Related papers: Synthetic Dimension in Photonics
The first quantum technology, which harnesses uniquely quantum mechanical effects for its core operation, has arrived in the form of commercially available quantum key distribution systems that achieve enhanced security by encoding…
A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.
Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.
Topology is a powerful framework for controlling and manipulating light, minimizing detrimental perturbations on the photonic properties. Combining nanophotonics with topological concepts presents opportunities for both fundamental physics…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional (3D) space. We study discrete diffraction in the linear regime, and predict the…
We propose an axiomatic approach to the concept of an intrinsic dimension of a dataset, based on a viewpoint of geometry of high-dimensional structures. Our first axiom postulates that high values of dimension be indicative of the presence…
Nanophotonics focuses on the control of light and the interaction with matter by the aid of intricate nanostructures. Typically, a photonic nanostructure is carefully designed for a specific application and any imperfections may reduce its…
Many ground-breaking advancements in machine learning can be attributed to the availability of a large volume of rich data. Unfortunately, many large-scale datasets are highly sensitive, such as healthcare data, and are not widely available…
The recent emerging field of synthetic dimension in photonics offers a variety of opportunities for manipulating different internal degrees of freedom of photons such as the spectrum of light. While nonlinear optical effects can be…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
It is shown how in 3+3 dimensions, it is possible to have a superparticle Lagrangian that has manifest supersymmetry both on the world line and in the target space.
The principal use of photonic crystals is to engineer the photonic density of states, which controls light-matter coupling. We theoretically show that strained 2D photonic crystals can generate artificial electromagnetic fields and highly…
The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…
Photonic circuits, engineered to couple optical modes according to a specific map, serve as processors for classical and quantum light. The number of components typically scales with that of processed modes, thus correlating system size,…
A short overview of basics aspects of hadronic interaction of the photon is presented.
Symmetric informationally complete measurements are both important building blocks in many quantum information protocols and the seminal example of a generalised, non-orthogonal, quantum measurement. In higher-dimensional systems, these…