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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 6196–6204

Laser mode hyper-combs

Alon Schwartz and Baruch Fischer  »View Author Affiliations

Optics Express, Vol. 21, Issue 5, pp. 6196-6204 (2013)

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Laser mode and frequency combs, as lasers, are commonly one-dimensional systems. Here we present a construction of multi-dimensional laser-mode lattices (mode hyper-combs) with unique properties. They are obtained from regular 1-dimensional combs by multi-frequency modulation in active mode-locking (AML). The hyper-comb, with near neighbor mode coupling and noise functioning as temperature, is mapped to interacting magnetic-spins lattices in the spherical-model which is one of the few statistical-mechanics systems soluble in all dimensions. The important result is that such systems have, in d>2 dimensions, a phase-transition to a global phase-ordered mode hyper-comb. It can therefore change the nature of AML lasers by capturing very broad coherent frequency bandwidths and obtaining ultimately short and robust pulses. Additionally, the hyper-combs can serve as a rare physical realization of the spherical-model in any dimension.

© 2013 OSA

OCIS Codes
(000.6590) General : Statistical mechanics
(140.4050) Lasers and laser optics : Mode-locked lasers

ToC Category:
Lasers and Laser Optics

Original Manuscript: January 3, 2013
Revised Manuscript: February 10, 2013
Manuscript Accepted: February 10, 2013
Published: March 5, 2013

Alon Schwartz and Baruch Fischer, "Laser mode hyper-combs," Opt. Express 21, 6196-6204 (2013)

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  1. T. R. Schibli, J. W. Kuzucu, J. W. Kim, E. P. Ippen, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, G. Angelow, “Toward single-cycle laser systems,” IEEE J. Select. Topics in Quantum. Electron. 9, 990–1001 (2003).
  2. F. X. Kärtner, E. P. Ippen, and S. T. Cundiff, “Femtosecond laser development,” in Femtosecond Optical Frequency Comb: Principle, Operation and Applications, J. Ye and S.T. Cundiff, eds., (Springer Verlag, 2005).
  3. Th. Udem, R. Holzwarth, T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002). [CrossRef] [PubMed]
  4. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef] [PubMed]
  5. M. Hentschel, R. Kienberger, Ch. Spielmann, G. A. Reider, N. Milosevic, T. Brabec, P. B. Corkum, U. Heinzmann, M. Drescher, F. Krausz, “Attosecond metrology,” Nature 414(6863), 509–513 (2001). [CrossRef] [PubMed]
  6. Z. Chang, P. B. Corkum, “Attosecond photon sources: the first decade and beyond,” J. Opt. Soc. Am. B 27(11), B9–B17 (2010). [CrossRef]
  7. J. Itatani, F. Quéré, G. L. Yudin, M. Y. Ivanov, F. Krausz, P. B. Corkum, “Attosecond streak camera,” Phys. Rev. Lett. 88(17), 173903 (2002). [CrossRef] [PubMed]
  8. H. C. Kapteyn, O. Cohen, I. Christov, M. M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007). [CrossRef] [PubMed]
  9. P. Popmintchev, M. C. Chen, P. Arpin, M. M. Murnane, H. C. Kapteyn, “The attosecond nonlinear optics of bright coherent X-ray generation,” Nat. Photonics 4(12), 822–832 (2010). [CrossRef]
  10. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1173–1185 (2000). [CrossRef]
  11. D. J. Kuizenga, A. E. Siegman, “Modulator frequency detuning effects in the FM-mode-locked laser,” IEEE J. Quantum Electron. QE-6, 803–808 (1970).
  12. A. Gordon, B. Fischer, “Phase transition theory of many-mode ordering and pulse formation in lasers,” Phys. Rev. Lett. 89(10), 103901 (2002). [CrossRef] [PubMed]
  13. A. Gordon, B. Vodonos, V. Smulakovski, B. Fischer, “Melting and freezing of light pulses and modes in mode-locked lasers,” Opt. Express 11(25), 3418–3424 (2003). [CrossRef] [PubMed]
  14. B. Vodonos, R. Weill, A. Gordon, A. Bekker, V. Smulakovsky, O. Gat, B. Fischer, “Formation and annihilation of laser light pulse quanta in a thermodynamic-like pathway,” Phys. Rev. Lett. 93(15), 153901 (2004). [CrossRef] [PubMed]
  15. O. Gat, A. Gordon, B. Fischer, “Light-mode locking: a new class of solvable statistical physics systems,” New J. Phys. 7, 151 (2005). [CrossRef]
  16. R. Weill, A. Rosen, A. Gordon, O. Gat, B. Fischer, “Critical behavior of light in mode-locked lasers,” Phys. Rev. Lett. 95(1), 013903 (2005). [CrossRef] [PubMed]
  17. A. Rosen, R. Weill, B. Levit, V. Smulakovsky, A. Bekker, B. Fischer, “Experimental observation of critical phenomena in a laser light system,” Phys. Rev. Lett. 105(1), 013905 (2010). [CrossRef] [PubMed]
  18. M. Katz, A. Gordon, O. Gat, B. Fischer, “Non-Gibbsian Stochastic light-mode dynamics of passive mode locking,” Phys. Rev. Lett. 97(11), 113902 (2006). [CrossRef] [PubMed]
  19. A. Gordon, B. Fischer, “Statistical-mechanics theory of active mode locking with noise,” Opt. Lett. 29(9), 1022–1024 (2004). [CrossRef] [PubMed]
  20. R. Weill, B. Fischer, O. Gat, “Light-mode condensation in actively-mode-locked lasers,” Phys. Rev. Lett. 104(17), 173901 (2010). [CrossRef] [PubMed]
  21. R. Weill, B. Levit, A. Bekker, O. Gat, B. Fischer, “Laser light condensate: Experimental demonstration of light-mode condensation in actively mode locked laser,” Opt. Express 18(16), 16520–16525 (2010). [CrossRef] [PubMed]
  22. B. Fischer, R. Weill, “When does single-mode lasing become a condensation phenomenon?” Opt. Express 20(24), 26704–26713 (2012). [CrossRef] [PubMed]
  23. T. H. Berlin, M. Kac, “The spherical model of a ferromagnet,” Phys. Rev. 86(6), 821–835 (1952). [CrossRef]
  24. G. S. Joyce, “Critical properties of the spherical model,” 2, Chapter 10, 375, in Phasetransitions and Critical Phenomena, C. Domb and M.S. Green, eds. (Academic Press, 1972).
  25. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, 1989).
  26. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University, 1971).
  27. H. E. Stanley, “Exact solution for a linear chain of isotropically interacting classical spins of arbitrary dimensionality,” Phys. Rev. 179(2), 570–577 (1969). [CrossRef]
  28. A. Siegman, Lasers (University Science Books, 1986).

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