Related papers: Optical Darboux Transformer
Broken-supersymmetry is used to define a reflectionless active cavity capable of amplifying electromagnetic radiation in the visible. The approach is analytical through the use of the Darboux transform for the generation of the optical…
The classical Darboux system governing rotation coefficients of three-dimensional metrics of diagonal curvature possesses an equivalent formulation as a sixth-order PDE for a scalar potential (related to the corresponding $\tau$-function).…
We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund…
Nanophotonics research has focused recently on the ability of non-linear optical processes to mediate and transform optical signals in a myriad of novel devices, including optical modulators, transducers, color filters, photodetectors,…
As the diffraction limit is approached, device miniaturization to integrate more functionality per area becomes more and more challenging. Here we propose a novel strategy to increase the functionality-per-area by exploiting the modal…
Digital micromirror devices are a popular type of spatial light modulators for wavefront shaping applications. While they offer several advantages when compared to liquid crystal modulators, such as polarization insensitivity and…
Following how the electrical transistor revolutionized the field of electronics,the realization of an optical transistor in which the flow of light is controlled optically should open the long-sought era of optical computing and new data…
Astronomical telescopes suffer from a tradeoff between field of view (FoV) and image resolution: increasing the FoV leads to an optical field that is under-sampled by the science camera. This work presents a novel computational imaging…
Using bidifferential calculus, we derive a vectorial binary Darboux transformation for the first member of the "negative" part of the AKNS hierarchy. A reduction leads to the first "negative flow" of the NLS hierarchy, which in turn is a…
In this letter we analyze an optical Fabry-P\'erot resonator as a time-periodic driving of the (2D) optical field repeatedly traversing the resonator, uncovering that resonator twist produces a synthetic magnetic field applied to the light…
Microresonator-based degenerate optical parametric oscillation (DOPO) has recently been explored as a compelling platform for all-optical computing and quantum information applications, such as truly random number generation and the…
We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…
We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o represent the number of pixels at the input and output…
We construct a Darboux transformation of a general $su(3)$-valued spin system called the $\Gamma$-spin system. Using this Darboux transformation we derive a recursive formula for the soliton solutions of this spin system. Then using these…
Active control and manipulation of electromagnetic waves are highly desirable for advanced photonic device technology, such as optical cloaking, active camouflage and information processing. Designing optical resonators with high…
Here, Darboux's classical results about transformations with differential substitutions for hyperbolic equations are extended to the case of parabolic equations of the form $L u = \big(D^2_{x} + a(x,y) D_x + b(x,y) D_y + c(x,y)\big)u=0$. We…
A central task in quantum information processing is to characterize quantum processes. In the realm of optical quantum information processing, this amounts to characterizing the transformations of the mode creation and annihilation…
We study a complex intertwining relation of second order for Schroedinger operators and construct third order symmetry operators for them. A modification of this approach leads to a higher order shape invariance. We analyze with particular…
All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and…
We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in…