Spontaneous emission between an unusual pair of plates

We compute the modification in the spontaneous emission rate for a two-level atom when it is located between two parallel plates of different nature: a perfectly conducting plate $(\epsilon\to \infty)$ and an infinitely permeable one $(\mu\to \infty)$. We also discuss the case of two infinitely permeable plates. We compare our results with those found in the literature for the case of two perfectly conducting plates.