One-dimensional transfer matrix formalism with localized losses for fast designing of quasiperiodic waveguide filters

Yann G. Boucher; Emmanuel Drouard; Ludovic Escoubas; Francois Flory

doi:10.1117/12.512980

18 February 2004 One-dimensional transfer matrix formalism with localized losses for fast designing of quasiperiodic waveguide filters

Yann G. Boucher, Emmanuel Drouard, Ludovic Escoubas, Francois Flory

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Proceedings Volume 5249, Optical Design and Engineering; (2004) https://doi.org/10.1117/12.512980
Event: Optical Systems Design, 2003, St. Etienne, France

Abstract

We present a new, one-dimensional, transfer matrix formalism for describing the spectral properties of a quasi-periodic integrated waveguide filter (reflection R, transmission T, overall losses L = 1 - R - T), where losses (essentially due to the modal mismatch between adjacent sections) are modeled as localized, Dirac-like singularities of the (complex) dielectric permittivity. As far as losses appear periodic, the coupling constant between propagating and contra-propagating waves is complex: such a distribution leads to a specific spectral response for L, different from that provided by homogeneous absorption. Besides, the transfer matrix of a unit cell (made of two quarter-wave sections of high and low indices) can be expressed rigorously in the frame of usual coupled-wave equations, even for arbitrary high index contrast. As a result, any periodic section can be represented by one transfer matrix only, whatever the number of unit cells. This can dramatically reduce the computational time by comparison with more accurate simulation tools such as Film Mode Matching (FMM) method.

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Yann G. Boucher, Emmanuel Drouard, Ludovic Escoubas, and Francois Flory "One-dimensional transfer matrix formalism with localized losses for fast designing of quasiperiodic waveguide filters", Proc. SPIE 5249, Optical Design and Engineering, (18 February 2004); https://doi.org/10.1117/12.512980

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KEYWORDS

Absorption

Waveguides

Interfaces

Refractive index

Dielectrics

Computer simulations

Wave propagation

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