We show that the set of two coupled differential equations governing a four-wave mixing (FWM) component and its associated idler in a one-pump fiber optical parametric amplifier are the same as for standard parametric amplification, but with additional source terms arising from FWM between already-calculated waves. We show how to solve this new set of equations in general: this involves multiplication by an exponential matrix and its inverse, and integration. Hence it is in principle possible to write the exact expressions for the cross-talk fields, in terms of a large number of exponentials. The results show that the power of the first- and second-order cross-talk terms scales, respectively, like the first and second power of the signal power. In the case of two input signals, the powers of the cross-talk terms are independent of the phases of the signals, hence phase control cannot be used for reducing cross talk. In a particular case, cross talk scales like the inverse of pump power, which confirms a general trend noted in numerical simulations, and experiments.
© 2008 Optical Society of America
Fiber Optics and Optical Communications
Original Manuscript: September 18, 2007
Revised Manuscript: February 19, 2008
Manuscript Accepted: March 5, 2008
Published: April 30, 2008
M. E. Marhic and J. M. Chavez Boggio, "Solutions for first- and second-order four-wave mixing cross talk in one-pump fiber optical parametric amplifiers," J. Opt. Soc. Am. B 25, 841-848 (2008)