  We introduce a reduced order model (ROM) methodology for inverse
electromagnetic wave scattering in layered lossy media, using data gathered by
an antenna which generates a probing wave and measures the time resolved
reflected wave. We recast the wave propagation problem as a passive
infinite-dimensional dynamical system, whose transfer function is expressed in
terms of the measurements at the antenna. The ROM is a low-dimensional
dynamical system that approximates this transfer function. While there are many
possible ROM realizations, we are interested in one that preserves passivity
and in addition is: (1) data driven (i.e., is constructed only from the
measurements) and (2) it consists of a matrix with special sparse algebraic
structure, whose entries contain spatially localized information about the
unknown dielectric permittivity and electrical conductivity of the layered
medium. Localized means in the intervals of a special finite difference grid.
The main result of the paper is to show with analysis and numerical simulations
that these unknowns can be extracted efficiently from the ROM.
