Accurate and efficient sensitivity extraction of complex structures using FDTD

Mohamed A. Swillam; Mohamed H. Bakr; Xun Li

doi:10.1117/12.779122

26 October 2007 Accurate and efficient sensitivity extraction of complex structures using FDTD

Mohamed A. Swillam, Mohamed H. Bakr, Xun Li

Proceedings Volume 6796, Photonics North 2007; 67963A (2007) https://doi.org/10.1117/12.779122
Event: Photonics North 2007, 2007, Ottawa, Canada

Abstract

We discuss a novel FDTD-based technique for estimating accurate sensitivities of the desired response. Our technique utilizes the central adjoint variable method (CAVM) for estimating the response sensitivities. This approach features accuracy comparable to that of the central finite difference (CFD) approximation at the response level. Using only two simulations, of the original and the adjoint photonic structures, the sensitivities with respect to all the designable parameters are obtained regardless of their number. Our approach uses the same update equations of the conventional FDTD for the adjoint problem, which simplifies the implementation. A self-adjoint approach based on CAVM (SA-CAVM) is also proposed to extract the sensitivities of the power reflectivity. Using this self-adjoint approach, only the original simulations are needed to evaluate the objective function and its sensitivities as well. Our approach can also supply wideband sensitivities. The additional cost in this case is mainly that of performing the discrete Fourier transform (DFT) which is negligible compared to the FDTD simulation cost. Our SA-CAVM approach is also utilized to minimize the power reflectivity of deeply etched waveguide terminators, and double layer antireflection coatings on laser diode (LD) facets which can be used as an optical amplifier. The accuracy of our approaches is illustrated by comparing the results with the second order accurate CFD. Our results show a very good agreement between the CAVM-based sensitivities and those obtained using the expensive central finite difference approximation.

Citation Download Citation

Mohamed A. Swillam, Mohamed H. Bakr, and Xun Li "Accurate and efficient sensitivity extraction of complex structures using FDTD", Proc. SPIE 6796, Photonics North 2007, 67963A (26 October 2007); https://doi.org/10.1117/12.779122

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KEYWORDS

Finite-difference time-domain method

Waveguides

Reflectivity

Antireflective coatings

Computer simulations

Matrices

Autoregressive models

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