The vector wave equation can be rewritten as a quasiscalar wave equation with one extra term -▽▽ • E (the depolarization term). Many authors utilize Poisson’s equation to replace it by ▽(E • ▽ln∊. However, fields E obtained as solutions of the ensuing equation must be made to obey Poisson’s equation (as they do not do so automatically, in general) or be rejected. Some examples are given, and it is shown why first-order solutions for ∊= 1 + δ∊ with δ∊ ≪1 are often correctly derived (unwittingly?) from an “incorrect” equation.
© 1979 Optical Society of America
D. A. de Wolf, "Depolarization term of the wave equation," J. Opt. Soc. Am. 69, 1313-1314 (1979)