Related papers: Squeeze operators in classical scenarios

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

The similarity between the Schr\"odinger equation and the paraxial wave equation permits numerous analogies linking these fields, which is pivotal in advancing both quantum mechanics and wave optics. In this study, we demonstrate the…

The phasor field has been shown to be a valuable tool for non-line-of-sight imaging. We present a formal analysis of phasor-field imaging using paraxial wave optics. Then, we derive a set of propagation primitives---using the two-frequency,…

We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian…

The classical Fourier transform on the line sends the operator of multiplication by $x$ to $i\frac{d}{d\xi}$ and the operator of differentiation $\frac{d}{d x}$ to the multiplication by $-i\xi$. For the Fourier transform on the Lobachevsky…

The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger particles, namely, charge carriers in semiconductor nanostructures within the…

By virtue of the parabose squeezed operator, propagator of a parabose parametric amplifier, explicit form of parabose squeezed number states and normalization factors of excitation states on a parabose squeezed vacuum atate are calculated…

The paraxial approximation of a classical spinning photon is shown to yield an "exotic particle" in the plane transverse to the propagation. The previously proposed and observed position shift between media with different refractive indices…

Here we outline a description of paraxial light propagation from a modal perspective. By decomposing the initial transverse field into a spatial basis whose elements have known and analytical propagation characteristics, we are able to…

Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$,…

The tremendous progress in light scattering engineering made it feasible to develop optical tweezers allowing capture, hold, and controllable displacement of submicronsize particles and biological structures. However, the momentum…

We apply the formalism of coherent states in quantum optics to pomeron evolution and show that evolving squeezed pomeron states are equivalent to pomeron fan diagrams at the leading order of perturbative expansion. Based on our results, we…

This article presents a squeezing transformation for quantum systems associated to finite vector spaces. The physical idea of squeezing here is taken from the action of the usual squeezing operator over wave functions defined on a real…

We employ quantum mechanical operator techniques to solve the equations of $(1+1)D$ and $(2+1)D$ for paraxial waves with initial conditions defined by Airy-type functions. In the first part, we find the expressions of $(1+1)D$ optical…

The ABCD matrix formalism describing paraxial propagation of optical beams across linear systems is generalized to arbitrary beam trajectories. As a by-product of this study, a one-to-one correspondence between the extended ABCD matrix…

We look for new steps on the dynamical operations that may squeeze simultaneously some families of quantum states, independently of their initial shape, induced by softly acting external fields which might produce the squeezing of the…

We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…

We investigate the mechanism of the nonparaxial propagation of the tightly focused beams in the view of Fourier optics. It shows that it is the phase of the angular spectrum which induces the interesting evolution of the tightly focused…

We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.

In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…