Relativistic analysis of field-kinetic and canonical electromagnetic systems

We demonstrate the relativistic electromagnetic force and power distributions of the field-kinetic and canonical electromagnetic subsystems with respect to light normally incident upon a moving, lossless magnetodielectric slab of material. Time-averaged and time-varying studies are preformed to demonstrate the continuum mathematical approach and discern between the physical characteristics of both field-kinetic and canonical subsystems. It is shown that when considering time-averaged fields, both subsystems are equivalent and thereby yield equivalent electromagnetic force and power results. The time-varying case demonstrates the differences between the field-kinetic and canonical subsystems, where the field-kinetic subsystem attempts to distort the media and the canonical subsystem satisfies global conservation principles.

Figure 1

A plane wave normally incident on a magnetodielectric slab with a refractive index, $n=c\sqrt{\epsilon \mu }$, moving with velocity $v=zt$.

Figure 2

The electromagnetic (a) force and (b) power versus velocity for the field-kinetic and canonical relativistic formulations are presented for a moving magnetodielectric slab of thickness $d={\lambda }_0/4n$. Here, the initial wavelength is ${\lambda }_0=640$ nm, where $\epsilon =5{\epsilon }_0, \mu =3{\mu }_0$, and $n=c\sqrt{\epsilon \mu }$, with $\beta =\frac{v}{c}$ as the normalized velocity.

Figure 3

The graphical representation of conservation, ${\overline{F}}_M·\overline{v}=P_M$, in terms of the Minkowski formulation. Here, $\epsilon =5{\epsilon }_0, \mu =3{\mu }_0, n=c\sqrt{\epsilon \mu }, {\lambda }_0=640$ nm, $d={\lambda }_0/4n$, and the velocity of the slab is $\overline{v}=\widehat{z}7c/10.$

Figure 4

The graphical representation of conservation, ${\overline{F}}_C·\overline{v}=P_C$, in terms of the Chu formulation. Here, $\epsilon =5{\epsilon }_0, \mu =3{\mu }_0, n=c\sqrt{\epsilon \mu }, {\lambda }_0=640$ nm, $d={\lambda }_0/4n$, and the velocity of the slab is $\overline{v}=\widehat{z}7c/10.$