Before revision: Luneburg method The method of obtaining equations of geometrical optics by analysing surfaces of discontinuities of solutions to Maxwell's equations was first described by Rudolf Karl Luneburg in 1944.Luneburg, R. K., Methematical Theory of Optics, Brown University Press 1944 [mimeographed notes], University of California Press 1964 It does not restrict the electromagnetic field to have a special form (in the Sommerfeld-Runge method it is not clear that a field whose amplitude is made to depend on would still yield the eikonal equation , i.e., a geometrical optics wave front).
After revision: Luneburg method The method of obtaining equations of geometrical optics by analysing surfaces of discontinuities of solutions to Maxwell's equations was first described by Rudolf Karl Luneburg in 1944.Luneburg, R. K., Methematical Theory of Optics, Brown University Press 1944 [mimeographed notes], University of California Press 1964 It does not restrict the electromagnetic field to have a special form required by the Sommerfeld-Runge method