Application of the Model of “Quantum” Metamaterials: Regular and Stochastic Dynamics of Nanolaser (Spaser)

  • Arkadi ChipoulineEmail author
  • Franko Küppers
Part of the Springer Series in Optical Sciences book series (SSOS, volume 211)


One of the main drawbacks of plasmonic nanostructures, restricting their potential application, is the intrinsic (ohmic) losses caused by the interaction of the free electrons of the metal with thermostat (irreversible losses) and radiative losses. The more localized light is to the metal surface, the more concentrated the plasmonic field fraction is inside the metal resulting in the appearance of higher dissipative losses (Maier in Opt Express 14:1957, 2006, 1).


  1. 1.
    S. Maier, Plasmonic field enhancement and SERS in the effective mode volume picture. Opt. Express 14, 1957 (2006)CrossRefGoogle Scholar
  2. 2.
    A.D. Boardman, Electromagnetic Surface Modes (Wiley, New York, 1982)Google Scholar
  3. 3.
    H. Raether, Surface Plasmons (Springer, New York, 1988)Google Scholar
  4. 4.
    C. Soukoulis, M. Wegener, Optical metamaterials—more bulky and less lossy. Science 330, 1633 (2010)CrossRefGoogle Scholar
  5. 5.
    A. Boltasseva, H. Atwater, Low-loss plasmonic metamaterials. Science 331, 290 (2011)CrossRefGoogle Scholar
  6. 6.
    S. Anlage, The physics and applications of superconducting metamaterials. J. Opt. 13, 024001 (2011)CrossRefGoogle Scholar
  7. 7.
    H.-T. Chen et al., Tuning the resonance in high-temperature superconducting terahertz metamaterials. PRL 105, 247402 (2010)Google Scholar
  8. 8.
    P. Berini, I. De Leon, Surface plasmon–polariton amplifiers and lasers. Nat. Photon. 6, 16 (2011)CrossRefGoogle Scholar
  9. 9.
    C. Soukoulis, M. Wegener, Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nat. Photon. 5, 523–530 (2011)CrossRefGoogle Scholar
  10. 10.
    W.L. Barnes, Fluorescence near interfaces: the role of photonic mode density. J. Mod. Opt. 45, 661 (1998)CrossRefGoogle Scholar
  11. 11.
    S. Ramakrishna, J. Pendry, Removal of absorption and increase in resolution in a near-field lens via optical gain. Phys. Rev. B 67, 201101(R) (2003)CrossRefGoogle Scholar
  12. 12.
    D.J. Bergman, M.I. Stockman, PRL 90, 027402 (2003)CrossRefGoogle Scholar
  13. 13.
    E.M. Purcell, Phys. Rev. 69, 681 (1946)CrossRefGoogle Scholar
  14. 14.
    A.F. Koenderink, On the use of Purcell factors for plasmon antennas. Opt. Lett. 35, 4208 (2010)CrossRefGoogle Scholar
  15. 15.
    N. Blombergen, R. Pound, Phys. Rev. 95, 8 (1954)CrossRefGoogle Scholar
  16. 16.
    M. Strandberg, Phys. Rev. 106, 617 (1957)CrossRefGoogle Scholar
  17. 17.
    F. Bunkin, A. Oraevsky, Izv. Vuzov. Radiophysika 2(2), 181 (1959)Google Scholar
  18. 18.
    O. Hess, J.B. Pendry, S.A. Maier, R.F. Oulton, J.M. Hamm, K.L. Tsakmakidis, Active nanoplasmonic metamaterials. Nat. Mater. 11, 573 (2012)CrossRefGoogle Scholar
  19. 19.
    N. Liu, L. Langguth, J.K.T. Weiss, M. Fleischhauer, T. Pfau, H. Giessen, Nat. Mater. 8, 758 (2009)CrossRefGoogle Scholar
  20. 20.
    C. Rockstuhl et al., Resonances of split-ring resonator metamaterials in the near infrared. Appl. Phys. B 84, 219–227 (2006)CrossRefGoogle Scholar
  21. 21.
    M. Husnik et al., Absolute extinction cross-section of individual magnetic split-ring resonators. Nat. Photon. 2, 614 (2008)CrossRefGoogle Scholar
  22. 22.
    D.E. Chang, A.S. Sorensen, P.R. Hemmer, M.D. Lukin, PRL 97, 053002 (2006)Google Scholar
  23. 23.
    D. Martin-Cano, L. Martin-Moreno, F. Garcia-Vidal, E. Moreno, Nano Lett. 10, 3129 (2010)CrossRefGoogle Scholar
  24. 24.
