OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 16, Iss. 8 — Aug. 1, 1999
  • pp: 1269–1279

Quantum theory of a second-order soliton based on a linearization approximation

Chen-Pang Yeang  »View Author Affiliations


JOSA B, Vol. 16, Issue 8, pp. 1269-1279 (1999)
http://dx.doi.org/10.1364/JOSAB.16.001269


View Full Text Article

Acrobat PDF (261 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A linearized perturbation quantum theory of second-order soliton propagation is developed. The theory shows that the quantum fluctuations of photon number, phase, momentum, and position at an arbitrary propagation distance are linear combinations of these fluctuations at zero distance. The evolutions of second-order soliton quantum fluctuations are evaluated and compared with the quantum-fluctuation evolutions of a fundamental soliton. Based on this theory, the squeezing effect of a second-order soliton is studied. It is shown that, like a fundamental soliton, a second-order soliton also exhibits squeezing along propagation when a proper combination of the number and phase operators is detected.

© 1999 Optical Society of America

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(270.0270) Quantum optics : Quantum optics
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(270.6570) Quantum optics : Squeezed states

Citation
Chen-Pang Yeang, "Quantum theory of a second-order soliton based on a linearization approximation," J. Opt. Soc. Am. B 16, 1269-1279 (1999)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-16-8-1269


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
  2. L. F. Mollenauer and R. H. Stolen, “The soliton laser,” Opt. Lett. 9, 13–15 (1984).
  3. J. P. Gordon and H. A. Haus, “Random walk of coherently amplified solitons in optical fiber transmission,” Opt. Lett. 11, 665–667 (1986).
  4. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13, 2226–2243 (1976).
  5. J. N. Hollenhorst, “Quantum limits on resonant-mass gravitational-radiation detectors,” Phys. Rev. D 19, 1669–1679 (1979).
  6. T. Hirano and M. Matsuoka, “Broadband squeezing of light by pulse excitation,” Opt. Lett. 15, 1153–1155 (1990).
  7. K. Bergman and H. A. Haus, “Squeezing in fibers with optical pulses,” Opt. Lett. 16, 663–665 (1991).
  8. M. Rosenbluth and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
  9. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1844 (1987).
  10. P. D. Drummond and S. J. Carter, “Quantum field theory of squeezing in solitons,” J. Opt. Soc. Am. B 4, 1565–1673 (1987).
  11. Y. Lai and H. A. Haus, “Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation,” Phys. Rev. A 40, 844–853 (1989).
  12. Y. Lai and H. A. Haus, “Quantum theory of solitons in optical fibers. II. Exact solution,” Phys. Rev. A 40, 854–856 (1989).
  13. H. A. Haus, K. Watanabe, and Y. Yamamoto, “Quantum-nondemolition measurement of optical solitons,” J. Opt. Soc. Am. B 6, 1138–1148 (1989).
  14. H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach,” J. Opt. Soc. Am. B 7, 386–392 (1990).
  15. Y. Lai, “Quantum theory of soliton propagation: a unified approach based on the linearization approximation,” J. Opt. Soc. Am. B 10, 475–484 (1993).
  16. J. Satsuma and N. Yajima, “Initial value problems of one-dimensional self-modulation of nonlinear wave in dispersive media,” Prog. Theor. Phys. Suppl. 55, 284–306 (1974).
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1995), Chap. 5.
  18. H. A. Haus, F. I. Khatri, W. S. Wang, E. P. Ippen, and K. R. Tamura, “Interaction of soliton with sinusoidal wave packet,” IEEE J. Quantum Electron. 32, 917–924 (1996).
  19. R. H. Stolen, L. F. Mollenauer, and W. J. Tomlinson, “Observation of pulse restoration at the soliton period in optical fibers,” Opt. Lett. 8, 186–188 (1983).
  20. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, “Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers,” Opt. Lett. 8, 289–291 (1983).
  21. J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrodinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
  22. D. J. Kaup, “Perturbation theory for solitons in optical fibers,” Phys. Rev. A 42, 5689–5694 (1990).
  23. K. J. Blow and N. J. Doran, “The asymptotic dispersion of soliton pulses in lossy fibres,” Opt. Commun. 52, 367–370 (1985).
  24. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1995), Chap. 8.
  25. P. D. Drummond and A. D. Hardman, “Simulation of quantum effects in Raman-active waveguides,” Europhys. Lett. 21, 279–284 (1993).
  26. Y. Lai and S.-S. Yu, “General quantum theory of nonlinear optical-pulse propagation,” Phys. Rev. A 51, 817–829 (1995).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited