Lefevre Yannick, Vermeulen Nathalie, Debaes Christof, Thienpont Hugo
Brussels Photonics Team (B-PHOT), Department of Applied Physics and Photonics, Vrije Universiteit Brussel, B-1050 Brussels, Belgium.
Opt Express. 2011 Sep 26;19(20):18810-26. doi: 10.1364/OE.19.018810.
We present a generic approach to determine the phase mismatch for any optical nonlinear process. When applying this approach, which is based on the evaluation of local phase changes, to Raman- and Kerr-based four-wave mixing in silicon waveguides, we obtain an expression for the phase mismatch which is more accurate as compared to the conventional definition; and which contains additional contributions due to the dispersion of the four-wave-mixing processes. Furthermore, starting from the general propagation equations for the involved pump, Stokes and anti-Stokes waves, we investigate the impact of this four-wave-mixing dispersion in silicon waveguides and examine how it is influenced by changing the frequency difference between the pump and Stokes input waves. We show by means of numerical simulations that, by detuning this frequency difference slightly away from Raman resonance, the four-wave-mixing conversion efficiency can be more than doubled, but can also lead to a decrease in efficiency of more than 10 dB. We also discuss how the pump-Stokes frequency difference that is optimal for wavelength conversion varies with the length of the silicon waveguides and with their dispersion characteristics. Finally, starting from the newly introduced phase mismatch formula we simplify the set of propagation equations such that they are less computationally intensive to solve while still giving accurate estimates of the optimal pump-Stokes frequency difference and the corresponding wavelength conversion efficiency.
我们提出了一种通用方法来确定任何光学非线性过程中的相位失配。当将这种基于局部相位变化评估的方法应用于硅波导中基于拉曼和克尔效应的四波混频时，我们得到了一个相位失配表达式，与传统定义相比，该表达式更精确；并且它包含了由于四波混频过程的色散而产生的额外贡献。此外，从所涉及的泵浦波、斯托克斯波和反斯托克斯波的一般传播方程出发，我们研究了这种四波混频色散在硅波导中的影响，并考察了它如何受到泵浦波和斯托克斯输入波之间频率差变化的影响。我们通过数值模拟表明，将该频率差略微偏离拉曼共振进行失谐时，四波混频转换效率可以提高一倍以上，但也可能导致效率降低超过10 dB。我们还讨论了对于波长转换而言最优的泵浦 - 斯托克斯频率差如何随硅波导的长度及其色散特性而变化。最后，从新引入的相位失配公式出发，我们简化了传播方程组，使其求解时计算量更小，同时仍能准确估计最优的泵浦 - 斯托克斯频率差以及相应的波长转换效率。
