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Universal single-mode lasing in fully chaotic two-dimensional microcavity lasers under continuous-wave operation with large pumping power [Invited]

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Abstract

For a fully chaotic two-dimensional (2D) microcavity laser, we present a theory that guarantees both the existence of a stable single-mode lasing state and the nonexistence of a stable multimode lasing state, under the assumptions that the cavity size is much larger than the wavelength and the external pumping power is sufficiently large. It is theoretically shown that these universal spectral characteristics arise from the synergistic effect of two different kinds of nonlinearities: deformation of the cavity shape and mode interaction due to a lasing medium. Our theory is based on the linear stability analysis of stationary states for the Maxwell–Bloch equations and accounts for single-mode lasing phenomena observed in real and numerical experiments of fully chaotic 2D microcavity lasers.

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DOI:10.1364/prj.5.000b39

基金项目:Waseda University10.13039/501100004423 (2017B-197).

收稿日期:2017-08-02

录用日期:2017-10-18

网络出版日期:2017-10-24

作者单位    点击查看

Takahisa Harayama:Department of Applied Physics, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Satoshi Sunada:Faculty of Mechanical Engineering, Institute of Science and Engineering, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan
Susumu Shinohara:Department of Applied Physics, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

联系人作者:Takahisa Harayama(harayama@waseda.jp)

【1】H.-J. St?ckmann, Quantum Chaos: An Introduction (Cambridge University, 1999).

【2】F. Haake, Quantum Signatures of Chaos (Springer, 2000).

【3】K. Nakamura, and T. Harayama, Quantum Chaos and Quantum Dots (Oxford University, 2004).

【4】O. Bohigas, M. J. Giannoni, and C. Schmit, “Characterization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett. 52 , 1–4 (1984).

【5】G. Casati, F. Valz-Gris, and I. Guarneri, “On the connection between quantization of nonintegrable systems and statistical theory of spectra,” Lett. Nuovo Cimento Soc. Ital. Fis. 28 , 279–282 (1980).

【6】M. V. Berry, “Quantizing a classically ergodic system: Sinai’s billiard and the KKR method,” Ann. Phys. (N.Y.) 131 , 163–216 (1981).

【7】M. V. Berry, “Semiclassical theory of spectral rigidity,” Proc. R. Soc. London Ser. A 400 , 229–251 (1985).

【8】M. Sieber, “Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems,” J. Phys. A 35 , L613–L619 (2002).

【9】S. Müller, S. Heusler, P. Braun, F. Haake, and A. Altland, “Periodic-orbit theory of universality in quantum chaos,” Phys. Rev. Lett. 93 , 014103 (2004).

【10】S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake, “Periodic-orbit theory of level correlations,” Phys. Rev. Lett. 98 , 044103 (2007).

【11】M. Sieber, and K. Richter, “Correlations between periodic orbits and their role in spectral statistics,” Phys. Scr. T90 , 128–133 (2001).

【12】R. A. Jalabert, H. U. Baranger, and A. D. Stone, “Conductance fluctuations in the ballistic regime: a probe of quantum chaos?” Phys. Rev. Lett. 65 , 2442–2445 (1990).

【13】C. M. Marcus, A. J. Rimberg, R. M. Westervelt, P. F. Hopkins, and A. C. Gossard, “Conductance fluctuations and chaotic scattering in ballistic microstructures,” Phys. Rev. Lett. 69 , 506–509 (1992).

【14】J. U. N?ckel, and A. D. Stone, “Ray and wave chaos in asymmetric resonant optical cavities,” Nature 385 , 45–47 (1997).

【15】C. Gmachl, F. Capasso, E. E. Narimanov, J. U. N?ckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280 , 1556–1564 (1998).

【16】S.-B. Lee, J.-H. Lee, J.-S. Chang, H.-J. Moon, S. W. Kim, and K. An, “Observation of scarred modes in asymmetrically deformed microcylinder lasers,” Phys. Rev. Lett. 88 , 033903 (2002).

