On the Majorana representation of the optical Dirac equation

We consider the representations of optical Dirac equation, especially ones where Hamiltonian is purely real-valued. This equivalent, for Maxwell's equations, to Majorana representation massless (Weyl) equation. draw analogies between Dirac, chiral and derive two new representations. Just as are related spin helicity states, these equation associated with linear polarisation light. provides a means compare electron electromagnetic wave equations in context classical field theory.