Exact Solutions of Field Vectors of Diffraction-Free Electromagnetic Waves

Diffraction-free beams of light have recently been studied by quite a few authors using the Helmholtz equation. The scalar theory of diffraction, however, is not a good approximation when the beam size is comparable to the wavelength. In this paper, Maxwell's equations are solved exactly to obtain the vectorial components of the diffraction-free beam. Solutions for the plane-polarized-electric (or magnetic) waves, and the TE (or TM) modes are given and their relations are discusssed. The exact solution shows that the diffraction-free beam should have longitudinal components of the electric and/or magnetic fields and that no mode has the exact J 0 intensity distribution. Relation to the non-transverse cylindrically symmetric wave with parallel electric and magnetic fields is also found.