定义：用于在透明晶体材料中实现非线性相互作用中准相位匹配的一种技术

非线性晶体材料的周期性极化是用于获得非线性相互作用中准相位匹配的技术。它涉及一种在非线性晶体中产生周期性畴反转（domain inversion），使得非线性系数的符号也发生改变。 

铁电畴工程学（Ferroelectric Domain Engineering） 
最常用的周期性极化技术是铁电畴工程学。其将一个强电场经由图案化的电极打到铁电晶体的晶体表面，该电极通常利用光刻工艺制备而成，具有几微米和几十微米的周期。极化周期（即电极的图案周期）决定了非线性过程中哪些波长可以满足准相位匹配条件。发生畴反转的电场需要大于所谓的矫顽场强度，对于同成分铌酸锂（congruent LiNbO3）而言，该强度约为21kV/mm。在施加如此强的电场时需要注意避免在空气中的放电和对晶体破坏。对于厚的样品（大于0.5mm），极化过程则变得很具有挑战性，因为有时只能在电极附近的区域获得较好的极化质量。另一个挑战是实现高质量的小极化周期（远低于10um），这种周期性极化结构的晶体可以用于倍频产生可见光。化学计量铌酸锂（Stoichiometric LiNbO3）的矫顽场强度约为2 kV/mm，从而极大地方便了周期性极化，即使对于更厚的样品也很容易获得好的极化质量。 

需要注意的是极化过程的需要对不同的非线性晶体进行细节调整，包括：晶体表面的制备，电极材料，电极的制造，电脉冲的持续时间、大小、形状（常常需要进行实时的监测控制），以及极化过程的温度。有时还有需要一些方法来抑制畴的反向变换，或利用畴的反向变换来实现高质量极化。

 适合实现周期性极化的铁电的非线性晶体材料包括：铌酸锂（LiNbO3），钽酸锂（LiTaO3），磷酸氧钛钾（KTP，KTiOPO4）和 砷酸氧钛钾（KTA，KTiOAsO4）。周期性极化的材料，常常在晶体名字前面加一个“PP”的开头，例如PPKTP（周期性极化KTP），PPLN（周期性极化铌酸锂）和PPLT（周期性极化钽酸锂）。PPLN和PPLT晶体通常用于光学参量振荡器和倍频器中，并且可以制备成非线性波导的结构形式。波导结构的PPLN使得即便功率较低时也可以获得较高效率的非线性相互作用。 

可以通过周期性极化的方法一次性的极化一整个晶体晶片，然后在将其切割成许多小晶体。利用这种方法可以实现低成本的大批量生产，而小批量生产周期性极化材料的单片成本则相对高很多。 

玻璃的周期性极化 
也有一些对于光纤进行的周期性极化的尝试。这种尝试是可能的，因为一个施加一个强电场（在真空室中，连同高温）一段时间后，可以使得最初各向同性的玻璃诱导产生χ(2)非线性。即使最终的非线性系数不是很高，但通过适当增加光纤长度依然可以在全光线结构中实现高效的非线性频率变换。
 

Definition: a technique for achieving quasi-phase matching of nonlinear interactions in a transparent crystal material

Periodic poling of nonlinear crystal materials is a technique for obtaining quasi-phase matching [1] of nonlinear interactions. It involves a process which generates a periodic reversal of the domain orientation (domain inversion) in a nonlinear crystal so that the sign of the nonlinear coefficient also changes.

Ferroelectric Domain Engineering

The most common technique for periodic poling is ferroelectric domain engineering [2]. This involves the application of a strong electric field to a ferroelectric crystal via patterned electrodes on the crystal surface, which typically have a period between a few microns and some tens of microns, and are usually produced with a photolithographic process. The poling period (i.e. the period of the electrode pattern) determines the wavelengths for which certain nonlinear processes can be quasi-phase-matched. Domain reversal occurs for a field strength above the so-called coercive field strength, which is e.g. ≈ 21 kV/mm in congruent lithium niobate (LiNbO₃). Such high field strengths have to be applied with great care to avoid discharges in air and destruction of the crystal.

The process is particularly challenging for thick samples (more than 0.5 mm), where the poling quality is sometimes good only near the electrodes. Another challenge is to achieve a high poling quality for small poling periods (well below 10 μm), as required, e.g., for frequency doubling to the visible spectral range. Stoichiometric lithium niobate (SLN) has a much lower coercive field strength of roughly 2 kV/mm, which greatly facilitates periodic poling, even for thicker samples.

Ferroelectric nonlinear crystal materials which are suitable for periodic poling with electric fields include lithium niobate (LiNbO₃), lithium tantalate (LiTaO₃), potassium titanyl phosphate (KTP, KTiOPO₄) and potassium titanyl arsenate (KTA, KTiOAsO₄). The periodically poled materials are often given a name beginning with “PP”, for example PPKTP (periodically poled KTP), PPLN (periodically poled lithium niobate) and PPLT (periodically poled lithium tantalate). PPLN and PPLT crystals are often used in, e.g., optical parametric oscillators and frequency doublers, and are also available in the form of nonlinear waveguides. The combination of the high nonlinearity of PPLN with strong confinement in a waveguide allows for efficient nonlinear interactions even at fairly low power levels.

Note that the details of the poling process have to be optimized for each particular type of nonlinear crystal; this can involve the preparation of crystal surfaces, the choice of electrode materials and details of electrode fabrication, the magnitude, shape and duration of applied electric pulses (often actively controlled with real-time monitoring e.g. of the flown electric charge or optical polarization changes), and the choice of temperature during the poling process. There are also methods to suppress domain back-switching, or to exploit backswitching for high-quality poling [4].

It is possible to periodically pole a large proportion of a whole crystal wafer, e.g. of lithium niobate or tantalate, in a single process, and later cut that wafer into many small crystals. In that way, the processing cost can be relatively low for fabrication of large quantities, whereas periodically poled materials are usually expensive when made in small quantities.

Periodic Poling of Glasses

There have also been interesting attempts to perform periodic poling of optical glass fibers. This is possible because the application of a strong electric field (often applied in a vacuum chamber, together with elevated temperature) for some time can induce a χ⁽²⁾ nonlinearity in the originally isotropic glass. Even if the effective nonlinear coefficient achieved is not very high, some moderate length of glass with a decent poling quality permits efficient nonlinear frequency conversion within all-fiber devices [6].

Fabrication of Orientation-patterned Semiconductors

It is also possible to fabricate semiconductor materials such as gallium arsenide (GaAs) with periodic patterns of domain orientation, which lead to a periodically changing sign of the effective nonlinear coefficient. However, this is not achieved by application of an electric field; gallium arsenide, for example, is not ferroelectric, so that such a technique could not work. Other techniques have been worked out for such periodic patterning, but they are usually not called periodic poling. The article on orientation-patterned semiconductors contains more details.

Bibliography