    V.V. Klimov, Nanoplasmonics. Phys. Usp. 51(8), 839–844 (2008)CrossRefGoogle Scholar
  25. 25.
    V.V. Klimov, Nanoplasmonika. ISBN 978-5-9221-1205-5 (2010) (in Russian)Google Scholar
  26. 26.
    M. Stockman, Spaser explained. Nat. Photonics 2, 327 (2008)CrossRefGoogle Scholar
  27. 27.
    M. Stockman, The spaser as a nanoscale quantum generator and amplifier. J. Opt. 12, 024004 (2010)CrossRefGoogle Scholar
  28. 28.
    M. Stockman, Spaser action, loss-compensation, and stability in plasmonic systems with gain. PRL 106, 156802 (2011)CrossRefGoogle Scholar
  29. 29.
    N. Zheludev, S. Prosvirin, N. Papasimakis, V. Fedotov, Lasing spaser. Nat. Photonics 2, 351 (2008)CrossRefGoogle Scholar
  30. 30.
    M. Noginov, G. Zhu, A. Belgrave, R. Bakker, V. Shalaev, E. Narimanov, S. Stout, E. Herz, T. Suteewong, U. Wiesner, Demonstration of a spaser-based nanolaser. Nature 460, 1110 (2009)CrossRefGoogle Scholar
  31. 31.
    R. Oulton, V. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, Plasmon lasers at deep subwavelength scale. Nature 461, 629 (2009)CrossRefGoogle Scholar
  32. 32.
    M. Hill, M. Marell, E. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. van Veldhoven, E. Jan Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, M. Smit, Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides. Opt. Express 17, 11107 (2009)CrossRefGoogle Scholar
  33. 33.
    Z. Zhu, H. Liu, S. Wang, T. Li, J. Cao, W. Ye, X. Yuan, S. Zhu, Optically pumped nanolaser based on two magnetic plasmon resonance modes. APL 94, 103106 (2009)Google Scholar
  34. 34.
    A. Banerjee, R. Li, H. Grebel, Surface plasmon lasers with quantum dots as gain media. APL 95, 251106 (2009)Google Scholar
  35. 35.
    M. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, Y. Fainman, Room-temperature subwavelength metallo-dielectric lasers. Nat. Photon. 4, 395 (2010)CrossRefGoogle Scholar
  36. 36.
    R.-M. Ma, R. Oulton, V. Sorger, G. Bartal, X. Zhang, Room-temperature sub-diffraction-limited plasmon laser by total internal reflection. Nat. Mater. 10, 110 (2011)CrossRefGoogle Scholar
  37. 37.
    R.A. Flynn, C.S. Kim, I. Vurgaftman, M. Kim, J.R. Meyer, A.J. Mäkinen, K. Bussmann, L. Cheng, F.-S. Choa, J.P. Long, A room-temperature semiconductor spaser operating near 1.5 μm. Opt. Express 19, 8954 (2011)CrossRefGoogle Scholar
  38. 38.
    C.-Y. Wu, C.-T. Kuo, C.-Y. Wang, C.-L. He, M.-H. Lin, H. Ahn, S. Gwo, Plasmonic green nanolaser based on a metal-oxide-semiconductor structure. Nano Lett. 11, 4256 (2011)CrossRefGoogle Scholar
  39. 39.
    E. Plum, V.A. Fedotov, P. Kuo, D.P. Tsai, N.I. Zheludev, Opt. Express 17, 8548 (2009)CrossRefGoogle Scholar
  40. 40.
    Y. Lu, C.-Y. Wang, J. Kim, H.-Y. Chen, M.-Y. Lu, Y.-C. Chen, W.-H. Chang, L.-J. Chen, M.I. Stockman, C.-K. Shih, S. Gwo, Nano Lett. 14, 4381 (2014)CrossRefGoogle Scholar
  41. 41.
    R. Ma, R. Oulton, V. Sorger, G. Bartal, X. Zhang, Nat. Mater. 10, 110 (2010)CrossRefGoogle Scholar
  42. 42.
    K. Ding, Z.C. Liu, L.J. Yin, M.T. Hill, M.J.H. Marell, P.J. van Veldhoven, R. Nöetzel, C.Z. van Ning, Phys. Rev. B 85, 041301(R) (2012)CrossRefGoogle Scholar
  43. 43.
    Y.-J. Lu, J. Kim, H.-Y. Chen, C.I. Wu, N. Dabidian, C.E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, S. Gwo, Science 337, 450 (2012)Google Scholar
  44. 44.
