Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model

Abstract

Whispering gallery modes supported by open circular dielectric cavities are embedded into a non-parametric 2-D frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided-wave scattering process, the response of the circuit to guided wave excitation. Transmission resonances can be characterized directly in terms of resonance frequency and linewidth by computing supermodes of the entire composite circuits, comprising both cavities and bus waveguides. Examples of single ring-and disk-filters, a coupledresonator optical waveguide, and a three-cavity photonic molecule in a reflector configuration allow the approach to be assessed.

Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver

“…Refs. [27,28]) 1 . The deviation appears to be slightly larger for the case of the TM 00 resonance, with less confined fields, i.e.…”

“…Ref. [27,28], a reasoning based on the "supermodes" associated with the "open system", comprising the actual cavity (the strip core) together with the outlet (the half-infinite slab), i.e. based on the (hybrid) leaky modes supported by the strip-slab configuration, can be applied.…”

Constructing a partially transparent computational boundary for UPPE using leaky modes

“…Using the formula (14) and our convention for the inverse Fourier transform (5) we can conclude that the modes in the second quadrant, determined by formula (34), are outgoing and exponentially growing in the transverse direction. From the formula for the propagation constants (15) it is also evident that they are decaying in the propagation direction. These are thus leaky modes.…”

Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings

“…Using Eqs. (15) and (19), it is possible to express the curls of the modal element fields through the exported fields directly, without resorting to numerical derivatives.…”

“…The respective "hybrid" analytical/numerical CMT variant (HCMT) was introduced in [16], at first applied to circuits with rectangular refractive index distributions, including the crossings of perpendicular waveguide channels, waveguide Bragg gratings and related filters, and systems of coupled square microcavities [16,17]. References [18,19] report on HCMT models of a series of micro-ring or -disk circuits. The most recent overviews of the quite versatile technique are found in [20,21]; all examples so far, however, were restricted to 2D.…”