Theoretical analysis of a log-periodic structure

An analysis of a two-dimensional log-periodic corrugated plane is presented as a perturbation series. The zero-order solution is that for which the structure is embedded in a medium of continuously variable refractive index, such that in a coordinate system in which the boundaries become periodic, the wave equation also admits a periodic solution. The solution in an actual physical medium, having a constant refractive index of unity, is treated by perturbation analysis.