Aberrations in Helmholtz optics

The scalar optics is based on a Hamiltonian derived using the Fermat's principle of least time. The same Hamiltonian can now be derived from the Maxwell equations. The Helmholtz equations has a striking mathematical similarity to the Klein-Gordon equation for the relativistic spin-0 particle. It is possible to make use of this strong similarity through quantum techniques and develop an alternative to the traditional approaches. The non-traditional formalism of Helmholtz optics reproduces the traditional results as expected. Moreover, it leads to the wavelength-dependent modifications of the paraxial as well as the aberrating behavior. To illustrate the formalism, we consider the propagation of light in optical fibers in substantial detail. We also consider the propagation of light through a graded index slab.