Analytical solutions of coupled-mode equations for multiwaveguide systems, obtained by use of Chebyshev and generalized Chebyshev polynomials

被引:15
作者
Meng, YC
Guo, QZ
Tan, WH
Huang, ZM
机构
[1] Shanghai Univ Sci & Technol, Inst Fiber Opt, Shanghai 201800, Peoples R China
[2] Shanghai Univ, Sch Commun & Informat Engn, Shanghai 200072, Peoples R China
[3] Shanghai Univ, Dept Phys, Shanghai 200436, Peoples R China
关键词
D O I
10.1364/JOSAA.21.001518
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
A novel approach is proposed for obtaining the analytical solutions of the coupled-mode equations (CMEs); the method is applicable for an arbitrary number of coupled waveguides. The mathematical aspects of the CMEs and their solution by use of Chebyshev polynomials are discussed. When mode coupling between only adjacent waveguides is considered (denoted weak coupling), the first and second kinds of the usual Chebyshev polynomials are appropriate for evaluating the CMEs for linearly distributed and circularly distributed multi-waveguide systems, respectively. However, when one is considering the coupling effects between nonadjacent waveguides also (denoted strong coupling), it is necessary to use redefined generalized Chebyshev polynomials to express general solutions in a form similar to those for the weak-coupling case. As concrete examples, analytical solutions for 2 x 2, 3 x 3, and 4 x 4 linearly distributed directional couplers are obtained by the proposed approach, which treats the calculation as a nondegenerate eigenvalue problem. In addition, for the 3 x 3 circularly distributed directional coupler, which gives rise to a degenerate eigenvalue problem, an analytical solution is obtained in an improved way. Also, for comparison and without loss of generality, to clarify the difference between the two coupling cases, analytical solutions for a 5 x 5 circularly distributed directional coupler are obtained by use of the usual and the redefined generalized Chebyshev polynomials. (C) 2004 Optical Society of America.
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页码:1518 / 1528
页数:11
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