  We study second harmonic generation in a negative index material cavity. The
transmission spectrum shows a gap between the electric and magnetic plasma
frequencies, so that localized and anti-localized states are allowed at the
band edges. The process is made efficient by local phase matching conditions
between a forward-propagating pump and a backward-propagating second harmonic
signal. By simultaneously exciting the cavity with counter-propagating pulses
one is able to enhance or inhibit absorption and stimulated processes. The
control parameter is the relative phase difference between the two incident
pulses which determines the interference properties of the fields inside the
cavity.
