Laser Applications Newsletter
9 October 1999
Laser Kinetics Inc.
Mtn. View, CA 94041
Issue 2 , Vol 3

For most material processing applications, laser beams must be focused. The size of the focused spot is critically important for many applications, but it's hard to determine experimentally and not straightforward to figure out. In this newsletter, I'll outline some of the issues related to laser focusing.

A) How is a laser beam characterized?
The beam from a laser has two important characteristics: Waist Diameter and Divergence (Strictly speaking, since laser beams are often not round, you have to look at the width and divergence in two orthogonal planes, but we won't do that here). The waist diameter is the beam's minimum size, and the divergence is the angle at which it increases its size. The waist may be located anywhere with respect to the laser, but is often at the output window or within the laser cavity.

For any given wavelength, there is a theoretical minimum to the divergence for a given waist diameter such that the product of the waist diameter and the divergence must exceed 4/pi times the wavelength. A beam which approaches this limit is often termed TEM00 or gaussian, neither of which is an accurate description. All real beams exceed the theoretical waist/divergence product. The ratio between the real and theoretical products is often referred to as "M squared" (M^^2).

When using industrial lasers, you must always be aware of M^^2 because it can be a large number. Some Nd:YAG lasers have M^^2 values around 80, so using calculations for TEM00 beams will cause gross errors.

It has tacitly been assumed that the diameter and divergence are known. These are slippery quantities, and different standards exist for what the size of a beam is. Beam measurement is a whole topic unto itself, and most of the time we use the laser manufacturer's specifications for the beam properties.

B) How is a laser beam focused?
In industry, both lenses and mirrors are used to focus laser beams. Lenses are simpler to use since they work on the optical axis, but mirrors are more durable. For high-power welding, lens life is typically unacceptably short, so mirrors are the standard focusing optics.

In theory, a paraboloidal mirror will focus a laser beam better than a lens because lenses have spherical aberration and paraboloid do not. In practice, lenses are usually made smoother and more accurately than mirrors, so lenses produce smaller spots. Another problem with mirrors is that they must be very accurately aligned to the incoming beam. An angular error of as little as 10 milliradians is enough to enlarge the focused spot. Lenses are much more tolerant of angular misalignment and will work perfectly well with a couple of degrees of error.

C) What size is the focused spot?
The answer to this is, "it depends". The focused spot size is often taken to be the lens focal length times the beam divergence. This is OK if the lens is near the waist, but quickly becomes inaccurate as the beam diverges. This effect can often be seen on moving beam systems where the distance between the laser and the lens changes. Sometimes, the process works well on some parts of the table but not on others. The exact spot size can be calculated using Self's equations, which are discussed on pages 57-59 of my book.

D) Where does the beam focus?
Surprisingly, not at the lens' focal length unless the lens is exactly 1 focal length beyond the beam waist. The focal point may be inboard or outboard of the lens' focus, and its location moves as the lens goes through the laser beam waist. Again, a computational tool such as Self's equations is needed to find the correct value.

Coming real soon:

International Congress on the Applications of Lasers and Electro-Optics
November 15-18, 1999
San Diego, CA

ICALEO is the world's premier laser applications conference, and this year it's in San Diego again (you should try to attend conferences in San Diego even if they're not of any use). At ICALEO, you can hear about the newest developments in laser processing and talk to the people who are doing them.

LIA's phone number is (407).380-1553 Fax: (407).380-5588

eedback is important to us. Do you want processing tips, news about developments in laser applications, laser fundamentals or something else? Do you have any comments on the material presented above? E-mail us at with your comments and suggestions.

Call 650 575-4919 or e-mail us for more information.