Related papers: Bohm approach to the Gouy phase shift
We present a framework for the paraxial wave equation based on propagation-dependent unitary transformations closely related to the Lewis-Ermakov invariant. This approach establishes a formal equivalence between free-space propagation and…
In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadratically on position and show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided…
Recently Gouy rotation was observed with focused non-relativistic electron vortex beams. If the electrons in vortex beams are very fast we have to take into account relativistic effects to completely describe the Gouy phase on them. Exact…
On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase…
A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the $4$-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but…
The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner…
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on $\chi^{(2)}$ interaction of optical fields, e.g. through birefringent crystals, and show that…
It is shown that field propagation in linear and quadratic gradient-index (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be {\it exported} to…
A connection between relativistic quantum mechanics in the Foldy-Wouthuysen representation and the paraxial equations is established for a Dirac particle in external fields. The paraxial form of the Landau eigenfunction for a relativistic…
We show how to transform the mathematical expression of any monochromatic paraxial light beam into the expression of a pulsed beam whose diffraction is switched from the axial direction to its temporal structure. We exemplify this…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…
We investigate the propagation characteristics of Cauchy-Riemann beams in gradient-index media. Our study reveals two key findings: a) the preservation of their form during propagation, and b) surprisingly, the feasibility of obtaining the…
The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization…
Exact Bateman-Hillion solutions of the wave equation are applied to Hermite-Gaussian beams using a space-time constraint condition that requires the field density to fall as the inverse square of distance from the focal point of the beam at…
The far-field intensity distribution of spatiotemporal Laguerre-Gaussian (STLG) modes propagating in free space exhibits a multi-petal pattern analogous to that observed in tilted Hermite-Gaussian modes. Here, we show that this phenomenon…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
The pion transition form factor $G(q^2)$ is computed on the entire domain of spacelike and timelike momenta using a quantum field theory continuum approach. In analytical continuation of the function $G(Q^2)$ we utilized the Gauge Technique…
The point-particle-like Hamiltonian of a biaxial spin particle with external magnetic field along the hard axis is obtained in terms of the potential field description of spin systems with exact spin-coordinate correspondence. The Zeeman…
We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the…
Assuming that the energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term,…