This paper is a study of an electromagnetic wave solution to the Riesz's Maxwell equation in free space, using Hestenes's spacetime algebra in Gibb's vector form. The amplitude of the electromagnetic wave is a sum of a spatial vector electric field and a spatial bivector magnetic field. The rotator of this electromagnetic field amplitude is the exponential of the sum of a scalar and a spatial vector. The scalar part is a product of angular velocity and time, while the vector part is product of the wave vector and distance of propagation. When this expression is used for the electromagnetic field expression in the Maxwell equation, the wave condition is satisfied. The energy-momentum of the electromagnetic wave is obtained by multiplying the Maxwell equation from the left by the electromagnetic wave expression. An identity relating the energy-momentum expression with its spatial inverse is similar in form to the Poincare sphere equation. Analogous expressions for the Stoke's parameters, coherency matrices, and Jones vectors fall naturally out from the proposed electromagnetic wave expression.

daniel@pusit.admu.edu.ph