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Transmission coefficients (TE polarization) for the light coupling between two 2D square lattice PCs with slightly different parameters( and , as shown in the inset) using the direct mode matching simulation and group-velocity-based approximation.
(Color online) Contours of constant group velocities (at =0.15 with TE polarization) for different design parameters of 2D rectangular lattice PCs. The lattice constant parallel to the interface, , is kept intact and normal incidence (along the direction) is considered. The dashed line shows the suggested path for an adiabatic transition and the circles highlight the designed parameters for the successive layers. The gray shaded region represents PC structures for which the operation frequency lies inside the band gap.
(a) Reflection from a square lattice PC structure (circular air holes in Si, ) is shown with no matching stage and with adiabatic matching stages. (b) For the same structure, the angular response of the ten-layer matching at is compared with that of the PC with no matching stage. (c) The shaded region shows reflections for 50 different random buffer stages (with 12 PC layers) with up to 5% perturbation in the sizes of holes compared to the original design.
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