定义：
衡量激光光束的聚焦程度。

激光光束的光束质量具有多个定义，通常被用来衡量激光光束在特定情况下（例如，有限的光束发散角的情况下）聚焦的程度。常用的量化光束质量的方法有： — 光束参数乘积（BPP），也就是束腰处的光束半径与远场光束发散角的乘积 — M2因子，定义为光束参数乘积与其相同波长的衍射极限高斯光束的BPP的比值 — M2的倒数，光束质量很高时这一值很大 
光束质量高代表波前平滑，因此采用透镜对光束聚焦时，当波前是平面时得到焦点。图1中的波前形状很难聚焦，也就是给定光斑大小的光束发散角变大了。 

图1：光束质量比较差的激光光束，该光束很难聚焦。 

衍射极限高斯光束的光束质量最好，这时M2 = 1。许多激光器的光束都接近这一值，尤其是单横向模式（参阅单模工作）的固态体激光器和采用单模光纤的光纤激光器，或者一些低功率激光二极管（尤其是VCSELs）。但是有些高功率激光器（例如，固态体激光器和半导体激光器，例如二极管激光阵列）的 M2值高达100甚至超过1000，这通常是由于增益介质中热效应引起的波前畸变或者激光晶体中有效模式面积和泵浦面积不匹配，而高功率半导体激光器中光束质量差是由于采用了多模波导。而上面的情形中，光束质量差通常与高阶共振模式被激发有关。 

聚焦衍射极限光束时（也就是该处光束半径为最小值），光波前是平的。由于光学元件质量差引起的波前不规则，例如透镜组的球形象差，增益介质的热效应，圆孔衍射或者寄生反射灯，都会使光束质量变差。对于单色光束，利用相位掩膜完全补偿波前畸变理论上可以保持光束质量，但是实际中非常困难，即使畸变是稳态的也是如此。可以采用更灵活的方案，将自适应光学与波前传感器相结合。 

采用非共振的模清洁器或者模清洁腔可以提高激光光束的光束质量。但是这会损失部分光功率。 
激光器的亮度由输出功率和光束质量决定。 

有时光束质量被定性的用于某些地方，表示的意义与之前描述的聚焦程度关系很小。有些应用中，需要得到非常平滑的光束强度截面，例如高斯型，这时不需要考虑光束发散角。光束的质量不需要采用之前采用的 M2，光束可以具有相对比较小的 M2值但是同时具有多个峰值，而也有光束具有非常平滑的光束形状但是发散角很大，因此 M2值很大。 

目录

1. 测量光束质量
2. 应用中光束质量的重要性
3. 一些激光器的光束质量
4. 优化激光光束质量
5. 非线性光学中的光束质量

测量光束质量 
根据ISO标准11146，可以采用拟合过程计算光束质量因子 M2，应用于测量光束在传输方向上光束半径的变化（如图2）。为了得到正确结果，在光束半径的严格定义和数据点的位置选取时，需要遵守一些规则。 

图2：根据测量的焦散面计算得到的光束质量。黑色的数据点是用来拟合曲线的点，忽略了灰色的数据点。（根据ISO标准11146，需要平均选取数据点，有些位于焦点附近，而其他的点则离焦点有一段距离） 

商用的光束分析仪可以在几秒内自动测量光束质量。仪器是测量不同位置处的光束剖面来得到光束质量的。采用不同原理的光束分析仪，例如，采用CCD和CMOS相机或者旋转刀边或旋转刀缝，在允许的光束半径范围，光功率，波长范围等方面是不同的。例如，缝或者刀边扫描仪可以扫描比相机系统更高的功率，对于近高斯型光束测量很准确，而采用相机系统更适用于复杂波形。如果光束功率随时间变化则会产生其它的问题，例如，调Q激光器的输出光。这时需要用一个快门与激光脉冲同步。 

为了消除移动部件对系统的影响，可以采用空间光调制器，而不需要移动探测器。 
另外的测量方法包括：采用光束通过模式匹配的被动光振荡器后的透射光测量，或者采用波前传感器，例如，Shack-Hartmann传感器。此时分析激光光束只需要分析某一平面的波前面即可。 

