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A useful fractional linear transformation for the riccati equation for reflection coefficients
Author(s) -
He Sailing
Publication year - 1995
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/mop.4650080614
Subject(s) - riccati equation , refractive index , mathematics , reflection (computer programming) , transformation (genetics) , mathematical analysis , algebraic riccati equation , reflection coefficient , derivative (finance) , index (typography) , optics , physics , differential equation , chemistry , computer science , biochemistry , financial economics , economics , gene , programming language , world wide web
The conventional Riccati equation for the reflection coefficient involves the spatial derivative of the refractive index, and thus it is not suitable for use when the refractive index is nondifferentiable and/or discontinuous. In the present article we introduce a fractional linear transformation to obtain a Riccati equation that does not involve the derivative of the refractive index. The transformed reflection coefficient is continuous everywhere in space for any refractive index profile. The transformed Riccati equation is also used to obtain an explicit solution for a multi‐layered structure in a straightforward way. © 1995 John Wiley & Sons. Inc.