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The loss of gauge invariance in models of light-matter interaction which arises from material and photonic space truncation can pose significant challenges to conventional quantum optical models when matter and light strongly hybridize. In…

The advent of dispersion-engineered and highly nonlinear nanophotonics is expected to open up an all-optical path towards the strong-interaction regime of quantum optics by combining high transverse field confinement with ultra-short-pulse…

Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions…

Optical focusing through/inside scattering media, like multimode fiber and biological tissues, has significant impact in biomedicine yet considered challenging due to strong scattering nature of light. Previously, promising progress has…

We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be…

Matter-wave optics is often viewed as a linear analogue of photonics, where noninteracting particles are coherently split, diffracted, and recombined, and interference arises from single-particle coherence. In ultracold quantum gases,…

In this report we show that vacuum is a nonlinear optical medium and we discuss what are the optical phenomena that should exist in the framework of the standard model of particle physics. We pay special attention to the low energy limit.…

A basic problem in linear particle optics is to find a symplectic transformation that brings the (symmetric) beam matrix to a special diagonal form, called normal form. The conventional way to do this involves an eigenvalue-decomposition of…

Vectorial structured light with spatially varying amplitude, phase, and polarization is reshaping many areas of modern optics, including nonlinear optics, as diverse parametric processes can be used to explore interactions between such…

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as…

Van der Waals (vdW) materials offer new ways to assemble artificial electronic media with properties controlled at the design stage, by combining atomically defined layers into interfaces and heterostructures. Their potential for…

We show set of transformations which allow to obtain analytic solutions in several quantum-optical problems. We start with the ion-laser (time dependent) interaction, continue with the problem of a slow atom interacting with a quantized…

We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…

This article is provides an introduction to the quantum theory of optics in nonlinear dielectric media. We begin with a short summary of the classical theory of nonlinear optics, that is nonlinear optics done with classical fields. We then…

We exploit free-space interactions between electron beams and tailored light fields to imprint on-demand phase profiles on the electron wave functions. Through rigorous semiclassical theory involving a quantum description of the electrons,…

Time-varying optical media, whose dielectric properties are actively modulated in time, introduce a host of novel effects in the classical propagation of light, and are of intense current interest. In the quantum domain, time-dependent…

All-optical image processing offers a high-speed, energy-efficient alternative to conventional electronic systems by leveraging the wave nature of light for parallel computation. However, traditional optical processors rely on bulky…

By harnessing the resonant nature of localized electromagnetic modes in a nanostructured silicon membrane, an all-dielectric metamaterial can act as nonlinear medium at optical telecommunications wavelengths. We show that such metamaterials…

We experimentally demonstrate the manipulation of optical diffraction, utilizing the atomic thermal motion in a hot vapor medium of electromagnetically-induced transparency (EIT). By properly tuning the EIT parameters, the refraction…

Transformation optics (TO) is a new method to design metamaterials that can manipulate electromagnetic fields. Inspired by the traditional TO techniques which is mostly based on the solid metamaterials with a limited range of tunability, a…