25 August 2017 The total energy-momentum tensor for electromagnetic fields in a dielectric
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Radiation pressure is an observable consequence of optically induced forces on materials. On cosmic scales, radiation pressure is responsible for the bending of the tails of comets as they pass near the sun. At a much smaller scale, optically induced forces are being investigated as part of a toolkit for micromanipulation and nanofabrication technology [1]. A number of practical applications of the mechanical effects of light–matter interaction are discussed by Qiu, et al. [2]. The promise of the nascent nanophotonic technology for manufacturing small, low-power, high-sensitivity sensors and other devices has likely motivated the substantial current interest in optical manipulation of materials at the nanoscale, see, for example, Ref. [2] and the references therein. While substantial progress toward optical micromanipulation has been achieved, e.g. optical tweezers [1], in this report we limit our consideration to the particular issue of optically induced forces on a transparent dielectric material. As a matter of electromagnetic theory, these forces remain indeterminate and controversial. Due to the potential applications in nanotechnology, the century-old debate regarding these forces, and the associated momentums, has ramped up considerably in the physics community. The energy–momentum tensor is the centerpiece of conservation laws for the unimpeded, inviscid, incompressible flow of non-interacting particles in the continuum limit in an otherwise empty volume. The foundations of the energy–momentum tensor and the associated tensor conservation theory come to electrodynamics from classical continuum dynamics by applying the divergence theorem to a Taylor series expansion of a property density field of a continuous flow in an otherwise empty volume. The dust tensor is a particularly simple example of an energy–momentum tensor that deals with particles of matter in the continuum limit in terms of the mass density ρm, energy density ρmc 2 , and momentum density ρmv. Newtonian fluids can behave very much like dust with the same energy–momentum tensor. The energy and momentum conservation properties of light propagating in the vacuum were long-ago cast in the energy–momentum tensor formalism in terms of the electromagnetic energy density and electromagnetic momentum density. However, extrapolating the tensor theory of energy–momentum conservation for propagation of light in the vacuum to propagation of light in a simple linear dielectric medium has proven to be problematic and controversial. A dielectric medium is not ”otherwise empty” and it is typically assumed that optically induced forces accelerate and decelerate nanoscopic material constituents of the dielectric. The corresponding material energy–momentum tensor is added to the electromagnetic energy–momentum tensor to form the total energy–momentum tensor, thereby ensuring that the total energy and the total momentum of the thermodynamically closed system remain constant in time.
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Michael E. Crenshaw, "The total energy-momentum tensor for electromagnetic fields in a dielectric", Proc. SPIE 10347, Optical Trapping and Optical Micromanipulation XIV, 103473B (25 August 2017); doi: 10.1117/12.2271859; https://doi.org/10.1117/12.2271859

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