WKB approximation in optics

Summary

The WKB approximation in optics describes waves in a medium whose refractive index changes slowly on the scale of a wavelength. It is the WKB approximation applied to the Helmholtz equation $\nabla^2 u + k_0^2 n^2 u = 0$ with the large parameter $k_0$. Its phase satisfies the eikonal equation and its amplitude a transport equation, which together give geometrical optics. In layered media it gives explicit approximate fields and the mode conditions of graded-index waveguides.