Tracing optical force fields within graded-index media

Abstract

The mechanical interaction between light and graded index media (both isotropic and anisotropic) is presented from the geometrical optics (GO) perspective. Utilizing Hamiltonian equations to determine ray trajectories combined with a description of the Lorentz force exerted on bound currents and charges, we provide a general method that we denote 'force tracing' for determining the direction and magnitude of the bulk and surface force density in arbitrarily anisotropic and inhomogeneous media. This technique provides the optical community with machinery which can give a good estimation of the force field distribution in different complex media, and with significantly faster computation speeds than full-wave methods allow. Comparison of force tracing against analytical solutions shows some unusual limitations of GO, which we also illustrate.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. like behavior to some extent, while black-body radiation, the photoelectric effect and the Compton effect are related to the particle-like nature of photons. Distinguishing these two characteristics is crucial in gaining an intuitive understanding of the physics of light, but sometimes it can be baffling when these two views of the nature of light lead to contradictory conclusions in some circumstances. One such puzzling case is the long-lasting Abraham-Minkowski controversy, which is related to the momentum of photons in matter and the distribution of optical force (or stress) and torque within a medium.From the early days of electromagnetic wave theory, the pressure exerted by light on a body was of great interest. In 1891, Maxwell, using his celebrated equations, was able to calculate the momentum density of light in free space and predicted that '[concentrated] rays falling on a thin metallic disc, delicately suspended in a vacuum, might perhaps produce an observable mechanical effect' [1]. At the same time, using the second law of thermodynamics, Bartoli reached a similar conclusion [2]. Not long after that, the idea proposed by Maxwell and Bartoli was experimentally validated by Lebedev [3] and later confirmed by experiments carried out by Nichols and Hull [4,5]. In 1908 Minkowski derived the momentum density of light in dielectrics analytically, reaching the conclusion that a photon inside a medium of refractive index n carries a momentum equal to np, where p is the momentum of the photon in vacuum [6,7]. Conversely, Abraham formulated electromagnetic momentum conservation in a different way, which resulted in the conclusion of p n for the momentum of the photon within a medium [8,9]. This was the start of a controversy which lasted for a century; during this long period of time, there have been many efforts made by theoretical [10][11][12][13][14][15][16][17][18][19][20][21][22] and experimental [23][24][25] researchers to advocate either o...

Lorentz force and the optical pulling of multiple rayleigh particles outside the dielectric cylindrical waveguides

“…However, most of the times optical pulling effects have been discussed from the point of view of quasi static analysis based on the external dipole force methods ; without considering much analysis on full electrodynamic calculation or the Lorentz force . Though Lorentz force analysis has been applied previously in to understand the mechanism of chirality induced force, Luneburg lenses, mechanical interaction between light and graded index media, cloaking effect, background effect on radiation pressure; such analysis has never been applied to understand the tractor beam like effect.…”

“…However, most of the times optical pulling effects have been discussed from the point of view of quasi static analysis based on the external dipole force methods ; without considering much analysis on full electrodynamic calculation or the Lorentz force . Though Lorentz force analysis has been applied previously in to understand the mechanism of chirality induced force, Luneburg lenses, mechanical interaction between light and graded index media, cloaking effect, background effect on radiation pressure; such analysis has never been applied to understand the tractor beam like effect. Our verifications on the consistency between the full electrodynamic analysis based external stress tensor and volume/Lorentz force method in three dimensional (3D) environment may open a new window to understand the physical mechanism of optical force not only for optical pulling but also for more complicated set‐ups reported in (where dipolar force does not lead to the consistent result).…”

“…Though Lorentz force analysis has been applied previously in to understand the mechanism of chirality induced force, Luneburg lenses, mechanical interaction between light and graded index media, cloaking effect, background effect on radiation pressure; such analysis has never been applied to understand the tractor beam like effect. Our verifications on the consistency between the full electrodynamic analysis based external stress tensor and volume/Lorentz force method in three dimensional (3D) environment may open a new window to understand the physical mechanism of optical force not only for optical pulling but also for more complicated set‐ups reported in (where dipolar force does not lead to the consistent result). Though in this article we have limited our discussion on non‐resonating dielectric Rayleigh particles (both non‐absorbing and absorbing), we believe that our proposed DWTB based pulling can also be applicable for resonating and plasmonic Rayleigh objects due to the dominance of the identical part of the Lorentz force.…”

The distribution of electromagnetic waves and forces in a dispersive chiral cylinder

“…In recent years, optical forces [1,2,3,4,5,6,7,8,9,10,11,12] in different structures and devices have been a subject of great interest because of theirs application in optical tweezers [2,3,4], tractor beams [5], etc. Most of these studies have been focused on the structures composed of passive materials [3,4], whereas forces on active media have received little attention.…”

“…Most of these studies have been focused on the structures composed of passive materials [3,4], whereas forces on active media have received little attention. Gain media with a positive imaginary part of the complex permittivity are simulated in Refs.…”