Spinor solutions to Maxwell's equations in free space

Abstract

Using the Hankel transform, we obtain, in their most general form, the spinor solutions of Maxwell's equations in free space for a light beam propagating along 0z with cylindrical symmetry around 0z. Then we compute a paraxial approximation of these solutions and we discuss the case of Gaussian beams. A comparison of the spinor solutions with the scalar ones supplied by the parabolic equation is also given.

Thermal Blooming of Laser Beams in the Framework of Spinor Formalism

“…the solutions of equation (1) satisfying the boundary condition (7) . Approximate solution in free space is given in [6] .…”

Spinor Formalism for Weakly Guiding Fibers

“…The Maxwell equations in cylindrical geometry are well known [1,3] and a simple calculation gives for μ = 1 ίβ(Η Γ +ίΗ φ )=-(0 Γ ±-5 φ )Η ζ ,…”

“…Then the comparison between (4) and (5) leads to the following identification: -2 (6) ιωε which defines the electromagnetic field E, H in terms of the components v|/ t , ψ 3 . From now on we assume that ε is a function of the transverse variable r but such that or ε may be neglected (weakly guiding approximation).…”