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Beyond Mean Field—Mode Locked Lasers

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Statistical Physics of Wave Interactions

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

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Abstract

In this Chapter we discuss how to extend the multimode laser model introduced in the previous Chapter, cf. Eq. (3.1), beyond the assumptions of narrow-bandwidth and extended modes.

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Notes

  1. 1.

    Graphics Processing Unit. The code, written in CUDA, have been running on Nvidia GTX680 and Nvidia Tesla K20.

  2. 2.

    In particular, if the quadruplets are formed by the four spins living in the edges of single plaquettes of an auxiliary hyper-cubic lattice, the local gauge transformation consists in flipping all spins corresponding to the edges incoming a given node of the auxiliary lattice.

  3. 3.

    The generalization to a more general class of models is in progress.

  4. 4.

    Note that here we are neglecting the influence of the moduli, but this is approximately correct since they are locked in the ML phase, cf. Fig. 4.11, and their small inhomogeneities are not expected to play a role.

  5. 5.

    We stress, once again, that in this case the validity of the results for the optical system can only be checked a posteriori, implementing a real dynamics of the electromagnetic modes.

  6. 6.

    Note that, as usual in this Thesis, we are considering the case of a continuous pumping (over the timescale on which the system is studied).

References

  1. A.D. Sokal, Monte Carlo Methods in Statistical Mechanics (EPFL, Lausanne, 1989)

    Google Scholar 

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

    Google Scholar 

  3. 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 

  4. L. Angelani et al., Mode-locking transitions in nanostructured weakly disordered lasers. Phys. Rev. B 76, 064202 (2007)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  7. M. Leonetti, C. Conti, C. Lopez, The mode-locking transition of random lasers. Nat. Photonics 5(10) 615–617 (2011)

    Google Scholar 

  8. 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 

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

    Google Scholar 

  10. T. Udem, R. Holzwarth, T.W. Hansch, Optical frequency metrology. Nature 416(877), pp. 233–237 (2002)

    Google Scholar 

  11. J.B. Kogut, An introduction to lattice gauge theory and spin systems. Rev. Mod. Phys. 51, 659–713 (1979)

    Google Scholar 

  12. O.G. Mouritsen, B. Frank, D. Mukamel, Cubic Ising lattices with four-spin interactions. Phys. Rev. B 27, 3018–3031 (1983)

    Google Scholar 

  13. J.P. Bouchaud, M. Mézard, Self induced quenched disorder: a model for the glass transition. J. Phys. I Fr. 4(8),1109–1114 (1994)

    Google Scholar 

  14. A. Lipowski, Glassy behaviour and semi-local invariance in Ising model with four-spin interaction. J. Phys. A: Math. Gen. 30(21), 7365 (1997)

    Google Scholar 

  15. A. Lipowski, D. Johnston, Cooling-rate effects in a model of glasses. Phys. Rev. E 61, 6375–6382 (2000)

    Google Scholar 

  16. A. Lipowski, D. Johnston, D. Espriu, Slow dynamics of Ising models with energy barriers. Phys. Rev. E 62, 3404–3410 (2000)

    Google Scholar 

  17. A. Lipowski, D. Johnston, Metastability in a four-spin Ising model. J. Phys. A: Math. Gen. 33(24), 4451 (2000)

    Google Scholar 

  18. Y. Nishiyama, Multicriticality of the three-dimensional Ising model with plaquette interactions: An extension of Novotny’s transfer-matrix formalism. Phys. Rev. E 70, 026120 (2004)

    Google Scholar 

  19. A. Cavagna, I. Giardina, T.S. Grigera, Glass and polycrystal states in a lattice spin model. J. Chem. Phys. 118(15), 6974–6988 (2003)

    Article  ADS  MATH  Google Scholar 

  20. R.L. Jack, J.P. Garrahan, D. Sherrington, Glassy behavior in an exactly solved spin system with a ferromagnetic transition. Phys. Rev. E 71, 036112 (2005)

