**Authors:** Ira Kohlberg

**Source:** FERMAT, Volume 5, Article 3, Sep-Oct., 2014

**Abstract:** We derive a system of propagation
equations in a Double Negative (DN) material in a way
that appears to differ from previous derivations—
although the end result is the same. Our derivation
assumes the Poynting vector theorem applies, real
materials always have some loss, () and () are
obtained from real materials, and wave energy traveling
in a specified direction must always be accompanied by a
loss of energy in that direction. Additional mathematics
beyond Maxwell’s equation is not required. Energy
losses per unit length of travel are finite, and can be
extremely small. Propagation in a lossless DN media is
found as the mathematical limiting solution of an
extremely small energy loss per unit length. When
developed along these principles, the equations
developed for designing leaky antennas are
straightforward.

**Index Terms:** Double Negative material, Poynting
vector theorem, Meta materials.

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