigen-equation of self-eonsistent field MATRIX theory for the propagation of scalar light wave quasiequivalence relation. 

分 类 号：N[自然科学总论]