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Schematic of the proposed semianalytic approach for analyzing a structure formed by a dielectric waveguide coupled to a semi-infinite photonic crystal (PhC) waveguide by using an especially designed two-defects configuration placed within a PhC taper. , , , and are the transmission and reflection matrixes calculated in mediums I–II while and are the forward and backward components of the forward (backward) propagating Bloch modes calculated at the interface layer between mediums I–II and medium II, which corresponds to a fixed cut position within the lattice period, , of the PhC. The axis indicates the propagation direction.
(Color online) (a) Transmission efficiency as a function of the defect radius normalized to the rod radius of the photonic crystal, , and of the relative position in the axis within the PhC taper normalized to the lattice constant, . (b) Transmission efficiency map of an additional single defect considering that a defect of radius is placed at within the PhC taper.
Transmission efficiency as a function of the normalized frequency for the structure shown in Fig. 1 and considering the PhC taper with and without the optimized two-defects configuration. Semianalytic results are compared with FDTD simulations.
(a) Coupled-cavity waveguide (CCW) coupled to a conventional single line defect PhC waveguide. The PhC waveguide is butt coupled to a wide dielectric waveguide by conveniently choosing the cut position to achieve negligible reflection back to the CCW. (b) Reflected power into the CCW as a function of the normalized frequency.
Transmission spectrum of a CCW of finite length calculated by using the Fabry-Perot formula (dashed line) and by using the FDTD method (solid line).
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