The quantum potential approach provides an intriguing perspective for studying optical beams, offering a more direct description of energy flow than conventional wave optics and connecting naturally to the de Broglie–Bohm interpretation of quantum mechanics. In recent years, this approach has been applied to structured light beams, yet its use in analyzing superposed light fields and interference phenomena remains largely unexplored. In this work, we develop an alternative formulation of the quantum potential that avoids direct calculation of amplitude and phase, and apply it to the interference of Hermite–Gaussian beams. A general analytical expression for the quantum potential of the interference field is derived, in which the total quantum potential is decomposed into a linear superposition term and an interference correction term modulated by the phase difference. Based on this expression, we investigate the mechanisms underlying the formation of optical vortices and interference fringes in Hermite–Gaussian beam interference. We show that the interference term creates sharp potential structures and strong quantum forces that guide the energy flow, leading to the formation of dark fringes, while phase differences capable of inducing angular momentum give rise to optical vortices. We also argue that the term $\frac{\partial \varphi}{\partial z}$ should not be neglected in the analysis of interference. Our results provide new theoretical tools for investigating interference phenomena in superposed structured light fields and highlight the decisive role of the quantum potential interference term, with potential applications in structured light, singular optics, and precision optical manipulation.
The quantum potential approach provides an intriguing perspective for studying optical beams, offering a more direct description of energy flow than conventional wave optics and connecting naturally to the de Broglie–Bohm interpretation of quantum mechanics. In recent years, this approach has been applied to structured light beams, yet its use in analyzing superposed light fields and interference phenomena remains largely unexplored. In this work, we develop an alternative formulation of the quantum potential that avoids direct calculation of amplitude and phase, and apply it to the interference of Hermite–Gaussian beams. A general analytical expression for the quantum potential of the interference field is derived, in which the total quantum potential is decomposed into a linear superposition term and an interference correction term modulated by the phase difference. Based on this expression, we investigate the mechanisms underlying the formation of optical vortices and interference fringes in Hermite–Gaussian beam interference. We show that the interference term creates sharp potential structures and strong quantum forces that guide the energy flow, leading to the formation of dark fringes, while phase differences capable of inducing angular momentum give rise to optical vortices. We also argue that the term ∂z∂φ should not be neglected in the analysis of interference. Our results provide new theoretical tools for investigating interference phenomena in superposed structured light fields and highlight the decisive role of the quantum potential interference term, with potential applications in structured light, singular optics, and precision optical manipulation.
The quantum potential approach provides an intriguing perspective for studying optical beams, offering a more direct description of energy flow than conventional wave optics and connecting naturally to the de Broglie–Bohm interpretation of quantum mechanics. In recent years, this approach has been applied to structured light beams, yet its use in analyzing superposed light fields and interference phenomena remains largely unexplored. In this work, we develop an alternative formulation of the quantum potential that avoids direct calculation of amplitude and phase, and apply it to the interference of Hermite–Gaussian beams. A general analytical expression for the quantum potential of the interference field is derived, in which the total quantum potential is decomposed into a linear superposition term and an interference correction term modulated by the phase difference. Based on this expression, we investigate the mechanisms underlying the formation of optical vortices and interference fringes in Hermite–Gaussian beam interference. We show that the interference term creates sharp potential structures and strong quantum forces that guide the energy flow, leading to the formation of dark fringes, while phase differences capable of inducing angular momentum give rise to optical vortices. We also argue that the term ∂z∂φ should not be neglected in the analysis of interference. Our results provide new theoretical tools for investigating interference phenomena in superposed structured light fields and highlight the decisive role of the quantum potential interference term, with potential applications in structured light, singular optics, and precision optical manipulation.
The paraxial wave equation is formally equivalent to the Schrödinger equation, enabling quantum-mechanical concepts to be applied to classical optical fields. Within this framework, we investigate the Bohmian dynamics of superpositions of Laguerre-Gaussian beams. We derive the velocity field and quantum potential and analyze the resulting trajectory dynamics. Interference between modes with different orbital angular momentum generates vortex formation, trajectory exclusion from nodal regions, and spiral motion around phase singularities. Remarkably, despite the complexity of the Bohmian trajectories, the vortex cores follow nearly linear paths along propagation. The dynamics are governed by the amplitude ratio and OAM indices, while the relative phase only induces global rearrangements. These results establish a coherent trajectory-based description of structured light and highlight vortex cores as robust topological features.
Interference is commonly regarded as the most direct manifestation of the superposition principle. This association is natural for the linear Schrödinger equation, where coherent alternatives combine at the level of probability amplitudes. However, the situation becomes less transparent when nonlinear couplings are present, or when the field is only partially coherent. In this work, we argue that a more robust organizing principle is provided by the local flow generated by phase variations. In this sense, phase-induced flow acts as a unifying mechanism for interference-like dynamics in nonlinear and partially coherent Schrödinger systems. The discussion is developed from a hydrodynamic, or Bohmian, perspective, understood here as a practical probing tool rather than as an additional ontology. Three representative situations are considered: interfering Bose--Einstein condensates described by the Gross--Pitaevskii equation, nonlinear Schrödinger dynamics obtained by modifying the quantum-potential contribution, and partially coherent Airy beams described through their cross-spectral density. Although these systems differ in physical origin and mathematical implementation, they share a common dynamical structure: density-related observables are shaped by velocity fields determined by phase, or ensemble-phase, information. From this viewpoint, interference-like traits, localization, self-acceleration and coherence loss can be interpreted in terms of the preservation, deformation or breaking of the symmetries displayed by the underlying flow. This provides a compact way of connecting interference, nonlinear dynamics, classicality, coherence loss, and structured-light propagation within a single trajectory-based framework.
Electromagnetically induced transparency (EIT) is an important phenomenon in quantum optics, and has a wide range of applications in the fields of quantum information processing and quantum precision metrology. Recently, with the rapid progress of the generation and detection of structured light, the EIT with structured light has attracted enormous interests and offers new and novel functionalities and applications. Here, we theoretically study the propagation and evolution of Gaussian vortex beams, a typical type of structured light, in an EIT medium with Λ-type three-level atoms. Based on the generalized Huygens-Fresnel principle, we derive the analytical expressions of fully and partially coherent Gaussian vortex beams propagating in the EIT medium, and study the evolution of the intensity and phase distributions of the beams and their dependencies on parameters such topological charge, coherence length, Rabi frequency, etc. It is shown that both the fully and partially coherent Gaussian vortex beams undergo focusing and diverging periodically during propagation. The phase singularity of the fully coherent beam keeps unchanged, while the phase singularity of the partially coherent beam experiences splitting and recombination periodically. In addition, new phase singularities with opposite topological charge are generated in the latter case. Our results not only advance the study of the interaction between structured light and coherent media, but also pave the avenue for manipulating structured light via EIT.
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams.
Orbital angular momentum (OAM) light is nowadays an intriguing resource in classical and quantum optics due to the richness of physical properties it shows in interaction with matter. A key ingredient needed to exploit the full potential of OAM light is the control of quantum interference, a crucial resource in fields like quantum communication and quantum optics. Here, we study the vortex four-wave mixing (FWM) via multi-photon quantum interference in an ultraslow propagation regime. We find that the structured information can be manipulated via two-photon detuning and three photon detuning, which manifests itself as a spatial modulation. The detailed explanations based on the dispersion relation are given, which are in good agreement with our simulations. Furthermore, in order to clearly show the modulated mechanism, we perform the interference between the FWM field and a same-frequency Gaussian beam. It is found that the interference patterns are also manipulated by adjusting the multi-photon detunings. This work may have some potential applications in quantum control based on OAM light.