Design and Analysis of High-Index-Contrast Gratings Using Coupled Mode Theory

We analyze high-refractive-index-contrast subwavelength grating structures using truncated coupled mode theory (CMT). CMT not only provides physical insight into the role of each mode in the overall response but also allows for improved design. An analytic expression is derived for the design of broadband reflectors, providing a near-optimal design that is within 0.08% of the maximum broadband reflectivity calculated by the finite-difference time-domain method. Furthermore, the CMT is used to design a high-quality narrow-band reflector with 28% improved quality factor over previously reported results, as quantified by rigorous coupled wave analysis.