## Autoresonant propagation of incoherent light-waves |

Optics Express, Vol. 18, Issue 17, pp. 17709-17718 (2010)

http://dx.doi.org/10.1364/OE.18.017709

Acrobat PDF (1003 KB)

### Abstract

We study, theoretically and experimentally, the evolution of optical waves with randomly-fluctuating phases in a spatially chirped nonlinear directional coupler. As the system crosses its linear resonance, we observe collective self-phase-locking (autoresonance) of all mutually-incoherent waves, each with its own pump, and simultaneous amplification until the pumps are exhausted. We show that the autoresonant transition in this system exhibits a sharp threshold, common to all mutually-incoherent waves comprising the light beam.

© 2010 OSA

## 1. Introduction

1. Y. Silberberg and G. I. Stegeman, “Nonlinear Coupling of Waveguide Modes,” Appl. Phys. Lett. **50**(13), 801–803 (1987). [CrossRef]

2. O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. **99**(5), 053902 (2007). [CrossRef] [PubMed]

3. G. Bartal, O. Manela, and M. Segev, “Spatial Four Wave Mixing in Nonlinear Periodic Structures,” Phys. Rev. Lett. **97**(7), 073906 (2006). [CrossRef] [PubMed]

2. O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. **99**(5), 053902 (2007). [CrossRef] [PubMed]

5. S. Somekh and A. Yariv, “Phase‐matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. **21**(4), 140–141 (1972). [CrossRef]

6. H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A **78**(6), 063821 (2008). [CrossRef]

7. S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. **76**(20), 201101 (2007). [CrossRef]

8. Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Effect of nonlinearity on adiabatic evolution of light,” Phys. Rev. Lett. **101**(19), 193901 (2008). [CrossRef] [PubMed]

9. F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. **34**(16), 2405–2407 (2009). [CrossRef] [PubMed]

10. A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett. **103**(12), 123901 (2009). [CrossRef] [PubMed]

11. L. Friedland, “Autoresonant Solutions of Nonlinear Schrodinger Equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **58**(3), 3865–3875 (1998). [CrossRef]

12. J. Fajans and L. Friedland, “Autoresonant (nonstationary) Excitation of Pendulums, Plutinos, Plasmas, and Other Nonlinear Oscillators,” Am. J. Phys. **69**(10), 1096–1102 (2001). [CrossRef]

13. M. Deutsch, B. Meerson, and J. E. Golub, “Strong plasma wave excitation by a “chirped” laser beat wave,” Phys. Fluids B **3**(7), 1773–1780 (1991). [CrossRef]

15. L. Friedland and A. G. Shagalov, “Resonant formation and control of 2D symmetric vortex waves,” Phys. Rev. Lett. **85**(14), 2941–2944 (2000). [CrossRef] [PubMed]

16. L. Friedland and A. G. Shagalov, “Excitation of Solitons by Adiabatic Multiresonant Forcing,” Phys. Rev. Lett. **81**(20), 4357–4360 (1998). [CrossRef]

17. L. Friedland, “Migration timescale thresholds for resonant capture in the Plutino problem,” Astrophys. J. **547**(1), L75–L79 (2001). [CrossRef]

18. A. I. Nicolin, M. H. Jensen, and R. Carretero-González, “Mode locking of a driven Bose-Einstein condensate,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **75**(3), 036208 (2007). [CrossRef] [PubMed]

19. O. Naaman, J. Aumentado, L. Friedland, J. S. Wurtele, and I. Siddiqi, “Phase-locking transition in a chirped superconducting Josephson resonator,” Phys. Rev. Lett. **101**(11), 117005 (2008). [CrossRef] [PubMed]

## 2. Theory

## 3. Experiments

## 4. Summary

## References and links

1. | Y. Silberberg and G. I. Stegeman, “Nonlinear Coupling of Waveguide Modes,” Appl. Phys. Lett. |

2. | O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. |

3. | G. Bartal, O. Manela, and M. Segev, “Spatial Four Wave Mixing in Nonlinear Periodic Structures,” Phys. Rev. Lett. |

4. | A. Yariv, |

5. | S. Somekh and A. Yariv, “Phase‐matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. |

6. | H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A |

7. | S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. |

8. | Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Effect of nonlinearity on adiabatic evolution of light,” Phys. Rev. Lett. |

