Analytic modal solution to transmission and collimation of light by one-dimensional nanostructured subwavelength metallic slits

Abstract

Light transmitting through a subwavelength slit on an ordinary metal plate is diffracted to all directions but if the exit plane of the slit is patterned with periodical nanostructures, the diffracted light may be compressed into a collimated beam within a small angle. In this paper, we develop a rigorous theoretical method for solving the surface wave induced beam collimation in nanostructured subwavelength metallic slits. The method combines the analytical modal expansion method, the supercell technique, the transfer-matrix method, and the conventional Kirchhoff’s diffraction theory. It allows for quantitative investigation of coupling of the incident light into the guided wave of the slit and coupling of the guided wave out of the nanostructured exit plane. We have used the method to examine light transmission through the nanostructured metallic slit and the corresponding diffraction and beam collimation behaviors. We have extensively analyzed the angular transmission spectrum as a function of the nanostructure period and the incident light wavelength and revealed the condition at which good beam collimation can take place. The result shows that the beam collimation is caused by the excitation of the surface waves supported on the periodical nanostructured pattern and subsequent coupling into the radiation light. Several scattering channels can coexist for coupling the surface waves into the observed diffraction waves and they can act constructively to create one or more collimation beams with excellent directionality and high brightness. The diffraction field patterns in the large area confirm the angular spectrum analysis.