Abstract
We present a general recipe for tailoring flat dispersion curves in photonic crystal waveguides. Our approach is based on the critical coupling criterion that equates the coupling strength of guided modes with their frequency spacing and results in a significant number of the modes lying collectively in the slow-light regime. We first describe the critical coupling scheme in photonic crystal waveguides using a simple coupled mode theory model. We also determine that canonical photonic crystal waveguides natively correspond to strongly coupled modes. Based on these analyses, our design recipe is as follows: Tune the profile of the first Fourier component of the waveguide periodic dielectric boundary to lower the coupling strength of the guided modes down to its critical value. We check that this generalized tuning may be accomplished by adjusting any desired optogeometric parameter such as hole size, position, index etc. We explore the validity of this general approach down to the narrow two-missing rows waveguides. The interest of this method is to circumvent most of the common trial-and-error procedures for flatband engineering.
Highlights
A simple wavelength-scale periodic boundary corrugation along a dielectric waveguide confers it the extraordinary ability to slow down light [1, 2]
We describe a framework to look at critical coupling in the modified context of hyperbolic dispersion relations, as is the case in photonic crystal (PhC) waveguides, and study the effect of varying modal coupling strength on the band shape
We have described a simple recipe for designing flatbands in a PhC waveguide
Summary
A simple wavelength-scale periodic boundary corrugation along a dielectric waveguide confers it the extraordinary ability to slow down light [1, 2]. Apart from laterally confining modes by the PBG effect, the periodic waveguide cladding acts a grating, giving rise to “resonant diffraction” [18] of certain guided modes These resonant conditions appear as zerogroup-velocity points on the dispersion diagram. 4kz range of the flatband (see Fig. 1(c)) translates into a large angular bandwidth 46, over which the mode does not apparently disperse and retains its resonant character This is made possible by the hybridization of the Littrow mode with the other interacting near-Littrow modes like type ‘3’ of Fig. 1(a).
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