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Stability of periodic paraxial optical systems
1Dipartimento di Fisica, Istituto Nazionale per la Fisica della Materia and CEQSE-CNR, Politecnico di Milano, Piazza L. da Vinci, 32 I-20133 Milano, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
Summary
Stable periodic optical systems become unstable with random perturbations, similar to Anderson localization. Finite aperture effects and complex paraxial optics restore stability in these focusing systems.
Area of Science:
- Optics and Photonics
- Wave Propagation
- Disordered Systems
Background:
- Periodic paraxial systems and optical resonators are fundamental in optics.
- Stochastic perturbations can significantly alter system behavior.
- Anderson localization describes wave behavior in disordered media.
Purpose of the Study:
- To investigate the stability of periodic paraxial systems under stochastic perturbations.
- To explore the connection between ray displacement and Anderson localization.
- To identify conditions for restoring stability in focusing systems.
Main Methods:
- Analysis of ray propagation using paraxial geometric optics.
- Mathematical modeling of stochastic perturbations in periodic sequences.
- Incorporation of finite aperture effects and complex paraxial optics.
Main Results:
- Periodic paraxial systems and optical resonators exhibit instability when subjected to stochastic perturbations.
- Ray displacements show exponential divergence, analogous to Anderson localization.
- Stability is re-established by considering finite aperture effects and complex paraxial optics.
Conclusions:
- Stochastic perturbations fundamentally destabilize periodic paraxial optical systems.
- The observed instability is closely related to Anderson localization phenomena.
- Finite aperture and complex paraxial optics are crucial for understanding and restoring stability in optical resonators.
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