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Inhomogeneous optical filter design with the use of a Riccati equation
Author(s) -
Chang Hosung,
Lee SangSun,
Choi MyungRyul,
Lim Sungkyoo
Publication year - 1999
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/(sici)1098-2760(19990720)22:2<140::aid-mop18>3.0.co;2-k
Subject(s) - riccati equation , discontinuity (linguistics) , filter (signal processing) , mathematical analysis , function (biology) , mathematics , nonlinear system , reflection (computer programming) , algebraic riccati equation , phase (matter) , microwave , differential equation , optics , control theory (sociology) , physics , computer science , control (management) , quantum mechanics , evolutionary biology , artificial intelligence , computer vision , biology , programming language
Inhomogeneous optical filter design based upon tapered transmission‐line theory is described by deriving an approximate spectral function from a nonlinear Riccati equation, which governs the reflection characteristics of tapered lines. We deal with the problem of discontinuity that may occur at both ends of the filter section, and pursue a solution of the nonlinear differential equation via iterations. It is shown that the derived spectral function Q(k) is equivalent to an improved Q(k)‐function used in the optical approach when the phase is not considered. Numerical examples are given to illustrate the role of the phase function to obtain refractive index profiles suitable for design specifications. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 140–144, 1999.