Abstract

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

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. S. A. Cummer, "Dynamics of causal beam refraction in negative refractive index materials," Appl. Phys. Lett. 82, 2008-2010 (2003).
    [CrossRef]
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    [CrossRef]
  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).
    [CrossRef]
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  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).
    [CrossRef]
  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).
    [CrossRef]
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    [CrossRef] [PubMed]
  43. D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
    [CrossRef]
  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).
    [CrossRef]
  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).
    [CrossRef] [PubMed]

2005 (2)

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).
[CrossRef]

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).
[CrossRef] [PubMed]

2004 (3)

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).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

2003 (5)

S. A. Cummer, "Dynamics of causal beam refraction in negative refractive index materials," Appl. Phys. Lett. 82, 2008-2010 (2003).
[CrossRef]

J. B. Pendry, "Focusing light using negative refraction," J. Phys.: Condens. Matter 15, 6345-6364 (2003).

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

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).
[CrossRef]

R. W. Ziolkowski, "Pulsed and cw Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
[CrossRef] [PubMed]

2002 (1)

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

2001 (5)

J. Pendry, "Electromagnetic materials enter the negative age," Phys. World 14, 47-51 (2001).

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

2000 (6)

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

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).
[CrossRef]

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).
[CrossRef]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

R. Ruppin, "Surface polaritons of a left-handed medium," Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

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).
[CrossRef]

1998 (1)

C.-F. Chen and S. Chi, "Subwavelength spatial solitons of TE mode," Opt. Commun. 157, 170-172 (1998).
[CrossRef]

1997 (3)

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
[CrossRef]

G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
[CrossRef]

1995 (2)

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).
[CrossRef]

D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
[CrossRef]

1994 (1)

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).
[CrossRef]

1993 (1)

1992 (1)

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).
[CrossRef]

1990 (1)

1984 (1)

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]

1974 (1)

H. F. Taylor, "Optical modulation in thin films," J. Vac. Sci. Technol. 11, 150-155 (1974).
[CrossRef]

1968 (2)

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1966 (1)

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).
[CrossRef]

Aceves, A. B.

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).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Y. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Aitchison, J. S.

Akhmediev, N.

N. Akhmediev and A. Ankieewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).

Ankieewicz, A.

N. Akhmediev and A. Ankieewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).

Bassi, P.

G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
[CrossRef]

Bellanca, G.

G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
[CrossRef]

Boardman, A. D.

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).
[CrossRef]

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]

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).
[CrossRef]

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).

Chae, K.

Chen, C.-F.

C.-F. Chen and S. Chi, "Subwavelength spatial solitons of TE mode," Opt. Commun. 157, 170-172 (1998).
[CrossRef]

Chi, S.

C.-F. Chen and S. Chi, "Subwavelength spatial solitons of TE mode," Opt. Commun. 157, 170-172 (1998).
[CrossRef]

Cummer, S. A.

S. A. Cummer, "Dynamics of causal beam refraction in negative refractive index materials," Appl. Phys. Lett. 82, 2008-2010 (2003).
[CrossRef]

Djafari-Rouhani, B.

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]

Drachev, V. P.

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).

Egan, P.

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]

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).
[CrossRef]

Gisin, B. V.

Granot, E.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Heyman, E.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Isbi, Y.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

Jackel, J. L.

Joseph, R. M.

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
[CrossRef]

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).
[CrossRef]

Judkins, J. B.

King, N.

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).
[CrossRef]

A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).

Kivshar, Y.

Y. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Kivshar, Y. S.

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).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Kunz, K. S.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

Kuzyuk, M.

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).
[CrossRef]

Lakhtakia, A.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Leaird, D. E.

Lee, H.

Lewis, A.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

Liu, J.

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).
[CrossRef]

Luebbers, R. J.

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

Malomed, B.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

Malomed, B. A.

Marinov, K.

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).
[CrossRef]

Mazur, P.

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]

McCall, M. W.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Moloney, J. V.

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).
[CrossRef]

Narimanov, E. E.

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).
[CrossRef]

Newell, A. C.

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).
[CrossRef]

Oliver, M. K.

Otto, A.

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

Park, S.

Pendry, J.

J. Pendry, "Electromagnetic materials enter the negative age," Phys. World 14, 47-51 (2001).

Pendry, J. B.

J. B. Pendry, "Focusing light using negative refraction," J. Phys.: Condens. Matter 15, 6345-6364 (2003).

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

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).
[CrossRef]

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).

Pushkarov, D. I.

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).
[CrossRef]

Rapoport, Y.

A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).

Rozanov, N. N.

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).
[CrossRef]

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).
[CrossRef]

Ruppin, R.

R. Ruppin, "Surface polaritons of a left-handed medium," Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Sarychev, A. K.

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).
[CrossRef]

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).

Schneider, J. B.

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).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schuster, A.

A. Schuster, An Introduction of the Theory of Optics (Edward Arnold, 1904).

Semenov, V. E.

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).
[CrossRef]

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).
[CrossRef]

Semprini, R.

G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
[CrossRef]

Shadrivov, I. V.

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).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shalaev, V. M.

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).
[CrossRef]

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).

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shivarova, A.

