Fast Exact Inversion of the Generalized Zakharov-Shabat Problem for Rational Scattering Data: Application to the Synthesis of Optical Couplers

An exact method is presented for the inversion of the generalized Zakharov-Shabat problem, for the case where the scattering data are (or are approximated by) rational functions. The presence of bound states is also accounted for. The problem is examined with the aim of obtaining an exact synthesis...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1988-06, Vol.48 (3), p.689-702
Main Authors: Bava, G. P., Ghione, G., Maio, I.
Format: Article
Language:English
Subjects:
Applied mathematics
Coupled mode theory
Coupling coefficients
Eigenvalues
Exact sciences and technology
Inverse problems
Inverse scattering
Mathematical functions
Mathematical procedures
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Optical waveguides
Ordinary differential equations
Propagation
Reflectance
Scattering functions
Sciences and techniques of general use
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Summary:An exact method is presented for the inversion of the generalized Zakharov-Shabat problem, for the case where the scattering data are (or are approximated by) rational functions. The presence of bound states is also accounted for. The problem is examined with the aim of obtaining an exact synthesis procedure for a class of two-mode optical couplers, including lossy and active structures. The present method yields a closed-form solution, thereby leading to very fast numerical implementation. The implications of the synthesis technique on the physical problem at hand are briefly discussed, and some numerical examples are presented.
ISSN:0036-1399
1095-712X
DOI:10.1137/0148039