  These notes, intended to be self contained and tutorial, present a direct,
macroscopic approach to quantizing light inside a linear-response dielectric
material when both spectral dispersion and spatial nonuniformity are present,
but the spectral region of interest is optically transparent so that explicit
treatment of the underlying physics of the medium is not needed. The approach
taken is based on the macroscopic Maxwell equations and a corresponding
Hamiltonian, without the use of Lagrangians or any dynamical model for the
medium, and uses a standard mode-based quantization method. The treatment
covers: energy density and flux in a dispersive dielectric; a summary of the
inverse permittivity formalism; a new derivation of the mode normalization
condition; a direct proof of the nonorthogonality of the modes; examples of
quantized field expressions for the general case and various special cases; the
relationship between group velocity and energy flux; the band approximation and
the continuum limit; and quantum optical treatment of waveguide modes.
