Related papers: Whispering gallery modes for a transmission proble…
We present an analytical method of studying "extended" electronic eigenstates of a diamond hierarchical lattice, which may be taken as the simplest of the hierarchical models recently proposed for stretched polymers. We use intuitive…
Tapered fibers with diameters ranging from 1-4 micron are widely used to excite the whispering-gallery (WG) modes of microcavities. Typically, the transmission spectrum of a WG cavity coupled to a waveguide around a resonance assumes a…
We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a $d$-dimensional…
We investigate the single-photon transport problem in the system of a Whispering-Gallery mode microresonator directionally coupled with a two-level quantum emitter (QE). This QE-microresonator coupling system can usually be studied by…
We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
Optical Whispering Gallery Modes (WGMs) derive their name from a famous acoustic phenomenon of guiding a wave by a curved boundary observed nearly a century ago. This phenomenon has a rather general nature, equally applicable to sound and…
Using Andreev and Lifshitz's supersolid hydrodynamics, we obtain the propagating longitudinal modes at non-zero applied pressure $P_{a}$ (necessary for solid 4He), and their generation efficiencies by heaters and transducers. For small…
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit…
Soliton microcombs have shown great potential in a variety of applications ranging from chip scale frequency metrology to optical communications and photonic data center, in which light coupling among cavity transverse modes, termed as…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
Space-time varying media with moving interfaces unlock new ways to manipulate electromagnetic waves. Yet, analytical solutions have been mostly limited to interfaces moving at constant velocity or constant proper acceleration. Here, we…
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution…
Scattering hinders the passage of light through random media and consequently limits the usefulness of optical techniques for sensing and imaging. Thus, methods for increasing the transmission of light through such random media are of…
Typical microresonators exhibit a large frequency spacing between resonances and a limited tunability. This impedes their use in a large class of applications which require a resonance of the microcavity to coincide with a predetermined…
Coupled-mode induced transparency is realized in a single microbubble whispering gallery mode resonator. Using aerostatic tuning, we find that the pressure induced shifting rates are different for different radial order modes. A finite…
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…
Quasi-transverse-electric and -transverse-magnetic fundamental whispering gallery modes in a polymer-coated silica microtoroid are theoretically investigated and demonstrated to possess very high-quality factors. The existence of a…
Layered media have been studied extensively both for their importance in imaging technologies and as an example of a hyperbolic PDE with discontinuous coefficients. From the perspective of acoustic imaging, the time limited impulse response…
We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…