Imperfections in Active Transmission Lines

In the present paper we consider the theory of active transmission lines (i.e., lines with gain) with discrete imperfections. Roth equally spaced, identical imperfections and random imperfections will be considered. This study was suggested by R. Kompfner as a rough mathematical model for the effects of imperfections in certain types of optical maser amplifiers, in which the optical signal is reflected back and forth through the active medium on essentially nonoverlapping paths by an array of mirrors. A. G. Fox has suggested that this mathematical model will also provide a description of a one-dimensional active medium (e.g., maser) with (one-dimensional) random inhomogencities. Consider an active transmission line that provides exponential gain to both forward and backward waves, and further provides distortionless amplification. The voltage (and current) then vary as e~Vz -- forward wave, +r« , , , c -- backward wave, 201 (D 262 T H E B E L L S Y S T E M TECHNICAL J O U R N A L , J A N U A R Y 1964