Nonparaxial focusing of wave beams in a graded-index medium

The minimum dimensions, limited by the nonparaxial effects, of the wave-bea m 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 longitudin al direction. It is shown that a ring-shaped structure of the distribution of the light intensity with a bright spot in the centre is formed in the fo cal plane. The linear dimensions of the spot may be considerably smaller th an the radiation wavelength and their reduction is due to the decrease in t he fraction of the energy concentrated in the spot. The longitudinal distri bution of the field intensity has a fine structure with linear dimensions c omparable with the radiation wavelength. It was established that an increas e in the refractive index on the waveguide axis reduces the size of the foc using area as a consequence of a weaker influence of the nonparaxial effect s.