Long-wave infrared surface plasmon grating coupler

We present a simplified analytic formula that may be used to design gratings intended to couple longwave infrared radiation to surface plasmons. It is based on the theory of Hessel and Oliner (1965). The recipe is semiempirical, in that it requires knowledge of a surface-impedance modulation amplitude, which is found here as a function of the grating groove depth and the wavelength for silver lamellar gratings at CO₂ laser wavelengths. The optimum groove depth for photon-to-surface-plasmon energy conversion was found by experiment and calculation to be ∼10%-15% of the wavelength. This value is about twice what has been reported previously in the visible spectral range for sinusoidal grating profiles.