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Héctor M. Moya-Cessa

Publications and source records attributed to Héctor M. Moya-Cessa.

At least 19 recordsLinked to original sources
arXiv2026

Syncopated Bessel beams

We introduce the syncopated Bessel beam, a new class of exact solutions to the paraxial equation obtained by means of a sinusoidal modulation of the azimuthal phase at the source. This modulation imposes a phase rhythm that deliberately breaks the azimuthal symmetry, analogous to musical syncopation, and triggers a topological transformation that deflects the propagation trajectory and shifts the beam's center of symmetry off the optical axis, while preserving its self-scaling invariance that can be explained by the Madelung-Bohm formalism. An exact analytical framework, supported by experimental validation, reveals the intrinsic structural robustness and preservation of topological properties through propagation.

physics.optics↗
arXiv2024

Integrated optical wave analyzer using the discrete fractional Fourier transform

Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study introduces an innovative methodology aimed at reconstructing the Wigner distribution function of optical signals; a crucial tool in comprehending the time-frequency behavior exhibited by these signals. The proposed approach integrates two robust mathematical tools: the discrete realization of fractional Fourier transform, and the propagator of the quantum harmonic oscillator in waveguide arrays. This integration offers a direct and efficient method for characterizing optical signals by reconstructing their Wigner distribution function in the scope of integrated optics. We provide evidence of how having knowledge of the signal propagation amid the phase-space reconstruction, has desirable advantages in respect to only knowing the signal state.

physics.optics↗
arXiv2024

Exact solutions to the Telegraph equation in terms of Airy functions

Two exact different solutions to the Telegraph equation in three-dimensional space are obtained in terms of Airy functions. As a result, these solutions unveil a distinctive propagation pattern along a coordinate that resembles a speed-cone-like coordinate of the system. This unique characteristic leads to effective Schrödinger-like equations, amenable to exact solutions through Airy functions.

physics.gen-ph↗
arXiv2023

Non-Hermitian propagation in Glauber-Fock optical lattices

The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock) waveguide array of the Hatano-Nelson-type. Several cases are analyzed and exact analytical solutions for both the Hermitian and non-Hermitian Schrödinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric (SUSY) transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.

physics.optics↗
arXiv2023

Non-Hermitian propagation in equally-spaced Hermitian waveguide arrays

A non-unitary transformation leading to a Hatano-Nelson problem is performed on an array of equally-spaced optical waveguides. Such transformation produces a non-reciprocal system of waveguides, as the corresponding Hamiltonian becomes non-Hermitian. This may be achieved by judiciously choosing an attenuation (amplification) of the injected (or exciting) field. The non-Hermitian transport induced by such transformation is studied for several cases and closed analytical solutions are obtained. The corresponding non-Hermitian Hamiltonian may represent an open system that interacts with the environment, either loosing to or being provided with energy from the exterior.

physics.optics↗
arXiv2023

Supersymmetric behavior of polarized electromagnetic waves in anisotropic media

A medium with specific anisotropic refractive indices can induce a supersymmetric behavior in the propagation of polarized electromagnetic waves, in an analogue fashion to a quantum mechanical system. The polarizations of the wave are the ones which behave as superpartners from each other. For this to happen, the anisotropy of the medium must be transverse to the direction of propagation of the wave, with different refractive indices along the direction of each polarization. These refractive indices must follow a very specific relation in order to trigger the supersymetric response of the electromagnetic wave, each of them with spatial dependence on the longitudinal (propagation) direction of the wave. In this form, in these materials, different polarized light can be used to test supersymmetry in an optical fashion.

physics.optics↗
arXiv2023

Moving mirror-field dynamics under intrinsic decoherence

We study the decaying dynamics in the mirror-field interaction by means of the intrinsic decoherence scheme. Factorization of the mirror-field Hamiltonian with the use of displacement operators, allows us to calculate the explicit solution to Milburn's equation for arbitrary initial conditions. We show expectation values, correlations, and Husimi functions for the solutions obtained.

