Abstract
In nonlinear electromagnetism in vacuum, a classical electromagnetic wave itself can generate another wave. A classical field can become a source for a nonlinear correction via the polarization and magnetization of vacuum. We elucidate that a resonant generation is intrinsic to the theoretical structure of nonlinear electromagnetism. The resonance can take place when the phases, or the cycles of the source and the nonlinear correction match. We demonstrate two specific systems as examples. For a plane wave and constant fields, nonlinear corrective electromagnetic fields are resonantly enhanced with distance. It is shown in a stationary special solution. For more realistic system, we have considered the case of a standing wave in a cavity with an appropriate initial and boundary conditions. As a result, the corrections are resonantly enhanced with time. The resonance effect in the cavity is shown to be observed more effectively by combining a static magnetic flux density. We have evaluated the resonant effect using concrete parameters of current experiments. The demonstrated resonance can be combined with existing proposals to enable experimental detection of nonlinear optical effects of vacuum easier.Graphical abstract
Highlights
Extended electromagnetic models have been considered [1,2,3]. These theories describe the electromagnetic nonlinearity of vacuum and have recently drawn attention across several fields, such as photon-photon scattering in quantum mechanics [4], radiation from stars in astrophysics [5,6,7], energy levels of hydrogen atom in atomic physics [8,9], and high intensity laser physics [10,11,12], where uncharted range of strong electromagnetic fields should be properly treated
In order to overcome the difficulty, we theoretically investigate nonlinear corrections that stem from classical electromagnetic fields
In a specific physical system, the nonlinear correction can increase resonantly and the resonance is intrinsic to nonlinear electromaga e-mail: shibata-ka@ile.osaka-u.ac.jp netism
Summary
Extended electromagnetic models have been considered [1,2,3]. These theories describe the electromagnetic nonlinearity of vacuum and have recently drawn attention across several fields, such as photon-photon scattering in quantum mechanics [4], radiation from stars in astrophysics [5,6,7], energy levels of hydrogen atom in atomic physics [8,9], and high intensity laser physics [10,11,12], where uncharted range of strong electromagnetic fields should be properly treated. One is that the nonlinearity requires extremely strong electromagnetic fields, e.g., the expected constraint given by the Schwinger limit Esch ≈ 1.32 × 1018(N/C) [3]. Another is that the nonlinear effects depend on electromagnetic fields through two Lorentz invariants [22], and not on energy density. It can occur that the energy density is large but the invariants are small. This theoretical structure has become a restriction on designing an efficient experimental setup
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