## Modes of random lasers |

Advances in Optics and Photonics, Vol. 3, Issue 1, pp. 88-127 (2011)

http://dx.doi.org/10.1364/AOP.3.000088

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### Abstract

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, directivity, and polarization. In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. We review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. The past decade has witnessed the emergence of the idea that even the low-Q resonances of such open systems could play a role similar to the cavity modes of a conventional laser and produce sharp lasing peaks. We focus here on the near-threshold single-mode lasing regime where nonlinear effects associated with gain saturation and mode competition can be neglected. We discuss in particular the link between random laser modes near threshold and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized (strong scattering) regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime, where it was observed that increasing the openness of such systems eventually resulted in measurable and increasing differences between quasi-bound states and lasing modes. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the threshold lasing modes are in fact distinct from QB states of the passive system and are better described in terms of a new class of states, the so-called constant-flux states. The correspondence between QB states and lasing modes is found to improve in the strong scattering limit, confirming the validity of initial work in the strong scattering limit.

© 2011 Optical Society of America

**OCIS Codes**

(140.3430) Lasers and laser optics : Laser theory

(140.3460) Lasers and laser optics : Lasers

(290.4210) Scattering : Multiple scattering

(260.2710) Physical optics : Inhomogeneous optical media

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: January 21, 2010

Revised Manuscript: August 4, 2010

Manuscript Accepted: August 6, 2010

Published: October 1, 2010

**Virtual Issues**

(2011) *Advances in Optics and Photonics*

**Citation**

J. Andreasen, A. A. Asatryan, L. C. Botten, M. A. Byrne, H. Cao, L. Ge, L. Labonté, P. Sebbah, A. D. Stone, H. E. Türeci, and C. Vanneste, "Modes of random lasers," Adv. Opt. Photon. **3**, 88-127 (2011)