    W. Zhou, M. Dridi, J.Y. Suh, C.H. Kim, D.T. Co, M.R. Wasielewski, G.C. Schatz, T.W. Odom, Nat. Nanotechnol. 8, 506 (2013)CrossRefGoogle Scholar
  45. 45.
    R.-M. Ma, S. Ota, Y. Li, S. Yang, X. Zhang, Nat. Nanotechnol. 9, 600 (2014)CrossRefGoogle Scholar
  46. 46.
    A. Yang, T.B. Hoang, M. Dridi, C. Deeb, M.H. Mikkelsen, G.C. Schatz, T.W. Odom, Nat. Commun. 6, 6939 (2015)CrossRefGoogle Scholar
  47. 47.
    X. Meng, A.V. Kildishev, K. Fujita, K. Tanaka, V.M. Shalaev, Nano Lett. 13, 4106 (2013)CrossRefGoogle Scholar
  48. 48.
    E.I. Galanzha, R. Weingold, D.A. Nedosekin, M. Sarimollaoglu, A.S. Kuchyanov, R.G. Parkhomenko, A.I. Plekhanov, M.I. Stockman, V.P. Zharov, arXiv:1501.00342
  49. 49.
    V. Apalkov, M.I. Stockman, Light Sci. Appl. 3, e191 (2014)CrossRefGoogle Scholar
  50. 50.
    Y. Yin, T. Qiu, J. Li, P. Chu, Plasmonic nano-lasers. Nano Energy 1, 25 (2012)CrossRefGoogle Scholar
  51. 51.
    J.A. Gordon, R.W. Ziolkowski, The design and simulated performance of a coated nano-particle laser. Opt. Express 15, 2622 (2007)CrossRefGoogle Scholar
  52. 52.
    S. Wuestner, A. Pusch, K. Tsakmakidis, J. Hamm, O. Hess, Gain and plasmon dynamics in active negative-index metamaterials. Phil. Trans. R. Soc. A 369, 3525 (2011)CrossRefGoogle Scholar
  53. 53.
    A. Sarychev, G. Tartakovsky, Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser, Phys. Rev. B 75, 085436 (2007)Google Scholar
  54. 54.
    E. Andrianov, A. Pukhov, A. Dorofeenko, A. Vinogradov, A. Lisyansky, Forced synchronization of spaser by an external optical wave. Opt. Express 19, 24849 (2011)CrossRefGoogle Scholar
  55. 55.
    V.M. Fain, Quantum Radio Physics, Vol. 1: Photons and Nonlinear Media (Sovetskoe Radio, Moscow, 1972) (in Russian)Google Scholar
  56. 56.
    G. Haken, Laser Light Dynamics (North Holland, Amsterdam, 1985)Google Scholar
  57. 57.
    S. Akhmanov, Y. D’yakov, A. Chirkin, Introduction to Statistical Radio Physics and Optics (Nauka, Moscow, 1981) (in Russian)Google Scholar
  58. 58.
    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001)Google Scholar
  59. 59.
    I. Protsenko, A. Uskov, O. Zaimidoroga et al., Phys. Rev. A 71, 063812 (2005)CrossRefGoogle Scholar
  60. 60.
    N. Arnold, B. Ding, C. Hrelescu, T.A. Klar, Beilstein J. Nanotechnol. 4, 974 (2013)CrossRefGoogle Scholar
  61. 61.
    R.R. Chance, A. Prock, R. Silbey, in Advances in Chemical Physics, vol. 37, ed. by I. Prigogine, S.A. Rice (Wiley, Hoboken, 1978)Google Scholar
  62. 62.
    H. Metiu, Prog. Surf. Sci. 17, 153 (1984)Google Scholar
  63. 63.
    V. Pustovit, A. Urbas, A. Chipouline, T. Shahbazyan, Coulomb and quenching effects in small nanoparticle-based spasers. PRB (2016)Google Scholar
  64. 64.
    J. Gersten, A. Nitzan, Spectroscopic properties of molecules interacting with small dielectric particles. J. Chem. Phys. 75(3), 1139 (1981)CrossRefGoogle Scholar
  65. 65.
    R. Ruppin, J. Chem. Phys. 76(4) (1982)Google Scholar
  66. 66.
    V.N. Pustovit, T.V. Shahbazyan, J. Chem. Phys. 136, 204701 (2012)CrossRefGoogle Scholar
  67. 67.
    N.E. Rehler, J.H. Eberly, Phys. Rev. A 3, 1735 (1971)CrossRefGoogle Scholar
  68. 68.
