OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 7 — Jul. 1, 2005
  • pp: 1443–1452

Ultra-narrow bright spatial solitons interacting with left-handed surfaces

Allan D. Boardman, Larry Velasco, Neil King, and Yuriy Rapoport  »View Author Affiliations

JOSA B, Vol. 22, Issue 7, pp. 1443-1452 (2005)

View Full Text Article

Acrobat PDF (696 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A vectorial finite-difference time-domain (FDTD) method is used to present a numerical study of very narrow spatial solitons interacting with the surface of what has become known as a left-handed medium. After a comprehensive discussion of the background and the family of surface modes to be expected on a left-handed material, bounded by dispersion-free right-handed material, it is demonstrated that robust outcomes of the FDTD approach yield dramatic confirmation of these waves. The FDTD results show how the linear and nonlinear surface modes are created and can be tracked in time as they develop. It is shown how they can move backward or forward, depending on either a critical value of the local nonlinear conditions at the interface or the ambient linear conditions. Several examples are given to demonstrate the power and versatility of the method and the sensitivity to the launching conditions.

© 2005 Optical Society of America

OCIS Codes
(160.0160) Materials : Materials
(190.0190) Nonlinear optics : Nonlinear optics
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(240.0240) Optics at surfaces : Optics at surfaces
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves

Allan D. Boardman, Larry Velasco, Neil King, and Yuriy Rapoport, "Ultra-narrow bright spatial solitons interacting with left-handed surfaces," J. Opt. Soc. Am. B 22, 1443-1452 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).
  2. A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
  3. H. F. Taylor, "Optical modulation in thin films," J. Vac. Sci. Technol. 11, 150-155 (1974).
  4. V. E. Semenov, N. N. Rozanov, and N. V. Vysotina, "Ultranarrow beams of electromagnetic radiation in media with a Kerr nonlinearity," JETP 89, 243-248 (1999).
  5. N. N. Rozanov, V. E. Semenov, and N. V. Vyssotina, "Optical needles in media with saturating self-focusing nonlinearities," J. Opt. B 3, S96-S99 (2001).
  6. E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
  7. C.-F. Chen and S. Chi, "Subwavelength spatial solitons of TE mode," Opt. Commun. 157, 170-172 (1998).
  8. E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
  9. B. V. Gisin and B. A. Malomed, "One- and two-dimensional subwavelength solitons in saturable media," J. Opt. Soc. Am. B 18, 1356-1361 (2001).
  10. J. S. Aitchison, J. S. Silberberg, A. M. Weiner, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, "Observation of spatial optical solitons in a nonlinear glass waveguide," Opt. Lett. 15, 471-473 (1990).
  11. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
  12. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
  13. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000). [CrossRef]
  14. R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001). [CrossRef]
  15. I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69, 016617 (2004). [CrossRef]
  16. J. Pendry, "Electromagnetic materials enter the negative age," Phys. World 14, 47-51 (2001).
  17. R. Ruppin, "Surface polaritons of a left-handed medium," Phys. Lett. A 277, 61-64 (2000).
  18. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef]
  19. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003). [CrossRef]
  20. M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
  21. R. W. Ziolkowski, "Pulsed and cw Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
  22. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
  23. A. K. Sarychev, V. P. Drachev, H. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksimenko, eds. Proc. SPIE 5219, 92-98 (2003).
  24. V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A, Pure Appl. Opt. 7, 32-37 (2005).
  25. J. B. Pendry, "Focusing light using negative refraction," J. Phys.: Condens. Matter 15, 6345-6364 (2003).
  26. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  27. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).
  28. R. M. Joseph and A. Taflove, "Spatial soliton deflection mechanism indicated by FD-TD Maxwell's equations modeling," IEEE Photonics Technol. Lett. 6, 1251-1254 (1994).
  29. K. L. Shlager and J. B. Schneider, "A selective survey of the finite-difference time-domain literature," IEEE Antennas Propag. Mag. 37, 39-56 (1995).
  30. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
  31. G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
  32. S. A. Cummer, "Dynamics of causal beam refraction in negative refractive index materials," Appl. Phys. Lett. 82, 2008-2010 (2003).
  33. R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
  34. A. D. Boardman, P. Egan, L. Velasco, and N. King, "Control of planar nonlinear guided waves and spatial solitons with a left-handed medium," J. Opt. A 7, 57-67 (2004).
  35. A. Schuster, An Introduction of the Theory of Optics (Edward Arnold, 1904).
  36. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  37. Y. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  38. N. Akhmediev and A. Ankieewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).
  39. A. D. Boardman, K. Marinov, D. I. Pushkarov, and A. Shivarova, "Influence of nonlinearly induced diffraction on spatial solitary waves," Opt. Quantum Electron. 32, 49-62 (2000).
  40. D. Sullivan, J. Liu, and M. Kuzyuk, "Three-dimensional optical pulse simulation using the FDTD method," IEEE Trans. Microwave Theory Tech. 48, 1127-1133 (2000).
  41. R. W. Ziolkowski and J. B. Judkins, "Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time," J. Opt. Soc. Am. B 10, 186-198 (1993).
  42. H. Lee, K. Chae, S. Yim, and S. Park, "Finite-difference time-domain analysis of self-focusing in a nonlinear Kerr film," Opt. Express 12, 2603-2609 (2004).
  43. D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
  44. J. V. Moloney, A. C. Newell, and A. B. Aceves, "Spatial soliton optical switches: a soliton-based equivalent particle approach," Opt. Quantum Electron. 24, S1269-S1293 (1992).
  45. P. Mazur and B. Djafari-Rouhani, "Effect of surface polaritons on the lateral displacement of a light beam at a dielectric interface," Phys. Rev. B 30, 6759-6762 (1984). [CrossRef]
  46. A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).
  47. I. V. Shadrivov, R. W. Ziolkowski, A. A. Zharov, and Y. S. Kivshar, "Excitation of guided waves in layered structures with negative refraction," Opt. Express 13, 481-492 (2005).

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