TY - JOUR
T1 - Exact and geometrical optics energy trajectories in Bessel beams via the quantum potential
AU - Silva-Ortigoza, Gilberto
AU - Julian-Macias, Israel
AU - Espindola-Ramos, Ernesto
AU - Silva-Ortigoza, Ramon
N1 - Publisher Copyright:
© 2023 Optica Publishing Group.
PY - 2023/3
Y1 - 2023/3
N2 - The aim of the present work is to show that any monochromatic solution to the scalar wave equation in free space defines a conservative Hamiltonian system, describing a particle of mass m D1=2 and energy E D1, under the influence of the so-called quantum potential.We remark that the integral curves of its Poynting vector, exact optics energy trajectories, define a particular subset of solutions to the correspondingHamilton equations. Furthermore, we introduce the zero quantum potential straight lines concept, as the family of tangent lines to the integral curves of the Poynting vector at the zeros of the quantum potential. These general results are applied to a family of plane waves and to Bessel beams. In the case of Bessel beams, we present a detailed study of the trajectories determined by the corresponding Hamiltonian system, and we show that the zero quantum potential straight lines coincide with the geometrical light rays, geometrical optics energy trajectories. Furthermore,we showthat the areal velocity, determined by the exact optics energy trajectories, for non-zero order Bessel beams is not a constant of motion. However, its projection along the Oz direction is a constant of motion because Lz is a constant.
AB - The aim of the present work is to show that any monochromatic solution to the scalar wave equation in free space defines a conservative Hamiltonian system, describing a particle of mass m D1=2 and energy E D1, under the influence of the so-called quantum potential.We remark that the integral curves of its Poynting vector, exact optics energy trajectories, define a particular subset of solutions to the correspondingHamilton equations. Furthermore, we introduce the zero quantum potential straight lines concept, as the family of tangent lines to the integral curves of the Poynting vector at the zeros of the quantum potential. These general results are applied to a family of plane waves and to Bessel beams. In the case of Bessel beams, we present a detailed study of the trajectories determined by the corresponding Hamiltonian system, and we show that the zero quantum potential straight lines coincide with the geometrical light rays, geometrical optics energy trajectories. Furthermore,we showthat the areal velocity, determined by the exact optics energy trajectories, for non-zero order Bessel beams is not a constant of motion. However, its projection along the Oz direction is a constant of motion because Lz is a constant.
UR - http://www.scopus.com/inward/record.url?scp=85152120953&partnerID=8YFLogxK
U2 - 10.1364/JOSAB.475745
DO - 10.1364/JOSAB.475745
M3 - Artículo
AN - SCOPUS:85152120953
SN - 0740-3224
VL - 40
SP - 620
EP - 630
JO - Journal of the Optical Society of America B: Optical Physics
JF - Journal of the Optical Society of America B: Optical Physics
IS - 3
ER -