Resonant production of millicharged scalars in $k^2>0$ electromagnetic wave background

We investigate the solution of the Klein-Gordon equation for a charged scalar particle in an electromagnetic plane wave background with $k^2>0$, which can be realized in a medium with a refractive index $n<1$. We reduce the equation of motion to the Mathieu equation, which has resonant solutions that grow exponentially for certain parameter ranges. We apply our results to derive constraints on scalar millicharged particles and compare them with existing experimental data.