Generalized source method for modeling nonlinear diffraction in planar periodic structures

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Generalized source method for modeling nonlinear diffraction in planar periodic structures

Weismann, M; Panoiu, NC; Gallagher, DFG; (2014) Generalized source method for modeling nonlinear diffraction in planar periodic structures. Proceedings of SPIE , 9131 , Article 913115. 10.1117/12.2052247. Green open access

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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. © 2014 SPIE.

Type:	Article
Title:	Generalized source method for modeling nonlinear diffraction in planar periodic structures
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1117/12.2052247
Publisher version:	http://dx.doi.org/10.1117/12.2052247
Language:	English
Additional information:	Copyright 2014 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI:	https://discovery.ucl.ac.uk/id/eprint/1433371