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Suppression of interactions in multimode random lasers in the Anderson localized regime

Nature Photonics volume 7, pages 66–71 (2013)Cite this article

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Abstract

Understanding random lasing is a formidable theoretical challenge. Unlike conventional lasers, random lasers have no resonator to trap light, they are highly multimode with potentially strong modal interactions, and they are based on disordered gain media, where photons undergo random multiple scattering. Interference effects notoriously modify the propagation of waves in such random media, but their fate in the presence of nonlinearity and interactions is poorly understood. Here, we present a semiclassical theory for multimode random lasing in the strongly scattering regime. We show that Anderson localization, a wave interference effect, is not affected by the presence of nonlinearities. To the contrary, its presence suppresses interactions between simultaneously lasing modes. Consequently, each lasing mode in a strongly scattering random laser is given by a single long-lived, Anderson localized mode of the passive cavity, the frequency and wave profile of which do not vary with pumping, even in the multimode regime when modes spatially overlap.

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Figure 1: Evolution of lasing modes as a function of pump strength D0 for a non-absorbing, Anderson localized, half-open 1d microcavity laser.
Figure 2: Overlapping lasing modes in the Anderson localized regime.
Figure 3: Stability of the lasing mode spatial profile.
Figure 4: Onset of modal interactions in an absorbing or weakly scattering cavity.

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References

  1. Ishimaru, A. Wave Propagation and Scattering in Random Media (Academic Press, 1978).

    MATH  Google Scholar 

  2. Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  3. Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    Article  ADS  Google Scholar 

  4. Lagendijk, A., van Tiggelen, B. & Wiersma, D. S. Fifty years of Anderson localization. Phys. Today 62, 24–29 (2009).

    Article  Google Scholar 

  5. Kuga, Y. & Ishimaru, A. Retroreflectance from a dense distribution of spherical particles. J. Opt. Soc. Am. A 1, 831–835 (1984).

    Article  ADS  Google Scholar 

  6. Van Albada, M. P. & Lagendijk, A. Observation of weak localization of light in a random medium. Phys. Rev. Lett. 55, 2692–2695 (1985).

    Article  ADS  Google Scholar 

  7. Wolf, P. E. & Maret, G. Weak localization and coherent backscattering of photons in disordered media. Phys. Rev. Lett. 55, 2696–2699 (1985).

    Article  ADS  Google Scholar 

  8. Meystre, P. & Sargent, M. Elements of Quantum Optics 3rd edn (Springer, 1999).

    Book  Google Scholar 

  9. Cao, H. et al. Random laser action in semiconductor powder. Phys. Rev. Lett. 82, 2278–2281 (1999).

    Article  ADS  Google Scholar 

  10. Frolov, S. V., Vardeny, Z. V., Yoshino, K., Zakhidov, A. & Baughman, R. H. Stimulated emission in high-gain organic media. Phys. Rev. B 59, R5284–R5287 (1999).

    Article  ADS  Google Scholar 

  11. Wiersma, D. S. The physics and applications of random lasers. Nature Phys. 4, 359–367 (2008).

    Article  ADS  Google Scholar 

  12. Zaitsev, O., Deych, L. & Shuvayev, V. Statistical properties of one-dimensional random lasers. Phys. Rev. Lett. 102, 043906 (2009).

    Article  ADS  Google Scholar 

  13. Jiang, X. & Soukoulis, C. M. Time dependent theory for random lasers. Phys. Rev. Lett. 85, 70–73 (2000).

    Article  ADS  Google Scholar 

  14. Vanneste, C. & Sebbah, P. Selective excitation of localized modes in active random media. Phys. Rev. Lett. 87, 183903 (2001).

    Article  ADS  Google Scholar 

  15. Apalkov, V. M., Raikh, M. E. & Shapiro, B. Almost localized photon modes in continuous and discrete models of disordered media. J. Opt. Soc. Am. B 21, 132–140 (2004).

    Article  ADS  Google Scholar 

  16. Vanneste, C., Sebbah, P. & Cao, H. Lasing with resonant feedback in weakly scattering random systems. Phys. Rev. Lett. 98, 143902 (2007).

    Article  ADS  Google Scholar 

  17. Türeci, H. E., Ge, L., Rotter, S. & Stone, A. D. Strong interactions in multimode random lasers. Science 320, 643–646 (2008).