【17】S.-Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C.-M. Kim, “Quasiscarred resonances in a spiral-shaped microcavity,” Phys. Rev. Lett. 93 , 164102 (2004).

【18】H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21 , 923–934 (2004).

【19】V. A. Podolskiy, E. Narimanov, W. Fang, and H. Cao, “Chaotic microlasers based on dynamical localization,” Proc. Natl. Acad. Sci. USA 101 , 10498–10500 (2004).

【20】J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97 , 253901 (2006).

【21】J. Wiersig, and M. Hentschel, “Combining directional light output and ultralow loss in deformed microdisks,” Phys. Rev. Lett. 100 , 033901 (2008).

【22】E. Bogomolny, R. Dubertrand, and C. Schmit, “Trace formula for dieletric cavities: I. General properties,” Phys. Rev. E 78 , 056202 (2008).

【23】S. Shinohara, T. Harayama, T. Fukushima, M. Hentschel, T. Sasaki, and E. E. Narimanov, “Chaos-assisted directional light emission from microcavity lasers,” Phys. Rev. Lett. 104 , 163902 (2010).

【24】Q. Song, L. Ge, B. Redding, and H. Cao, “Channeling chaotic rays into waveguides for efficient collection of microcavity emission,” Phys. Rev. Lett. 108 , 243902 (2012).

【25】R. Sarma, L. Ge, J. Wiersig, and H. Cao, “Rotating optical microcavities with broken chiral symmetry,” Phys. Rev. Lett. 114 , 053903 (2015).

【26】H. Cao, and J. Wiersig, “Dielectric microcavities: model systems for wave chaos and non-Hermitian physics,” Rev. Mod. Phys. 87 , 61–111 (2015).

【27】T. Harayama, and S. Shinohara, “Two-dimensional microcavity lasers,” Laser Photon. Rev. 5 , 247–271 (2011).

【28】S. Sunada, T. Fukushima, S. Shinohara, T. Harayama, and M. Adachi, “Stable single-wavelength emission from fully chaotic microcavity lasers,” Phys. Rev. A 88 , 013802 (2013).

【29】S. Sunada, S. Shinohara, T. Fukushima, and T. Harayama, “Signature of wave chaos in spectral characteristics of microcavity lasers,” Phys. Rev. Lett. 116 , 203903 (2016).

【30】M. Fisher, “The renormalization group in the theory of critical behavior,” Rev. Mod. Phys. 46 , 597–616 (1974).

【31】T. Harayama, P. Davis, and K. S. Ikeda, “Stable oscillations of a spatially chaotic wave function in a microstadium laser,” Phys. Rev. Lett. 90 , 063901 (2003).

【32】T. Harayama, S. Sunada, and K. S. Ikeda, “Theory of two-dimensional microcavity lasers,” Phys. Rev. A 72 , 013803 (2005).

【33】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).

【34】H. E. Türeci, A. D. Stone, and L. Ge, “Theory of the spatial structure of nonlinear lasing modes,” Phys. Rev. A 76 , 013813 (2007).

【35】W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134 , A1429–A1450 (1964).

【36】M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, 1974).

【37】M. Sargent, “Theory of a multimode quasiequilibrium semiconductor laser,” Phys. Rev. A 48 , 717–726 (1993).

【38】T. Harayama, T. Fukushima, S. Sunada, and K. S. Ikeda, “Asymmetric stationary lasing patterns in 2D symmetric microcavities,” Phys. Rev. Lett. 91 , 073903 (2003).

【39】H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320 , 643–646 (2008).

【40】L. Ge, R. J. Tandy, A. D. Stone, and H. E. Türeci, “Quantitative verification of ab initio self-consistent laser theory,” Opt. Express 16 , 16895–16902 (2008).

【41】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).

【42】L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82 , 063824 (2010).

【43】A. Cerjan, and A. D. Stone, “Steady-state ab initio theory of lasers with injected signals,” Phys. Rev. A 90 , 013840 (2014).

