Theoretical analyses and optimizations for wavelength conversion by quasi-phase-matching difference frequency generation

Under the undepleted-punip approximation, the conversion efficiency eta and bandwidth Delta gimel, based on quasi-phase-matching (QPM) difference frequency generation (DFG), are theoretically studied in detail and their expressions are obtained. The theoretical results show that, for the uniform grating, eta logarithmically increases with L, whereas Delta gimel decreases under the perfect phase matching. Contrarily, when eta reaches the minimum, the bandwidth Delta gimel, which is independent of the second-order nonlinearity, the pump, and the signal power, reaches the maximum under the imperfect phase matching. The expression of eta for the arbitrary chirp QPM grating In the typical DFG process is obtained in this paper for the first time. Optimized examples for two-, three-, and four-segment chirp grating are given, respectively. The numerically optimized results show that both the pump and signal bandwidth Delta gimel can apparently be widened in the chirp grating although eta may decrease a little, and that, with the adding of segment numbers, Delta gimel can increase.