    R. Friedberg, S.R. Hartmann, Phys. Rev. A 10, 1728 (1974)CrossRefGoogle Scholar
  69. 69.
    B. Coffey, R. Friedberg, Phys. Rev. A 17, 1033 (1978)CrossRefGoogle Scholar
  70. 70.
    S. Wuestner, J.M. Hamm, A. Pusch, F. Renn, K. Tsakmakidis, O. Hess, Control and dynamic competition of bright and dark lasing states in active nanoplasmonic metamaterials. Phys. Rev. B 85, 201406(R) (2012)CrossRefGoogle Scholar
  71. 71.
    J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, T. Pertsch, Multipole approach to metamaterials. Phys. Rev. B 78, 043811 (2008)CrossRefGoogle Scholar
  72. 72.
    S. Xiao, V. Drachev, A. Kildishev, X. Ni, U. Chettiar, H.-K. Yuan, V. Shalaev, Loss-free and active optical negative-index metamaterials. Nat. Lett. 466, 735 (2010)CrossRefGoogle Scholar
  73. 73.
    V. Pustovit, T. Shahbazyan, Phys. Rev. B 82, 075429 (2010)CrossRefGoogle Scholar
  74. 74.
    A. Schawlow, C. Townes, Phys. Rev. 112, 1940 (1958)CrossRefGoogle Scholar
  75. 75.
    V.S. Troitskii, Zh. Eksp. Teor. Fiz. 34, 390 (1958) [Sov. Phys. JETP 7, 271 (1958)]. Radiotekhn. Elektron. 3, 1298, (1958)Google Scholar
  76. 76.
    J. Singer, Masers (Wiley, New York, 1959)Google Scholar
  77. 77.
    A. Malakhov, Fluctuations in Self Oscillatory Systems (Nauka, Moscow, 1968) (in Russian)Google Scholar
  78. 78.
    F. Arecchi, M. Scully, H. Haken, W. Weidlich, Quantum Fluctuations of Laser Emission (Mir, Moscow, 1974) (in Russian)Google Scholar
  79. 79.
    M. Lax, in Statistical Physics, Phase Transitions and Superfluidity, vol. 271, ed. by M. Chrétien, E.P. Gross, S. Deser (Gordon and Breach, New York, 1968)Google Scholar
  80. 80.
    A. Yariv, Quantum Electronics, 2nd edn. (Wiley, New York, 1975)Google Scholar
  81. 81.
    Y. Klimontovich (ed.), Wave and Fluctuation Processes in Lasers (Nauka, Moscow, 1974) (in Russian)Google Scholar
  82. 82.
    A. Oraevsky, J. Opt. Soc. Am. B 5, 933 (1988)CrossRefGoogle Scholar
  83. 83.
    M. Scully, M. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997)CrossRefGoogle Scholar
  84. 84.
    G. Strakhovskii, A. Uspenskii, Fundamentals of Quantum Electronics (Vysshaia Shkola, Moscow, 1973) (in Russian)Google Scholar
  85. 85.
    R. Pantell, H. Puthoff, Fundamentals of Quantum Electronics (Wiley, New York, 1969)Google Scholar
  86. 86.
    S. Akhmanov, Y. D’yakov, A. Chirkin, Statistical Radiophysics and Optics. Random Oscillations and Waves in Linear Systems (Fizmatlit, Moscow, 2010) (in Russian)Google Scholar
  87. 87.
    S. Kuppens, M. van Exter, J. Woerdman, Quantum limited linewidth of a bad-cavity laser. PRL 72, 3815 (1994)CrossRefGoogle Scholar
  88. 88.
    A.Z. Khoury, M.I. Kolobov, L. Davidovich, Quantum-limited linewidth of a bad-cavity laser with inhomogeneous broadening. Phys. Rev. A 53, 1120 (1996)CrossRefGoogle Scholar
  89. 89.
    M. Exter, S. Kuppens, J. Woerdman, Theory for the linewidth of a bad-cavity laser. Phys. Rev. A 51, 809 (1995)CrossRefGoogle Scholar
  90. 90.
    A.S. Chirkin, A.V. Chipouline, Generalized expression for the natural width of the radiation spectrum of quantum oscillators. JETP Lett. 93, 114 (2011)CrossRefGoogle Scholar
  91. 91.
    P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability) (Springer, Berlin, 2011)Google Scholar

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Authors and Affiliations

  1. 1.Institute of Microwave Engineering and PhotonicsTechnical University of DarmstadtDarmstadtGermany
  2. 2.Department of Electrical Engineering and Information TechnologiesTechnical University of DarmstadtDarmstadtGermany

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