Scattering from anisotropic geometries of arbitrary shape is relatively difficult to interpret physically, involving the intricate interplay between material and geometric effects. Insights into complex scattering mechanisms are often enabled by modal methods that decompose the response into the well-understood multipolar resonances. Here, we extend the generalized normal mode expansion to lossy and anisotropic scatterers. Unique to the method is that it decomposes the total response of any anisotropic resonator into the modes of the corresponding isotropic resonator. This disentangles the material and geometric contributions to the scattering of any anisotropic resonator. Furthermore, the method can identify absorption and scattering resonances with separate sets of modes. We illustrate our method by considering an infinitely long cylinder with concentric metallic/dielectric layers, targeting the complex case of an effective hyperbolic response. We show that by scanning the material composition of the hyperbolic medium, we can achieve any desired scattering effect, including backscattering cancellation.
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Special attention is given in the eigensolver routine of Eq. (5). Depending on the case that is being treated, pre-arrangement of the matrix of overlap integrals ease the calculation. In our case, since the permittivity tensor (9) is diagonal, there is no mode mixing between modes of different azimuthal orders (see Appendix C). Thus, we can re-arrange the matrix of overlap integrals to be block diagonal and solve Eq. (5) for each azimuthal order independently.
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