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B. M. Rodriguez-Lara

Publications and source records attributed to B. M. Rodriguez-Lara.

10 recordsLinked to original sources
arXiv2026

Self-similar rigid rotation in anisotropic squeezed Laguerre--Gaussian beams

We introduce anisotropic squeezed Laguerre--Gaussian beams as an analytically complete family of structured paraxial scalar beams with Gouy-phase-controlled rigid rotation. Our construction organizes the Laguerre--Gaussian transverse modal Hilbert space into circular modal subspaces carrying parity-resolved single-mode $\mathrm{su}(1,1)$ representations. The resulting optical Bargmann bases support squeezed states whose lowest-weight forms factor into Gaussian beam phases, parity-dependent polynomials, and elliptically anisotropic Gaussian envelopes. Excited seeds are polynomial deformations of the same squeezed envelope, extending the analytic construction to the full family. The Gouy-dressed squeezing parameter sets the semi-axis widths, aspect ratio, handedness, and orientation, while propagation rotates the profile by the accumulated Gouy phase without changing the scaled transverse shape. We generate these fields with synthetic phase holograms and experimentally confirm their self-similar rigid rotation. Our scalar-beam family provides a tunable anisotropic structured-light platform whose transverse orientation encodes propagation distance and may support axial localization, range finding, optical manipulation, and modal diagnostics.

physics.optics↗
arXiv2026

From Gaussian beams to Helmholtz waves

We identify the scale ratio between the Helmholtz transverse-wavenumber scale and the paraxial Gaussian-beam-width scale as the physical parameter connecting separable Gaussian beams with Helmholtz waves. Our optical scale ratio factors the Helmholtz-to-paraxial angular-spectrum restriction with the paraxial-to-Helmholtz large-Rayleigh-range limit. It turns the algebraic Inönü--Wigner contraction and the Cayley--Klein deformation into optical limits governed by scale. Our spectral contraction connects Hermite, Laguerre, Ince, and Boyer--Wolf Gaussian beam families with plane, Bessel, Mathieu, and Weber wave families, respectively, at the coordinate, differential wave equation, algebraic deformation, separation operator, separated differential equation, and separation-spectrum levels.

physics.optics↗
arXiv2026

Routes to Chaos in Class-B laser Dimer Necklaces

Linear $\mathcal{PT}$-symmetric dimer necklaces use cyclic coupling to organize phase-locked modes, while class-B laser--resonator dimers use carrier inversion to destabilize gain--loss dynamics and produce routes to chaos. We study a cyclic necklace of class-B laser--resonator dimers to determine how inter-dimer coupling and cyclic phase constraints modify carrier-mediated instabilities. The carrier inversion turns the necklace into an amplitude--phase--carrier system whose active-site gain controls intensities, while the linewidth-enhancement factor shifts phases. We derive the real dynamical equations, identify uniform fixed points above threshold, and classify their phase configurations under cyclic closure. Even necklaces support full synchronization, a uniform $π$ shift, and two alternating phase configurations; odd necklaces support only the first two. Linear stability of these configurations partitions the coupling plane into sixteen possible regions, including one region with no stable uniform fixed point. Long-time simulations for representative two- and three-dimer necklaces show stable lasing, multistability, and irregular lasing controlled by pump ratio and coupling strengths. Increasing the pump ratio expands stable domains and suppresses the region without stable uniform fixed points.

physics.optics↗
arXiv2026

Grid-state deformation in a no-jump non-Hermitian bosonic dimer

We study the no-jump evolution of ideal grid states in a lossy bosonic dimer with differential decay. The effective non-Hermitian quadratic dynamics induces a complex symplectic flow in phase space that deforms both the primitive lattice vectors and the origin seed. The average decay rate controls common attenuation, while coherent hopping and differential decay control the reduced dimer deformation. The reduced sector contains elliptic, parabolic, and hyperbolic regimes with imaginary spectra, an exceptional point, and real spectra, producing oscillatory, linear, and exponential lattice deformations. Although projected lattice areas can change, the deformation comes from a determinant-one complex symplectic flow on the full four-dimensional phase space. For a Gaussian regularization of the origin seed, we derive the associated complex width matrix and identify the positivity conditions that preserve Gaussian form. For an initial two-mode qunaught product state, the lossless limit recovers the standard beam-splitter generation of a square GKP$+$ Bell pair, while the no-jump dynamics produces its non-Hermitian deformation with a postselection cost set by the no-jump probability.

