定义：将非线性晶体放置于激光谐振腔内的倍频方法

倍频和很多其他非线性频率变换效应一样，只有在打到非线性晶体材料上的光强足够大时才会具有较高的频率变换效率。这对于平均功率较低的情况，尤其是连续光的情况，则很难实现。腔内倍频则是解决这一问题的一种有效方法，在这种方法中，倍频晶体被放置于激光谐振腔（或者是光学参量振荡器的谐振腔）中。这种方法对于倍频效率的提升主要源自于以下两个方面： 

1. 在谐振腔中，光功率和光强都会强很多，从而可以大幅提高单次通过下的倍频效率，通常会提高一个量级； 
2. 虽然单次通过的倍频效率依然不是很高，但是由于未被转换的泵浦光依然还在腔内，因此最终的倍频效率会大幅提升。 

因此，利用腔内倍频有可能产生一个高功率的倍频光，而该倍频光的功率比起没有倍频晶体时直接输出的未倍频的光的功率并不会低很多。 
腔内倍频的谐振腔必须包含一个双色镜，该双色镜对于倍频光束具有高的透射率，从而用于输出倍频光。腔内所有谐振镜对于基频光都具有高反射率。（原有的输出分束器将不再被使用）。
对于线性谐振腔，倍频将会在两个传播方向都反生。这两个光束可被合束为一个光束。如果端镜没有寄生损耗并具有理想的相对相位变化，那么线性腔的腔内倍频的转换效率可以是单通的四倍。 
关于偏振和相位匹配，也有不同的选择： 

• I型相位匹配的倍频可以在偏振发射的激光中使用。 
• II型相位匹配的倍频器适于非偏振光发射的激光。 

在这两种情况下，倍频光都是线性偏振。 
许多连续光的绿色和蓝色激光光源都是基于腔内倍频的，现在已经有产生几十W输出功率的这种激光器。这种技术也适用于红光激光器，其利用了1342nm的钒激光器。 

典型技术问题
对于连续光激光器使用腔内倍频会有一些负面的问题。其中一个非常困扰人的问题是在某些情况下，激光会具有显著的强度噪声。这是谐振器模式的非线性效应导致的，它不仅受到非线性频率变换的影响，但受到空间烧孔和高阶谐振模式的影响。
偏振问题也是需要重视的，特别是对于II型相位匹配的情况。对于不同的情况下，其不稳定性可以通过一些不同的激光设计技术来消除。例如，使用一个相对较长的谐振腔的（增加的谐振模式的数量），或稳定的单频模式。
非线性晶体的热效应通常不会到来很大的问题，因为相对激光晶体其热效应小很多。 
如果增益带宽比所述非线性晶体的相位匹配带宽大，激光波长就会大于非线性变换的波长区域，这将导致非常低的转换效率。这个问题可以用一个腔内的滤光器来消除，这个滤波器正好与非线性变换的波长相匹配。 
当晶体温度不合适使得相位匹配不满足的情况发生，从而导致倍频器不工作时，基频光的腔内功率将会变得相当高（特别是在调Q激光器中）。激光器的设计应该保证不会发生激光损伤。

 其他途径
仅在极少数情况下，调Q激光器或锁模激光器会用于腔内倍频。这是因为这种脉冲激光的峰值功率通常能够实现高效率转化，并且非线性元件会对脉冲形成产生不利影响。在调Q激光器中，腔内倍频会显著减缓脉冲积聚，并且在被动锁模激光器中由于其部分抵消了可饱和吸收体的作用，从而使得超短脉冲难以产生。 
一种替代技术，同时适用于单频激光器和锁模激光器，是在激光器外部利用谐振的增强腔（参阅谐振倍频）。通常情况下，腔内倍频和谐振倍频两个技术只会使用一种。通常情况下，这两种技术都不适合的高功率光纤激光器：腔内倍频的谐振腔损耗过高从而无法实现高效的倍频，而谐振倍频的系统搭建和操作则较为复杂。但将这两种方法组合起来则会获得很好的效果：长的光纤激光器谐振强与短的倍频谐振腔的谐振频率一致，谐振增强仅发生在非线性晶体中，而不会在光纤中发生，因此，在光纤部分的高损耗并不会带来问题。 
另外，也可以利用激光谐振腔实现其他类型的非线性频率变换：如受激拉曼散射、和频/差频产生以及光学参量振荡器。

Definition: frequency doubling with a nonlinear crystal within the laser resonator

More general terms: nonlinear frequency conversion

Frequency doubling, similar to other processes of nonlinear frequency conversion, can have a high power conversion efficiency only if sufficiently high optical intensities are reached in the nonlinear crystal material. This is often not possible for low- or moderate-power continuous-wave lasers. A good solution in such cases – particularly for solid-state lasers – can be intracavity frequency doubling (or intracavity SHG = second-harmonic generation), where the frequency doubler crystal is placed within the laser resonator (or similarly within the resonator of an optical parametric oscillator). There are actually two different reasons why intracavity frequency doubling works well:

• Within the laser resonator, the optical powers and thus the intensities achievable are much higher, increasing the conversion efficiency per path by often more than an order of magnitude.
• It is normally sufficient to achieve a single-pass conversion efficiency of just a few percent, because the unconverted power remains in the laser resonator rather than being lost.

