Nonparaxial focusing of wave beams in a graded-index medium

The minimum dimensions, limited by the non-paraxial effects, of the wave-beam focusing area were determined. These effects lead to a significant change in the transverse distribution of the light intensity in the focusing area and to an asymmetric distribution of the field intensity in the longitudinal direction. It is shown that a ringshaped structure of the distribution of the light intensity with a bright spot in the centre is formed in the focal plane. The linear dimensions of the spot may be considerably smaller than the radiation wavelength and their reduction is due to the decrease in the fraction of the energy concentrated in the spot. The longitudinal distribution of the field intensity has a fine structure with linear dimensions comparable with the radiation wavelength. It was established that an increase in the refractive index on the waveguide axis reduces the size of the focusing area as a consequence of a weaker influence of the nonparaxial effects.