Influence of pumping laser bandwidth on the quantum fluctuation chracteristic of non-degenerate optical parametric amplifier

Usually the quantum fluctuation characteristic of the non-degenerate optical parametric amplifier is analysed under the assumption of monochromatic pumping. However, in experiments, the driving beam with finite bandwidth is used to obtain the non-degenerate signal and idler beam amplifications. On account of that, we derive an analytical solution for the non-degenerate optical parametric amplification system with finite bandwidth laser pumping, and evaluate the associated quantum fluctuation. Finally, the application of the V₁ criterion to the bipartite entanglement is discussed.