## Dynamic behavior of spatial solitons propagating along Scarf II parity–time symmetric cells |

JOSA B, Vol. 29, Issue 11, pp. 3057-3062 (2012)

http://dx.doi.org/10.1364/JOSAB.29.003057

Enhanced HTML Acrobat PDF (848 KB)

### Abstract

Using a nonstationary state solution to the nonlinear Schrödinger equation (NLSE), we report the results of our numerical investigation on the swing behavior of spatial solitons propagating along waveguides whose refractive indices in the transverse direction are perturbed by Scarf II type parity–time symmetric profiles. We show that solitons, after entering parity–time symmetry (PTS) cells with Scarf II profiles will, in general, swing along the waveguide with nonuniform amplitude and period. Nevertheless, it is demonstrated that when the average incident position in the transverse direction is set at the center of the profile symmetry and the amplitude of the incident soliton exceeds a specific value, the soliton behavior could be approximated by a stationary-state solution to the NLSE and say it is almost self-trapped. Simulation also shows that, depending on the soliton’s initial average transverse input position, the swing behavior could be greatly influenced by the nonreciprocity of PTS cells.

© 2012 Optical Society of America

**OCIS Codes**

(190.3270) Nonlinear optics : Kerr effect

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 1, 2012

Revised Manuscript: September 19, 2012

Manuscript Accepted: September 21, 2012

Published: October 16, 2012

**Citation**

Mina Nazari, Fakhroddin Nazari, and Mohammad Kazem Moravvej-Farshi, "Dynamic behavior of spatial solitons propagating along Scarf II parity–time symmetric cells," J. Opt. Soc. Am. B **29**, 3057-3062 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-11-3057

Sort: Year | Journal | Reset

### References

- T. Kato, Perturbation Theory for Linear Operators (Springer Verlag, 1966).
- C. M. Bender and S. Bottcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998). [CrossRef]
- C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999). [CrossRef]
- A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005). [CrossRef]
- O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009). [CrossRef]
- 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]
- K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010). [CrossRef]
- 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]
- 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]
- F. Nazari, M. Nazari, and M. K. Moravvej-Farshi, “A 2×2 spatial optical switch based on PT-symmetry,” Opt. Lett. 36, 4368–4370 (2011). [CrossRef]
- 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]
- A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (2010). [CrossRef]
- H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010). [CrossRef]
- Z. Lu and Z. Zhang, “Defect solitons in parity-time symmetric superlattices,” Opt. Express 19, 11457–11462 (2011). [CrossRef]
- F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011). [CrossRef]
- D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in the harmonic PT-symmetric potential,” Phys. Rev. A 85, 043840(2012). [CrossRef]
- M. Ebnali-Heidary, M. K. Moravvej-Farshi, and A. Zarifkar, “Multichannel wavelength conversion using fourth-order soliton decay,” J. Lightwave Technol. 25, 2571–2578(2007). [CrossRef]
- F. Garzia, C. Sibilia, and M. Bertolotti, “New phase modulation technique based on spatial soliton switching,” J. Lightwave Technol. 19, 1036–1042 (2001). [CrossRef]
- N. J. Doran and D. Wood, “Soliton processing element for all-optical switching and logic,” J. Opt. Soc. Am. B 4, 1843–1846 (1987). [CrossRef]
- X. D. Cao and D. D. Meyerhofer, “All-optical switching by means of collisions of spatial vector solitons,” Opt. Lett. 19, 1711–1713 (1994). [CrossRef]
- L. Lefort and A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photon. Technol. Lett. 9, 1364–1366 (1997). [CrossRef]
- A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989). [CrossRef]
- A. Suryanto and E. van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258, 264–274 (2006). [CrossRef]
- F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997). [CrossRef]
- M. Ebnali-Heidari, M. K. Moravvej-Farshi, and A. Zarifkar, “Swing effect of spatial solitons propagating through Gaussian and triangular waveguides,” Appl. Opt. 48, 5005–5014 (2009). [CrossRef]
- Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282, 343–348 (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.