    Google Scholar 

  21. R.V. Ambartzumian et al., Alternative model of random surfaces. Phys. Lett. B 275(1–2), 99–102 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  22. G.K. Savvidy, K.G. Savvidy, Interaction hierarchy. Phys. Lett. B 337(3–4), 333–339 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. D. Espriu et al., Evidence for a first-order transition in a plaquette three-dimensional Ising-like action. J. Phys. A: Math. Gen. 30(2), 405 (1997)

    Google Scholar 

  24. M.R. Swift et al., Glassy behavior in a ferromagnetic p-spin model. Phys. Rev. B 62, 11494–11498 (2000)

    Google Scholar 

  25. P. Dimopoulos et al., Slow dynamics in the three-dimensional gonihedric model. Phys. Rev. E 66, 056112 (2002)

    Google Scholar 

  26. C. Castelnovo, C. Chamon, D. Sherrington, Quantum mechanical and information theoretic view on classical glass transitions. Phys. Rev. B 81, 184303 (2010)

    Google Scholar 

  27. J.E. Moore, D.-H. Lee, Geometric effects on T-breaking in p+ip and d+id superconducting arrays. Phys. Rev. B 69, 104511 (2004)

    Google Scholar 

  28. C. Xu, J.E. Moore, Strong-weak coupling self-duality in the two-dimensional quantum phase transition of p + ip superconducting arrays. Phys. Rev. Lett. 93, 047003 (2004)

    Google Scholar 

  29. K. Binder, D. Heermann, Monte Carlo Simulation in Statistical Physics: An Introduction (Springer, 2010)

    Google Scholar 

  30. D.J. Earl, M.W. Deem, Parallel tempering: theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7(23), 3910–3916 (2005)

    Google Scholar 

  31. M.I. Berganza, L. Leuzzi, Critical behavior of the XY model in complex topologies. Phys. Rev. B 88, 144104 (2013)

    Google Scholar 

  32. F.D. Nobre, A.A. Júnior, The parallel updating in a fullyfrustrated Ising model: a damage-spreading analysis. Phys. Lett. A 288(5–6), 271–276 (2001)

    Google Scholar 

  33. H. Gibbs, Optical Bistability: Controlling Light with Light (Elsevier, Amsterdam, 1985)

    Google Scholar 

  34. A. Baas et al., Optical bistability in semiconductor microcavities. Phys. Rev. A 69, 023809 (2004)

    Google Scholar 

  35. A. Baas et al., Optical bistability in semiconductor microcavities in the nondegenerate parametric oscillation regime: analogy with the optical parametric oscillator. Phys. Rev. B 70, 161307 (2004)

    Google Scholar 

  36. M.I. Berganza, P. Coletti, A. Petri, Anomalous metastability in a temperature-driven transition. EPL (Europhysics Letters) 106(5), 56001 (2014)

    Google Scholar 

  37. T. Brabec, F. Krausz, Intense few-cycle laser fields: frontiers of nonlinear optics. Rev. Mod. Phys. 72(2), 545–591 (2000)

    Google Scholar 

  38. H.A. Haus, Mode-locking of lasers. IEEE J. Quantum Electron. 6(6), 1173–1185 (2000)

    Article  Google Scholar 

  39. H.A. Haus, Mode-locking of lasers. Sel. Top. Quantum Electron. IEEE J. 6(6), 1173–1185 (2000)

    Google Scholar 

  40. M. Horowitz et al., Narrow-linewidth, singlemode erbium-doped fibre laser with intracavity wave mixing in saturable absorber. Electron. Lett. 30(8), 648–649 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  41. M. Horowitz et al., Linewidth-narrowing mechanism in lasers by nonlinear wavemixing. Opt. Lett. 19(18), 1406–1408 (1994)

    Google Scholar 

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Authors and Affiliations

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

    Fabrizio Antenucci

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  1. Fabrizio Antenucci
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Correspondence to Fabrizio Antenucci .

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Antenucci, F. (2016). Beyond Mean Field—Mode Locked Lasers. In: Statistical Physics of Wave Interactions. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41225-2_4

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