Adjoint variable method for general material models towards efficient sensitivity analysis of subwavelength structures

Osman S. Ahmed; Mohamed H. Bakr; Xun Li; Tsuyoshi Nomura

doi:10.1117/12.2038645

11 October 2013 Adjoint variable method for general material models towards efficient sensitivity analysis of subwavelength structures

Osman S. Ahmed, Mohamed H. Bakr, Xun Li, Tsuyoshi Nomura

Author Affiliations +

Proceedings Volume 8915, Photonics North 2013; 89151Q (2013) https://doi.org/10.1117/12.2038645
Event: Photonics North 2013, 2013, Ottawa, Canada

Abstract

In this paper, we propose to extend the adjoint variable method (AVM) to the sensitivity analysis of dispersive materials. In the optical range, most common materials are frequency dependent. The complexity of the modeling approaches of these materials delayed the development of simulation-based AVM techniques. We circumvent the mathematical difficulties through utilizing the Z-domain representation of the dispersive models. We exploit the time domain modeling technique (transmission line modeling) for efficient calculation of the structure sensitivities. The theory is developed for general dispersive materials modeled by Drude or Lorentz models. Adjoint variable method is known to be the ultimate efficient sensitivity calculation modality. The sensitivity is calculated with respect to all the designable parameters utilizing at most one extra simulation. This is far more efficient than the regular finite difference approaches with a computational overhead that scales linearly with the number of design parameters. The theory has been successfully applied to a subwavelength structure of 180° bend utilizing metamaterial slab where the design variables are the shape parameters and material parameters of the metamaterial slab. The results are compared to the accurate yet expensive finite difference approach and good agreement is achieved.

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Osman S. Ahmed, Mohamed H. Bakr, Xun Li, and Tsuyoshi Nomura " Adjoint variable method for general material models towards efficient sensitivity analysis of subwavelength structures ", Proc. SPIE 8915, Photonics North 2013, 89151Q (11 October 2013); https://doi.org/10.1117/12.2038645

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