Mode structure of a broadband high gain parametric amplifier

High gain parametric amplifier with a single-pass pulsed pump is known to generate broadband twin photon fields that are entangled in amplitude and phase but have complicated spectral correlation. Fortunately, they can be decomposed into independent temporal modes. But the common treatment of interaction Hamiltonian does not consider issue time ordering problem thus leads incorrect conclusion mode structure functions do change as increases. In this paper, we use an approach usually employed for treating nonlinear interferometers avoids issue. This allows us derive evolution equation differential-integral form. Numerical solutions high situation indicate gain-dependent has its distributions changed broadened