Two-dimensional grating for narrow-band filtering with large angular tolerances.

Evgeny Popov,Anne-Laure Fehrembach,Guillaume Demésy,Yoann Brûlé,Philippe Boyer

doi:10.1364/oe.24.014974

Abstract

A two-dimensional periodic sub-wavelength array of vertical dielectric cylinders on a glass substrate is studied numerically using three different electromagnetic approaches. It is shown that such structure can present a narrow-band spectral resonance characterized by large angular tolerances and 100% maximum in reflection. In particular, in a two-nanometer spectral bandwidth the reflectivity stays above 90% within angles of incidence exceeding 10 degrees for unpolarized light. Bloch modal analysis shows that these properties are due to the excitation of a hybrid mode that is created in the structure by a guided-like mode and a localized cavity mode. The first one is due to the collective effect of the array, while the second one comes from the mode(s) of a single step-index fiber.

Highlights

Realizing a spectral filtering function with nanopatterned structures is not new but it is a still dynamic field of research
Another advantage is that nanopatterned filters with different spectral characteristics can be created on a single chip, their filtering function can be differentiated by varying only few parameters of the pattern, preserving the same thickness of the assembly of different filters
Narrow-band spectral filters can be achieved with the so-called Guided mode resonance filters (GMRF) composed of a subwavelength grating and a planar waveguide

Summary

Introduction

Realizing a spectral filtering function with nanopatterned structures is not new but it is a still dynamic field of research. Called “High contrast grating”, the coupling between a mode similar to the guided mode of a planar waveguide and a cavity mode leads to a hybrid mode [10], which presents a high angular tolerance, and having either a high spectral selectivity in the reflectivity [7,8,9] or a high reflectivity over a wide spectral range suitable to create broadband mirrors [11,12] This phenomenon can be interpreted in terms of modes propagating along the ridges for two-dimensional (2D) structures [13,14] (invariant along one direction). The incident polarization is linear and is defined with respect to the plane of incidence: as usual, it is called transverse electric (TE), when the electric field vector is perpendicular to the plane of incidence, and transverse magnetic (TM), when the electric field vector lies inside the plane of incidence

Reflectivity behavior

Modal analysis

Electric field distributions