Mass-polariton theory of light in dispersive media

Abstract

We have recently shown that the electromagnetic pulse in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the coupled state of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. We show that the total momentum and the transferred mass of the light pulse can be determined in a straightforward way if we know the field energy of the pulse and the dispersion relation of the medium. In analogy to the nondispersive case, we also find unambiguous correspondence between the MP and OCD theories. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum p MP = n ph ω/c, where n p is the phase refractive index. The field's share of the MP momentum is equal to p field =hω/(n g c), where n g is the group refractive index and the share of the MDW is equal to p MDW = p MP − p field . Thus, as in a nondispersive medium, the total momentum of the MP is equal to the Minkowski momentum and the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media. We also carry out simulations for optimal measurements of atomic displacements related to the MDW in silicon. In the simulations, we consider different waveguide cross sections and optical pulse widths and account for the breakdown threshold irradiance of materials. We also compare the MP theory to previous theories of the momentum of light in a dispersive medium. We show that our generalized MP theory resolves all the problems related to the Abraham-Minkowski dilemma in a dispersive medium.

Lagrangian dynamics of the coupled field-medium state of light

“…The MP SEM tensor then obtains in the L frame exactly the same form as given in equation (B4) in appendix B of our original work in [10]. In the OCD simulations of our previous works [10,11,13], these approximations have been verified within the numerical accuracy of 7 digits. However, one must remember that both the numerical accuracy and the approximation n (A) =n (L) are much more accurate than the approximation of a nondispersive medium for any realistic material.…”

“…Once we know the electric field E (L) and the magnetic flux density B (L) , we can express the electromagnetic field tensor F αβ in terms of these fields as presented in equation (6). After this, we can write the electromagnetic displacement tensor  ab by using equation (11), where the atomic velocity ( ) v a L in the matrix h αβ is unknown at this stage. We find that the fields D (L) and H (L) are given in terms of the fields E (L) and B (L) as e = .…”

“…Very recently, the mass-polariton (MP) theory of light has provided a unique resolution to the Abraham-Minkowski controversy [10][11][12]. The MP theory shows that light propagating in a medium must be described as a coupled state of the field and the medium.…”

An Integrodifferential Equation for Electromagnetic Fields in Linear Dispersive Media

“…, as expected. (ii) Note that wave equations (9) and (10) are linear in the electromagnetic fields so that linear superpositions of their solutions are also solutions of these equations. At this point, it is important to emphasize that the Fourier components of the fields, E(r, ω) = ∞ −∞ E(r, t)e iωt dt, satisfy the well-known Helmholtz equation…”

“…In spite of its long history, many important aspects of dispersive media are still at the forefront of research. Amongst many contributions, we can mention the analysis of, the angular momentum of optical fields and the electromagnetic helicity in these media ( [5,6]), the investigation of the very definition of light momentum (in the context of the hundred year old Abraham-Minkowski controversy, see [7] and references therein), and the new results on polariton excitations in dispersive media ( [8,9]). Since Sommerfeld, most treatments of electromagnetic wave propagation are given in Fourier space, in contrast to what is usually done in (non-dispersive) free space.…”