Incompatible case of perfect conductor approximation in vacuum nonlinear electromagnetism

Abstract

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.