http://www.opticsinfobase.org/aop/abstract.cfm?URI=aop-3-1-88

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### References

- D. S. Wiersma, “The smallest random laser,” Nature 406, 132–135 (2000). [CrossRef]
- H. Cao, “Random lasers with coherent feedback,” in Optical Properties of Nanostructured Random MediaV.M.Shalaev, ed., Vol. 82 of Topics in Applied Physics (Springer-Verlag, 2002), pp. 303–330
- H. Cao, “Lasing in random media,” Waves Random Complex Media 13, R1–R39 (2003). [CrossRef]
- H. Cao, J. Y. Xu, Y. Ling, A. L. Burin, E. W. Seeling, X. Liu, and R. P. H. Chang, “Random lasers with coherent feedback,” IEEE J. Sel. Top. Quantum Electron. 9, 111–118 (2003). [CrossRef]
- D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4, 359–367 (2008). [CrossRef]
- P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109, 1492 (1958). [CrossRef]
- C. Gouedart, D. Husson, C. Sauteret, F. Auzel, and A. Migus, “Generation of spatially incoherent short pulses in laser pumped neodymium stoichiometric crystal powders,” J. Opt. Soc. Am. B 10, 2358–2363 (1993). [CrossRef]
- N. M. Lawandy, R. M. Balachandra, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368, 436–438 (1994). [CrossRef]
- W. L. Sha, C. H. Liu, and R. R. Alfano, “Spectral and temporal measurements of laser action of Rhodamine 640 dye in strongly scattering media,” Opt. Lett. 19, 1922–1924 (1994). [CrossRef]
- H. Cao, Y. G. Zhao, H. C. Ong, S. T. Ho, J. Y. Dai, J. Y. Wu, and R. P. H. Chang, “Ultraviolet lasing in resonators formed by scattering in semiconductor polycristalline films,” Appl. Phys. Lett. 73, 3656–3658 (1998). [CrossRef]
- H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang, and R. P. H. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82, 2278–2281 (1999). [CrossRef]
- H. Cao, Y. G. Zhao, H. C. Ong, and R. P. H. Chang, “Far-field characteristics of random lasers,” Phys. Rev. B 59, 15107–15111 (1999). [CrossRef]
- S. V. Frolov, Z. V. Vardeny, K. Yoshino, A. Zakhidov, and R. H. Baughman, “Stimulated emission in high-gain organic media,” Phys. Rev. B 59, R5284–R5287 (1999). [CrossRef]
- H. Cao, J. Y. Xu, D. Z. Zhang, S.-H. Chang, S. T. Ho, E. W. Seelig, X. Liu, and R. P. H. Chang, “Spatial confinement of laser light in active random media,” Phys. Rev. Lett. 84, 5584–5587 (2000). [CrossRef]
- H. Cao, Y. Ling, J. Y. Xu, C. Q. Cao, and C. Q. Cao, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86, 4524–4527 (2001). [CrossRef]
- A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009). [CrossRef]
- V. Milner and A. Z. Genack, “Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization,” Phys. Rev. Lett. 94, 073901 (2005). [CrossRef]
- K. L. van der Molen, R. W. Tjerkstra, A. P. Mosk, and A. Lagendijk, “Spatial extent of random laser modes,” Phys. Rev. Lett. 98, 143901 (2007). [CrossRef]
- V. M. Apalkov, M. E. Raikh, and B. Shapiro, “Random resonators and prelocalized modes in disordered dielectric films,” Phys. Rev. Lett. 89, 016802 (2002). [CrossRef]
- V. M. ApalkovM. E. Raikh, and B. Shapiro, “Almost localized photon modes in continuous and discrete models of disordered media,” J. Opt. Soc. Am. B 21, 132–140 (2004). [CrossRef]
- S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93, 053903 (2004). [CrossRef]
- S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76, 033807 (2007). [CrossRef]
- A. A. Chabanov, Z. Q. Zhang, and A. Z. Genack, “Breakdown of diffusion in dynamics of extended waves in mesoscopic media,” Phys. Rev. Lett. 90, 203903 (2003). [CrossRef]
- J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nat. Photonics 3, 279–282 (2009). [CrossRef]
- X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85, 70–73 (2000). [CrossRef]
- C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001). [CrossRef]
- P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66, 144202 (2002). [CrossRef]
- C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98, 143902 (2007). [CrossRef]
- C. Vanneste and P. Sebbah, “Complexity of two-dimensional quasimodes at the transition from weak scattering to Anderson localization,” Phys. Rev. A 79, 041802(R) (2009). [CrossRef]
- X. Wu, W. Fang, A. Yamilov, A. A. Chabanov, A. A. Asatryan, L. C. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74, 053812 (2006). [CrossRef]
- H. E. Türeci, A. D. Stone, and B. Collier, “Self-consistent multimode lasing theory for complex or random lasing media,” Phys. Rev. A 74, 043822 (2006). [CrossRef]
- H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76, 013813 (2007). [CrossRef]
- H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320, 643 (2008). [CrossRef]
- L. Ge, R. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16, 16895 (2008). [CrossRef]
- H. E. Türeci, A. D. Stone, L. Ge, S. Rotter, and R. J. Tandy, “Ab initio self-consistent laser theory and random lasers,” Nonlinearity 22, C1–C18 (2009). [CrossRef]
