Abstract
We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed in an external cavity lead to the emission of temporal dissipative solitons. These are vectorial solitons because they appear as localized pulses in the polarized output, but leave the total intensity constant. When the cavity roundtrip time is much longer than the soliton duration, several independent solitons as well as bound states (molecules) may be hosted in the cavity. All these solitons coexist together and with the background solution. The experimental results are well described by a theoretical model that can be reduced to a single delayed equation for the polarization orientation, which allows the vectorial solitons to be interpreted as polarization kinks. A Floquet analysis is used to confirm the mutual independence of the observed solitons.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Akhmediev, N. & Ankiewicz, A. (eds) Dissipative Solitons (Springer, 2005).
Akhmediev, N. & Ankiewicz, A. (eds) Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).
Ackemann, T., Firth, W. J. & Oppo, G. in Advances in Atomic Molecular, and Optical Physics Vol. 57 (eds Arimondo, E., Berman, P. R. & Lin, C. C.) 323–421 (Academic Press, 2009).
Descalzi, O., Clerc, M., Residori, S. & Assanto, G. (eds) Localized States in Physics: Solitons and Patterns (Springer, 2011).
Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nature Photon. 6, 84–92 (2012).
Fauve, S. & Thual, O. Solitary waves generated by subcritical instabilities in dissipative systems. Phys. Rev. Lett. 64, 282–284 (1990).
Rosanov, N. N. & Khodova, G. V. Autosolitons in bistable interferometers. Opt. Spectrosc. 65, 449–450 (1988).
Tlidi, M., Mandel, P. & Lefever, R. Localized structures and localized patterns in optical bistability. Phys. Rev. Lett. 73, 640–643 (1994).
Firth, W. J. & Scroggie, A. J. Optical bullet holes: robust controllable localized states of a nonlinear cavity. Phys. Rev. Lett. 76, 1623–1626 (1996).
Barland, S. et al. Cavity solitons as pixels in semiconductor microcavities. Nature 419, 699–702 (2002).
Lugiato, L. Introduction to the feature section on cavity solitons: an overview. IEEE J. Quantum Electron. 39, 193–196 (2003).
Coullet, P., Riera, C. & Tresser, C. Stable static localized structures in one dimension. Phys. Rev. Lett. 84, 3069–3072 (2000).
Nicolis, G. & Prigogine, I. Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order through Fluctuations (Wiley, 1977).
Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nature Photon. 4, 471–476 (2010).
Elsass, T. et al. Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber. Appl. Phys. B 98, 327–331 (2010).
Genevet, P., Barland, S., Giudici, M. & Tredicce, J. R. Cavity soliton laser based on mutually coupled semiconductor microresonators. Phys. Rev. Lett. 101, 123905 (2008).
Tang, D. Y., Man, W. S., Tam, H. Y. & Drummond, P. D. Observation of bound states of solitons in a passively mode-locked fiber laser. Phys. Rev. A 64, 033814 (2001).
Grelu, P. & Soto-Crespo, J. in Dissipative Solitons: From Optics to Biology and Medicine (eds Akhmediev, N. & Ankiewicz, A) 1–37 (Springer, 2008).
Jang, J. K., Erkintalo, M., Murdoch, S. G. & Coen, S. Ultraweak long-range interactions of solitons observed over astronomical distances. Nature Photon. 7, 657–663 (2013).
Chouli, S. & Grelu, P. Soliton rains in a fiber laser: an experimental study. Phys. Rev. A 81, 063829 (2010).
Cundiff, S. T., Soto-Crespo, J. M. & Akhmediev, N. Experimental evidence for soliton explosions. Phys. Rev. Lett. 88, 073903 (2002).
Kang, J. U., Stegeman, G. I., Aitchison, J. S. & Akhmediev, N. Observation of Manakov spatial solitons in AlGaAs planar waveguides. Phys. Rev. Lett. 76, 3699–3702 (1996).
Williams, Q. L., García-Ojalvo, J. & Roy, R. Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: inclusion of stochastic effects. Phys. Rev. A 55, 2376–2386 (1997).
Zhang, H., Tang, D. Y., Zhao, L. M. & Wu, X. Observation of polarization domain wall solitons in weakly birefringent cavity fiber lasers. Phys. Rev. B 80, 052302 (2009).
Lecaplain, C., Grelu, P. & Wabnitz, S. Polarization-domain-wall complexes in fiber lasers. J. Opt. Soc. Am. B 30, 211–218 (2013).
Choquette, K. D., Richie, D. A. & Leibenguth, R. E. Temperature dependence of gain-guided vertical-cavity surface emitting laser polarization. Appl. Phys. Lett. 64, 2062–2064 (1994).