应用中光束质量的重要性 
当需要紧聚焦光束时，高的光束质量非常必要。在激光材料加工、印刷、标记、切割和钻探中需要很高的光束质量，而焊接和其它表面处理则相对不太需要很高的光束质量，因为它们采用的光斑较大，因此可以采用光束质量稍差的高功率激光二极管。激光切割和远程焊接中，需要光束质量相对较高（M2值不要大于10）用于较大工作距离（也就是工件与聚焦目标之间距离），这样是为了保护光学元件避免烟雾和损伤。在光束传输系统中，光束质量高可以减小光束直径，这样可以采用更小更便宜的光学元件（例如，镜子和棱镜）。还有，增大有效瑞利长度（给定光斑大小）可以提高纵向对准允差。 

光束质量高可以允许工作距离比较大，这在设计二极管泵浦激光器时也非常重要，因为泵浦光束在进入激光器晶体前需要通过很多光学元件（例如，二向色镜）。 
干涉仪、光学数据记录、激光显微镜等类似领域通常需要很高的光束质量（近于衍射极限）和高空间相干性。 
锁模激光器需要具有很高的光束质量，因为高阶纵向模式的激发会干扰脉冲形成过程。 

一些激光器的光束质量 
通常来讲，光束质量不依赖于激光器类型，但是也存在一些规律： — 大多数低功率二极管泵浦固态激光器的光束质量很高（接近衍射极限）。 — 许多气体激光器与上相同，例如氦氖激光器和二氧化碳激光器。 — 一些高功率固态激光器的光束质量很差，主要是因为激光器晶体的强热学效应引起光束畸变。另外，需要在高光束质量和高功率效率之间权衡，或者高光束质量和低对准灵敏度之间。 — 低功率激光二极管通常具有比较高的光束质量，而高功率激光二极管的光束质量则比较差。这主要是因为功率高需要辐射孔径大，因此采用的波导具有多个模式。（不能减小数值孔径） 

优化激光光束质量 
为了得到高光束质量的固态体激光器，关键因素为： — 优化谐振腔设计得到合适的模式面积（尤其是在增益介质中）和对热透镜效应的低灵敏度 — 谐振腔对准 — 将热效应最小化，尤其是增益介质中的热透镜效应 — 高质量光学元件（尤其是增益介质） — 优化的泵浦强度分布（有时需要泵浦光源光束质量比较高），采用端泵浦比边泵浦更简单 

非线性光学中的光束质量 
不仅激光器中需要考虑光束质量，非线性频率转换中也需要考虑。由于只有当平均功率很高时，非线性晶体材料中才存在热透镜效应（因为只有弱寄生吸收产生热），还存在其它效应会影响光束质量： — 空间游走会使相互作用光束发生偏移，因此交叠变小，相互作用在空间上不对称。 — 在倍频或者光参量放大器等强频率转换过程中，在光束轴向的泵浦光束存在很强的损耗甚至会背向转换，极限情况下会形成明显的环形结构。增益导引会使这一问题更加严重。光束质量问题会限制高增益非线性频率转换装置的功率扩展性。对于超短脉冲，群速度失配和其它效应甚至会使光束质量随时间变化。 

在非线性频率转换装置中，如果采用的激光的光束质量很差会极大的降低转换效率。 非线性光学中光束质量的影响可以采用一些数值模型来研究，表征光束空间分布（甚至随时间的分布）的变化情况。

Definition: a measure for how well a laser beam can be focused

The beam quality of a laser beam is an important aspect of laser beam characterization. It can be defined in different ways, but is normally understood as a measure of how tightly a laser beam can be focused under certain conditions (e.g. with a limited beam divergence). The most common ways to quantify the beam quality are:

• the beam parameter product (BPP), i.e., the product of beam radius at the beam waist with the far-field beam divergence angle
• the M² factor, defined as the beam parameter product divided by the corresponding product for a diffraction-limited Gaussian beam with the same wavelength

Low values of BPP or M² factor imply a high beam quality.

