Exact analytical representations for broadband transmission properties of 
quarter-wave multilayers

Grigoriev, Victor; Biancalana, Fabio

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Exact analytical representations for broadband transmission properties of quarter-wave multilayers

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Biancalana, Fabio
Biancalana Research Group, Research Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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Grigoriev, V., & Biancalana, F. (2011). Exact analytical representations for broadband transmission properties of quarter-wave multilayers. OPTICS LETTERS, 36(19), 3774-3776.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-6981-8

Abstract

The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact analytical formula for the transmission spectrum, which is valid for the full spectral range and which contains only a limited number of parameters for structures satisfying the quarter-wave condition. These parameters are related to the poles of the scattering matrix, and we present an efficient algorithm to find them, which is based on considering the ray propagation inside the structure and subsequent application of the harmonic inversion technique. These results are significant for analyzing the reshaping of ultrashort pulses in multilayered structures. (C) 2011 Optical Society of America