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Encyclopedia of Laser Physics and Technology

© Dr. Rüdiger Paschotta

Last update: 2008-05-14

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

The beam quality of a laser beam can be defined in different ways, but is essentially 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
• the M² factor, defined as the beam parameter product divided by the corresponding product for a diffraction-limited Gaussian beam with the same wavelength
• the inverse M² factor, which is high (ideally 1) for beams with high beam quality

The best possible beam quality is achieved for a diffraction-limited Gaussian beam, having M² = 1. This 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 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 nonresonant mode cleaner or a mode cleaner cavity. This, however, is accompanied by some loss of optical power.

The brightness of a laser 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 "nice" (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.

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). 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 1: 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 focus 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.

Alternative measurement methods are based on the transmission through a mode-matched passive optical resonator or on wavefront sensors, e.g. Shack-Hartmann 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 require high beam qualities, whereas welding and various 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 poor beam quality 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.

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
• 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
• good resonator alignment, and low sensitivity of resonator design with respect to misalignment

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

See also: diffraction-limited beams, Gaussian beams, M² factor, beam radius, beam divergence, beam parameter product, brightness, beam profilers, end pumping, side pumping, thermal lensing, resonator design, mode cleaner cavities, beam shapers, Spotlight article 2007-04-01, Spotlight article 2007-06-11

Category: general optics

This encyclopedia is authored by Dr. Rüdiger Paschotta, the founder and executive of RP Photonics Consulting GmbH. Contact this distinguished expert in laser technology, nonlinear optics and fiber optics, and find out how his technical consulting services (e.g. product designs, problem solving, independent evaluations, or staff training) could become very valuable for your business!