Propagating Bloch modes above the lightline on a periodic array of cylinders

Abstract

Optical bound states in the radiation continuum (BICs) have interesting properties and potentially important applications. On periodic structures, the BICs are guided modes above the lightline, and they can be either standing waves or propagating Bloch modes. A one-dimensional (1D) array of circular dielectric cylinders is probably the simplest structure on which different types of BICs exist. Using a highly efficient numerical method, we perform an extensive numerical study for propagating BICs on 1D arrays of circular dielectric cylinders. In addition to the known Bloch BIC which is symmetric with respect to the axis of the array, we obtain a new BIC which is antisymmetric. The existence domains (in the plane of radius and dielectric constant of the cylinders) of both BICs are determined. The boundaries of these domains correspond to either standing waves which are not protected by symmetry or the opening of the second diffraction channel. Numerical results are also presented to illustrate the discontinuities of transmission and reflection coefficients at the BICs, and the resonant behavior near the BICs.

Light Trapping above the Light Cone in One-Dimensional Arrays of Dielectric Spheres

“…As soon as one deviates from the BSC point in the parametric space the BSC emerges in the form of a collapsing Fano resonance. That phenomenon was observed in scattering of EM waves by arrays of rods [30,33,37,40,44,45,52,62]. The Fano resonance for the present system can be interpreted as interference of two optical paths, one through the spheres and another between the spheres.…”

“…The Bloch BSCs in a single array of cylindrical dielectric rods in air were also reported in Refs. [37,49,62]. Such travelling wave Bloch BSCs with the eigenfrequencies above the light cone are interesting because the array serves as a waveguide although only for fixed β (see summary of BSCs in Figure 5) in contrast to the bound states below the light cone [24].…”

Bound states with complex frequencies near the continuum on lossy periodic structures

“…where a 11 = Ω φB 1 dr, a 12 = Ω φB 2 dr, a 21 = Ω ϕB 1 dr, a 22 = Ω ϕB 2 dr, b 1j = Ω φC j dr, b 2j = Ω ϕC j dr.…”

“…A particularly simple structure supporting BICs is a slab waveguide with anisotropic core and substrate [11,12]. Many recent works are concerned with BICs on periodic structures, including two-dimensional (2D) structures with one periodic direction [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], threedimensional (3D) biperiodic structures [28][29][30][31][32][33][34][35][36][37], and 3D rotationally symmetric structures [38,39]. In these studies, the periodic structures are sandwiched between or surrounded by homogeneous media, the BICs are guided Bloch modes above the lightline, and the radiative waves are propagating plane waves in the homogeneous media.…”

Revealing photonic symmetry-protected modes by the finite-difference-time-domain method

“…Thus, two obvious solutions exist to break the symmetry: an intrinsic one by modifying the geometry of the structure itself [6][7][8][9][10] or an extrinsic one induced by modifying the illumination conditions (oblique incidence for instance) [3,11,12]. Two-dimensional (2D) [8] or three-dimensional (3D) [9,[13][14][15][16] structures were proposed in this context to present symmetry protected modes at normal incidence. The spatial discretization exercised in the FDTD combined with the Yee scheme [17], for which two different components of the electromagnetic field are located at two different spatial positions, leads to naturally break the geometrical symmetry of the structure.…”