Abstract: The quasi phase-matched Optical Parametric Amplification (OPA) gain formula, within the undepleted pump approximation, is developed with the aid of the Rotating Wave Approximation (RWA). THe RWA keeps only the nearly phase-matched terms in the coupled Maxwell's equations for the signal and idler beam. The basis for dripping all the other terms is that they are rapidly oscillating on the length scale over which the nearly phase-matched terms vary appreciably and therefore will average to zero. This permits a closed from solution for the gain formula to be obtained. From the gain formula, important quantities such as the spectral, temperature, and angular bandwidth can be calculated. The RWA solution is compared with exact numerical solution. !12
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