4π-spherically focused electromagnetic wave: diffraction optics approach and high-power limits.

The focused field and its intensity distribution achieved by the 4π-spherical focusing scheme are investigated within the framework of diffraction optics. Generalized mathematical formulas describing the spatial distributions of the focused electric and magnetic fields are derived for the transverse magnetic and transverse electric mode electromagnetic waves with and without the orbital angular momentum attribute. The mathematical formula obtained shows no singularity in the field in the focal region and satisfies the finite field strength and electromagnetic energy conditions.