Adjoint sensitivity analysis with dispersive materials
In all the previously discussed cases, we assumed that the materials utilized in the FDTD simulations are nondispersive. This means that all material properties (permittivity, permeability, and conductivity) do not change with frequency. In many interesting applications, however, this is not the case. For example, in the emerging area of metamaterials, the effective permittivity and permeability show strong dependency on frequency . In the area of plasmonics, all metals have dispersive properties [2-5]. The same applies to modeling materials in the THz and infrared frequency regimes [6,7]. It is thus of prime importance to be able to estimate the sensitivities of different responses with respect to all geometrical and material parameters of structures with dispersive material properties. In this chapter, we develop a general theory for adjoint sensitivity analysis of high frequency dispersive structures. This formulation applies to materials with commonly used types of dispersion profiles such as Lorentz [8,9], Drude [10-12], and Debye [13,14]. We show that only one dispersive adjoint simulation is required to estimate the sensitivities of the desired response with respect to all parameters. We illustrate this approach through one example.