  Vector and scalar potential formulation is valid from quantum theory to
classical electromagnetics. The rapid development in quantum optics calls for
electromagnetic solutions that straddle quantum physics as well as classical
physics. The vector potential formulation is a good candidate to bridge these
two regimes. Hence, there is a need to generalize this formulation to
inhomogeneous media. A generalized gauge is suggested for solving
electromagnetic problems in inhomogenous media which can be extended to the
anistropic case. The advantages of the resulting equations are their absence of
low-frequency catastrophe. Hence, usual differential equation solvers can be
used to solve them over multi-scale and broad bandwidth. It is shown that the
interface boundary conditions from the resulting equations reduce to those of
classical Maxwell's equations. Also, classical Green's theorem can be extended
to such a formulation, resulting in similar extinction theorem, and surface
integral equation formulation for surface scatterers. The integral equations
also do not exhibit low-frequency catastrophe as well as frequency imbalance as
observed in the classical formulation using E-H fields. The matrix
representation of the integral equation for a PEC scatterer is given.
