准相位匹配

非线性过程通过非线性系数实现耦合。除能量守恒，非线性耦合还要求动量守恒，即相位匹配，当相位匹配时，可以获得很高的转换效率，反之，非线性过程就很弱。通常可以采用角度匹配，温度匹配，准相位匹配等方法实现相位匹配。但前二者对光波的传播方向和偏振态要明确要求，一般也不能利用到晶体较大的非线性系数，同时对于不同波长的匹配也很困难，多个非线性过程同时实现更是困难。而准相位匹配则能较好解决这些问题。可以通过一个三波耦合说明准相位匹配原理。考虑一个三波（${\displaystyle \mathbf {\omega } _{1}}$,${\displaystyle \mathbf {\omega } _{2}}$,${\displaystyle \mathbf {\omega } _{3}}$）的相互作用${\displaystyle \mathbf {\omega } _{3}=\mathbf {\omega } _{1}+\mathbf {\omega } _{2}}$，它们的波矢分别为${\displaystyle \mathbf {k} _{1}}$,${\displaystyle \mathbf {k} _{2}}$,${\displaystyle \mathbf {k} _{3}}$,通常，由于频率色散的存在，它们的相位不匹配，即相位失配量${\displaystyle \Delta \mathbf {k} =\mathbf {k} _{3}-\mathbf {k} _{2}-\mathbf {k} _{1}}$。而在准相位匹配结构中，由于非线性系数被周期性调制，因此它是空间${\displaystyle \mathbf {r} }$的函数。通常可以用一个结构函数${\displaystyle f(\mathbf {r} )}$来描述这种周期性调制。对结构函数${\displaystyle f(\mathbf {r} )}$可进行傅里叶展开，${\displaystyle f(\mathbf {r} )=\sum _{m,n}f_{m,n}exp(i\mathbf {G} _{m,n}.\mathbf {r} )}$,其中，${\displaystyle \mathbf {G} _{m,n}}$准相位结构提供的倒格矢，${\displaystyle f_{m,n}}$为相应的傅里叶系数，m,n 为整数。可以看到，准相位匹配结构可以提供多个倒格矢，这样可以需要选择和合适的倒格矢，从而实现相位匹配。例如选择合适的${\displaystyle \mathbf {G} _{m,n}}$,可以得到${\displaystyle \mathbf {k} _{3}-\mathbf {k} _{2}-\mathbf {k} _{1}+\mathbf {G} _{m,n}=0}$，即相位匹配，从而获得高效率的非线性频率转换。

1. 电极化制作PPLN
2. 大块PPLN的实现
3. 单束光单晶体直接三倍频
4. 三原色激光器

一维

1. 综述文章 Y.Y. Zhu and N.B. Ming, "Dielectric superlattices for nonlinear optical effects ",Optical and Quantum Electronics,31,1093-1128,(1999),doi:10.1023/A:1006932103769.

2.准周期结构

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997). doi: 10.1126/science.278.5339.843

K. F. Kashi and A. Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum Electron. 35, 1649–1655 (1999). doi:10.1109/3.798088

3.非周期结构 B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75, 2175-2177 (1999).doi:10.1063/1.124956

4.非周期结构 H. Liu, Y. Y. Zhu, S. N. Zhu, C. Zhang, and N. B. Ming, “Aperiodic optical superlattices engineered for optical frequency conversion,” Appl. Phys. Lett. 79, 728-730 (2001)doi:10.1063/1.1381569

5. 非周期结构 T. Kartaloğlu, Z. Gürkan Figen, and O. Aytür, “Simultaneous phase matching of optical parametric oscillation and second-harmonic generation in aperiodically poled lithium niobate,” J. Opt. Soc. Am. B 20, 343-350 (2003)doi:10.1364/JOSAB.20.000343

6.啁啾结构 K. L. Baker, “Single-pass gain in a chirped quasi-phase-matched optical parametric oscillator,” Appl. Phys. Lett. 82, 3841-3843 (2003). doi:10.1063/1.1579848

二维

1. 综述文章 A. Arie, A. Bahabad and N. Habshoosh, “Nonlinear interactions in periodic and quasi-periodic nonlinear photonic crystals,” in Ferroelectric Crystals for Photonic Applications (eds. P. Ferraro, S. Grilli and P. De Natale ) ch.10,259-294 (Springer Verlag, 2008).doi:10.1007/978-3-540-77965-0

2.第一块二维非线性光子晶体 N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, “Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal,” Phys. Rev. Lett. 84, 4345–4348 (2000).doi: 10.1103/PhysRevLett.84.4345

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