Exact solution of four-wave mixing of copropagating light beams in a Kerr medium

Optimisation of amplitude limiters for phase preservation based on the exact solution to degenerate four-wave mixing

“…Attempting to solve FWM of copropagating waves using coupled equations often results in the adoption of an undepletable pump approximation [10]. Such solutions are naturally of no use in understanding saturated FWM.…”

“…Such solutions are naturally of no use in understanding saturated FWM. By instead considering a single initial field consisting of multiple oscillating terms, an exact solution to FWM in the dispersionless case can be derived in which the evolution of harmonics as they propagate through the medium is descibed by the sum of two Bessel functions of differing order [10,11]. In opting for this model, we cannot easily incorporate dispersion, which in general affects phase matching and FWM efficiency, however such effects are well understood and are studied in [3,11,12].…”

“…We apply the Bessel function model of FWM [10,11] to extract the conditions under which amplitude squeezing of a signal can be achieved. Under these conditions, we derive expressions for the terms responsible for amplitude noise to phase noise conversion.…”

Optical Predistortion Enabling Phase Preservation in Optical Signal Processing Demonstrated in FWM-Based Amplitude Limiter

“…In the following description of the proposed scheme, we shall make use of the theoretical results presented in [7], which were obtained by making use of an exact solution to FWM in the dispersionless case [11], [17], [18]. Figure 2 outlines the procedure followed in the scheme.…”

“…In the first step (illustrated by Figure 2 -1), a pump, P 0 is multiplexed with the signal P 1 and then allowed to undergo FWM in a medium of length L 1 and nonlinear coefficient γ 1 in the second step (Figure 2 -2), after which the conjugate of the signal is selected using an optical bandpass filter. The output power and phase of this conjugate can be shown [7], [11], [18] to be given by Equations 4 and 5, respectively, where J n is the nth Bessel function of the first kind, and J 2 n its square. In [7] we identified two sources of amplitude to phase noise conversion which can be seen to originate from the following phase shift terms in Equation 5: SPM, given by ∆φ SP M = γ 1 L 1 P 1 and Bessel Order Mixing (BOM), given by ∆φ BOM = arctan…”