We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite-Gaussian laser modes we detail how Laguerre-Gaussian laser modes can be obtained by the direct conversion of the Hermite-Gaussian output. A Mach-Zehnder interferometer allows the phase structure of the Laguerre-Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre- Gaussian modes, which is the origin of the orbital angular momentum associated with each of them. (C) 1996 American Association of Physics Teachers.

doi:10.1119/1.18283