Bound states in the continuum on periodic structures: perturbation theory and robustness

Bifurcation of bound states in the continuum in periodic structures

In lossless dielectric structures with a single periodic direction, a bound state in the continuum (BIC) is a special resonant mode with an infinite quality factor (Q factor). The Q factor of a resonant mode near a typical BIC satisfies Q∼1/(β-β ∗)2, where β and β ∗ are the Bloch wavenumbers of the resonant mode and the BIC, respectively. However, for some special BICs with β ∗=0 (referred to as super-BICs by some authors), the Q factor satisfies Q ∼ 1/β6. Although super-BICs are usually obtained by merging a few BICs through tuning a structural parameter, they can be precisely characterized by a mathematical condition. In this Letter, we consider arbitrary perturbations to structures supporting a super-BIC. The perturbation is given by δF(r), where δ is the amplitude and F(r) is the perturbation profile. We show that for a typical F(r), the BICs in the perturbed structure exhibit a pitchfork bifurcation around the super-BIC. The number of BICs changes from one to three as δ passes through zero. However, for some special profiles F(r), there is no bifurcation, i.e., there is only a single BIC for δ around zero. In that case, the super-BIC is not associated with a merging process for which δ is the parameter.

Non-generic bound states in the continuum in waveguides with lateral leakage channels

For optical waveguides with a layered background which itself is a slab waveguide, a guided mode is a bound state in the continuum (BIC), if it coexists with slab modes propagating outwards in the lateral direction; i.e., there are lateral leakage channels. It is known that generic BICs in optical waveguides with lateral leakage channels are robust in the sense that they still exist if the waveguide is perturbed arbitrarily. However, the theory is not applicable to non-generic BICs which can be defined precisely. Near a BIC, the waveguide supports resonant and leaky modes with a complex frequency and a complex propagation constant, respectively. In this paper, we develop a perturbation theory to show that the resonant and leaky modes near a non-generic BIC have an ultra-high Q factor and ultra-low leakage loss, respectively. Recently, many authors studied merging-BICs in periodic structures through tuning structural parameters. It has been shown that resonant modes near a merging-BIC have an ultra-high Q factor. However, the existing studies on merging-BICs are concerned with specific examples and specific parameters. Moreover, we analyze an arbitrary structural perturbation given by δF(r) to waveguides supporting a non-generic BIC, where F(r) is the perturbation profile and δ is the amplitude, and show that the perturbed waveguide has two BICs for δ > 0 (or δ < 0) and no BIC for δ < 0 (or δ > 0). This implies that a non-generic BIC can be regarded as a merging-BIC (for almost any perturbation profile F) when δ is considered as a parameter. Our study indicates that non-generic BICs have interesting special properties that are useful in applications.

Double-Strip Array-Based Metasurfaces with BICs for Terahertz Thin Membrane Detection

A double-strip array-based metasurface that supports the sharp quasi-bound states in the continuum (quasi-BICs) is demonstrated in terahertz regions. By tuning the structural parameters of metal strips, the conversion of BICs and quasi-BICs is controllable. The simulated results exhibit an achieved maximum Q-factor for quasi-BICs that exceeds 500, corresponding to a bandwidth that is less than 1 GHz. The optical response of quasi-BICs is mainly affected by the properties of substrates. Resonant frequencies decrease linearly with increasing refractive index. The bandwidth of quasi-BICs decreases to 0.9 GHz when n is 2.2. The sharp quasi-BICs are also sensitive to changes in material absorption. Low-loss materials show higher Q-factors. Thus, the selection of a suitable substrate material will be beneficial in achieving resonance with a high Q value. The sensitivity of DSAs for molecules is assessed using a thin membrane layer. The DSAs show high sensitivity, which achieves a frequency shift of 70 GHz when the thickness of the membrane is 10 μm, corresponding to a sensitivity of 87.5 GHz/RIU. This metasurface with sharp quasi-BICs is expected to perform well in THz sensing.

