  Exploiting the similarities between the Helmholtz wave equation and the
Klein-Gordon equation, the former is linearized using the Feschbach-Villars
procedure used for linearizing the Klein-Gordon equation. Then the
Foldy-Wouthuysen iterative diagonalization technique is applied to obtain a
Hamiltonian description for a system with varying refractive index. Besides
reproducing all the traditional quasiparaxial terms, this method leads to
additional terms, which are dependent on the wavelength, in the optical
Hamiltonian. This alternate prescription to obtain the aberration expansion is
applied to the axially symmetric graded index fiber. This results in the
wavelength-dependent modification of the paraxial behaviour and the aberration
coefficients. Explicit expression for the modified coefficients of the
aberration to third-order are presented. Sixth and eighth order Hamiltonians
are derived for this system.