- P. Sebbah, D. Sornette, and C. Vanneste, “Anomalous diffusion in two-dimensional Anderson-localization dynamics,” Phys. Rev. B 48, 12506–12510(1993). [CrossRef]
- F. A. Pinheiro, M. Rusek, A. Orlowski, and B. A. van Tiggelen, “Probing Anderson localization of light via decay rate statistic,” Phys. Rev. E 69, 026605 (2004). [CrossRef]
- The idea of considering localized modes for random lasing can already be found in P. Sebbah, D. Sornette, and C. Vanneste, “Wave automaton for wave propagation in the time domain,” Advances in Optical Imaging and Photon Migration, R.R.Alfano, ed., Vol. 21 of OSA Proceedings Series (Optical Society of America, 1994), p.68 (1994), and Ref. .
- P. Sebbah, “A new approach for the study of wave propagation and localization,” Ph.D. thesis (Université de Nice—Sophia Antipolis, 1993).
- A. E. Siegman, Lasers (University Science Books, 1986).
- A. Taflove, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech House, 1995).
- J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1995). [CrossRef]
- X. Jiang and C. M. Soukoulis, “Localized random lasing modes and a path for observing localization,” Phys. Rev. E 65, 025601(R) (2002). [CrossRef]
- A. G. Fox and T. Li, “Resonant modes in an optical maser,” Proc. IRE 48, 1904–1905 (1960).
- A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
- S. M. Dutra and G. Nienhuis, “Quantized mode of a leaky cavity,” Phys. Rev. A 62, 063805 (2000). [CrossRef]
- J. C. J. Paasschens, T. Sh. Misirpashaev, and C. W. J. Beenakker, “Localization of light: dual symmetry between absorption and amplification,” Phys. Rev. B 54, 11887–11890 (1996). [CrossRef]
- A. A. Asatryan, N. A. Nicorovici, L. C. Botten, M. C. de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57, 13535–13549 (1998). [CrossRef]
- X. Jiang, Q. Li, and C. M. Soukoulis, “Symmetry between absorption and amplification in disordered media,” Phys. Rev. B 59, R9007–R9010 (1999). [CrossRef]
- X. Wu, J. Andreasen, H. Cao, and A. Yamilov, “Effect of local pumping on random laser modes in one dimension,” J. Opt. Soc. Am. B 24, A26–A33 (2007). [CrossRef]
- D. Felbacq, G. Tayeb, and D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 11, 2526–2538 (1994). [CrossRef]
- E. Centeno and D. Felbacq, “Characterization of defect modes in finite bidimensional photonic crystals,” J. Opt. Soc. Am. A 16, 2705–2712 (1999). [CrossRef]
- A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. M. de Sterke, and N. A. Nicorovici, “Two-dimensional Green tensor and local density of states in finite-sized two-dimensional photonic crystals,” Waves Random Complex Media 13, 9–25 (2003). [CrossRef]
- A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E 63, 046612 (2001). [CrossRef]
- A. A. Asatryan, L. C. Botten, N. A. Nicorovici, R. C. McPhedran, and C. Martijn de Sterke, “Frequency shift of sources embedded in finite two-dimensional photonic clusters,” Waves Random Complex Media 16, 151–165 (2006). [CrossRef]
- K. M. Lo, R. C. McPhedran, I. M. Bassett and G. W. Milton, “An electromagnetic theory of optical wave-guides with multiple embedded cylinders,” J. Lightwave Technol. 12, 396–410 (1994). [CrossRef]
- T. P. White, B. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers I: formulation,” J. Opt. Soc. Am. B 10, 2322–2330 (2002). [CrossRef]
- B. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. Martijn de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers II: implementation and results,” J. Opt. Soc. Am. B 10, 2331–2340 (2002). [CrossRef]
- D. P. Fussell, R. C. McPhedran, C. Martijn de Sterke, and A. A. Asatryan, “Three-dimensional local density of states in a finite two-dimensional photonic crystal composed of cylinders,” Phys. Rev. E 67, 045601(R) (2003). [CrossRef]
- J. Jin, The Finite Element Method in Electromagnetics (Wiley, 1993).
- M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1982).
- H. Haken, Light: Laser Dynamics (North-Holland, 1985), vol. 2.
- Recently it was shown that one can define a variant of the CF states, termed the threshold constant flux (TCF) states, for which one TCF state is the TLM. Above threshold additional TCF states are needed to describe the lasing modes, but in general fewer than for the CF states defined here. The above threshold theory using these TCF states is almost identical to the theory described in . Details are in L. Ge, Y. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” arXiv.org, arXiv:1008.0628v1 (submitted to Phys. Rev. A).
- Ü. Pekel and R. Mittra, “A finite-element-method frequency-domain application of the perfectly matched layer (PML) concept,” Microwave Opt. Technol. Lett. 9(3) 117–122 (2007). [CrossRef]
- P. Ambre, “Modélisation et caractérisation des fibres microstructurées air/silice pour application aux télécommunications optiques,” Ph.D. thèses (Université de Limoges, 2003).

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