1 May 2012 Analytic design of chirped planar photonic crystals in the metamaterial regime
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Abstract
We report an analytic approach to describe all-dielectric graded periodical media (namely graded photonic crystals) operating in the homogeneous regime. Beneath this condition, the method is based on the equations of Hamiltonian optics and provides an analytical expression of the two-dimensional refraction index needed to make light follow prescribed paths. It is applied to a proof-of-concept structure (light 90° bend), which behaviour is investigated by considering a two-dimensional planar silicon on insulator slab waveguide drilled by a sub-wavelength air-hole lattice with a gradual filling factor corresponding to the required optical index map. The electromagnetic properties of the considered structure are then verified using Finite Difference Time Domain simulation. As a whole, the proposed method is an alternative solution to conformal space coordinate transforms applied to all-dielectric photonic metamaterials and could help the design of new structures in forthcoming works.
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Eric Cassan, Eric Cassan, Khanh Van Do, Khanh Van Do, Delphine Marris-Morini, Delphine Marris-Morini, Laurent Vivien, Laurent Vivien, } "Analytic design of chirped planar photonic crystals in the metamaterial regime", Proc. SPIE 8423, Metamaterials VII, 84231X (1 May 2012); doi: 10.1117/12.921984; https://doi.org/10.1117/12.921984
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