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

JOSA A, Vol. 21, Issue 8, pp. 1518-1528 (2004)

http://dx.doi.org/10.1364/JOSAA.21.001518

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### Abstract

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 multiwaveguide 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

© 2004 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(130.2790) Integrated optics : Guided waves

(230.7370) Optical devices : Waveguides

**History**

Original Manuscript: November 3, 2003

Revised Manuscript: February 19, 2004

Manuscript Accepted: February 19, 2004

Published: August 1, 2004

**Citation**

Yi-Chao Meng, Qi-Zhi Guo, Wei-Han Tan, and Zhao-Ming Huang, "Analytical solutions of coupled-mode equations for multiwaveguide systems, obtained by use of Chebyshev and generalized Chebyshev polynomials," J. Opt. Soc. Am. A **21**, 1518-1528 (2004)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-8-1518

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