Angle-dependent optical transmission through a narrow slit in a thick metal film

The theory of optical transmission through a narrow slit in a thick metal screen was formulated previously for normal incidence [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)]. In this work, the theory is generalized to include the parallel angle dependence of the optical transmission for angles in the plane of the slit. A fully analytic formulation of the parallel angle-dependent reflection coefficient and transmission is provided. It is shown that the slit width has a strong influence on the angle tuning of the Fabry-P\'erot resonances, which is caused by the angle dependence of the reflection coefficient. The theory agrees quantitatively with recent experiments and predicts angle-dependent variations that may readily be observed in future experiments over a wider angle and wavelength range.