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.
Abstract Bohmian mechanics is a deterministic account of quantum phenomena in terms of particle trajectories. Guided by a quantum force, the gradient of a quantum potential, trajectories bend to account for quantum interference. The quantum potential is expressible in terms of weak values, complex numbers that characterize quantum systems for which both the initial and final states are predetermined. In Berry and Shukla (2010 J. Phys. A: Math. Theor. 43 354024), the typical probabilities of weak values were calculated. In this paper, expressing the quantum potential in terms of weak values, we find the typical probability distribution of the quantum potential for randomly selected states. The latter allows the calculation of the typical probability of semiclassical superoscillation, a generalization of superoscillations (functions that oscillate faster than their fastest Fourier component) to functions that are not band-limited.