Figure 1: Photograph of the VERDI green laser from Coherent. A unidirectional ring laser resonator is used, enabling low-noise single-frequency operation. The image was kindly provided by Coherent.

It is therefore possible to generate a frequency-converted output power which is not much lower than that achievable with the same laser head at the unconverted wavelength (without a frequency doubler, and with a suitable output coupler for the fundamental wavelength).

The laser resonator must contain a dichroic mirror which has a high transmissivity for the frequency-doubled beam, and all resonator mirrors should be highly reflective for the fundamental wavelength. (In general, an ordinary output coupler mirror will not be used.) For linear resonators, frequency doubling occurs in both propagation directions. However, the two resulting beams can be combined to a single output beam when there is a folding mirror with significant transmittance for the frequency-doubled wavelength. For ideal relative phase changes on the end mirror and without parasitic losses, the double-pass conversion efficiency can be four times the single-pass value.

Concerning polarization and phase matching, there are different options:

• A type I phase-matched frequency doubler may be used within a laser with polarized emission.
• A type II phase-matched frequency doubler is suitable for a laser with unpolarized emission.

In both cases, the frequency-doubled light is linearly polarized.

Many continuous-wave green and blue laser sources are actually based on intracavity frequency doubling. There are versions generating tens of watts of output power. The technique is also applicable to red laser sources, based e.g. on 1342-nm vanadate lasers.

Typical Technical Issues

Power Instabilities

There are some possible negative side effects of intracavity doubling in continuous-wave lasers. A very disturbing issue can be that under certain circumstances the laser can exhibit very strong intensity noise (“green problem”). This is a result of the introduced nonlinear dynamics of the resonator modes, which can be influenced not only by the nonlinear frequency conversion but also be spatial hole burning and oscillation of higher-order resonator modes. Aspects of polarization can also be important, particularly for frequency doubling with a type II phase-matched crystal.

Depending on the situation, the instabilities can be eliminated by applying different techniques in the laser design. Examples are the use of a relatively long resonator (increasing the number of oscillating resonator modes) or to design for stable single-frequency operation. (Somewhat surprisingly, single-frequency operation can even be stabilized by an intracavity doubler.)

Laser Wavelength Escaping the Nonlinear Conversion

If the gain bandwidth is larger than the phase-matching bandwidth of the nonlinear crystal, the laser wavelength may “escape” the wavelength region where the nonlinear conversion occurs, and this can result in an extremely low conversion efficiency. This problem can be eliminated with an intracavity optical filter, which essentially fixes the laser wavelength.

Excessive Fundamental Laser Power

In the case that the frequency doubler does not work, e.g. due to a crystal temperature which does not allow for phase matching, the intracavity power of the fundamental wave can become fairly high (particularly in a Q-switched laser). The design should be such that laser-induced damage of optical components is nevertheless avoided.

Effects on Pulses in Q-switched and Mode-locked Lasers

Only in rare cases is intracavity frequency doubling used with Q-switched or mode-locked lasers. This is partly because the peak powers of such pulsed lasers are anyway sufficiently high for efficient conversion, and partly because the nonlinear element can have a detrimental impact on the pulse formation. In Q-switched lasers, an intracavity frequency doubler can significantly slow the pulse build-up, and in a passively mode-locked laser it can prevent the generation of ultrashort pulses by counteracting the effect of the saturable absorber.

Other Approaches

An alternative technique, applicable to both single-frequency lasers and mode-locked lasers, is the use of a resonant enhancement cavity (→ resonant frequency doubling) external to the laser. Here, not only mode matching is required, but also precise matching of the resonance frequency.

Normally, only one of the two techniques (intracavity doubling or external resonant doubling) is used. However, Ref. [15] demonstrates the unusual combination of both techniques. Here, the frequency-doubling resonator has been placed within the laser resonator of a fiber laser. Normally, neither technique would be ideal for a high-power fiber laser: the resonator losses are too high for efficient intracavity doubling, and frequency-stabilized narrowband operation for external resonant doubling is not very convenient. The combination of both methods, however, works well: the long fiber laser resonator automatically operates on frequencies which are resonant in the short doubling resonator (a ring resonator), and the resonant enhancement takes place only in the nonlinear crystal, but not in the fiber, so that the higher losses in the fiber part are not relevant.

It is also possible to perform other kinds of nonlinear frequency conversion within a laser resonator; examples are stimulated Raman scattering, sum and difference frequency generation, and optical parametric oscillation.

Bibliography