Theory of Optical Transmission Through a Near-Field Probe With a Dissipative Matter in its Core

We develop a theory of light transmission through an aperture-type near-field optical probe with a dissipative matter in its semiconducting core described by a complex frequency-dependent dielectric function. We evaluate the near-field transmission coefficient of a metallized silicon probe with a large taper angle of in the visible and near-infrared wavelength range. It is shown that in this spectral range the use of a short silicon probe instead of a glass one allows to achieve a strong (up to 10$^2-10^{3}$) enhancement in the transmission efficiency.