https://doi.org/10.1140/epjd/s10053-022-00550-z
Regular Article – Nonlinear Dynamics
Long timescale behavior of large self-modulation of electromagnetic wave caused by vacuum nonlinearity
Institute of Laser Engineering, Osaka University, 2-6 Yamada-Oka, 565-0871, Suita, Osaka, Japan
a
shibata-ka@ile.osaka-u.ac.jp
Received:
25
August
2022
Accepted:
5
November
2022
Published online:
16
November
2022
The vacuum is expected to exhibit electromagnetic nonlinearity via virtual electron–positron pairs. An electromagnetic wave is modulated. The self-modulation has been believed to be vanishingly small. However, a large self-modulation can appear in a long timescale, even though the intensity of electromagnetic wave is not extremely strong. To demonstrate this assertion, we theoretically consider standing electromagnetic waves with modest intensity confined in a two-dimensional rectangular cavity. We first calculate in a short timescale by applying a perturbative linear approximation. We show a secular term. Then, beyond the linear approximation, we derive differential equations for slowly varying amplitude and phase in a long timescale. A large self-modulation of polarization, phase, and energy ratio of each mode are obtained by solving the equations. In particular, the energy ratio is classified into three types. Namely, it keeps oscillating, eventually converges, or stays constant.
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