    Article  ADS  Google Scholar 

  18. Mujumdar, S., Ricci, M., Torre, R. & Wiersma, D. S. Amplified extended modes in random lasers. Phys. Rev. Lett. 93, 053903 (2004).

    Article  ADS  Google Scholar 

  19. Tulek, A., Polson, R. C. & Vardeny, Z. V. Naturally occurring resonators in random lasing of π-conjugated polymer films. Nature Phys. 6, 303–310 (2010).

    Article  ADS  Google Scholar 

  20. Van der Molen, K. L., Tjerkstra, R. W., Mosk, A. P. & Lagendijk, A. Spatial extent of random laser modes. Phys. Rev. Lett. 98, 143901 (2007).

    Article  ADS  Google Scholar 

  21. Fallert, J. et al. Co-existence of strongly and weakly localized random laser modes. Nature Photon. 3, 279–282 (2009).

    Article  ADS  Google Scholar 

  22. Milner, V. & Genack, A. Z. Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization. Phys. Rev. Lett. 94, 073901 (2005).

    Article  ADS  Google Scholar 

  23. Starykh, O. A., Jacquod, P. R. J., Narimanov, E. E. & Stone, A. D. Signature of dynamical localization in the resonance width distribution of wave-chaotic dielectric cavities. Phys. Rev. E 62, 2078–2084 (2000).

    Article  ADS  Google Scholar 

  24. Türeci, H. E., Stone, A. D. & Collier, B. Self-consistent multimode lasing theory for complex or random lasing media. Phys. Rev. A 74, 043822 (2006).

    Article  ADS  Google Scholar 

  25. Türeci, H. E., Stone, A. D. & Ge, L. Theory of the spatial structure of nonlinear lasing modes. Phys. Rev. A 76, 013813 (2007).

    Article  ADS  Google Scholar 

  26. Ivanov, D. A., Skvortsov, M. A., Ostrovsky, P. M. & Fominov, Ya. V. Hybridization of wave functions in one-dimensional localization. Phys. Rev. B 85, 035109 (2012).

    Article  ADS  Google Scholar 

  27. Haken, H. Light: Laser Light Dynamics Vol. 2 (North-Holland, 1985).

    Google Scholar 

  28. Mirlin, A. D. Statistics of energy levels and eigenfunctions in disordered systems. Phys. Rep. 326, 259–382 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  29. Andreasen, J. & Cao, H. Numerical study of amplified spontaneous emission and lasing in random media. Phys. Rev. A 82, 063835 (2010).

    Article  ADS  Google Scholar 

  30. Liu, J. et al. An Anderson-localized random nanolaser. Preprint at http://arXiv.org/abs/1210.4764 (2012).

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Acknowledgements

The authors thank A. Cerjan, L. Ge, A.D. Stone and H. Türeci for helpful discussions on various aspects of their lasing theory, and D. Ivanov for discussions on wavefunction correlations with Anderson localization. This work was supported by the National Science Foundation (grant no. PHY-1001017). P.J. acknowledges support from the Swiss Center of Excellence MANEP and P.S. acknowledges support from SCIEX and CE SAV QUTE NFP26240120022.

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Authors and Affiliations

  1. Institute of Physics, Slovak Academy of Sciences, Bratislava, 845 11, Slovakia

    Peter Stano

  2. Department of Physics, University of Basel, Klingelbergstrasse 82, Basel, CH-4056, Switzerland

    Peter Stano

  3. Physics Department, University of Arizona, 1118 E 4th Street, Tucson, 85721, Arizona, USA

    Philippe Jacquod

  4. College of Optical Sciences, University of Arizona, Tucson, 85721, Arizona, USA

    Philippe Jacquod

  5. Départment de Physique Théorique, Université de Genève, Genève, CH-1211, Switzerland

    Philippe Jacquod

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  1. Peter Stano
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  2. Philippe Jacquod
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P.S. wrote the numerical codes and performed the numerical calculations. Both authors worked on the theoretical calculations and participated in discussion of the data and writing of the manuscript.

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Correspondence to Philippe Jacquod.

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The authors declare no competing financial interests.

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Stano, P., Jacquod, P. Suppression of interactions in multimode random lasers in the Anderson localized regime. Nature Photon 7, 66–71 (2013). https://doi.org/10.1038/nphoton.2012.298

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