Abstract
The question of whether it is possible to suppress ray oscillations in light waveguides is important for the design of light communications systems. With the help of Liouville's theorem of statistical mechanics it is shown that it is impossible to reduce simultaneously the amplitudes and the angles of ray oscillations if the ray originates in and returns to a region of low index of refraction. A reduction of both ray amplitudes and angles can be achieved only if the ray moves from a region of low to one of high index of refraction. Liouville's theorem is used to derive a condition relating the output position and slope of a ray which traverses an optical transformer to its input position and slope. With p <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> , x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> denoting the canonically conjugate variables of the output ray and p <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> , x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</inf> those of the input ray, the condition derived from Liouville's theorem states that the Jacobian of the transformation is one.
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