Under the undepleted-pump approximation, the conversion efficiency and bandwidth , 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, logarithmically increases with L, whereas decreases under the perfect phase matching. Contrarily, when reaches the minimum, the bandwidth , 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 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 can apparently be widened in the chirp grating although may decrease a little, and that, with the adding of segment numbers, can increase.
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