Enhancement and Inhibition of Stimulated Processes in a Negative Index Cavity

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.