Maximum power transfer in a real metal slit: an analytic approach

We present a fully analytic theory to study the power and field enhancement inside a real metal slit. A generalized formula for the reflection coefficient at the interface of the slit is derived. The resulting expression is purely analytic and the reflection coefficient can be simply evaluated to provide physical insight, while not requiring complicated numerical simulations. The calculated values of reflection phase and amplitude are then used in the Fabry-Pérot formalism to compute the electric field and the power inside the slit. It is shown that the power attains its maximum value when the scattering and the absorption cross-sections of the slit are equal, a confirmation of the maximum power transfer theorem for this case. The analytic results agree well with numerical simulations, which is promising for optimizing performance in applications ranging from modulators to optical tweezers.