【44】S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K. G. Makris, and A. D. Stone, “Scalable numerical approach for the steady-state ab initio laser theory,” Phys. Rev. A 90 , 023816 (2014).

【45】A. Pick, A. Cerjan, D. Liu, A. W. Rodriguez, A. D. Stone, Y. D. Chong, and S. G. Johnson, “Ab initio multimode linewidth theory for arbitrary inhomogeneous laser cavities,” Phys. Rev. A 91 , 063806 (2015).

【46】A. I. Shnirelman, “Ergodic properties of eigenfunctions,” Usp. Mat. Nauk 29 , 181–182 (1974).

【47】Y. Colin de Verdie’re, “Ergodicité et fonctions propres du laplacien,” Commun. Math. Phys. 102 , 497–502 (1985).

【48】S. Zelditch, “Uniform distribution of eigenfunctions on compact hyperbolic surfaces,” Duke Math. J. 55 , 919–941 (1987).

【49】B. Helffer, A. Martinez, and D. Robert, “Ergodicité et limite semiclassique,” Commun. Math. Phys. 109 , 313–326 (1987).

【50】S. Zelditch, and M. Zworski, “Ergodicity of eigenfunctions for ergodic billiards,” Commun. Math. Phys. 175 , 673–682 (1996).

【51】A. B?cker, R. Schubert, and P. Stifter, “Rate of quantum ergodicity in Euclidean billiards,” Phys. Rev. E 57 , 5425–5447 (1998).

【52】H. Schomerus, and J. Tworzydlo, “Quantum-to-classical crossover of quasibound states in open quantum systems,” Phys. Rev. Lett. 93 , 154102 (2004).

【53】S. Nonnenmacher, and M. Zworski, “Fractal Weyl laws in discrete models of chaotic scattering,” J. Phys. A 38 , 10683–10702 (2005).

【54】J. P. Keating, M. Novaes, S. D. Prado, and M. Sieber, “Semiclassical structure of chaotic resonance eigenfunctions,” Phys. Rev. Lett. 97 , 150406 (2006).

【55】D. L. Shepelyansky, “Fractal Weyl law for quantum fractal eigenstates,” Phys. Rev. E 77 , 015202(R) (2008).

【56】M. Novaes, “Resonances in open quantum maps,” J. Phys. A 46 , 143001 (2013).

【57】T. Harayama, and S. Shinohara, “Ray-wave correspondence in chaotic dielectric billiards,” Phys. Rev. E 92 , 042916 (2015).

【58】E. G. Altmann, “Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics,” Phys. Rev. A 79 , 013830 (2009).

【59】B. Redding, A. Cerjan, X. Huang, M. L. Lee, A. D. Stone, M. A. Choma, and H. Cao, “Low-spatial coherence electrically-pumped semiconductor laser for speckle-free full-field imaging,” Proc. Natl. Acad. Sci. USA 112 , 1304–1309 (2015).

【60】M. Choi, S. Shinohara, and T. Harayama, “Dependence of far-field characteristics on the number of lasing modes in stadium-shaped InGaAsP microlasers,” Opt. Express 16 , 17544–17559 (2008).

【61】A. Cerjan, B. Redding, L. Ge, S. F. Liew, H. Cao, and A. D. Stone, “Controlling mode competition by tailoring the spatial pump distribution in a laser: a resonance-based approach,” Opt. Express 24 , 26006–26015 (2016).

【62】S. Sunada, T. Harayama, and K. S. Ikeda, “Multimode lasing in fully chaotic cavity lasers,” Phys. Rev. E 71 , 046209 (2005).

【63】H. Fu, and H. Haken, “Multifrequency operation in a short-cavity standing-wave laser,” Phys. Rev. A 43 , 2446–2454 (1991).

引用该论文

Takahisa Harayama, Satoshi Sunada, and Susumu Shinohara, "Universal single-mode lasing in fully chaotic two-dimensional microcavity lasers under continuous-wave operation with large pumping power [Invited]," Photonics Research 5(6), B39 (2017)

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