Rays and beams

Focusing a laser beam

A laser beam cannot be focused to a point. A lens squeezes it to a waist whose size is set by the wavelength and the angle the beam converges at, and the beam stays near that size over the Rayleigh range.

What you are looking at

A 1 mm laser beam passes a 100 mm lens. The profiler sits at the focus and measures the waist.

How the bench is set up

HeNe laser (1 mm waist), thin lens f = 100 mm, beam profiler 100 mm behind the lens.

The theory

A Gaussian beam of width $w$ at a lens of focal length $f$ focuses to

w_0 \approx \frac{\lambda f}{\pi w},

and stays within $\sqrt2\,w_0$ for a Rayleigh range $z_R = \pi w_0^2/\lambda$ either side of the waist.

What to measure

Waist w₀ = λf/πw; Rayleigh range πw₀²/λ

Read the profiler’s width: about 20 µm.
Move the profiler 1 mm at a time with the arrow keys and find where the width is $\sqrt2$ larger.

What the model leaves out

The lens has no aberrations, and the beam is a perfect TEM₀₀.

Things to try

Raise the laser’s M² to 3: the focus grows three times.
Use a shorter lens for a tighter focus, and see the Rayleigh range shrink.

References

A. E. Siegman (1986), Lasers, University Science Books.
B. E. A. Saleh and M. C. Teich (2019), Fundamentals of Photonics, 3rd edition, Wiley.

More experiments, and how the lab works, are in the laser lab’s overview.