A high beam quality implies smooth wavefronts (i.e., strong phase correlation across the beam profile), such that focusing the beam with a lens allows one to obtain a focus where the wavefronts are plane. Scrambled wavefronts (see Figure 1) make beam focusing more difficult, i.e., the beam divergence for a given spot size is increased.

Figure 1: A laser beam with poor beam quality. In contrast to an ideal Gaussian beam, the wavefronts are somewhat scrambled, which makes it more difficult to tightly focus the beam.

The highest possible beam quality in terms of M² is achieved for a diffraction-limited Gaussian beam, having M² = 1. That value is closely approached by many lasers, in particular by solid-state bulk lasers operating on a single transverse mode (→ single-mode operation) and by fiber lasers based on single-mode fibers, also by some low-power laser diodes (particularly VCSELs). On the other hand, in particular some high-power lasers (e.g. solid-state bulk lasers and semiconductor lasers such as diode bars) can have a very large M² of more than 100 or even well above 1000. In solid-state lasers, this is often a result of thermally induced wavefront distortions in the gain medium and/or a mismatch of effective mode area and pumped area in the laser crystal, whereas in high-power semiconductor lasers the poor beam quality results from operation with a highly multimode waveguide. In both cases, the poor beam quality is associated with the excitation of higher-order resonator modes.

In the focus (beam waist) of a diffraction-limited beam (i.e., at the location where the beam radius reaches its minimum), the optical wavefronts are flat. Any scrambling of the wavefronts, e.g. due to optical components with poor quality, spherical aberrations of lenses, thermal effects in a gain medium, diffraction at apertures, or by parasitic reflections, can spoil the beam quality. For monochromatic beams, the beam quality could in principle be restored e.g. with a phase mask which exactly compensates the wavefront distortions, but this is usually difficult in practice, even in cases where the distortions are stationary. A more flexible approach is to use adaptive optics in combination with a wavefront sensor.

It is possible to some extent to improve the beam quality of a laser beam with a non-resonant mode cleaner or a mode cleaner cavity. This, however, leads to some loss of optical power.

The brightness of a laser, or more precisely its radiance, is determined by its output power together with its beam quality.

Note that the term beam quality is sometimes used with a qualitative meaning which has little to do with the focusability as discussed above. For some applications, it is vital to obtain a smooth beam intensity profile, e.g. of Gaussian shape, whereas the beam divergence is not of interest. The “quality” of a laser beam may then not be characterized e.g. with an M² as discussed below: one beam may have a relatively small M² value but a multi-peaked beam profile, whereas another beam may have a smooth beam shape but a high divergence and thus a large M² value.

Some laser applications such as lithography require the uniform illumination of a large area. If the term beam quality appears in that context, it may have nothing to do with focusability as discussed in this article. One may then even prefer beams with a rather low spatial and temporal coherence.

Measurement of Beam Quality

According to ISO Standard 11146, the beam quality factor M² can be calculated with a fitting procedure, applied to the measured evolution of the beam radius along the propagation direction (the so-called caustic, see Figure 2). For correct results, a number of rules have to be observed, e.g. concerning the exact definition of the beam radius and the placing of data points.

Figure 2: Calculation of the beam quality from the measured caustic. The black data points are those used for the fitting procedure, whereas the gray points are ignored. (A balanced selection of data points, with some near the beam waist and others at a sufficient distance from it, is required according to ISO Standard 11146.)

There are commercially available beam profilers which can automatically perform beam quality measurements within a few seconds. They are normally based on the measurement of the beam profile at different positions. Beam profilers based on different measurement principles, e.g. CCD and CMOS cameras or rotating knife edges or slits, differ considerably in terms of the allowed ranges of beam radius and optical power, wavelength range, sensitivity to artifacts, etc. For example, slit or knife-edge scanners can usually handle higher powers than cameras and can be precise for nearly Gaussian-shaped beams, whereas camera-based systems are usually more appropriate for complicated beam shapes. Other issues come into play for beams with temporally varying powers, e.g. for the output of Q-switched lasers. It may then be necessary to synchronize a shutter with the laser pulses.

