We suggest a geometrical framework in which to discuss periodic layered structures in the unit disk. Bandgaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic period allows for a classification in three families of orbits with quite different properties. The laws of convergence of the iterates to the unit circle can then be considered universal features of the reflection.
© 2003 Optical Society of America
(000.3860) General : Mathematical methods in physics
(120.5700) Instrumentation, measurement, and metrology : Reflection
(230.4040) Optical devices : Mirrors
(230.4170) Optical devices : Multilayers
Alberto G. Barriuso, Juan J. Monzón, and Luis L. Sánchez-Soto, "General unit-disk representation for periodic multilayers," Opt. Lett. 28, 1501-1503 (2003)