General recipe for flatbands in photonic crystal waveguides

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.

Control of dispersion in photonic crystal waveguides using group symmetry theory

“…the so-called photonic wires, the dispersion can be controlled by changing the height and the width of the high index silicon wire on top of the silica layer [3]. The ability to generate a prescribed dispersion function, also referred as dispersion engineering [4,5], is a more demanding goal. By offering many degrees of freedom in the design, photonic crystals (PhC) fibers [6] and waveguides [7,8,9,4,10] have proven to enable dispersion engineering.…”

Wideband slow light in photonic crystal slab waveguide based on geometry adjustment and optofluidic infiltration

“…2(a), the dispersion curves for the waveguide guided mode (WGM) have a positive slope resulting in a U-shaped n g curve. Based on coupled mode theory (CMT) [29], the coupling between forward and backward propagating modes generates PBG, and the width of the gap is determined by the coupling strength. In the same way, the coupling between the contradirectional propagating modes generates the gap in the PhCSW.…”

Broad periodic waveguides with critically coupled modes for open resonator operation

“…Figure 1 illustrates how the modes are transformed (coupled mode theory, CMT). Gaps open at every crossing, but as discussed recently [2], if the coupling has an adequate strength, the so-called critical coupling regime (CCR) optimally flat bands are formed at the Brillouin zone edge [3,4]. In some more details, the set of coupled modes has a locally hyperbolic behavior [4], with wiggles reminiscent of the initial modes superimposed on it.…”