We present some of our recent works in developing novel classes of meta-materials, including 3D isotropic high-index meta-materials, and non-Maxwellian meta-materials. We also introduce a theoretical formalism of the photonic band structure of optical meta-materials in terms of a Hermitian eigenvalue problem, and show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general.
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