Instead of a moving a detector through the beam, one can use a spatial light modulator to avoid any moving parts [8].

Alternative measurement methods are based on the transmission through a mode-matched passive optical resonator or on wavefront sensors, e.g. Shack–Hartmann wavefront sensors. The full characterization of the laser beam then only requires analysis in a single plane.

Importance of Beam Quality for Applications

A high beam quality can be important e.g. when strong focusing of a beam is required. In the area of laser material processing, printing, marking, cutting and drilling often require high beam qualities, whereas welding, soldering, hardening and various other kinds of surface treatment are less critical in this respect, because they work with larger spots, so that direct application of high-power laser diodes with comparatively poor beam quality (direct diode lasers) is possible. For cutting and remote welding, a relatively high beam quality (with M² not much larger than 10) makes it possible to use a large working distance (i.e., a large distance between workpiece and focusing objective), which is highly desirable e.g. in order to protect the optics against debris and fumes. Also, a high beam quality reduces the beam diameters in a beam delivery system, so that smaller and thus cheaper optical elements (e.g. mirrors and lenses) can be used. Furthermore, the increased effective Rayleigh length (for a given spot size) increases the tolerance for longitudinal alignment.

A large working distance, made possible by a high beam quality, is also important for the design of diode-pumped lasers when the pump beam has to go through various pieces of optics (e.g. a dichroic mirror) before reaching the laser crystal.

A very high (close to diffraction-limited) beam quality, associated with a high spatial coherence, is often required for interferometers, optical data recording, laser microscopy, and the like.

Mode-locked lasers always have to have a high beam quality, since the excitation of higher-order transverse modes would disturb the pulse formation process.

Typical Beam Quality of Certain Lasers

Generally, the beam quality is not determined by the type of laser, but there are some typical trends:

• Most low-power diode-pumped solid-state lasers exhibit a high (close to diffraction-limited) beam quality.
• The same applies to various gas lasers such as helium–neon lasers and CO₂ lasers.
• Some high-power solid-state lasers exhibit a poor beam quality, essentially because strong thermal effects in the laser crystal lead to beam distortions. Also, there can be design trade-off between high beam quality and high power efficiency, or high beam quality and low alignment sensitivity.
• Low-power laser diodes normally have a rather high beam quality, whereas high-power laser diodes basically always have a poor beam quality. Essentially, this is because high powers require large emitting apertures which make the used waveguides highly multimode. (The numerical aperture cannot be strongly reduced.)

Optimizing Laser Beam Quality

Crucial factors for obtaining a high beam quality from a solid-state bulk laser are:

• an optimized resonator design with suitable mode area (particularly in the gain medium) and low sensitivity to thermal lensing
• good resonator alignment
• minimized thermal effects, particularly from thermal lensing in the gain medium
• high-quality optical components (particularly concerning the gain medium)
• an optimized pump intensity distribution (sometimes requiring a pump source with good beam quality) – more easily achieved with end pumping than with side pumping

Beam Quality in Nonlinear Optics

Beam quality is an issue not only for lasers, but also for nonlinear frequency conversion. While thermal lensing in nonlinear crystal materials occurs only at very high average power levels (because heating occurs only through weak parasitic absorption), the beam quality can be affected by other effects:

• Spatial walk-off can spatially shift the interacting beams, so that the overlap becomes weaker, and the interaction becomes spatially asymmetric.
• For strong conversion e.g. in a frequency doubler or an optical parametric amplifier, there can be strong depletion of the pump beam near the beam axis or even backconversion, in extreme cases leading to pronounced ring structures. Gain guiding can make such problems more severe. Beam quality issues have been shown to limit the power scalability of high-gain nonlinear frequency conversion devices [5].
• For ultrashort pulses, the group velocity mismatch and other effects can even lead to time-dependent beam quality.

Further, the use of a laser beam with poor beam quality in a nonlinear frequency conversion device can significantly spoil the conversion efficiency.

Beam quality effects in nonlinear optics can be investigated with numerical computer models, which can simulate the evolution of the spatial (and possibly temporal) profiles of the involved beams.

Bibliography