Waveguide mode in the box with an extraordinary flat dispersion curve

Abstract

The extraordinary flattening of the dispersion curve of the so-called cavity resonator integrated guided-mode resonance filters (CRIGFs) is analyzed and explained as due to the intramode coupling imposed by the external Bragg resonators. CRIGFs are composed of a grating coupler (guided-mode resonance filter, GMRF) put between two distributed Bragg reflectors (DBRs). They form a cavity box in which the excited guided mode is confined. This confinement provides resonances with small spectral width (smaller than 1 nm for optical wavelengths) and extraordinary wide angular acceptance (several degrees). At a first glance, one may think that similar performances could be obtained while putting the GMRF and the DBR one above the other, forming a so-called "doubly periodic" grating, as in this configuration also the DBR confines the mode. Yet, the angular acceptance of CRIGFs is an order of magnitude greater than in classical gratings, even with complex pattern. The aim of the present paper is to identify the phenomenon responsible for the extraordinary large angular acceptance of CRIGFs. We numerically calculate, for the first time to the best of our knowledge, the dispersion curve of the mode excited in the CRIGF. The dispersion curve shows a flat part, where the resonance wavelength is quasi-independent of the angle of incidence, and the flattening grows with the width of the Bragg reflector. We develop an approximate coupled four-wave model, which predicts the extraordinary flattening as a consequence of an additional coupling of the waveguide modes of the GMRF provided by the Bragg grating, that does not exist in the "doubly periodic" gratings.

Recent Advances in Resonant Waveguide Gratings

“…When the reflectance of both DBRs is 100%, the guided wave power is accumulated enough to cancel the direct transmission or reflection. This particular configuration provides a high wavelength selectivity even with small (micrometer‐size) apertures, whilst preserving a high angular acceptance . CRIGFs were first developed to have high‐efficiency coupling before being implemented as filters working with a miniaturized aperture size .…”

“…b) CRIGF with the superposition of DBR and coupling grating. Reproduced with permission . Copyright 2015, OSA.…”

“…This particular configuration provides a high wavelength selectivity even with small (micrometer-size) apertures, whilst preserving a high angular acceptance. [349,350] CRIGFs were first developed to have high-efficiency coupling [289,351] before being implemented as filters working with a miniaturized aperture size. [352,353] The relative position between the coupling grating and the DBRs, the cavity length [354,355] as well as the waveguide thickness, [356] have to be properly tuned for phase adjustment of the waves resulting from out-coupling of the forward and backward guided waves.…”

Bimodal Resonance Phenomena—Part II: High/Low-Contrast Grating Resonators

“…R ESONATORS are key blocks in a vast multitude of applications in electronics, microwaves, optics and several other subjects. Focusing the discussion on optics, several implementations of resonators exhibiting a high quality factor (Q) have been attempted based on microrings [1], photonic crystals [2] and gratings, such as the cavity resonator integrated guided-mode-resonance filter (CRIGF) [3], [4]. A very interesting possibility relies on high-contrast gratings (HCGs).…”

Design of guided-mode resonance mirrors for short laser cavities

“…There have been reports on various configurations including curved gratings [23], a channel waveguide [24], a nonuniform coupling coefficient [25], and twodimensionally crossed gratings [26]. Applications to external mirrors were reported for wavelength stabilization of a laser [27] and for wide acceptable incidence angle [28,29].…”