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A simple expression is derived for the band structure of a one-dimensional periodic potential in terms of two solutions of the Schroedinger equation within the unit cell, one with a zero-derivative boundary condition on the left-hand end of…
We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended…
We propose and demonstrate a method to increase the momentum separation between the arms of an atom interferometer and thus its area and measurement precision, by using Bloch oscillations (BOs) in an excited band of a pulsed optical…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
Bloch's theorem is the centerpiece of topological band theory, which itself has defined an era of quantum materials research. However, Bloch's theorem is broken by a perpendicular magnetic field, making it difficult to study topological…
Bloch's theorem was a major milestone that established the principle of bandgaps in crystals. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations for Bloch's theorem, this…
In most of standard Finite Element (FE) codes it is not easy to calculate dispersion relations from periodic materials. Here we propose a new strategy to calculate such dispersion relations with available FE codes using user element…
Baryon acoustic oscillations (BAO) provide a robust standard ruler, and can be used to constrain the expansion history of the Universe at low redshift. Standard BAO analyses return a model-independent measurement of the expansion rate and…
The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis…
Small-size acoustic arrays exploit spatial diversity to achieve capabilities beyond those of single-element devices, with applications ranging from teleconferencing to immersive multimedia. A key requirement for broadband array processing…
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of…
Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation…
The introduction of structural defects in otherwise periodic media is well known to grant exceptional space control and localization of waves in various physical fields, including elasticity. Despite the variety of designs proposed so far,…
The accurate modeling of mode hybridization and calculation of radiative relaxation rates have been crucial to the design and optimization of superconducting quantum devices. In this work, we introduce a spectral theory for the…
Using Brillouin light scattering spectroscopy and dynamical matrix method calculations, we study collective spin waves in dense arrays of periodically double-side width-modulated Permalloy nanowires. Width modulation is achieved by creating…
Plasmonic devices with feature sizes of a few nanometers exhibit effects which can be described by the nonlocal hydrodynamic Drude model. We demonstrate how to exploit contour integral methods for computing eigenfrequencies and resonant…
We develop an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of…
Five methods of calculating electrical field distributions in one dimensional wave-guide arrays are reviewed. We analytically solve the scalar Helmholtz Equation and, based on the computed Bloch functions and associated bands of propagation…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the…
We develop a mathematical and numerical framework for studying evanescent waves in subwavelength band gap materials. By establishing a link between the complex Brillouin zone and various Hermitian and non-Hermitian phenomena, including…