Covariant theory of light in a dispersive medium

Abstract

The relativistic theory of the time- and position-dependent energy and momentum densities of light in glasses and other low-loss dispersive media, where different wavelengths of light propagate at different phase velocities, has remained a largely unsolved challenge until now. This is astonishing in view of the excellent theoretical understanding of Maxwell's equations and the abundant experimental measurements of optical phenomena in dispersive media. The challenge is related to the complexity of the interference patterns of partial waves and to the coupling of the field and medium dynamics by the optical force. In this work, we use the mass-polariton theory of light [Phys. Rev. A 96, 063834 (2017)] to derive the stress-energy-momentum (SEM) tensors of the field and the dispersive medium. Our starting point, the fundamental local conservation laws of energy and momentum, is close to that of a recent theoretical work on light in dispersive media by Philbin [Phys. Rev. A 83, 013823 (2011)], which however, excludes the power-conversion and force density source terms describing the coupling between the field and the medium. In the general inertial frame, we present the SEM tensors in terms of Lorentz scalars, four-vectors, and field tensors that reflect in a transparent way the Lorentz covariance of the theory. The SEM tensors of the field and the medium are symmetric, form-invariant, and in full accordance with the covariance principle of the special theory of relativity. The SEM tensor of the coupled field-medium state of light also has zero four-divergence. Therefore, light in a dispersive medium has well-defined four-momentum and rest frame. The volume integrals of the total energy and momentum densities of light agree with the model of mass-polariton quasiparticles having a nonzero rest mass. The predictions of our work are directly accessible to experiments.

References in corpus (9)

• Optical Momentum, Spin, and Angular Momentum in Dispersive Media
• Observation of a push force on the end face of a nm fiber taper exerted by outgoing light
• Optical momentum and angular momentum in complex media: From the Abraham-Minkowski debate to unusual properties of surface plasmon-polaritons
• Momentum exchange between light and a single atom: Abraham or Minkowski?
• Mass-polariton theory of light in dispersive media
• Electromagnetic energy and momentum in moving media
• Radiation pressure measurement using a macroscopic oscillator in an ambient environment
• Quantitative in situ measurement of optical force along a strand of cleaved silica optical fiber induced by the light guided therewithin
• Negative radiation pressure in metamaterials explained by light-driven atomic mass density rarefication waves

Cited by in corpus (10)

• Time-dependent theory of optical electro- and magnetostriction
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Time-dependent optical force theory for optomechanics of dispersive 3D photonic materials and devices
• The Microscopic Ampère formulation for the electromagnetic force density in linear dielectrics
• Negative radiation pressure in metamaterials explained by light-driven atomic mass density rarefication waves
• QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity
• A local model for the optical energy and momentum transfer in dielectric media and the microscopic origin of Abraham's force density
• Recoil momentum of an atom absorbing light in a gaseous medium and the Abraham-Minkowski debate
• Optical force density and surface displacements in transparent dielectrics due to non-ionizing sub-picosecond laser excitation
• Chiral-stress-energy-momentum tensor for covariant description of spin and torque densities of light