The direction of the laser output beam is subject to some fluctuations in beam pointing, which can cause major problems in certain situations - for example, when the beam has to be coupled into a single-mode fiber or when the beam has to hit a target at a large distance with high precision. For these reasons, a quantitative measure of the beam pointing stability can be important.

Physical origins of beam pointing fluctuations:

Beam pointing fluctuations of bulk lasers can have different sources:

Mechanical vibrations (e.g. picking up from the ground) and drifts (e.g. caused by thermal effects) can affect the alignment of optical components, in particular the mirrors of the laser resonator. In this way, the position of the resonator modes and therefore the position of the output beam can be affected.

There can also be direct thermal effects on the beam position. In particular, thermal lensing in the gain medium (e.g. laser crystal) may be associated not only with focusing effects but also with some beam offsets. This is particularly the case when the pump beam profile is not completely symmetrical or is not well aligned with the resonator axis.

It is important to note that a certain tilt of the resonator mirrors does not necessarily translate into an equally large tilt of the output beam. Instead, it usually results in some combination of a (greater or lesser) tilt and some shift (offset) of the beam. The type of effect depends on the overall resonator design (as discussed in the article on alignment sensitivity). For a linear resonator, the alignment sensitivity can be very different in the two stability regions, and even diverge near the edges of such regions. The alignment sensitivity of different resonator mirrors can also vary greatly. Such issues have important implications for optimizing pointing stability.

Quantification of Beam Pointing Stability:

The beam pointing stability of commercial laser products is usually specified quantitatively. Unfortunately, such specifications are often imprecise or even meaningless. A useful angular fluctuation specification must adhere to some important issues:

It must be clear whether the quoted figures apply to the beam's deviation from some reference axis, to the total width of the possible angular range, or to the maximum angular variation within some time interval.

It should be clear whether the figures are typical values, absolute limits (not to be exceeded for operation under specified conditions), or r.m.s. (root mean square) values.

Operating conditions need to be specified, including, for example, stability of ambient temperature, required warm-up time (during which large fluctuations may occur), operation at constant or variable output power, etc.

In addition, the time scale or frequency range must be specified. Ideally, a noise frequency range is specified, where lower numbers relate to the maximum measurement time and higher numbers to the measurement bandwidth. Specifications with smaller, low-noise frequencies include long-term drift. In other cases, where only fast fluctuations are of interest, a frequency range of, for example, 100 Hz to 10 kHz may be appropriate.

Finally, of course, it must be clear to which beam the numbers apply: for example, the beam obtained directly from the laser, or the beam after it has passed through a collimating lens. This is very important, since optics outside the laser often change the pointing stability of the beam (see below).

The magnitude of the angular fluctuations alone is often not actually sufficient to calculate the impact of beam pointing fluctuations in an application; how large the parallel beam deflections are, and how these deflections relate to the angular fluctuations, are also important.

The impact of external optics on beam pointing stability:

If the laser beam is sent through some optics, in general this will change the magnitude and type of beam pointing fluctuations, even if the optics are absolutely stable. The following two examples illustrate this.

If a collimated beam hits a focusing lens, the focal point behind the lens will exhibit lateral motion according to the angular fluctuations of the input beam, while such lateral shifts of the input beam only affect the beam direction in the focal point. If the input beam acquires an angular shift equal to the beam divergence, the focal point behind the lens will be shifted laterally by one beam radius (measured at the beam waist).

Consider a beam expander with a magnification factor of M=2, placed in the collimated beam of a laser. The output beam will not only have twice the beam radius, but also half the r.m.s. value of the angular fluctuations.

This behavior can be understood by purely geometric reasoning, e.g. based on the ABCD matrix algorithm.

In order to judge the angular beam stability of a laser, not only the magnitude of the angular fluctuations but also the beam radius must be considered. It is of interest to compare the angular fluctuations with the diffraction-limited beam divergence, i.e. the beam divergence of a Gaussian beam with a certain magnitude. The larger the radius of such a beam, the smaller its divergence angle and the more severe the effect of the directivity fluctuations for a given angular fluctuation.

Of course, vibrations of the optical elements will further increase the magnitude of the directivity fluctuations.

Optimizing beam pointing stability:

Laser designs that optimize beam pointing stability must take various factors into account.

Mechanical vibrations of the resonator mirrors should be minimized by a stable setup and possibly some mechanical decoupling from the ground.

Long-term drifts of heat sources should be minimized by a number of measures. For example, heating components such as laser diodes or electronic circuits should be shielded from the resonator optics. In high-power lasers, parasitic beams (e.g. beams transmitted by highly reflective mirrors) must be prevented from hitting the resonator mirrors.

The resonator design should be optimized for minimal alignment sensitivity. In some cases, this involves a trade-off with other desired characteristics, such as high beam quality.

With a good laser design, the angular beam pointing fluctuations of the laser can be a very small fraction of the beam divergence. This is equivalent to a phase change of the entire beam profile that is much smaller than one radian.

Further reduction of pointing fluctuations can be achieved by active stabilization schemes. For example, the beam position at a certain point can be monitored with a four-quadrant photodiode and corrected by pressing the mirror.

For an existing laser, directivity fluctuations are typically minimized by careful alignment to achieve maximum output power.