Transmission and reflection of the evanescent waves from a nanometric exit hole in a cylindrical waveguide

Abstract

The results of theoretical considerations of the electromagnetic-field behavior in a truncated cylindrical waveguide with a subwavelength-sized exit hole are reported. We develop a self-consistent approach to the description of the transverse-magnetic (TM) and transverse-electric (TE) fields inside the waveguide and in the free space behind the exit aperture of the waveguide. The approach takes into account the transformation of the initial wave into all possible modes that appear upon reflection from the exit aperture of the waveguide. It allows us to evaluate the amplitude reflection coefficients for the evanescent TM and TE waves and express them in terms of the impedance of an infinite waveguide and the impedance of the exit aperture at the interface of the truncated waveguide and the free space. We determine the complex optical flow through a nanometric hole and the transmission coefficient to the far-field zone and express them through the reflection coefficient. It is shown that the reflection and transmission coefficients strongly depend on the ratio of the aperture radius to the light wavelength, the dielectric constants of the waveguide core and the surrounding matter, and the type of waveguide modes. It is demonstrated that, in the case of a metallic matter at the waveguide exit, there is a strong enhancement in the amplitude of the reflected wave and, hence, in the resulting amplitude of the tangential component of the electric field. This enhancement is a result of the plasmon-supported effects in a metallic substrate.