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In this Chapter we briefly recall and summarize the main linear optics concepts of the accelerators beam dynamics theory. In doing so we put our emphasis on the related computational aspects: the reader will be provided with the basic…

Graphene, Silicene, $\mathrm{MoS}_2$ and other similar two-dimensional structures have unusual electronic properties that lend themselves to exotic device applications. These properties emanate from the fact that the electrons are endowed…

In this paper we establish a hypoellipticity result for second order linear operators comprised by a linear combination, with infinite vanishing coefficients, of subelliptic operators in separate spaces. This generalizes previous known…

Nonlinear optical effects provide a natural way of light manipulation and interaction, and form the foundation of applied photonics -- from high-speed signal processing and telecommunication, to ultra-high bandwidth interconnects and…

The magneto-optical effect breaks time-reversal symmetry, a unique property that makes it indispensable in nonreciprocal optics and topological photonics. Unfortunately, all natural materials have a rather weak magneto-optical response in…

Light-matter interactions in two-dimensional (2D) materials have gained significant interest due to their distinctive optical and electronic properties. Recently, silicates have emerged as a promising new class of 2D materials, but their…

Higher order nonclassical properties of fields propagating through a codirectional asymmetric nonlinear optical coupler which is prepared by combining a linear wave guide and a nonlinear (quadratic) wave guide operated by second harmonic…

The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This…

The paper theoretically establishes and studies the sub-Doppler linear optical Ramsey resonances that arise under certain conditions near centers of optical transitions in the absorption of a sufficiently weak monochromatic light beam…

We present a novel method to synthesize non-trivial speckles that can enable superresolving second-order correlation imaging. The speckles acquire a unique anti-correlation in the spatial intensity fluctuation by introducing the blue noise…

Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate…

The refractive index of a matter is foundational to quantify the light-matter interaction of the medium. However, the classical description of refractive index is based on macroscopic homogenization and is limited to describing the local…

Hyperbolic materials are natural or engineered artificial structures that provide means to manipulate and control electromagnetic radiation, leading to a variety of strong light-matter interactions at the nanoscale. In this work, we explore…

We observe experimentally two-dimensional solitons in superlattices comprising alternating deep and shallow waveguides fabricated via the femtosecond laser direct writing technique. We find that the symmetry of linear diffraction patterns…

We observed and studied strong reduction of optical reflection from the surface of InP wafers after high-temperature annealing. The effect is observed over a wide range of the incident wavelengths, and in the transparency band of the…

The formal properties of the recently derived set of linearly independent invariant amplitudes for the electromagnetic production of a pseudoscalar particle from a spin-one particle have been further exploited. The crossing properties are…

This paper is a summary of my talk at SPIE2013. The organizers were kind enough to invite me to talk about anything I wanted, and I chose to bring up the notion of higher order complementarity and the fact that it may not be monotonic. I…

We use all-order relativistic many-body perturbation theory to study 5s^2 nl configurations of In I and Sn II. Energies, E1-amplitudes, and hyperfine constants are calculated using all-order method, which accounts for single and double…

This paper is the next step of an ambitious program to develop conformally equivariant quantization on supermanifolds. This problem was considered so far in (super)dimensions 1 and 1|1. We will show that the case of several odd variables is…

The existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with…