The parameters of the transfer matrix describing a first-order optical system that is a cascade of <i>k</i> identical subsystems defined by the transfer matrix <i>M</i> 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.
© 1999 Optical Society of America
Tatiana Alieva and Martin J. Bastiaans, "Powers of transfer matrices determined by means of eigenfunctions," J. Opt. Soc. Am. A 16, 2413-2418 (1999)