We investigate the modes of coupled waveguides in a hexagonal photonic crystal. We find that for a substantial parameter range the coupled waveguide modes have dispersion relations exhibiting multiple intersections, which we explain both intuitively and using a rigorous tight-binding argument.
We derive effective photon modes that facilitate an intuitive and convenient picture of photon dynamics in a structured Kramers-Kronig dielectric in the limit of weak absorption. Each mode is associated with a mode field distribution that includes the effects of both material and structural dispersion, and an effective line-width that determines the temporal decay rate of the photon. These results are then applied to obtain an expression for the Beer-Lambert-Bouguer law absorption coefficient for unidirectional propagation in structured media consisting of dispersive, weakly absorptive dielectric materials.
We derive the dispersion relations of the guided modes in wire media slabs using a transmission and reflection matrix approach, providing a physically insightful perspective into wave propagation in wire media slabs. We find new approximations to the dispersion relations, and assess their accuracy and the regimes for which they hold. We do so both analytically, and against exact calculations of the electromagnetic fields without reference to effective media. We then analyze the effects of the background refractive index on the guided modes, proposing explanations for the observed behavior.
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