PIER B
 
Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 29 > pp. 83-103

DERIVATION OF THE EFFECTIVE NONLINEAR SCHRÖDINGER EQUATIONS FOR DARK AND POWER LAW SPATIAL PLASMON-POLARITON SOLITONS USING NANO SELF-FOCUSING

By S. H. Crutcher and A. Osei

Full Article PDF (428 KB)

Abstract:
An effective Nonlinear Schrödinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a surface plasmonic interaction. Starting with Maxwell's Nonlinear Equations a model is proposed for TM polarized type spatial solitons on a metal dielectric interface. Two separate systems are considered in which one metal dielectric interface has a dielectric Kerr medium that has self-defocusing and another similar interface which the dielectric Kerr medium that has self-focusing depending on the modulus of the electric field to some power law variable p. The beam dynamics are analytically studied for these nanowaveguides.

Citation:
S. H. Crutcher and A. Osei, "Derivation of the Effective Nonlinear SchrÖDinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing," Progress In Electromagnetics Research B, Vol. 29, 83-103, 2011.
doi:10.2528/PIERB11020306

References:
1. Kivshar, Y. S. and G. P. Agrawal, Optical Solitons from Fibers to Photonic Crystal, Academic Press, 2003.

2. Stegeman, G. I., L. Jankovic, H. Kim, S. Polyakov, S. Carrasco, L. Torner, C. Bosshard, P. Gunter, M. Katz, and D. Eger, "Generation of and interactions between quadratic spatial solitons in non-critically-phase-matched crystals," Journal of Nonlinear Optical Physics & Materials, Vol. 12, No. 4, 447-466, 2003.
doi:10.1142/S0218863503001572

3. Hasegawa, A. and Y. Kodama, Solitons in Optical Communications, Oxford University Press, 1995.

4. Reitze, A. D., H. Weiner, and D. E. Leaird, "High power femtosecond optical pulse compression using spatial solitons," Optics Letters, Vol. 16, 1409-1411, 1991.
doi:10.1364/OL.16.001409

5. Scheuer, J. and M. Orenstein, "Interactions and switching of spatial soliton pairs in the vicinity of a nonlinear interface," Optics Letters, Vol. 24, 1735-1737, 1999.
doi:10.1364/OL.24.001735

6. Pramono, Y. H., M. Geshiro, and T. Kitamura, "Optical Logic OR-AND-NOT and NOR Gates in waveguides consisting of nonlinear material," IEICE Transactions on Electronics, Vol. 11, 1755-1762, 2000.

7. Gisin, B. and B. A. Malomed, "One and two dimensional subwavelength solitons in saturable media," Journal of Optical Society of America B, Vol. 18, 1356-1361, 2001.
doi:10.1364/JOSAB.18.001356

8. Gisin, B. and B. A. Malomed, "Subwavelength spatial solitons in optical media with non-Kerr nonlinearities," Journal of Optics A: Pure and Applied Optics, Vol. 3, 284-290, 2001.
doi:10.1088/1464-4258/3/4/309

9. Sarid, D. and W. Challener, Modern Introduction to Surface Plasmons, Cambridge Press, 2010.

10. Maier, S. A., Plasmonics: Fundamentals and Applications, Springer-Verlag, Berlin, 2007.

11. Bozhevolnyi, S. I., Plasmonic Nanoguides and Circuits, Pan Stanford Publ., Singapore, 2009.

12. Calzzani, F. A., R. Sileshi, A. Kassu, J. M. Taguenang, A. Chowdhury, A. Sharma, P. B. Ruffin, C. Brantley, and E. Edwards, "Detection of residual traces of explosives by surface enhance Raman scattering using gold coated substrates produced by nanospheres imprint technique," Proceedings of SPIE, Vol. 6949, 69451O, 2008.
doi:10.1117/12.777072

13. Vincenti, M. A., et al., "Enhanced transmission and second harmonic generation from subwavelength slits on metal substrates," Proceedings of SPIE, Vol. 6987, 698700, 2008.

