GAUSS: Gaussian Beams & Near-field diffraction
The purpose of this experiment is to extend simplified notions geometric optics (ray-tracing) and of far-field (Fraunhofer) diffraction to the near-field regime essential for Gaussian beams -- the natural beams of lasers -- and essential for Fresnel diffraction which produces the famous phenomenon of the Spot of Arago (Poisson’s spot).
No light can actually come to a point focus, the way that raytracing, or geometrical optics, would suggest. Instead, for tiny spots diffraction will always be an issue, and we describe this kind of optics using the paraxial wave equation. The solution of the paraxial wave equation which ties to laser cavities and laser beams is called a gaussian beam. Therefore this experiment is central to everything about lasers and quantum optics.
This experiment asks you to image the intensity distribution of a gaussian laser beam for a number of positions before and through its focal spot. Closely related to changes in the intensity distribution, the phase fronts of a gaussian beam change curvature in surprising ways -- the apparatus lets you find the relationship R(z) between wavefront radius of curvature R and axial position z, by reflecting a laser beam exactly back on itself from surfaces of different radius of curvature R.Finally, this kind of phase-front interference optics lets you discover near-field diffraction, the optical physics that is in play for a gaussian beam near its smallest spot-size at focus, and the counterintuitive phenomenon that a solid object doesn't only make a shadow, but can create a bright spot of concentrated light.
Numerous Nobel Prizes over the years have recognized the importance of lasers, since the 1964 Nobel Prize to Townes, Basov, and Prokhorov, including, among many others, Schawlow in 1981 (Schawlow was a Univ. of Toronto student, and lived in the Annex), and of course Ashkin, Mourou, and Strickland in 2018.
Write-Up in PDF Format or Microsoft Word Format (Word without appendices).
(The experiment is currently located in MP227. This is an experiment introduced in Spring 2019 and most recently revised in September 2020.)
Additional resources:
- Instructions for Beam-Profiling using Image J.
- Using speckle to find laser focal spot [VIDEO] One way to easily find the focal spot of a laser beam through a lens is to use the light reflected from a fine rough surface. The pattern made by coherent light interfering, from all the rough features, is called a speckle pattern. For a large spot, the pattern is very fine; for a tiny spot the pattern is much coarser -- so searching for the coarsest speckle pattern tells you you're arrived at the tightest focus. (ref: correlation theorem for Fourier transforms)
- Aligning a lens to a laser beam [VIDEO] How a lens is aligned to a laser beam affects the quality of the focal spot. Here's a short tutorial on how to put the optical centre of a lens exactly on the axis of a laser beam. At the centre of a lens, the planes tangent to front and back surfaces are parallel to each other. So although the surfaces may produce beams that converge, or diverge, those reflections will go back in the same direction.
- Identifying second-surface reflections from an optic [VIDEO] There are reflections of light as a laser beam goes into an optic, and out again the other side -- both make beams going backwards. Sometimes it's important to know which reflection is which, in the reflected light. This shows a typical way people find which reflected light comes from the *second* surface.
Focussing onto dull-side aluminum foil, to use speckle scatter for finding focus, in new setup August 2020.
Ball and flat mirror to match wavefront surfaces in gaussian beam, in new setup August 2020.