volume | PIER Journals

Abstract

In this paper, we have extended the recently introduced theory of coupled propagation of two coaxially co-propagating and mutually incoherent bright 1-D beams to coupled propagation of two 2-D (cylindrical) bright beams and investigated the propagation behavior and spatial soliton pair formation of such beams by a recently introduced simple approach. We have considered saturable form of the nonlinear medium in this paper as 2-D spatial solitons are unstable in Kerr type media. We found that many of the propagation features of two 2-D beams in saturable media are same that of 1-D beams in Kerr type media. However, many features are different and to the best of our knowledge, reported in this paper for the first time. The present version of the theory is applicable in all possible physical situations and parameters.

1. Segev, M., B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media ," Phys. Rev. Lett., Vol. 68, No. 7, 923-926, 1992.
doi:10.1103/PhysRevLett.68.923 Google Scholar

2. Torruellas, W. E., Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, "Observation of two-dimensional spatial solitary waves in a quadratic medium," Phys. Rev. Lett., Vol. 74, No. 25, 5036-5039, 1995.
doi:10.1103/PhysRevLett.74.5036 Google Scholar

3. Tikhonenko, V., J. Christou, and B. Luther-Davies, "Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium," Phys. Rev. Lett., Vol. 76, No. 15, 2698-2701, 1996.
doi:10.1103/PhysRevLett.76.2698 Google Scholar

4. Sturdevant, B., D. A. Lott, and A. Biswas, "Topological solitons in 1+2 dimensions with time-dependent coe±cients," Progress In Electromagnetics Research Letters, Vol. 10, 69-75, 2009.
doi:10.2528/PIERL09070804 Google Scholar

5. Segev, M., M. Shih, and G. Valley, "Photorefractive screening solitons of high and low intensity," J. Opt. Soc. Am. B, Vol. 13, No. 4, 706-718, 1996.
doi:10.1364/JOSAB.13.000706 Google Scholar

6. Kivshar, Y., "Dark solitons in nonlinear optics," IEEE J. Quantum Electron., Vol. 29, No. 1, 250-264, 1993.
doi:10.1109/3.199266 Google Scholar

7. Snyder, A. W., D. J. Mitchell, and Y. Kivshar, "Unification of linear and nonlinear wave optics," Mod. Phys. Lett. B, Vol. 9, No. 23, 1479-1506, 1995.
doi:10.1142/S0217984995001480 Google Scholar

8. Lan, S., M. Shih, G. Mizell, J. A. Giordmaine, Z. Chen, C. Anastassiou, J. Martin, and M. Segev, "Second-harmonic generation in waveguides induced by photorefractive spatial solitons," Opt. Lett., Vol. 24, No. 16, 1145-1147, 1999.
doi:10.1364/OL.24.001145 Google Scholar

9. De La Fuente, R. and A. Barthelemy, "Spatial solitons pairing by cross phase modulation," Opt. Commun., Vol. 88, No. 4-6, 419-423, 1992.
doi:10.1016/0030-4018(92)90067-2 Google Scholar

10. Chen, Z., M. Segev, T. H. Coskun, D. N. Christodoulides, and Y. Kivshar, "Coupled photorefractive spatial-soliton pairs," J. Opt. Soc. Am. B, Vol. 14, No. 11, 3066-3077, 1997.
doi:10.1364/JOSAB.14.003066 Google Scholar

11. Medhekar, S., R. K. Sarkar, and P. P. Paltani, "Coupled spatial soliton pairs in saturable nonlinear media," Opt. Lett., Vol. 31, No. 1, 77-79, 2006.
doi:10.1364/OL.31.000077 Google Scholar

12. Medhekar, S., R. K. Sarkar, and P. P. Paltani, "Soliton pairing of two coaxially co-propagating mutually incoherent 1-D beams in Kerr type media," Optica Applicata, Vol. 37, No. 3, 243-259, 2007. Google Scholar

13. Scheuer, J. and M. Orenstein, "Interaction and switching of spatial soliton pairs in the vicinity of a nonlinear interface," Opt. Lett., Vol. 24, No. 23, 1735-1737, 1999.
doi:10.1364/OL.24.001735 Google Scholar

14. Scheuer, J. and M. Orenstein, "All-optical gates facilitated by soliton interactions in a multilayered Kerr medium," J. Opt. Soc. Am. B, Vol. 22, No. 6, 1260-1267, 2005.
doi:10.1364/JOSAB.22.001260 Google Scholar

Dr. Ram Krishna Sarkar

Professor Sarang Medhekar