Rigorous three-dimensional analysis of surface-relief gratings using a spectral collocation method

Palle Geltzer Dinesen; Jan S. Hesthaven; Jens-Peter Lynov

doi:10.1117/12.379350

10 March 2000 Rigorous three-dimensional analysis of surface-relief gratings using a spectral collocation method

Palle Geltzer Dinesen, Jan S. Hesthaven, Jens-Peter Lynov

Proceedings Volume 3951, Diffractive/Holographic Technologies and Spatial Light Modulators VII; (2000) https://doi.org/10.1117/12.379350
Event: Symposium on Integrated Optoelectronics, 2000, San Jose, CA, United States

Abstract

We present a general 3-D spectral collocation method for the analysis of diffractive optical elements (DOEs). The method computes a direct solution to the Maxwell's equations in the time domain. The computational domain is decomposed into a number of small subdomains in which a high-order Chebyshev spectral collocation scheme is used to approximate the spatial derivates in Maxwell's equations. The local solutions in each subdomain are integrated using a Runge-Kutta scheme, and the global solution is reconstructed by using the characteristic variables of the strongly hyperbolic set of equations. A smooth mapping technique is used to correctly model curvi- linear boundaries thus making the method a strong tool for analyzing, e.g., grating couplers with analog surface reliefs. The accuracy and efficiency of the method is verified using simple test cases and examples of the analysis of analog grating couplers of finite length are given. The examples demonstrate the superior properties of the method such as the low number of points per wavelength needed to accurately resolve wave propagation and the absence of numerical dispersion.

Citation Download Citation

Palle Geltzer Dinesen, Jan S. Hesthaven, and Jens-Peter Lynov "Rigorous three-dimensional analysis of surface-relief gratings using a spectral collocation method", Proc. SPIE 3951, Diffractive/Holographic Technologies and Spatial Light Modulators VII, (10 March 2000); https://doi.org/10.1117/12.379350

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KEYWORDS

Maxwell's equations

Dielectrics

Diffraction

Analog electronics

Interfaces

Waveguides

Diffraction gratings

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