VISUALIZING THE GOUY PHASE OF A LASER BEAM Thomas E. Videbaek, Marty Cohen and John Noé Laser Teaching Center, Department of Physics & Astronomy, Stony Brook University The propagation of laser beams is described by a precise theory that specifies the amplitude, curvature and phase of the evolving wavefronts as a function of radius r and distance z. The simplest such beams have a radially-symmetric Gaussian intensity profile I(r) which remains Gaussian-shaped as the beam propagates through space or radially-symmetric optical elements. The changing beam radius w(z) follows a hyperbola, and the point of minimum radius w0 at a "focus" is called the waist. An interesting and easily over-looked feature of the theory is the Gouy phase [1], a small correction to the on-axis wavefront phase compared to a reference plane wave; it varies from -pi/2 to +pi/2 as a beam moves through a waist. The Gouy phase can be visualized using a Mach-Zehnder interferometer setup by placing a suitable lens in one arm. Peatross and Pack [2] have described an alternative method that utilizes the "ghost beam" created by internal reflections in an uncoated plano-convex (PC) lens. When the PC lens is used to collimate diverging laser light the weak ghost beam forms a compact waist within the broad main beam and the resulting ring-shaped interference patterns can be viewed with a camera. The intensity pattern inverts as the camera is moved through the waist as a result of the changing Gouy phase. In this project we investigated the ghost-beam method and compared it to the classic interferometer setup. We found that the former method has numerous advantages, including several not mentioned in Ref. [2]. We also found that the secondary lens used [2] to control the divergence of the beam incident on the primary PC lens is unnecessary. It is sufficient to pick a primary lens that matches the intrinsic divergence of the laser beam, which is easily determined by beam profile measurements at one or more distances from the laser. Our recorded interference patterns are in generally good agreement with a model of the interference process that we created in Mathematica. Finally, we were able to derive some interesting mathematical relationships relevant to our simplified ghost-beam method. This work was supported by the National Science Foundation (Phy-0851594). [1] R.W. Boyd, J. Opt. Soc. Am. 70, 877-880 (1980). [2] J. Peatross and M.V. Pack, Am. J. Phys. 69, 1169-117 (2001).