Exact solution is obtained for the diffraction of plane electromagnetic waves by an elliptic cylindrical lens surrounding an infinitely long parallel slit in a perfectly conducting plane. Results are expressed in terms of Mathieu functions. Approximate expressions for the expansion coefficients for the diffracted waves, the scattered intensity at infinity, and the transmission coefficients are also obtained in the long-wavelength (Rayleigh scattering) limit. Possible numerical investigations are discussed.
C. YEH, "Exact Solution to a Lens Problem," J. Opt. Soc. Am. 55, 860-867 (1965)