Amplitude and phase representation of monochromatic fields in physical optics

The conservation equation for a monochromatic field with arbitrary polarization propagating in an inhomogeneous transparent medium is expressed in terms of amplitude and phase variables. The expressions obtained for linearly polarized fields are compared with the results obtained in the eikonal approximation. The electric field wave equation is written in terms of intensity and phase variables. The transport equations for the irradiance and the phase are shown to be particular cases of these derivations. The conservation equation arising from the second-order differential wave equation is shown to be equivalent to that obtained from Poynting's theorem.