Quasi-bound Modes Research Articles

From high- to low-contrast: the role of asymmetries in dielectric gratings supporting bound states in the continuum

One-dimensional sub-wavelength gratings are versatile photonic platforms supporting diverse resonances, including symmetry-protected bound states in the continuum. However, practical access to these bound modes relies on their quasi-bound form, which necessitates the introduction of perturbations in either geometry or material properties. Despite having a large, finite quality factor, quasi-bound modes retain their characteristically strong field confinement. Gaining control over field localization and leakage of quasi-bound modes requires an investigation not limited to studying the degree of asymmetry and the incoming polarization. Here, we demonstrate that by carefully combining specific types of asymmetries and refractive index contrast between the grating and its surrounding environment, one can tailor field localization and Q-factor almost at will. Our findings reveal a strategic roadmap for optimizing quasi-bound mode implementation, dramatically improving their use in applications such as optical communication, sensing, and nonlinear optical processes.

Exploiting Zone-Folding Induced Quasi-Bound Modes to Achieve Highly Coherent Thermal Emissions.

Thermal emissions with high coherence, although not as high as those of lasers, still play a crucial role in many practical applications. In this work, by exploiting the geometric perturbation-induced optical lattice tripling and the associated Brillion zone folding effect, we propose and investigate thermal emissions in the mid-infrared with simultaneous high temporal and spatial coherence. In contrast with the case of period-doubling perturbation in our previous work, the steeper part of the guided mode dispersion band will be folded to the high-symmetry Γ point in the ternary grating. In this case, a specific emission wavelength corresponds to only a very small range of wavevectors. Consequently, apart from the high temporal coherence characterized by an experimental bandwidth around 30 nm, the achieved thermal emissions also feature ultrahigh spatial coherence. Calculations show that at the thermal emission wavelengths in the mid-infrared, the spatial coherence length can easily reach up to mm scale.

Open boundary conditions for the simulation of leaky modes

We propose an open-boundary method for the simulation of the modes of confining dielectric structures. The technique is inclusive of normal modes, but is especially advantageous for the simulation of quasi-normal, or leaky, modes. The central idea is to utilize the asymptotic form of targeted solutions to eliminate the outer part of the computational domain and bring the numerical boundary close to the simulated structure. While a similar approach was previously demonstrated for scalar quantum models, here we put forward a generalization for fully vectorial fields. Accuracy in this new context is validated using step-index and tube-type hollow core fiber geometries. The method has broad applicability, as quasi-bound modes are intrinsic to many systems of interest in optics and photonics.

Dynamical signatures of black holes in massive Chern-Simons gravity: Quasibound modes and time evolution

Dynamical Chern-Simons (dCS) gravity is a promising extension of general relativity (GR), arising naturally from the low-energy limit of some string motivated theories. Even though dCS possesses an additional scalar degree of freedom, interestingly, the Schwarzschild black hole is an exact solution of it. Concerning dynamical phenomena, however, gravitational and scalar perturbations couple with each other, generating possible scenarios to understand the differences between dCS and GR. We study dynamical signatures of dCS considering that the scalar field potential has a mass term. We analyze the influence of the theory's parameter into the quasibound states and in the time evolution of purely gravitational initial profiles. We find that the coupling can make the dipolar modes \textit{less stable} and that at late times initial gravitational perturbations become contaminated with the scalar sector, presenting an oscillation that depends on the quasibound state frequencies. These results may be interesting in the light of superradiant instabilities in rotating systems and to find signatures of alternative theories in gravitational wave detections.

New results for electromagnetic quasinormal and quasibound modes of Kerr black holes

The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations governing the late-time ring-down of the perturbations of the Kerr metric, the Teukolsky Angular Equation and the Teukolsky Radial Equation, can be solved analytically in terms of confluent Heun functions. In this article, we solve numerically the spectral system formed by those exact solutions and we obtain the electromagnetic (EM) spectra of the Kerr black hole. Because of the novel direct way of imposing the boundary conditions, one is able to discern three different types of spectra: the well-known quasinormal modes (QNM), the symmetric with respect to the real axis quasibound modes (QBM) and a spurious spectrum who is radially unstable. This approach allows clearer justification of the term "spurious" spectrum, which may be important considering the recent interest in the spectra of the electromagnetic counterparts of events producing gravitational waves.

