title: 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.
authors.forename: N
authors.initials: N
authors.lastname: Rassem
authors.forename: A-L
authors.initials: AL
authors.lastname: Fehrembach
authors.forename: E
authors.initials: E
authors.lastname: Popov