Abstract
We present the interface diffraction method (IDM), an efficient technique to determine the response of planar photonic crystal waveguides and couplers containing arbitrary defects. Field profiles in separate regions of a structure are represented through two contrasting approaches: the plane wave expansion method in the cladding and a scattering matrix method in the core. These results are combined through boundary conditions at the interface between regions to model fully a device. In the IDM, the relevant interface properties of individual device elements can be obtained from unit cell computations, stored, and later combined with other elements as needed, resulting in calculations that are over an order of magnitude faster than supercell simulation techniques. Dispersion relations for photonic crystal waveguides obtained through the IDM agree with the conventional plane wave expansion method to within 2.2% of the stopband width.
Highlights
Photonic crystals provide a flexible platform for the realization of many optical components including passive, active, and nonlinear devices
In this paper we demonstrate that simulations conducted over photonic crystal unit cells alone are sufficient to determine the response of photonic crystal waveguides and couplers with complex defect regions
We demonstrate the flexibility of the interface diffraction method (IDM) with several types of photonic crystal waveguides and a novel coupler design, at each step verifying its accuracy with comparisons to numerical simulations
Summary
Photonic crystals provide a flexible platform for the realization of many optical components including passive, active, and nonlinear devices. We have recently introduced a method that uses the Bloch modes of infinite photonic crystals to calculate the reflection, transmission, and diffraction of light at photonic crystal interfaces [16] These coefficients, similar to the Fresnel coefficients for dielectric interfaces, can be used to model photonic crystal devices that include interfaces between photonic crystals and homogeneous materials as a succession of effective materials, with propagation inside each material described by its respective band structure. This method has been shown to simulate efficiently the response of point defect cavities, as well as line defect waveguides and waveguide couplers [17]. We demonstrate the flexibility of the IDM with several types of photonic crystal waveguides and a novel coupler design, at each step verifying its accuracy with comparisons to numerical simulations
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