OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Grover Swartzlander
  • Vol. 31, Iss. 8 — Aug. 1, 2014
  • pp: 1861–1866

Modulation instability in nonlinear complex parity-time symmetric periodic structures

Amarendra K. Sarma  »View Author Affiliations


JOSA B, Vol. 31, Issue 8, pp. 1861-1866 (2014)
http://dx.doi.org/10.1364/JOSAB.31.001861


View Full Text Article

Enhanced HTML    Acrobat PDF (349 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We carry out a modulation instability (MI) analysis in nonlinear complex parity-time (PT) symmetric periodic structures. All three regimes defined by the PT-symmetry breaking point or threshold, namely, below threshold, at threshold, and above threshold, are discussed. It is found that MI exists even beyond the PT-symmetry threshold, indicating the possible existence of solitons or solitary waves, in conformity with some recent reports. We find that MI does not exist at the PT-symmetry breaking point in the case of normal dispersion below a certain nonlinear threshold. However, in the case of the anomalous dispersion regime, MI does exist even at the PT-symmetry breaking point.

© 2014 Optical Society of America

OCIS Codes
(190.3100) Nonlinear optics : Instabilities and chaos
(190.3270) Nonlinear optics : Kerr effect
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: March 25, 2014
Revised Manuscript: May 11, 2014
Manuscript Accepted: June 19, 2014
Published: July 17, 2014

Citation
Amarendra K. Sarma, "Modulation instability in nonlinear complex parity-time symmetric periodic structures," J. Opt. Soc. Am. B 31, 1861-1866 (2014)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-31-8-1861


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT-symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998). [CrossRef]
  2. C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999). [CrossRef]
  3. C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002). [CrossRef]
  4. C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007). [CrossRef]
  5. A. Mostafazadeh, “Exact PT-symmetry is equivalent to Hermiticity,” J. Phys. A 36, 7081–7091 (2003). [CrossRef]
  6. C. E. Ruter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6, 192–195 (2010). [CrossRef]
  7. A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity–time synthetic photonic lattices,” Nature 488, 167–171 (2012). [CrossRef]
  8. L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013). [CrossRef]
  9. J. Schindler, A. Li, M. C. Zheng, F. M. Ellis, and T. Kottos, “Experimental study of active LRC circuits with PT symmetries,” Phys. Rev. A 84, 040101 (2011). [CrossRef]
  10. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric periodic optical potentials,” Int. J. Theor. Phys. 50, 1019–1041 (2011). [CrossRef]
  11. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT-symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008). [CrossRef]
  12. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011). [CrossRef]
  13. L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal light propagation in a silicon photonic circuit,” Science 333, 729–733 (2011). [CrossRef]
  14. T. Kottos, “Optical physics: broken symmetry makes light work,” Nat. Phys. 6, 166–167 (2010). [CrossRef]
  15. M. A. Miri, P. L. Wa, and D. N. Christodoulides, “Large area single-mode parity–time-symmetric laser amplifiers,” Opt. Lett. 37, 764–766 (2012). [CrossRef]
  16. Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106, 093902 (2011). [CrossRef]
  17. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (2010). [CrossRef]
  18. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008). [CrossRef]
  19. M. Nazari, F. Nazari, and M. K. Moravvej-Farshi, “Dynamic behavior of spatial solitons propagating along Scarf II parity–time symmetric cells,” J. Opt. Soc. Am. B 29, 3057–3062 (2012). [CrossRef]
  20. M. A. Miri, A. B. Aceves, T. Kottos, V. Kovanis, and D. N. Christodoulides, “Bragg solitons in nonlinear-symmetric periodic potentials,” Phys. Rev. A 86, 033801 (2012). [CrossRef]
  21. V. E. Zakharov and L. A. Ostrosvsky, “Modulation instability: the beginning,” Physica D 238, 540–548 (2009). [CrossRef]
  22. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  23. A. K. Sarma and M. Saha, “Modulational instability of coupled nonlinear field equations for pulse propagation in a negative index material embedded into a Kerr medium,” J. Opt. Soc. Am. B 28, 944–948 (2011). [CrossRef]
  24. M. J. Potasek, “Modulation instability in an extended nonlinear Schrödinger equation,” Opt. Lett. 12, 921–923 (1987). [CrossRef]
  25. P. K. Shukla and J. J. Rasmussen, “Modulational instability of short pulses in long optical fibers,” Opt. Lett. 11, 171–173 (1986). [CrossRef]
  26. A. K. Sarma, “Modulational instability of few-cycle pulses in optical fibers,” Europhys. Lett. 92, 24004 (2010). [CrossRef]
  27. Y. Xiang, X. Dai, S. Wen, and D. Fan, “Modulation instability in metamaterials with saturable nonlinearity,” J. Opt. Soc. Am. B 28, 908–916 (2011). [CrossRef]
  28. A. K. Sarma and P. Kumar, “Modulation instability of ultrashort pulses in quadratic nonlinear media beyond the slowly varying envelope approximation,” Appl. Phys. B 106, 289–293 (2012). [CrossRef]
  29. N. Akhmediev and A. Ankiewicz, “Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation,” Phys. Rev. E 83, 046603 (2011). [CrossRef]
  30. E. Kengne, S. T. Chui, and W. M. Liu, “Modulational instability criteria for coupled nonlinear transmission lines with dispersive elements,” Phys. Rev. E 74, 036614 (2006). [CrossRef]
  31. Z. Xu, L. Li, Z. Li, and G. Zhou, “Modulation instability and solitons on a cw background in an optical fiber with higher-order effects,” Phys. Rev. E 67, 026603 (2003). [CrossRef]
  32. M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107, 253901 (2011). [CrossRef]
  33. C. M. de Sterke, “Theory of modulational instability in fiber Bragg gratings,” J. Opt. Soc. Am. B 15, 2660–2667 (1998). [CrossRef]
  34. R. Ganapthy, K. Senthilnathan, and K. Porsezian, “Modulational instability in a fibre and a fibre Bragg grating,” J. Opt. B 6, S436–S452 (2004). [CrossRef]
  35. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2007).
  36. S. K. Gupta and A. K. Sarma, “Solitary waves in parity-time (PT)–symmetric Bragg grating structure and the existence of optical rogue waves,” Europhys. Lett. 105, 44001 (2014). [CrossRef]
  37. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef]
  38. D. N. Christodoulides and R. I. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989). [CrossRef]
  39. W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004). [CrossRef]
  40. N. M. Litchinitser, C. J. McKinstrie, C. M. de Sterke, and G. P. Agrawal, “Spatiotemporal instabilities in nonlinear bulk media with Bragg gratings,” J. Opt. Soc. Am. B 18, 45–54 (2001). [CrossRef]

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