Parametric resonance in periodic paraxial optical systems

It is theoretically shown that parametric resonance is a commonplace phenomenon in ray and wave propagation through periodic paraxial optical systems subjected to modulation of parameters, such as lensguide structures and optical resonators with time-varying parameters. The analysis is based on the well-known ABCD matrix propagation method of paraxial wave optics and is capable of capturing the occurrence of parametric resonances by use of a multi-scale asymptotic expansion of the difference equations governing ray and wave propagation through the lensguide. Due to the discreteness of the chain, it is shown that resonances usually occur for strictly not-periodic modulation of parameters. The effects of soft (Gaussian) apertures on parametric resonance are also discussed. (C) 2000 Elsevier Science B.V. All rights reserved.