Parametric resonance in periodic paraxial optical systems

It is theoretically shown that parametric resonance is a commonplace phenom enon in ray and wave propagation through periodic paraxial optical systems subjected to modulation of parameters, such as lensguide structures and opt ical resonators with time-varying parameters. The analysis is based on the well-known ABCD matrix propagation method of paraxial wave optics and is ca pable of capturing the occurrence of parametric resonances by use of a mult i-scale asymptotic expansion of the difference equations governing ray and wave propagation through the lensguide. Due to the discreteness of the chai n, it is shown that resonances usually occur for strictly not-periodic modu lation of parameters. The effects of soft (Gaussian) apertures on parametri c resonance are also discussed. (C) 2000 Elsevier Science B.V. All rights r eserved.