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Proceedings Paper

Generalized source method for modeling nonlinear diffraction in planar periodic structures
Author(s): Martin Weismann; Dominic F. G. Gallagher; Nicolae C. Panoiu
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Paper Abstract

We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and twodimensional (1D, 2D) diffraction gratings with arbitrary profile made of non-centrosymmetric optical materials. Our method extends the generalized source method (GSM), which is a highly efficient alternative to the conventional Fourier modal method, to quadratically nonlinear diffraction gratings. The proposed method consists of a two-stage algorithm. Initially, the electromagnetic field at the fundamental frequency is computed in order to obtain the second-harmonic polarization using the known second-order nonlinear susceptibility. Then the optical field at the second-harmonic frequency is computed using this polarization as an additional source term in the GSM. We show how to integrate this source term into the GSM framework without changing the structure of the basic algorithm. We use the proposed algorithm to investigate a doubly resonant mechanism that leads to strong enhancement of SHG in a nonlinear 2D circular GaAs grating mounted on top of a GaAs slab waveguide. We design this optical device such that slab waveguide modes at the fundamental and second-harmonic are simultaneously excited and phase matched by the grating. The numerically obtained resonance frequencies show good agreement with analytically computed resonance frequencies of the unperturbed slab waveguide.

Paper Details

Date Published: 1 May 2014
PDF: 11 pages
Proc. SPIE 9131, Optical Modelling and Design III, 913115 (1 May 2014); doi: 10.1117/12.2052247
Show Author Affiliations
Martin Weismann, Univ. College London (United Kingdom)
Photon Design Ltd. (United Kingdom)
Dominic F. G. Gallagher, Photon Design Ltd. (United Kingdom)
Nicolae C. Panoiu, Univ. College London (United Kingdom)


Published in SPIE Proceedings Vol. 9131:
Optical Modelling and Design III
Frank Wyrowski; John T. Sheridan; Jani Tervo; Youri Meuret, Editor(s)

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