Choquette, K., Schneider, R., Lear, K. & Leibenguth, R. Gain-dependent polarization properties of vertical-cavity lasers. IEEE J. Sel. Top. Quantum Electron. 1, 661–666 (1995).
Marino, F., Furfaro, L. & Balle, S. Cross-gain modulation in broad-area vertical-cavity semiconductor optical amplifier. Appl. Phys. Lett. 86, 151116 (2005).
Virte, M., Panajotov, K., Thienpont, H. & Sciamanna, M. Deterministic polarization chaos from a laser diode. Nature Photon. 7, 60–65 (2013).
Giacomelli, G. & Politi, A. Relationship between delayed and spatially extended dynamical systems. Phys. Rev. Lett. 76, 2686–2689 (1996).
Javaloyes, J. & Balle, S. Multimode dynamics in bidirectional laser cavities by folding space into time delay. Opt. Express 20, 8496–8502 (2012).
Perez-Serrano, A., Javaloyes, J. & Balle, S. Spectral delay algebraic equation approach to broad area laser diodes. IEEE Sel. J. Top. Quantum Electron. 19, 1502808 (2013).
Marconi, M., Javaloyes, J., Barland, S., Giudici, M. & Balle, S. Robust square-wave polarization switching in vertical-cavity surface-emitting lasers. Phys. Rev. A 87, 013827 (2013).
Javaloyes, J., Marconi, M. & Giudici, M. Phase dynamics in vertical-cavity surface-emitting lasers with delayed optical feedback and cross-polarized reinjection. Phys. Rev. A 90, 023838 (2014).
Javaloyes, J., Mulet, J. & Balle, S. Passive mode locking of lasers by crossed-polarization gain modulation. Phys. Rev. Lett. 97, 163902 (2006).
Arecchi, F. T., Giacomelli, G., Lapucci, A. & Meucci, R. Two-dimensional representation of a delayed dynamical system. Phys. Rev. A 45, R4225–R4228 (1992).
Bödeker, H. U. et al. Noise-covered drift bifurcation of dissipative solitons in a planar gas-discharge system. Phys. Rev. E 67, 056220 (2003).
Kartashov, Y. V., Vysloukh, V. A. & Torner, L. Brownian soliton motion. Phys. Rev. A 77, 051802 (2008).
San Miguel, M., Feng, Q. & Moloney, J. V. Light-polarization dynamics in surface-emitting semiconductor lasers. Phys. Rev. A 52, 1728–1739 (1995).
Klausmeier, C. A. Floquet theory: a useful tool for understanding nonequilibrium dynamics. Theor. Ecol. 1, 153–161 (2008).
Acknowledgements
J.J. acknowledges financial support from the Ramón y Cajal fellowship and useful discussions with B. Krauskopf. J.J. and S.B. acknowledge financial support from project RANGER (TEC2012-38864-C03-01). M.G. acknowledges discussions with G. Giacomelli and C. Miniatura. The INLN group acknowledges funding from Région Provence-Alpes-Cote d'Azur with the “Projet Volet Général 2011: Génération et Détection des Impulsions Ultra Rapides (GEDEPULSE)”, project ANR “OPTIROC” and project ANR – Jeunes Chercheurs “MOLOSSE”.
Author information
Authors and Affiliations
Contributions
M.M. performed the experimental characterization under the supervision of M.G. and assisted by S. Barland. M.M., S.B. and M.G. performed the statistical analysis of the experimental data. J.J. developed the theoretical and the numerical analysis and wrote the manuscript together with S.B. and M.G. All the authors participated in the interpretation of the results.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 28047 kb)
Rights and permissions
About this article
Cite this article
Marconi, M., Javaloyes, J., Barland, S. et al. Vectorial dissipative solitons in vertical-cavity surface-emitting lasers with delays. Nature Photon 9, 450–455 (2015). https://doi.org/10.1038/nphoton.2015.92
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphoton.2015.92
This article is cited by
-
Fitted Difference Scheme on a Non-uniform Mesh for Singularly Perturbed Parabolic Reaction–Diffusion with Large Negative Shift and Non-local Boundary Condition
International Journal of Applied and Computational Mathematics (2023)
-
Uniformly Convergent Numerical Scheme for Solving Singularly Perturbed Parabolic Convection-Diffusion Equations with Integral Boundary Condition
Differential Equations and Dynamical Systems (2023)
-
A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition
Journal of Applied Mathematics and Computing (2023)
-
Time crystal dynamics in a weakly modulated stochastic time delayed system
Scientific Reports (2022)
-
Amplitude Death, Bifurcations, and Basins of Attraction of a Planar Self-Sustained Oscillator with Delayed Feedback
Brazilian Journal of Physics (2022)