14. Scalora, M., G. D'Aguanno, N. Mattiucci, M. J. Bloemer, D. De Ceglia, M. Centini, A. Mandatori, C. Sibilia, N. Akozbek, M. G. Cappeddu, M. Fowler, and J. W. Haus, "Negative refraction and sub-wavelength focusing in the visible range using transparent metallo-dielectric stacks," Optics Express, Vol. 15, 508, 2007.
doi:10.1364/OE.15.000508

15. Davoyan, A. R., I. V. Shadrivov, and Y. S. Kivshar, "Self-focusing and spatial plasmon-polariton solitons," Optics Express, Vol. 17, No. 24, 21732-21737, 2009.
doi:10.1364/OE.17.021732

16. Edwards, M., S. H. Crutcher, M. D. Aggarwal, A. K. Batra, H. M. Jaenisch, A. J. Osei, and S. R. Bairavarasu, "Optical solitons in inhomogeneous media," Proceedings of SPIE, Vol. 5525, 2004.

17. Crutcher, S. H., M. Edwards, and A. Osei, Optical spatial solitons, the power law, and the swing effect, Vol. 7056, 70560Q-1, Proceedings of SPIE, 2008.

18. Crutcher, S. H., M. E. Edwards, A. Biswas, and M. D. Aggarwal, "Oscillatory behavior of spatial soltions in two dimensional waveguides and stationary temporal power law solitons in optical fibers," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 761-772, 2006.
doi:10.1163/156939306776143361

19. Trillo, S. and W. Torruellas, Optical Spatial Solitons, Springer Series in Optical Sciences, 2001.

20. Prade, B., J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructure with negative dielectric constant," Physical Review B, Vol. 44, No. 24, 556-572, 1991.
doi:10.1103/PhysRevB.44.13556

21. Bliokh, K. Y., Y. P. Bliokh, and A. Ferrando, "Resonant plasmon-soliton interaction," Physical Review A, Vol. 79, No. 24, 041803(R), 2009.

22. Feigenbaum, E. and M. Orenstein, "Plasmon-soliton," Optics Letters, Vol. 32, No. 6, 674-676, 2007.
doi:10.1364/OL.32.000674

23. Snyder, A. W. and D. J. Mitchell, "Spatial solitons of power law nonlinearity," Optics Letters, Vol. 18, No. 2, 101-103, 1993.
doi:10.1364/OL.18.000101

24. Mihalacke, D., M. Bertolotti, and C. Sibilia, Progress in Optics XXVII, E. Wolf (ed.), 228-309, Elsevier, Amsterdam, 1989.

25. Biswas, A., "Quasi-stationary optical solitons with power law nonlinearity," Journal of Physics A: Mathematical and Theoretical, Vol. 36, 4581-4589, 2003.

26. Biswas, A. and S. Konar, Introduction to Non-Kerr Law Optical Solitons, Chapman & Hall, 2007.

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

28. Biswas, A., "1-soliton solution of (1 + 2)-dimensional nonlinear Schrödinger's equation in dual power law media," Physics Letters A, Vol. 372, 5941-5943, 2008.
doi:10.1016/j.physleta.2008.07.052

29. Biswas, A., "Optical solitons in a parabolic law media with fourth order dispersion," Applied Mathematics and Computation, Vol. 208 , 299-302, 2009.
doi:10.1016/j.amc.2008.12.004

30. Biswas, A., "1-soliton solution of 1 + 2 dimensional nonlinear Schrödinger's equation in power law media," Communication in Nonlinear Science and Numerical Simulations, Vol. 14, 1830-1833, 2009.
doi:10.1016/j.cnsns.2008.08.003

31. Boardman, A. D., G. S. Cooper, A. A. Maradudin, and T. P. Shen, "Surface --- polariton solitons," Physical Review B, Vol. 34, 8273-8278, 1986.
doi:10.1103/PhysRevB.34.8273

32. Agranovich, V. M., V. S. Babichenko, and V. Ya Chernyak, "Nonlinear surface polaritons," Soviet Physics. JETP Letters, Vol. 32, 512-515, 1980.

33. Stegeman, G. H., C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, "Nonlinear electromagnetic waves guided by a single interface," Journal of Applied Physics, Vol. 58, 2453-2459, 1985.
doi:10.1063/1.335920

34. Boardman, A. D., G. H. Stegeman, A. A. Maradudin, T. Twardowski, and E. M. Wright, "Exact theory of nonlinear p-polarized optical waves," Physical Review A, Vol. 35, 1159-1164, 1987.
doi:10.1103/PhysRevA.35.1159


© Copyright 2010 EMW Publishing. All Rights Reserved