Robust and non-robust bound states in the continuum in rotationally symmetric periodic waveguides

A fiber grating and a one-dimensional (1D) periodic array of spheres are examples of rotationally symmetric periodic (RSP) waveguides. It is well known that bound states in the continuum (BICs) may exist in lossless dielectric RSP waveguides. Any guided mode in an RSP waveguide is characterized by an azimuthal index m, the frequency ω, and Bloch wavenumber β. A BIC is a guided mode, but for the same m, ω and β, cylindrical waves can propagate to or from infinity in the surrounding homogeneous medium. In this paper, we investigate the robustness of nondegenerate BICs in lossless dielectric RSP waveguides. The question is whether a BIC in an RSP waveguide with a reflection symmetry along its axis z, can continue its existence when the waveguide is perturbed by small but arbitrary structural perturbations that preserve the periodicity and the reflection symmetry in z. It is shown that for m = 0 and m ≠ 0, generic BICs with only a single propagating diffraction order are robust and non-robust, respectively, and a non-robust BIC with m ≠ 0 can continue to exist if the perturbation contains one tunable parameter. The theory is established by proving the existence of a BIC in the perturbed structure mathematically, where the perturbation is small but arbitrary, and contains an extra tunable parameter for the case of m ≠ 0. The theory is validated by numerical examples for propagating BICs with m ≠ 0 and β ≠ 0 in fiber gratings and 1D arrays of circular disks.

On the robustness of bound states in the continuum in waveguides with lateral leakage channels

Bound states in the continuum (BICs) are trapped or guided modes with frequencies in radiation continua. They are associated with high-quality-factor resonances that give rise to strong local field enhancement and rapid variations in scattering spectra, and have found many valuable applications. A guided mode of an optical waveguide can also be a BIC, if there is a lateral structure supporting compatible waves propagating in the lateral direction; i.e., there is a channel for lateral leakage. A BIC is typically destroyed (becomes a resonant or a leaky mode) if the structure is slightly perturbed, but some BICs are robust with respect to a large family of perturbations. In this paper, we show (analytically and numerically) that a typical BIC in optical waveguides with a left-right mirror symmetry and a single lateral leakage channel is robust with respect to any structural perturbation that preserves the left-right mirror symmetry. Our study improves the theoretical understanding on BICs and can be useful when applications of BICs in optical waveguides are explored.

All-Dielectric Active Terahertz Photonics Driven by Bound States in the Continuum

The remarkable emergence of all-dielectric meta-photonics governed by the physics of high-index dielectric materials offers a low-loss platform for efficient manipulation and subwavelength control of electromagnetic waves from microwaves to visible frequencies. Dielectric metasurfaces can focus electromagnetic waves, generate structured beams and vortices, enhance local fields for advanced sensing, and provide novel functionalities for classical and quantum technologies. Recent advances in meta-photonics are associated with the exploration of exotic electromagnetic modes called the bound states in the continuum (BICs), which offer a simple interference mechanism to achieve large quality factors (Q) through excitation of supercavity modes in dielectric nanostructures and resonant metasurfaces. Here, a BIC-driven terahertz metasurface with dynamic control of high-Q silicon supercavities that are reconfigurable at a nanosecond timescale is experimentally demonstrated. It is revealed that such supercavities enable low-power, optically induced terahertz switching and modulation of sharp resonances for potential applications in lasing, mode multiplexing, and biosensing.

Oblique evanescent excitation of a dielectric strip: A model resonator with an open optical cavity of unlimited Q

A rectangular dielectric strip at some distance above an optical slab waveguide is being considered, for evanescent excitation of the strip through the semi-guided waves supported by the slab, at specific oblique angles. The 2.5-D configuration shows resonant transmission properties with respect to variations of the angle of incidence, or of the excitation frequency, respectively. The strength of the interaction can be controlled by the gap between strip and slab. For increasing distance, our simulations predict resonant states with unit extremal reflectance of an angular or spectral width that tends to zero, i.e. resonances with a Q-factor that tends to infinity, while the resonance position approaches the level of the guided mode of the strip. This exceptionally simple system realizes what might be termed a "bound state coupled to the continuum".