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.
We propose an adjoint variable method (AVM) for efficient wideband sensitivity analysis of the dispersive plasmonic structures. Transmission Line Modeling (TLM) is exploited for calculation of the structure sensitivities. The theory is developed for general dispersive materials modeled by Drude or Lorentz model. Utilizing the dispersive AVM, sensitivities are calculated with respect to all the designable parameters regardless of their number using at most one extra simulation. This is significantly more efficient than the regular finite difference approaches whose computational overhead scales linearly with the number of design parameters. A Z-domain formulation is utilized to allow for the extension of the theory to a general material model. The theory has been successfully applied to a structure with teethshaped plasmonic resonator. The design variables are the shape parameters (widths and thicknesses) of these teeth. The results are compared to the accurate yet expensive finite difference approach and good agreement is achieved.
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