9. | F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. |

10. | A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett. |

11. | L. Friedland, “Autoresonant Solutions of Nonlinear Schrodinger Equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

12. | J. Fajans and L. Friedland, “Autoresonant (nonstationary) Excitation of Pendulums, Plutinos, Plasmas, and Other Nonlinear Oscillators,” Am. J. Phys. |

13. | M. Deutsch, B. Meerson, and J. E. Golub, “Strong plasma wave excitation by a “chirped” laser beat wave,” Phys. Fluids B |

14. | M. S. Livingston, |

15. | L. Friedland and A. G. Shagalov, “Resonant formation and control of 2D symmetric vortex waves,” Phys. Rev. Lett. |

16. | L. Friedland and A. G. Shagalov, “Excitation of Solitons by Adiabatic Multiresonant Forcing,” Phys. Rev. Lett. |

17. | L. Friedland, “Migration timescale thresholds for resonant capture in the Plutino problem,” Astrophys. J. |

18. | A. I. Nicolin, M. H. Jensen, and R. Carretero-González, “Mode locking of a driven Bose-Einstein condensate,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

19. | O. Naaman, J. Aumentado, L. Friedland, J. S. Wurtele, and I. Siddiqi, “Phase-locking transition in a chirped superconducting Josephson resonator,” Phys. Rev. Lett. |

20. | M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. |

21. | M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. |

22. | M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. |

23. | M. Segev, M.- Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B |

24. | N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

25. | J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature |

26. | H. Buljan, A. Siber, M. Soljacic, and M. Segev, “Propagation of incoherent “white” light and modulation instability in non-instantaneous nonlinear media,” Phys. Rev. E. Rapid Communication |

27. | T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett. |

28. | T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. |

29. | A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. |

30. | A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

31. | A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

32. | H. Buljan, M. Segev, and A. Vardi, “Incoherent matter-wave solitons and pairing instability in an attractively interacting Bose-Einstein condensate,” Phys. Rev. Lett. |

33. | W. Tong, M. Wu, L. D. Carr, and B. A. Kalinikos, “Formation of random dark envelope solitons from incoherent waves,” Phys. Rev. Lett. |

**OCIS Codes**

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(190.5940) Nonlinear optics : Self-action effects

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 23, 2010

Revised Manuscript: July 21, 2010

Manuscript Accepted: July 21, 2010

Published: August 2, 2010

**Citation**

Assaf Barak, Yuval Lamhot, Lazar Friedland, and Mordechai Segev, "Autoresonant propagation of incoherent
light-waves," Opt. Express **18**, 17709-17718 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17709

