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Chapter 15:
Light Tubes, Wigner Diagrams, and Optical Wave Propagation Simulation
Light propagating in a tube does not spread out, but instead remains confined to the dimensions of the tube. Some years ago Adolf Lohmann used the term light tube to describe the effect of a positive lens in the observation of Fraunhofer patterns. Normally, of course, light spreads as it propagates under conditions of Fraunhofer diffraction, and the size of the Fraunhofer pattern is scaled in proportion to the propagation distance z. A lens has the effect of bringing infinity up into its back focal plane and can be used to project the Fraunhofer pattern of an aperture onto an observation screen without the large-scale spreading associated with the lens-free case; a sufficiently powerful lens can keep the light confined to a tube, from input to Fraunhofer plane. In this chapter I show how one particular light tube can be used advantageously in connection with the numerical simulation of optical wave propagation. The analysis of this system is aided significantly by the use of the Wigner diagram: a powerful graphical tool that describes, both simply and concisely, the spreading of lightwaves with propagation and the corresponding effect on that spreading that is introduced by light transmission through a lens. Lohmann has been one of the major contributors to the use of Wigner diagrams in the analysis of optical systems, and it is he, along with others with whom he has worked, who is largely responsible for introducing me to the great power of this tool.
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