  We introduce a new notion of "matrix potential" to nonlinear optical systems.
In terms of a matrix potential $g$, we present a gauge field theoretic
formulation of the Maxwell-Bloch equation that provides a semiclassical
description of the propagation of optical pulses through resonant multi-level
media. We show that the Bloch part of the equation can solved identically
through $g$ and the remaining Maxwell equation becomes a second order
differential equation with reduced set of variables due to the gauge invariance
of the system. Our formulation clarifies the (nonabelian) symmetry structure of
the Maxwell-Bloch equations for various multi-level media in association with
symmetric spaces $G/H$. In particular, we associate nondegenerate two-level
system for self-induced transparency with $G/H=SU(2)/U(1)$ and three-level $\L
$- or V-systems with $G/H = SU(3)/U(2)$. We give a detailed analysis for the
two-level case in the matrix potential formalism, and address various new
properties of the system including soliton numbers, effective potential energy,
gauge and discrete symmetries, modified pulse area, conserved topological and
nontopological charges. The nontopological charge measures the amount of
self-detuning of each pulse. Its conservation law leads to a new type of pulse
stability analysis which explains nicely earlier numerical results.
