Incompatible case of perfect conductor approximation in vacuum nonlinear electromagnetism

Abstract

The perfect conductor approximation is the most practical way to treat light reflection by a mirror. We demonstrate that the approximation and nonlinear electromagnetism in vacuum are not always compatible. In the presence of external magnetic flux density, we prove that there is no solution for the nonlinear Maxwell’s equations if a perfect conductor mirror is folded by 90 degrees. Demonstrated results show that the perfect conductor approximation can be inappropriate. We also suggest an approach to avoid the incompatibility.

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

“…We expect that the minimum corrective term is a good approximation of the exact corrective term in a short timescale, i.e., E (0) n ≈ E n . In the following calculations, at least one of B sx and B sy is zero to avoid the situation of no solution [34].…”