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Transmission Line Formulation for Optical Maser Amplification

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Abstract

The optical maser amplifier is treated from the point of view of distributed lines. Transmission line analogues are set up generally for a system consisting of air, reflector, active medium, reflector, and air again. It is postulated that, in the active medium, the growth of the wave can be looked upon as due to the presence of an effectively negative conductivity. The problem is discussed for three media: air, ruby, air, and the five-media case: air, reflector, ruby, reflector, and air. Calculations are carried out showing that the five-layer case for special conditions can be reduced to a three-layer case. Equations for amplification and oscillation are developed which give the same results as Maiman’s criteria for oscillation and Smiley’s Fabry–Perot analysis for gain. The effective length of the line is estimated and one-dimensional wave propagation is justified on the basis of the small spreading angle. Some of the more recent predictions of gain as a function of length and negative attenuation factor are explained in terms of the impedance matching of an electromagnetic wave in air to the impedance seen at the front surface of the crystal.

© 1964 Optical Society of America

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