  A special non-linear equation of curvilinear electromagnetic wave is
presented. The particularity of this equation lies in the fact that in matrix
form it is mathematically equivalent to the Dirac electron equation. It is
shown that the solution of this is the motion of the plane-polarized
electromagnetic wave on a circular trajectory. It is also shown that such
twirled wave can be considered as a massive charge particle with a spin of one
half, similar to electron. The non-linear equation and its Lagrangian of these
EM particles are founded.
