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A modal impedance‐angle formalism: Schemes for accurate graded‐index bent‐slab calculations and optical fiber mode counting
Author(s) -
de Hon Bastiaan P.,
Bingle Marianne
Publication year - 2003
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2001rs002570
Subject(s) - bent molecular geometry , mathematical analysis , mathematics , physics , optics , geometry , organic chemistry , chemistry
The propagation coefficients of guided modes along bent slabs and optical fibers may be calculated with the aid of a complex‐power‐flow, variational scheme. This scheme can be cast in the form of a Newton iterative scheme for a characteristic equation in terms of impedances rather than fields. Singularities of the associated Riccati equations for the impedances are circumvented via a generalized coordinate transformation, involving an angle for bent slabs, or a matrix of angles for optical fibers. Adopting the resulting impedance‐angle formalism for bent slabs, numerical difficulties disappear, and accuracy ensues. The analysis of the vectorial optical‐fiber problem benefits from its scalar bent‐slab counterpart. In particular, the connection between the power flow and the impedance‐angle formalism forms the physical underpinning for understanding that beyond a certain distance from the fiber core the derivative of the impedance matrix with respect to the propagation coefficient is positive definite. In turn, this provides the basis for the full‐wave generalization for optical fibers of the mode‐counting scheme developed in 1975 by Kuester and Chang for scalar wave propagation along a straight slab. With these key results, root‐finding can be rendered more robust and efficient. A companion paper contains the necessary proofs for the complex‐power‐flow variational scheme and the mode‐counting and mode‐bracketing theorems.