Skip to main content
SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Statistical Physics of Wave Interactions

Part of the book series: Springer Theses ((Springer Theses))

  • 545 Accesses

Abstract

The application of the statistical mechanics tools to the study of optics was introduced in the seminal works of Fisher and coworkers in the early 00’s [1, 2].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The time dependent modulation is usually achieved with an acousto-optic or electro-optic modulator. If the modulation is synchronized with the resonator round trips, ultra-short pulses can be generated: a pulse with the “correct” timing can pass the modulator at times where the losses are at a minimum and the wings of the pulse are attenuated, which leads to (slight) pulse shortening in each round trip [7]. The pulse duration is typically in the picosecond range.

  2. 2.

    The light transmissivity through a fast saturable absorber is an increasing function of the instantaneous input intensity. In this way the saturable absorber destabilizes the laser operation into configurations where most of the power is concentrated in short pulses.

  3. 3.

    In a finite system this picture is only precise when the spectral correlation length is shorter than the finite bandwidth, so that the number of modes involved in the laser dynamic is large enough.

  4. 4.

    This is exactly true for the usual harmonic modulation. If instead, the modulation is a not-smooth function of time with a power law singularity, the system undergoes a continuous (unlike the passive mode locking case) phase transition to a Bose-Einstein Condensate (BEC) phase transition [11–13].

  5. 5.

    We refer, in particular, to the so-called Frequency Matching Condition, mentioned in Eq. (1.1).

  6. 6.

    The quality factor (or Q factor) of a resonator is the ratio between the resonance frequency and the full width at half-maximum bandwidth of the resonance.

  7. 7.

    The Ioffe-Regel criterion [36] for light localization states that, if the ratio of photon wave-vector k to mean free-path length l (of a photon not colliding with anything) is such that \(kl < 1\), then there is a finite probability that photons will become trapped, similarly to electrons under Anderson localization.

  8. 8.

    Levy distributions are characterized by a slowly decaying (power-law) tail, so they have infinite variance and describe the occurrence of rare but very large values.

References

  1. A. Gordon, B. Fischer, Phase transition theory of many-mode ordering and pulse formation in lasers. Phys. Rev. Lett. 89, 103901 (2002)

    Google Scholar 

  2. A. Gordon, B. Fischer, Phase transition theory of pulse formation in passively mode-locked lasers with dispersion and Kerr nonlinearity. Opt. Commun. 223(1–3), 151 (2003)

    Google Scholar 

  3. H. Haken, Synergetics (Springer, 1977)

    Google Scholar 

  4. P.-T. Ho, Phase and amplitude fluctuations in a mode-locked laser. IEEE J. Quant. Electron. 21(11), 1806–1813 (1985)

    Google Scholar 

  5. F. Rana, R.J. Ram, H. Haus, Quantum noise of actively mode-locked lasers with dispersion and amplitude/phase modulation. IEEE J. Quant. Electron. 40(1), 41–56 (2004)

    Google Scholar 

  6. A. Gordon, B. Fischer, Inhibition of modulation instability in lasers by noise. Opt. Lett. 28(15), 1326–1328 (2003)

    Google Scholar 

  7. D.J. Kuizenga, A.E. Siegman, FM and AM mode locking of the homogeneous laser—Part I: Theory. IEEE J. Quant. Electron. 6(11), 694–708 (1970)

    Google Scholar 

  8. H.A. Haus, Theory of mode locking with a fast saturable absorber. J. Appl. Phys. 46(7), 3049–3058 (1975)

    Article  ADS  Google Scholar 

  9. A. Gordon, B. Fischer, Statistical-mechanics theory of active mode locking with noise. Opt. Lett. 29(9), 1022–1024 (2004)

    Google Scholar 

  10. T.H. Berlin, M. Kac, The spherical model of a ferromagnet. Phys. Rev. 86, 821–835 (1952)

    Google Scholar 

  11. R. Weill, B. Fischer, O. Gat, Light-mode condensation in actively-mode-locked lasers. Phys. Rev. Lett. 104, 173901 (2010)

    Google Scholar 

  12. A. Fratalocchi, Mode-locked lasers: light condensation. Nat. Photonics 4(8), 502–503 (2010)

    Google Scholar 

  13. G. Oren, A. Bekker, B. Fischer, Classical condensation of light pulses in a loss trap in a laser cavity. Optica 1(3), 145–148 (2014)

    Google Scholar 

  14. O. Gat, A. Gordon, B. Fischer, Solution of a statistical mechanics model for pulse formation in lasers. Phys. Rev. E 70, 046108 (2004)

    Google Scholar 

  15. B. Vodonos et al., Formation and annihilation of laser light pulse quanta in athermodynamic-like pathway. Phys. Rev. Lett. 93, 153901 (2004)

    Google Scholar 

  16. C. Van den Broeck, J.M.R. Parrondo, R. Toral, Noise-induced nonequilibrium phase transition. Phys. Rev. Lett. 73, 3395–3398 (1994)

    Google Scholar 

  17. R. Weill et al., Critical behavior of light in mode-locked lasers. Phys. Rev. Lett. 95, 013903 (2005)

    Google Scholar 

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

    Google Scholar 

  19. V.S. Letokhov, Generation of light by a scattering medium with negative resonance absorption. Sov. J. Exp. Theor. Phys. 26, 835 (1968)

    Google Scholar 

  20. V.M. Markushev, V.F. Zolin, Ch.M. Briskina, Luminescence and stimulated emission of neodymium in sodium lanthanum molybdate powders. Sov. J. Quant. Electron. 16(2), 281 (1986)

    Google Scholar 

  21. C. Gouedard et al., Generation of spatially incoherent short pulses in laserpumped neodymium stoichiometric crystals and powders. JOSA B 10(12), 2358–2363 (1993)

