Optical fields inside a conical waveguide with a subwavelength-sized exit hole

Studies of the spatial distribution of time-harmonic optical fields inside a metallized cone, tapered to a subwavelength diameter, are reported. We consider the electric-type (TMmn) wave with the lowest-order indices m = 0 and n = 1. For these waves we obtain exact analytical results for electromagnetic fields inside a conical waveguide with a loss-free dielectric core and perfectly conducting metallic walls. The contributions of different field components to the energy density distributions are explicitly expressed as functions of the radial and angular coordinates. We outline a technique for the evaluation of the optical fields in the near-field zone beyond the exit aperture. This provides tools for the calculation of the amplitude reflection coefficient taking into account the influence of a plane interface between the truncated cone and free space. Particular attention is paid to the calculations of the energy density at the exit aperture and the near-field transmission coefficient of an optical probe with a glass core. We present a detailed analysis of the optical transmission of such a waveguide as a function of the wavelength for large taper angles and various values of the aperture diameter reaching similar tolambda/40. The results obtained yield the range of the cone parameters and wavelengths in which one can achieve a high spatial resolution capability and sufficiently high transmission efficiency.