Related papers: Optical Spectral Singularities as Threshold Resona…
We establish necessary and sufficient conditions for complex potentials in the Schr\"odinger equation to enable spectral singularities (SSs) and show that such potentials have the universal form $U(x) = -w^2(x) - iw_x(x) + k_0^2$, where…
Causality - the principle stating that the output of a system cannot temporally precede the input - is a universal property of nature. Here, we show that analogous input-output relations can also be realized in the spectral domain by…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Speckle patterns are used in a broad range of applications including microscopy, imaging, and light-matter interactions. Tailoring speckles' statistics can dramatically enhance their performance in applications. We present an experimental…
We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and…
The optical properties of PT-symmetric periodic stack of the layers with balanced loss and gain are examined. We demonstrate that tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries…
It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, significant advantage in measurement precision can be gained from exploiting phase singularities in a…
Highest resolution laser spectroscopy has generally been limited to single trapped ion systems due to rapid decoherence which plagues neutral atom ensembles. Here, precision spectroscopy of ultracold neutral atoms confined in a trapping…
A phonon laser based on an optomechanical system consisting of two optical modes interacting with each other via a phononic mode is considered. An external wave exciting one of the optical modes plays a role of the pumping. It is shown that…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure…
In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense $G_\delta$.
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
It is known that the perfect absorption of two identical waves incident on a complex potential from left and right can occur at a fixed real energy and that the time-reversed setting of this system would act as a laser at threshold at the…
An obstacle $K \subset \R^n,\: n \geq 3,$ $n$ odd, is called trapping if there exists at least one generalized bicharacteristic $\gamma(t)$ of the wave equation staying in a neighborhood of $K$ for all $t \geq 0.$ We examine the…
We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
Conventional lens-based imaging techniques have long been limited to capturing only the intensity distribution of objects, resulting in the loss of other crucial dimensions such as spectral data. Here, we report a spectral lens that…