quant-ph↗
arXiv2026

Total Angular Momentum Coherent State Fields

Structured light fields exploit spin and orbital angular momentum for precision manipulation, advanced imaging, and high-capacity communication. Orbital angular momentum coherent state beams interpolate between Hermite- and Laguerre-Gaussian beams, enabling continuous spatial control. We introduce a symmetry-based framework for joint control of polarization and spatial structure under the shared \$su(2)\$ Lie algebra of spin and orbital angular momentum. Within this structure, we construct total angular momentum fields as superpositions of circular polarization and Laguerre-Gaussian beams, and define their \$su(2)\$ coherent states within fixed-angular-momentum subspaces. A single complex parameter controls both polarization and spatial degrees of freedom, enabling continuous, symmetry-preserving tuning.

physics.optics↗
arXiv2026

Non-Hermitian $\mathrm{sl}(3, \mathbb{C})$ three-mode couplers

Photonic systems with exceptional points, where eigenvalues and corresponding eigenstates coalesce, have attracted interest due to their topological features and enhanced sensitivity to external perturbations. Non-Hermitian mode-coupling matrices provide a tractable analytic framework to model gain, loss, and chirality across optical, electronic, and mechanical platforms without the complexity of full open-system dynamics. Exceptional points define their spectral topology, and enable applications in mode control, amplification, and sensing. Yet $N$-mode couplers, the minimal setting for $N$th-order exceptional points, are often studied in specific designs that overlook their algebraic structure. We introduce a general $\mathrm{sl}(N,\mathbb{C})$ framework for arbitrary $N$-mode couplers in classical and quantum regimes, and develop it explicitly for $N=3$. This case admits algebraic diagonalization, where a propagation-dependent gauge aligns local and dynamical spectra and reveals the geometric phase connecting adiabatic and exact propagation. An exact Wei--Norman propagator captures the full dynamics and makes crossing exceptional points explicit. Our framework enables classification of coupler families. We study the family spanning $\mathcal{PT}$-symmetric and non-Hermitian cyclic couplers, where two exceptional points of order three lie within a continuum of exceptional points of order two, ruling out pure encircling. As an application, we study these exceptional points for a lossy three-leg beam splitter and reveal its propagation dynamics as a function of initial states, such as Fock and NOON states. Our approach provides a systematic route to analyze non-Hermitian mode couplers and guide design in classical and quantum platforms.

quant-ph↗
arXiv2019

Spectral Collapse in the two-photon quantum Rabi model

Spectral collapse, the transition from discrete to continuous spectrum, is a characteristic in quantum Rabi models. We explore this phenomenon in the two-photon quantum Rabi model in optical phase space and find that, in the so-called degenerate qubit regime, the collapse is similar to that happening in the transition from a quantum harmonic to an inverted quadratic potential with the free-partical potential as transition point. In this regime, it is possible to construct Dirac-normalizable eigenfunctions for the model that show well defined parity. In the general model, we use parity to diagonalize the system in the qubit basis and numerically find that the qubit frequency does not change the critical point where spectral collapse occurs.

quant-ph↗
arXiv2009

A single structured light beam as an atomic cloud splitter

We propose a scheme to split a cloud of cold non-interacting neutral atoms based on their dipole interaction with a single structured light beam which exhibits parabolic cylindrical symmetry. Using semiclassical numerical simulations, we establish a direct relationship between the general properties of the light beam and the relevant geometric and kinematic properties acquired by the atomic cloud as its passes through the beam.

quant-ph↗
arXiv2009

Interference with polarized light beams: Generation of spatially varying polarization

Using a scheme based on a Mach-Zehnder interferometer, we propose an analysis of the superposition of polarized laser beams at a given angle. The focus of our study is the spatially varying polarization state of the resulting field, also known as a polarization grating, generated by this setup. Our proposal combines a theoretical description of the resulting field in terms of its Stokes parameters with an experimental demonstration of the existence of such a polarization grating due to the effects of polarization on beam interference experiments.

physics.optics↗