    Article  ADS  Google Scholar 

  22. D.S. Wiersma, A. Lagendijk, Light diffusion with gain and random lasers. Phys. Rev. E 54, 4256–4265 (1996)

    Google Scholar 

  23. D.S. Wiersma, The physics and applications of random lasers. Nat. Phys. 4(5), 359–367 (2008)

    Google Scholar 

  24. S.V. Frolov et al., Stimulated emission in high-gain organic media. Phys. Rev. B 59, R5284–R5287 (1999)

    Google Scholar 

  25. R.C. Polson, A. Chipouline, Z.V. Vardeny, Random lasing in \(\pi \)-conjugated films and infiltrated opals. Adv. Mater. 13(10), 760–764 (2001)

    Article  Google Scholar 

  26. H. Cao et al., Photon statistics of random lasers with resonant feedback. Phys. Rev. Lett. 86, 4524–4527 (2001)

    Google Scholar 

  27. K.L. van der Molen et al., Spatial extent of random laser modes. Phys. Rev. Lett. 98, 143901 (2007)

    Google Scholar 

  28. M. Bahoura, K.J. Morris, M.A. Noginov, Threshold and slope efficiency of Nd0.5La0.5Al3(BO3)4 ceramic random laser: effect of the pumped spot size. Opt. Commun. 201(4–6), 405–411 (2002)

    Google Scholar 

  29. M. Bahoura, M.A. Noginov, Determination of the transport mean free path in a solid-state random laser. J. Opt. Soc. Am. B 20(11), 2389–2394 (2003)

    Google Scholar 

  30. H. Cao et al., Microlaser made of disordered media. Appl. Phys. Lett. 76(21), 2997–2999 (2000)

    Article  ADS  Google Scholar 

  31. X. Wu et al., Random lasing in weakly scattering systems. Phys. Rev. A 74, 053812 (2006)

    Google Scholar 

  32. S. John, Electromagnetic absorption in a disordered medium near a photon mobility edge. Phys. Rev. Lett. 53, 2169–2172 (1984)

    Google Scholar 

  33. P.W. Anderson, The question of classical localization a theory of white paint? Philos. Mag. Part B 52(3), 505–509 (1985)

    Google Scholar 

  34. Ad. Lagendijk, M.P. Van Albada, M.B. van der Mark, Localization of light: the quest for the white hole. Phys. A: Stat. Mech. Appl. 140(1–2), 183–190 (1986)

    Google Scholar 

  35. P.A. Lee, T.V. Ramakrishnan, Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985)

    Google Scholar 

  36. A.F. Ioffe, A.R. Regel, Progress in Semiconductors vol. 4, ed. by A.F. Gibson, F.A. Kroger, R.E. Burgess (Heywood, London, 1960), p. 237

    Google Scholar 

  37. E. Abrahams et al., Scaling theory of localization: absence of quantum diffusion in two dimensions. Phys. Rev. Lett. 42, 673–676 (1979)

    Google Scholar 

  38. S. Mujumdar et al., Chaotic behavior of a random laser with static disorder. Phys. Rev. A 76, 033807 (2007)

    Google Scholar 

  39. J. Fallert et al., Co-existence of strongly and weakly localized random laser modes. Nat. Photonics 3(5), 279–282 (2009)

    Google Scholar 

  40. D. Anglos et al., Random laser action in organic-inorganic nanocomposites. J. Opt. Soc. Am. B 21(1), 208–213 (2004)

    Google Scholar 

  41. K.L. van der Molen, A.P. Mosk, A. Lagendijk, Intrinsic intensity fluctuations in random lasers. Phys. Rev. A 74, 053808 (2006)

    Google Scholar 

  42. D. Sharma, H. Ramachandran, N. Kumar, Lévy statistics of emission from a novel random amplifying medium: an optical realization of the Arrhenius cascade. Opt. Lett. 31(12), 1806–1808 (2006)

    Google Scholar 

  43. S. Lepri et al., Statistical regimes of random laser fluctuations. Phys. Rev. A 75, 063820 (2007)

    Google Scholar 

  44. G. Parisi, Complex systems: a physicist’s viewpoint, May 2002. arXiv:condmat/0205297

  45. L. Angelani et al., Glassy behavior of light. Phys. Rev. Lett. 96, 065702 (2006)

    Google Scholar 

  46. M. Mézard, G. Parisi, M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)

    MATH  Google Scholar 

  47. W. Gotze, L. Sjogren, Relaxation processes in supercooled liquids. Rep. Prog. Phys. 55(3), 241 (1992)

    Google Scholar 

  48. K. Fisher, J.A. Hertz, Spin Glasses (Cambridge University Press, 1991)

    Google Scholar 

  49. L. Angelani et al., Glassy behavior of light in random lasers. Phys. Rev. B 74, 104207 (2006)

    Google Scholar 

  50. L. Leuzzi et al., Phase diagram and complexity of mode-locked lasers: from order to disorder. Phys. Rev. Lett. 102, 083901 (2009)

    Google Scholar 

  51. C. Conti, L. Leuzzi, Complexity of waves in nonlinear disordered media. Phys. Rev. B 83, 134204 (2011)

    Google Scholar 

  52. E. Bolthausen, Random Media and Spin Glasses: An Introduction into Some Mathematical Results and Problems (Springer, 2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Sapienza University of Rome, Rome, Italy

    Fabrizio Antenucci

Authors
  1. Fabrizio Antenucci
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fabrizio Antenucci .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Antenucci, F. (2016). Introduction. In: Statistical Physics of Wave Interactions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41225-2_1

Download citation

Publish with us

Policies and ethics

Search

Navigation