Quality of paraxial electromagnetic beams

The full wave theory of focused waves is developed and the radiation intensity distribution is determined. In the appropriate limit, the full wave theory correctly reproduces the paraxial beams. The limitations of paraxial beam theories are discussed. The method of treatment of full waves is presented with reference to the scalar Bessel-Gauss beam and wave. The necessary theoretical formulas for other beams and waves are also given. For the scalar Bessel-Gauss wave, the beam shape parameter can be adjusted to yield a flat-topped radiation pattern. The ratio of the power in the paraxial beam to that in the full wave is used as a parameter to measure the quality of the paraxial beam approximation. Lower-order waves are found to have better paraxial beam quality than do higher-order waves. The difference in the paraxial beam quality increases as kw0 is decreased where k is the wavenumber and w0 is the waist of the paraxial beam. The radiation patterns of waves are presented for some tightly focused waves.