More precisely, if the time-dependence of an electromagnetic wave can be assumed to be of the form sin(\omega t)... It's not quite true. It assumes that the el

More precisely, if the time-dependence of an electromagnetic wave can be assumed to be of the form sin(\omega t)... It's not quite true. It assumes that the electric field oscillates with the same phase at every point. Normally the Helmholtz equation is solved assuming that the time dependence is exp(I\omega t), where I is the imaginary unit, and we search for a complex E(x) solution. arg(E(x)) deals with the phase factor, abs(E(x)) is the amplitude. Re( E(x)exp(I\omega t) ) is a solution to the Maxwell equations.