Multipole surface plasmons in metallic nanohole arrays

The quasibound electromagnetic modes for the arrays of nanoholes perforated in thin gold film are analyzed both numerically by the rigorous coupled wave analysis (RCWA) method and semianalytically by the coupled mode method. It is shown that when the size of the nanohole occupies a large portion of the unit cell, the surface plasmon polaritons (SPPs) at both sides of the film are combined by the higher order waveguide modes of the holes to produce multipole surface plasmons: coupled surface plasmon modes with multipole texture on the elec-tric field distributions. Further, it is revealed that the multipole texture either enhances or suppresses the couplings between SPPs depending on their diffraction orders and also causes band inversion and reconstruction in the coupled SPP band structure. Due to the multipole nature of the quasibound modes, multiple dark modes coexist to produce a variety of Fano resonance structures on the transmission and reflection spectra.

Ab initio investigation of lasing thresholds in photonic molecules

We investigate lasing thresholds in a representative photonic molecule composed of two coupled active cylinders of slightly different radii. Specifically, we use the recently formulated steady-state ab initio laser theory (SALT) to assess the effect of the underlying gain transition on lasing frequencies and thresholds. We find that the order in which modes lase can be modified by choosing suitable combinations of the gain center frequency and linewidth, a result that cannot be obtained using the conventional approach of quasi-bound modes. The impact of the gain transition center on the lasing frequencies, the frequency pulling effect, is also quantified.

Schwarzschild scalar wigs: Spectral analysis and late time behavior

Using the Green's function representation technique, the late time behavior of localized scalar field distributions on Schwarzschild spacetimes is studied. Assuming arbitrary initial data we perform a spectral analysis, computing the amplitude of each excited quasi-bound mode without the necessity of performing dynamical evolutions. The resulting superposition of modes is compared with a traditional numerical evolution with excellent agreement; therefore, we have an efficient way to determine final black hole wigs. The astrophysical relevance of the quasi-bound modes is discussed in the context of scalar field dark matter models and the axiverse.

Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities

The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced ???chaotic??? modes for the generic case. The wavevector quantization rule for the quasi-bound modes is derived and given a simple physical interpretation in terms of Fresnel reflection; quasi-bound modes are explictly constructed and compared to numerical results. The effect of discrete symmetries of the resonator is analyzed and shown to give rise to quasi-degenerate multiplets; the average splitting of these multiplets is calculated by methods from quantum chaos theory.

Optical mode structure of the plasma waveguide

The quasibound modes of an evolving plasma waveguide were investigated by using variably delayed end-injected and side-injected probe pulses. The use of these different coupling geometries allowed the probing of the waveguide's optical modes during two temporal regimes: early-time plasma channel development, characterized by leaky optical confinement, and later channel hydrodynamic expansion characterized by stronger confinement. The wave equation was solved to determine the available quasiguided optical modes and their confinement for experimentally measured electron density profiles. The guided intensity patterns and spectra measured at the waveguide exit were successfully explained in terms of these mode solutions. The spectrum of broadband end-coupled probe pulses was found to be unaffected by the guiding process, mainly because those modes which survived to the waveguide exit were well-bound, and for strongly bound fields, the transverse mode profiles are wavelength independent. By contrast, side coupling to the quasibound modes of the plasma waveguide was seen to be highly mode and frequency selective.

Frequency Selective Tunnel Coupling to the Plasma Fiber

The optical resonances of plasma fibers are observed by monitoring the spectrum and spatial profile of their quasibound modes, which are excited through side or tunnel coupling. The features of the coupling compare favorably to calculations based on the measured electron-density profiles. This is the first direct observation of optical electromagnetic resonances of a plasma structure.

Detailed Study of Quasi-bound Modes in Leaky Structures

Abstract The inconsistency of the progressive wave boundary conditions for the quasi-bound modes in open leaky structures is shown and a new boundary value formulation is developed. The results obtained are tested for leaky waveguides with delta function barriers for which a simple analytical characteristic equation is available. The method is applied for the determination of eigenvalues of prism-loaded multilayer waveguides. The influence of the prism coupler on the waveguide modes is investigated in detail for slab and four-layer waveguides. The method is compared with several approximate methods.