Left-handed materials (LHM) have the unusual
property of having negative magnetic permittivity
mu < 0 and dielectric constant epsilon <
0. Due to their counter-intuitive refractive
properties, LHMs have been recently proposed for
making novel lenses. While LHMs do not occur in
nature, they can be designed from naturally occurring
building blocks. We present the results of
numerical and analytic modeling of such a
medium. The new composite medium is periodic in two
dimensions, and consists of two materials with
different dielectric constants, epsilon_1 > 0 and
epsilon_2 < 0. Conceptually, this medium can be
thought of as the periodic network of plasma
channels. This periodic structure is conceptually
simple and does not involve the complicated split
ring resonators which were employed for constructing
the LHM in the microwave range. Therefore, the
proposed composite material shows the path to
extending LHMs to terahertz or optical frequency
bands. Depending on the desired frequency, the
plasma-like medium can be composed of a
phonon-polariton material (e.g., LiTaO3) or thin
wires. We present the mean-field description of the
thin-wire meshes in two and three dimensions.