Electromagnetic resonance of nonlinear vacuum in one-dimensional cavity

Abstract

Nonlinear corrections on electromagnetic fields in vacuum have been expected. In this study, we have theoretically considered nonlinear Maxwell’s equations in a one-dimensional cavity for a classical light and external static electromagnetic fields. A general solution for the electromagnetic corrective components including that of a longitudinal standing wave was derived after a linearization. The main purpose is to give a detailed feature of the previously reported resonant behavior [Shibata, Euro. Phys. J. D 74:215 (2020)], such as the effect of external static fields and the polarization fluctuation. These results favor the development of new and effective method for experiment. Graphic abstract

Incompatible case of perfect conductor approximation in vacuum nonlinear electromagnetism

“…It will also be valuable to compare the present study and the calculations performed in a one-dimensional cavity [24,25,41]. In these previous papers, the perfect conductor approximation is employed and the nonlinear correction is consistently calculated without yielding to a situation of no solution, even in the appearance of an external magnetic flux density.…”

“…If the nonlinear correction is sufficiently small, we can regard that the correction is generated by the wave sources ρ c and j c , which are obtained by substituting the classical term into the right-hand sides of equation (4). This is a linear approximation and the corresponding correction has been especially referred to as 'minimum corrective term' [24,25] in order to distinguish it from a general 'corrective term' which is calculated without the linear approximation. We express the minimum corrective term by a subscript n and a superscript (0), such as E n 0 ( ) and B n 0 ( ) .…”

“…However, this equation cannot hold in general. For example, if the mirror M 2 is a plane such that f = 0, then the left-hand side is zero because of equation (25). On the other hand, the right-hand side can remain nonzero.…”

“…As for the birefringence in a cavity, several experiments were performed, i.e., the PVLAS (Polarizzazione del Vuoto con LASer) [12][13][14][15][16], BMV (Biréfringence Magnétique du Vide) [17], and OVAL (Observing VAcuum with Laser) [18] experiments. A cavity system is often considered in theoretical studies [19][20][21][22][23][24][25]. Several other systems have also been studied, for example, a waveguide [20,26,27], a ring laser [28], the Michelson interferometer [29], and a propagation between two mirrors [30,31].…”

Long time self-modulation of nonlinear electromagnetic wave in two-dimensional cavity

“…The resonant terms are partially calculated in Ref. [19]. The behavior that is proportional to time T is the same as the resonance discussed in a one-dimensional system [18][19].…”