quant-ph↗
arXiv2023

Non-unitary transformation approach to $\mathcal{PT}$ dynamics

We show that several Hamiltonians that are $\mathcal{PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

quant-ph↗
arXiv2022

Supersymmetric relativistic quantum mechanics in time-domain

A supersymmetric relativistic quantum theory in the temporal domain is developed for bi-spinor fields satisfying the Dirac equation. The simplest time-domain supersymmetric theory can be postulated for fields with time-dependent mass, showing an equivalence with the bosonic supersymmetric theory in time-domain. Solutions are presented and they are used to produce probability oscillations between mass states. As an application of this idea, we study the two-neutrino oscillation problem, showing that flavour state oscillations may emerge from the supersymmetry originated by the time-dependence of the unique mass of the neutrino.

quant-ph↗
arXiv2021

Intrinsic decoherence for the displaced harmonic oscillator

By using the complete solution of the Milburn equation (beyond the Lindblad form that it is generally used) that describes intrinsic decoherence, we study the decaying dynamics of a displaced harmonic oscillator. We calculate the expectation values of position quadrature, and the number operator in initial coherent and squeezed states.

quant-ph↗
arXiv2021

Coherent states for equally spaced, homogeneous waveguide arrays

Coherent states for equally spaced, homogeneous waveguide arrays are defined, in the infinite, semiinfinite and finite cases, and resolutions of the identity are constructed, using different methods. In the infinite case, which corresponds to Euclidean coherent states, a resolution of the identity with coherent states on the circle and involving a nonlocal inner product is reviewed. In the semiinfinite case, which corresponds to London coherent states, various construction are given (restricting to the circle with a non-local scalar product, rescaling the coherent states, modifying them, or using a non-tight frame). In the finite case, a construction in terms of coherent states on the circle is given, and this construction is shown to be a regularization of the infinite and semiinfinite cases.

quant-ph↗
arXiv2021

Bohm approach to the Gouy phase shift

By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent despite the fact that the Hamiltonian is itself time-independent. We finally show that the effective Bohm {\it index of refraction} generates a GRIN medium that produces the focusing needed for the Gouy phase.

physics.optics↗
arXiv2021

Intrinsic decoherence dynamics in the three-coupled harmonic oscillators interaction

Applying the Milburn equation to describe intrinsic decoherence, we study the interaction of three-coupled quantum harmonic oscillators or quantized fields. We give an explicit solution for the complete equation, i.e., beyond the usual second order approximation used to arrive to the Lindblad form. Then we calculate the expectation value of the number operator of each oscillator or mode for one of the modes given in an initial coherent

quant-ph↗
arXiv2021

Airy eigenstates and their relation to coordinate eigenstates

We study the eigenvalue problem for a linear potential Hamiltonian and, by writing Airy equation in terms of momentum and position operators define Airy states. We give a solution of the Schrödinger equation for the symmetrical linear potential in terms of the squeeze and displacement operators. Finally, we write the unit operator in terms of Airy states and find a relation between them and position and momentum eigenstates.

quant-ph↗
arXiv2021

Generation of Talbot-like fields

We present an integral of diffraction based on particular eigenfunctions of the Laplacian in two dimensions. We show how to propagate some fields, in particular a Bessel field, a superposition of Airy beams, both over the square root of the radial coordinate, and show how to construct a field that reproduces itself periodically in propagation, i.e., a field that renders the Talbot effect. Additionally, it is shown that the superposition of Airy beams produces self-focusing.

physics.optics↗
arXiv2021

Bohm potential is real and its effects are measurable

We analyze Bohm's potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using theoretical arguments as well as experimental evidence. We find that the effects produced by Bohm's potential are both theoretically responsible for the early success of Quantum Mechanics correctly describing atomic and nuclear phenomena and, more recently, by confirming surprising accelerating behavior of free waves and particles experimentally, for instance.

quant-ph↗
arXiv2021

Bohm potential for the time dependent harmonic oscillator

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 the time dependent term in the phase obeys an Ermakov equation.

quant-ph↗