Mode Structure of a Broadband High Gain Parametric Amplifier

TL;DR

This paper investigates the mode structure of broadband high gain parametric amplifiers, revealing that the mode distributions and functions evolve with gain when properly accounting for the time ordering of the interaction Hamiltonian.

Contribution

It introduces a method that avoids the time ordering problem, showing that the mode structure changes with gain, contrary to previous assumptions.

Findings

Mode distributions broaden with increasing gain

Mode functions become more diverse at higher gain

Proper treatment of time ordering affects mode structure analysis

Abstract

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 parametric interaction Hamiltonian does not consider the issue of time ordering problem of interaction Hamiltonian and thus leads to incorrect conclusion that the mode structure and the temporal mode functions do not change as the gain increases. In this paper, we use an approach that is usually employed for treating nonlinear interferometers and avoids the time ordering issue. This allows us to derive an evolution equation in differential-integral form. Numerical solutions for high gain situation indicate a gain-dependent mode structure that has its mode distributions changed and mode functions broadened as the gain increases.