OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 8 — Aug. 30, 2004
  • pp: 1518–1528

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

Yi-Chao Meng, Qi-Zhi Guo, Wei-Han Tan, and Zhao-Ming Huang  »View Author Affiliations


JOSA A, Vol. 21, Issue 8, pp. 1518-1528 (2004)
http://dx.doi.org/10.1364/JOSAA.21.001518


View Full Text Article

Enhanced HTML    Acrobat PDF (236 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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 2×2,3×3, and 4×4 linearly distributed directional couplers are obtained by the proposed approach, which treats the calculation as a nondegenerate eigenvalue problem. In addition, for the 3×3 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 5×5 circularly distributed directional coupler are obtained by use of the usual and the redefined generalized Chebyshev polynomials.

© 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

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited