"Walking the Beam": The Process of Laser Alignment

Simone Agha, Herricks High School, New Hyde Park, NY; Daniel Minkin, Portledge School, Locust Valley, NY; Harold Metcalf and John No�, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University.

Beam alignment is a constant concern in optics. It is a necessary and repetitive task of steering a laser beam so that it is collinear with two arbitrary points in space. This "walking the beam" is used, for example, when aligning interferometers or coupling light into an optical fiber.

In our project, the iterative process of aligning a beam was investigated mathematically. Using the concepts of a "position mirror" and an "angle mirror" it was possible to calculate the convergence of a beam through two pinholes while adjusting only two mirrors.

Our approach was to consider the optical setup as a line diagram in which all the optical components were collinear. The first mirror or the position mirror was used to center the beam on the first pinhole. The second mirror or the angle mirror was then adjusted to center the beam on the second mirror. The resulting offset from pinhole 1 was a distance d1. To converge the beam onto both pinholes, d1 distance must be zero when the beam is centered on pinhole 2 (offset distance d2 = 0).

Following the procedure above, we derived equations that describe the offset distances in terms of the mirror angles. These equations were inserted into Quattro Pro where we were able to model the process. By manipulating the starting values of the equations, we also were able to change the rate of convergence. The fastest rate of convergence is achieved when the angle mirror is close to the first pinhole.

An alternative method to the procedure we analyzed requires "overshooting" the centers of the pinholes. While faster, it requires some degree of expertise so that the beam does not diverge instead. Although the method we mathematically modeled is not the most efficient, it can be followed to reliably align a laser beam.

We would like to thank the Simons Foundation for funding this research.