Optical Physics: "Light Beams in High-Order Modes

A recent project that we have been working on involves the geometric phase that results from cyclic changes in the modes of a higher-order Gaussian beam. A set of the beam modes of a Gaussian beam carry orbital angular momentum. Patrick Crawford (Summer 2002), Matt Pysher (Summer 2002), Henry Sztul (Spring 2000 and 2001) and PJ Haglin (Summer 2000) have been working on this project. We have done the first measurements of this phase for optical beams. An article on this work appeared recently in Physical Review Letters [PRL 90, 203901 (2003)].

When you have a collimated beam of light the wave equation in three dimensions becomes the paraxial wave equation. This equation can be solved in either Cartesian or cylindrical coordinates. The solution in Cartesian coordinates gives a family of solutions expressed in terms of Hermite polynomials multiplied by a Gaussian envelope. These Hermite-Gauss solutions (or modes) are categorized by their indices (n,m) and 'order' N=n+m. The Hermite-Gauss (HGnm) of order zero, HG00 is the usual output of an ordinary laser (TEM00): "
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