相关论文: Fundamental lower size limit in wavelength selecti…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
We derive a lower limit to the amount of absorptive loss present in passive linear optical devices such as a beam splitter. We choose a particularly simple beam splitter geometry, a single planar slab surrounded by vacuum, which already…
Experiments involving micro- and nanomechanical resonators need to be carefully designed to reduce mechanical environmental noise. A small scale on-chip approach is to add an additional resonator to the system as a mechanical low-pass…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of…
We study the formation of the photonic band structure in small clusters of dielectric spheres. The first signs of the band structure, an attribute of an infinite crystal, can appear for clusters of 5 particles. Density of resonant states of…
Optical resonances in 1D photonic crystal microcavities are investigated numerically using finite-element light scattering and eigenmode solvers. The results are validated by comparison to experimental and theoretical findings from the…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…
The term `sub-wavelength' is commonly used to describe innovative sound-absorbing structures usually labeled as `metamaterials'. Such structures, however, inherently do not bring groundbreaking advancements. This study addresses the…
Asymptotic solution to many-body wave scattering problem is given in the case of many small scatterers. The small scatterers can be particles whose physical properties are described by the boundary impedances, or they can be small…
The inability of standard models to explain the flux ratios in many 4-image gravitational lenses has been cited as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling,…
The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous…
Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index…
Electromagnetic properties depend on the composition of materials, i.e. either angstrom scales of molecules or, for metamaterials, subwavelength periodic structures. Each material behaves differently in accordance with the frequency of an…
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modeling to everyday life devices. The eigenfrequencies of conventional…
The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an…
We investigate the ability to constrain oscillatory features in the primordial power spectrum using current and future cosmic microwave background observations. In particular, we study the observability of an oscillation arising from…
A general model is presented for coupling of high-$Q$ whispering-gallery modes in optical microsphere resonators with coupler devices possessing discrete and continuous spectrum of propagating modes. By contrast to conventional high-Q…
Interferometry with Heisenberg limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors, and in quantum information science. For experimental implementations the robustness of…
The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied…