Spectral Galerkin mode-matching method for applications in photonics.

Many engineered photonic devices can be decomposed into parts where the material properties are independent of one or more spatial variables. Numerical mode-matching methods are widely used to simulate such photonic devices due to the efficiency gained by treating the separated variables analytically. Existing mode-matching methods based on piecewise polynomials are more accurate than those based on the global Fourier basis or low-order finite difference, finite-element schemes, but they may exhibit numerical instability when a large number of eigenmodes are used.

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 ∼1/(- ), where β and are the Bloch wavenumbers of the resonant mode and the BIC, respectively. However, for some special BICs with =0 (referred to as super-BICs by some authors), the Q factor satisfies Q ∼ 1/β.

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.

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.

Cochlear implantation in a patient with congenital microtia, cochlear hypoplasia, venous anomalies of the temporal bone and laryngomalacia: Challenges and surgical considerations.

Rationale And Patient Concerns: Congenital hearing loss is often caused by an inner ear malformation, in such cases, the presence of other anomalies, such as microtia, and venous anomalies of the temporal bone and laryngomalacia makes it challenging to perform cochlear implantation surgery.

Diagnoses: This study reports the case of a 28-month-old girl with congenital profound hearing loss, laryngomalacia, and malformed inner ear, who received cochlear implantation surgery. The bony structure, vessels and nerves were first assessed through magnetic resonance imaging and computed tomography before exploring the genetic basis of the condition using trio-based whole exome sequencing.

Computing diffraction anomalies as nonlinear eigenvalue problems.

When a plane electromagnetic wave impinges on a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the outgoing waves in one or more radiation channels vanish. Zero reflection, zero transmission, and perfect absorption are important examples of diffraction anomalies, and they are useful for manipulating electromagnetic waves and light.

Complex modes in optical fibers and silicon waveguides.

In an open optical waveguide, complex modes that are confined around the waveguide core and have a complex propagation constant may exist, even though the waveguide consists of lossless isotropic dielectric materials. However, the existing studies on complex modes are very limited. In this Letter, we consider circular fibers and silicon waveguides, study the formation mechanism of complex modes, and calculate the dispersion relations for several complex modes in each waveguide.

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.

Complex modes in an open lossless periodic waveguide.

Guided modes of an open periodic waveguide, with a periodicity in the main propagation direction, are Bloch modes confined around the waveguide core with no radiation loss in the transverse directions. Some guided modes can have a complex propagation constant, i.e.

Computing resonant modes of circular cylindrical resonators by vertical mode expansions.

Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background.

Analyzing bowtie structures with sharp tips by a vertical mode expansion method.

Bowtie structures of metallic nanoparticles are very effective in producing strong local fields needed in many applications. Existing numerical studies on bowtie structures are limited to those with rounded tips. Due to the field singularities at sharp edges and corners, accurate numerical solutions for bowtie structures with mathematically sharp tips are difficult to obtain.

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

On periodic structures, a bound state in the continuum (BIC) is a standing or propagating Bloch wave with a frequency in the radiation continuum. Some BICs (e.g.

Calculating corner singularities by boundary integral equations.

Accurate numerical solutions for electromagnetic fields near sharp corners and edges are important for nanophotonics applications that rely on strong near fields to enhance light-matter interactions. For cylindrical structures, the singularity exponents of electromagnetic fields near sharp edges can be solved analytically, but in general the actual fields can only be calculated numerically. In this paper, we use a boundary integral equation method to compute electromagnetic fields near sharp edges, and construct the leading terms in asymptotic expansions based on numerical solutions.

Vertical mode expansion method for numerical modeling of biperiodic structures.

Due to the existing nanofabrication techniques, many periodic photonic structures consist of different parts where the material properties depend only on one spatial variable. The vertical mode expansion method (VMEM) is a special computational method for analyzing the scattering of light by structures with this geometric feature. It provides two-dimensional (2D) formulations for the original three-dimensional problem.

Nonlinear standing waves on a periodic array of circular cylinders.

