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-cons...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.展开更多
Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material ...Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material was put forward. The effects of shear modulus and Poisson＇s ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating/（i of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson＇s ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson＇s ratio on the stress singularity near the tip of notch was obtained.展开更多
文摘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.
基金supported by the Ministry of Education of China(No.208152)Gansu Natural Science Foundation(No.3ZS061-A52-47).
文摘Based on Zak＇s stress function, the eigen-equation of stress singularity ofbi-materials with a V-notch was obtained. A new definition of stress intensity factor for a perpendicular interfacial V-notch of bi-material was put forward. The effects of shear modulus and Poisson＇s ratio of the matrix material and attaching material on eigen-values were analyzed. A generalized expression for calculating/（i of the perpendicular V-notch of bi-materials was obtained by means of stress extrapolation. Effects of notch depth, notch angle and Poisson＇s ratio of materials on the singular stress field near the tip of the V-notch were analyzed systematically with numerical simulations. As an example, a finite plate with double edge notches under uniaxial uniform tension was calculated by the method presented and the influence of the notch angle and Poisson＇s ratio on the stress singularity near the tip of notch was obtained.
