The parameters of the transfer matrix describing a first-order optical syst
em that is a cascade of K identical subsystems defined by the transfer matr
ix M are determined from consideration of the subsystem's eigenfunctions. A
condition for the cascade to be cyclic is derived. Particular examples of
cyclic first-order optical systems are presented. Structure and properties
of eigenfunctions of cyclic transforms are considered. A method of optical
signal encryption by use of cyclic first-order systems is proposed. (C) 199
9 Optical Society of America [S0740-3232(99)02610-1].