A periodic array of parallel and infinitely long dielectric circular cylinders surrounded by air can be regarded as a simple two-dimensional periodic waveguide. For linear cylinders, guided modes exist continuously below the lightline in various frequency intervals, but standing waves, which are special guided modes with a zero Bloch wavenumber, could exist above the lightline at a discrete set of frequencies. In this paper, we consider a periodic array of nonlinear circular cylinders with a Kerr nonlinearity, and show numerically that nonlinear standing waves exist continuously with the frequency and their amplitudes depend on the frequency.

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background.

The vertical mode expansion method (VMEM) [J. Opt. Soc.

Efficient vertical mode expansion method for scattering by arbitrary layered cylindrical structures.

A relatively simple and efficient numerical method is developed for analyzing the scattering of light by a layered cylindrical structure of arbitrary cross section surrounded by a layered background. The method significantly extends an existing vertical mode expansion method (VMEM) for circular or elliptic cylindrical structures. The original VMEM and its extension give rise to effective two-dimensional formulations for the three-dimensional scattering problems of layered cylindrical structures.

Bilateral symmetry breaking in nonlinear circular cylinders.

Symmetry breaking is a common phenomenon in nonlinear systems, it refers to the existence of solutions that do not preserve the original symmetries of the underlying system. In nonlinear optics, symmetry breaking has been previously investigated in a number of systems, usually based on simplified model equations or temporal coupled mode theories. In this paper, we analyze the scattering of an incident plane wave by one or two circular cylinders with a Kerr nonlinearity, and show the existence of solutions that break a lateral reflection symmetry.

Vertical mode expansion method for transmission of light through a single circular hole in a slab.

An efficient method is developed for rigorously analyzing the scattering of light by a layered circular cylindrical object in a layered background, and it is applied to the study of the transmission of light through a subwavelength hole in a metallic film, where the hole may be filled by a dielectric material. The method relies on expanding the electromagnetic field (subtracted by one-dimensional solutions of the layered media) in one-dimensional modes, where the expansion "coefficients" are functions satisfying two-dimensional Helmholtz equations. A system of equations is established on the boundary of the circular cylinder to solve the expansion "coefficients.

Asymptotic solutions of eigenmodes in slab waveguides terminated by perfectly matched layers.

For numerical modeling of optical wave-guiding structures, perfectly matched layers (PMLs) are widely used to terminate the transverse variables of the waveguide. The PML modes are the eigenmodes of a waveguide terminated by PMLs, and they have found important applications in the mode matching method, the coupled mode theory, and so on. In this paper, we consider PML modes for two-dimensional slab waveguides.

Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities.

Improved Dirichlet-to-Neumann map method for scattering by circular cylinders on a lattice.

A simple model for two-dimensional photonic crystal devices consists of a finite number of possibly different circular cylinders centered on lattice points of a square or triangular lattice and surrounded by a homogeneous or layered background medium. The Dirichlet-to-Neumann (DtN) map method is a special method for analyzing the scattering of an incident wave by such a structure. It is more efficient than existing numerical or semianalytic methods, such as the finite element method and the multipole method, since it takes advantage of the underlying lattice structure and the simple geometry of the unit cells.

High order integral equation method for diffraction gratings.

Conventional integral equation methods for diffraction gratings require lattice sum techniques to evaluate quasi-periodic Green's functions. The boundary integral equation Neumann-to-Dirichlet map (BIE-NtD) method in Wu and Lu [J. Opt.

Complex modes and instability of full-vectorial beam propagation methods.

Full-vectorial beam propagation methods (FVBPMs) are widely used to model light waves propagating in high-index-contrast optical waveguides. We show that the paraxial FVBPM and wide-angle FVBPMs based on diagonal Padé approximants are analytically unstable for waveguides with complex modes. The instability cannot be removed by enlarging the computational domain, increasing the numerical resolution, or using perfectly matched layers, because the complex modes are highly confined around the waveguide core.

Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y.