Complex flow and reflection of evanescent waves from a nanometer-sized hole in a cylindrical waveguide

The results of the theoretical studies on the leakage of the optical radiation through a truncated waveguide with a subwavelength-sized exit hole are reported. We develop a self-consistent approach for the description of the fields behavior by taking into account the transformation of the initial wave into all possible modes, which appear due to the influence of the exit aperture. Our approach allows us to evaluate the amplitude reflection coefficient for the initial evanescent wave and to establish its relationship with the impedance of an infinite waveguide and the impedance of the exit aperture coupling a truncated waveguide with a free space. We determine the complex flow through the exit hole and the transmission coefficient to the far-field zone and express them through the reflection coefficient. Special attention in the work is paid to the evaluation of specific dependencies of the reflection and transmission coefficients on the ratio of the aperture radius to the light wavelength, on the dielectric constants of the waveguide core and the surrounding matter, and on the type of the waveguide mode. It is demonstrated that in the case of a metallic matter at the exit of a waveguide there is a strong resonance enhancement in the amplitude of the reflected wave and in the resulting amplitude of the tangential component of the electric field.