Optical wave chaos in a macroscopic open resonator

Jos Dingjan, M.P. van Exter, J.P. Woerdman

Huygens Laboratory
Leiden University, The Netherlands

In recent years, microwave resonators have lead to tremendous experimental progress in the field of wave chaos. Most notably, stadium type billiards have been spectacularly successful. Optical wave chaos has not benefited from this, and progress here has been modest. The primary reason for this is the inherent difficulty in producing and controlling stadium-type resonators in the optical range. Recently, we have put forward a radically new approach to optical wave chaos, using a system that is highly macroscopic, therefore offers unsurpassed control, and allows a wealth of different experimental techniques. We have demonstrated that an open, three-mirror, folded optical cavity can show chaotic dynamics [1]. The key ingredient in this resonator is a curved folding mirror, introducing, even at very modest numerical aperture, considerable aberrations through its use at non-normal incidence. These aberrations cause the paraxial approximation to be violated, making the wave equation describing the intra-cavity field non-separable. The strength of these aberrations crucially influences the chaos in the system. These aberrations, as introduced by the folding mirror, may be modified in two distinct ways: by varying the folding angle of the resonator (changing the angle of incidence on the curved folding mirror), and by varying the effective numerical aperture of the system. In line with expectations, increasing the folding angle of the resonator from 0$^\circ$ to 90$^\circ$ shows a smooth transition from a non-chaotic to a chaotic resonator. Also, increasing the effective numerical aperture, thereby preferentially exciting modes that have appreciable amplitude far from the optical axis of the resonator, leads to increased chaotic behaviour. We expect that this highly versatile and promising approach will boost research into optical wave chaos. At the same time, it may serve as an excellent model system to study many intriguing phenomena in wave chaos in general.

References
[1] J. Dingjan, E. Altewischer, M.P. van Exter, and J.P. Woerdman, Phys. Rev. Lett. 88, 064101 (2002)