Balance Equations of Electromagnetic Angular Momentum

Abstract

We give theoretical foundation to torque densities proposed in the past, like the one used by Beth to study experimentally the action of circularly polarized radiation on a birefringent material, or that proposed by Mansuripur to resolve a seeming paradox concerning the Lorentz force law and relativity. Our results provide new insights into electromagnetic theory, since they provide a unified and general treatment of the balance of lineal and angular momentum that permits a better assessment of some torques. Thus in this work we extend the derivations we have made of balance equations for electromagnetic linear momentum to balance equations for electromagnetic angular momentum. These balance equations are derived from the macroscopic Maxwell equations by means of vector and tensor identities and from the different ways in which these equations are written in terms of fields E, D, B, and H, as well as polarizations P, and M. Therefore these balance equations are as sound as the macroscopic Maxwell equations, with the limitations of the constitutive relations.

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

“…Although the stress tensor (127) is asymmetric, one can formulate the balance equation of angular momentum using the approach proposed in [64].…”

The additional optical angular momentum flux in media with nonlocality of nonlinear optical response

“…According to this law, if a system has rotational symmetry around some axis, the angular momentum component directed along this axis is conserved [1]. In optics, this law describes the relation between the angular momentum density and the angular momentum flux density of light [2][3][4][5]. In this case, the rotational symmetry condition reduces to the existence of the symmetry axis of infinite order of the medium in which light propagates.…”

Intrinsic symmetry of nonlocal nonlinear optical susceptibility tensor in degenerate multi-wave mixing

“…Using minus sign in F(−ω l ) above emphasizes that ω l is the first frequency in the sequence of frequency arguments of γ and its sign is changed when this frequency is permutated with any other frequency. Among the intrinsic symmetry relations ( 18), ( 26), ( 27), ( 28) only (28) will be changed if we use constitutive equations with γ instead of ( 14)- (16). In this equation the first term will have the coefficient [F(−ω n+1 )F(ω m )] −1 , the second one-[F(ω l )F(−ω n+1 )] −1 and the third one-[F(ω m )F(ω l )] −1 with the exact value of each of these coefficients being determined by the first and the last frequencies in the sequence of frequency arguments of each term.…”