BEAM TRACING AND APPLICATIONS.
Antenna Lab. technical rept. no. 79,
ILLINOIS UNIV URBANA ENGINEERING EXPERIMENT STATION
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Graphical methods are introduced to describe the transformations of a beam as it goes through an optical system. The beams considered here are defined by a real Gaussian distribution of the field at some reference cross-section but can also include higher order modes defined by HermiteGaussian functions, or the beam-modes considered by Goubau. A complex variance is introduced which describes at once the effective area of a cross-section of the beam and the curvature of its phase front. In free space propagation, and at the crossing of a leans, the complex variance transforms in a simple manner which may be compared to impedance transformation through a reactive ladder network. The graphical constructions described allow us to trace the variations of a beam cross-section and curvature through a system. They correspond to some formulas already given by Goubau but they lead to some insight in the operation of non-confocal resonators and beam waveguides with unequally spaced lenses. This is illustrated by several examples including the design of an antenna for concentrating in a narrow beam the radiation from a beam waveguide. Related graphical constructions for multi-transit resonators are presented and the resonance condition can be compared to that of higher mode resonances. Author