Quantum chaos in optical microcavities

• Applicant: Professor Dr. Jan Wiersig
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2007 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 24367642

• Final Report Year: 2014

Final Report Abstract

The topic of project P6 have been optical microcavities in the context of basic research – model systems for quantum chaos – as well as with a strong reference to applications – the emission properties of optical microlasers with the holy grail to achieve unidirectional light emission from high quality modes. The first funding period showed that both aspects merged: The unstable manifold of the chaotic saddle, a really mathematical object, determines the far-field emission pattern and explains all its properties (its robustness, its independence on the resonance chosen) in a very nice, very obvious way. It is also a paradigm example of ray-wave correspondence in open systems. In the second funding period we have, on the one-hand side, deepened our understanding of single optical microcavities and extended it to coupled cavities. We kept close relations to a number of experimental groups with fruitful results. We extended the system class considered by (i) adding Kerrnonlinearities to the index of refraction, (ii) addressing cavities with negative refraction, (iii) investigating lasing vs. non-lasing cavities, (iv) studying fully asymmetric cavities in the context of exceptional points, and (v) considering wavelength-scale cavities that may become relevant for cavity quantum electrodynamics, thereby anticipating the experimental trend and demand. Driven by the application potential, we have continued our search for microcavities with directional emission properties by either perturbing the boundary of single resonators or combining disk resonators. We found interesting and also surprising results that in turn required new models to explain the findings. A central topic have again been semiclassical corrections to the ray dynamics in form of Goos-Hänchen shift and Fresnel filtering. Here we are close to a description that also takes curvature effects into account which rounds-up our achievements on this topic and will help correctly predict the far-field properties of microlasers based on a simple ray-model based description.

Publications

• Directional laser emission from a wavelength-scale chaotic microcavity, Phys. Rev. Lett. 105, 103902 (2010)
  Q.H. Song, L. Ge, A.D. Stone, H.Cao, J. Wiersig, J.-B. Shim, J. Unterhinninghofen, W. Fang, and G. S. Solomon
  
• Electromagnetic modes in cavities made of negative-index metamaterials, Phys. Rev. A 81, 023809 (2010)
  J. Wiersig, J. Unterhinninghofen, H. Schomerus, U. Peschel, M. Hentschel
  
• Whispering-gallery mode resonators for highly unidirectional laser action, Proceedings of Nat. Acad. of Sci. USA 107, 22407 (2010)
  Q. J. Wang, C. Yan, N. Yu, J. Unterhinninghofen, J. Wiersig, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso
  
• Measurement of the Goos-Hänchen shift in a microwave cavity, New J. Phys. 13, 023013 (2011)
  J. Unterhinninghofen, U. Kuhl, J. Wiersig, H.-J. Stöckmann, and M. Hentschel
  
• Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities, Phys. Rev. A 84, 023845 (2011)
  E] J. Wiersig, A. Eberspächer, J.-B. Shim, J.-W. Ryu, S. Shinohara, M. Hentschel, and H. Schomerus
  
• U.S. Patent No. 61/417,650: Highly unidirectional microcavity resonators, Dec 2011
  F. Capasso, Q. J. Wang, N. Yu and J. Wiersig, J. Unterhinninghofen
  
• Whispering gallery modes formed by partial barriers in ultrasmall deformed microdisks, Phys. Rev. E 84, 035202(R) (2011)
  J.-B. Shim, J. Wiersig, and H. Cao
  
• Designing coupled microcavity lasers for high-Q modes with unidirectional light emission, Opt. Lett. 36, 1116 (2012)
  J.-W. Ryu, M. Hentschel
  
• Local Chirality of Optical Resonances in Ultrasmall Resonators, Phys. Rev. Lett. 108, 253902 (2012)
  B. Redding, L. Ge, Q.H. Song, J. Wiersig, G. S. Solomon, and H. Cao
  
• Phase-space analysis of lasing modes in a chaotic microcavity, Phys. Rev. A 88, 023855 (2013)
  T.-Y. Kwon, S.-Y. Lee, J.-W. Ryu, M. Hentschel