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### References

- Y. Silberberg and G. I. Stegeman, “Nonlinear Coupling of Waveguide Modes,” Appl. Phys. Lett. 50(13), 801–803 (1987). [CrossRef]
- O. Cohen, X. Zhang, A. L. Lytle, T. Popmintchev, M. M. Murnane, and H. C. Kapteyn, “Grating-Assisted Phase Matching in Extreme Nonlinear Optics,” Phys. Rev. Lett. 99(5), 053902 (2007). [CrossRef] [PubMed]
- G. Bartal, O. Manela, and M. Segev, “Spatial Four Wave Mixing in Nonlinear Periodic Structures,” Phys. Rev. Lett. 97(7), 073906 (2006). [CrossRef] [PubMed]
- A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
- S. Somekh and A. Yariv, “Phase‐matchable nonlinear optical interactions in periodic thin films,” Appl. Phys. Lett. 21(4), 140–141 (1972). [CrossRef]
- H. Suchowski, D. Oron, A. Arie, and Y. Silberberg, “Geometrical representation of sum frequency generation and adiabatic frequency conversion,” Phys. Rev. A 78(6), 063821 (2008). [CrossRef]
- S. Longhi, G. Della Valle, M. Ornigotti, and P. Laporta, “Coherent tunneling by adiabatic passage in an optical waveguide system,” Phys. Rev. 76(20), 201101 (2007). [CrossRef]
- Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Effect of nonlinearity on adiabatic evolution of light,” Phys. Rev. Lett. 101(19), 193901 (2008). [CrossRef] [PubMed]
- F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34(16), 2405–2407 (2009). [CrossRef] [PubMed]
- A. Barak, Y. Lamhot, L. Friedland, and M. Segev, “Autoresonant dynamics of optical guided waves,” Phys. Rev. Lett. 103(12), 123901 (2009). [CrossRef] [PubMed]
- L. Friedland, “Autoresonant Solutions of Nonlinear Schrodinger Equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(3), 3865–3875 (1998). [CrossRef]
- J. Fajans and L. Friedland, “Autoresonant (nonstationary) Excitation of Pendulums, Plutinos, Plasmas, and Other Nonlinear Oscillators,” Am. J. Phys. 69(10), 1096–1102 (2001). [CrossRef]
- M. Deutsch, B. Meerson, and J. E. Golub, “Strong plasma wave excitation by a “chirped” laser beat wave,” Phys. Fluids B 3(7), 1773–1780 (1991). [CrossRef]
- M. S. Livingston, High-Energy Particle Accelerators (Interscience, New York, 1954).
- L. Friedland and A. G. Shagalov, “Resonant formation and control of 2D symmetric vortex waves,” Phys. Rev. Lett. 85(14), 2941–2944 (2000). [CrossRef] [PubMed]
- L. Friedland and A. G. Shagalov, “Excitation of Solitons by Adiabatic Multiresonant Forcing,” Phys. Rev. Lett. 81(20), 4357–4360 (1998). [CrossRef]
- L. Friedland, “Migration timescale thresholds for resonant capture in the Plutino problem,” Astrophys. J. 547(1), L75–L79 (2001). [CrossRef]
- A. I. Nicolin, M. H. Jensen, and R. Carretero-González, “Mode locking of a driven Bose-Einstein condensate,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(3), 036208 (2007). [CrossRef] [PubMed]
- O. Naaman, J. Aumentado, L. Friedland, J. S. Wurtele, and I. Siddiqi, “Phase-locking transition in a chirped superconducting Josephson resonator,” Phys. Rev. Lett. 101(11), 117005 (2008). [CrossRef] [PubMed]
- M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of Self-Trapped Spatially Incoherent Light Beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997). [CrossRef]
- M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-Trapping of Partially Spatially Incoherent Light,” Phys. Rev. Lett. 77(3), 490–493 (1996). [CrossRef] [PubMed]
- M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994). [CrossRef] [PubMed]
- M. Segev, M.- Shih, and G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13(4), 706–718 (1996). [CrossRef]
- N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, “Discrete solitons in photorefractive optically induced photonic lattices,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(4 ), 046602 (2002). [CrossRef] [PubMed]
- J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422(6928), 147–150 (2003). [CrossRef] [PubMed]
- H. Buljan, A. Siber, M. Soljacic, and M. Segev, “Propagation of incoherent “white” light and modulation instability in non-instantaneous nonlinear media,” Phys. Rev. E. Rapid Communication 66, 35601 (2002).
- T. Schwartz, T. Carmon, H. Buljan, and M. Segev, “Spontaneous pattern formation with incoherent white light,” Phys. Rev. Lett. 93(22), 223901 (2004). [CrossRef] [PubMed]
- T. H. Coskun, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, “Coherence enhancement of spatially incoherent light beams through soliton interactions,” Opt. Lett. 25(11), 826–828 (2000). [CrossRef]
- A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. 86(10), 2010–2013 (2001). [CrossRef] [PubMed]
- A. Picozzi, C. Montes, and M. Haelterman, “Coherence properties of the parametric three-wave interaction driven from an incoherent pump,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 056605 (2002). [CrossRef]
- A. Picozzi and P. Aschieri, “Influence of dispersion on the resonant interaction between three incoherent waves,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(4), 046606 (2005). [CrossRef] [PubMed]
- H. Buljan, M. Segev, and A. Vardi, “Incoherent matter-wave solitons and pairing instability in an attractively interacting Bose-Einstein condensate,” Phys. Rev. Lett. 95(18), 180401 (2005). [CrossRef] [PubMed]
- W. Tong, M. Wu, L. D. Carr, and B. A. Kalinikos, “Formation of random dark envelope solitons from incoherent waves,” Phys. Rev. Lett. 104(3), 037207 (2010). [CrossRef] [PubMed]

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