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).
[CrossRef]

Shlager, K. L.

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).
[CrossRef]

Silberberg, J. S.

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

Smith, P. W. E.

Sternklar, S.

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "Subwavelength spatial solitons," Opt. Lett. 22, 1290-1292 (1997).
[CrossRef]

Sukhorukov, A. A.

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]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Sullivan, D.

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).
[CrossRef]

Sullivan, D. M.

D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
[CrossRef]

Taflove, A.

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
[CrossRef]

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).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Taylor, H. F.

H. F. Taylor, "Optical modulation in thin films," J. Vac. Sci. Technol. 11, 150-155 (1974).
[CrossRef]

Velasco, L.

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).
[CrossRef]

A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vogel, E. M.

Vysotina, N. V.

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).
[CrossRef]

Vyssotina, N. V.

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).
[CrossRef]

Weiglhofer, W. S.

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

Weiner, A. M.

Yee, K. S.

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).
[CrossRef]

Yim, S.

Yuan, H.

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).

Zharov, A. A.

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).
[CrossRef] [PubMed]

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]

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).
[CrossRef]

Ziolkowski, R. W.

Appl. Phys. Lett. (2)

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).
[CrossRef]

S. A. Cummer, "Dynamics of causal beam refraction in negative refractive index materials," Appl. Phys. Lett. 82, 2008-2010 (2003).
[CrossRef]

Eur. J. Phys. (1)

M. W. McCall, A. Lakhtakia, and W. S. Weiglhofer, "The negative index of refraction demystified," Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

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).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

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).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

R. M. Joseph and A. Taflove, "FDTD Maxwell's equations models for nonlinear electrodynamics and optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997).
[CrossRef]

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).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

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).
[CrossRef]

D. M. Sullivan, "Nonlinear FDTD formulations using Z transforms," IEEE Trans. Microwave Theory Tech. 43, 676-682 (1995).
[CrossRef]

J. Opt. A (1)

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).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

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).
[CrossRef]

J. Opt. B (1)

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).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys.: Condens. Matter (1)

J. B. Pendry, "Focusing light using negative refraction," J. Phys.: Condens. Matter 15, 6345-6364 (2003).

J. Vac. Sci. Technol. (1)

H. F. Taylor, "Optical modulation in thin films," J. Vac. Sci. Technol. 11, 150-155 (1974).
[CrossRef]

JETP (1)

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).
[CrossRef]

Opt. Commun. (2)

C.-F. Chen and S. Chi, "Subwavelength spatial solitons of TE mode," Opt. Commun. 157, 170-172 (1998).
[CrossRef]

E. Granot, S. Sternklar, Y. Isbi, B. Malomed, and A. Lewis, "On the existence of subwavelength spatial solitons," Opt. Commun. 178, 431-435 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Opt. Quantum Electron. (3)

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).
[CrossRef]

G. Bellanca, R. Semprini, and P. Bassi, "FDTD modeling of spatial soliton propagation," Opt. Quantum Electron. 29, 233-241 (1997).
[CrossRef]

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).
[CrossRef]

Phys. Lett. A (1)

R. Ruppin, "Surface polaritons of a left-handed medium," Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Phys. Rev. B (1)

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]

Phys. Rev. E (3)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative-refractive-index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

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]

Phys. Rev. Lett. (2)

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 85, 2933-2936 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Phys. World (1)

J. Pendry, "Electromagnetic materials enter the negative age," Phys. World 14, 47-51 (2001).

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Z. Phys. (1)

A. Otto, "Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968).
[CrossRef]

Other (9)

A. D. Boardman, N. King, Y. Rapoport, and L. Velasco, "Gyrotropic impact upon negative refracting surfaces," New J. Phys. (to be published).

A. D. Boardman, Electromagnetic Surface Modes (Wiley, 1982).

A. Schuster, An Introduction of the Theory of Optics (Edward Arnold, 1904).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Y. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

N. Akhmediev and A. Ankieewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, 1997).

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).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).

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Figures (7)

Fig. 1
Fig. 1

Sketches of the field profile intensities as a function of the y coordinate normal to the boundary between (a) a RHM linear dielectric and a RHM Kerr-type nonlinear dielectric and (b) TE surface waves at a RHM linear dielectric and a LHM linear dispersive plasma. Both (a) and (b) satisfy the TE boundary conditions.

Fig. 2
Fig. 2

Stable propagation of a 1-λ-wide beam soliton over a substantial distance (upper panel) compared with the distance shown in the middle figure for a beam width of 0.5 λ . The bottom panel indicates the destructive effects caused by interactions. x and y are measured in units of cell λ 33 .

Fig. 3
Fig. 3

(a) Time-averaged electric field amplitude over the time step (a) T = 12000 , (b) 7000, and (c) 12 000 units. LHM–air interface, Y = 300 . In (a) the air–nonlinear glass interface is at Y = 310 ; the inset displays the characteristic surface-wave profile taken at X = 0 , with interfaces marked by solid (LHM–air) and dashed (air–glass) lines. In (b) the air-linear glass (n=1.53) interface is at Y = 330 . In (c) the air-linear glass (n=1.53) interface is at Y = 310 ; the inset displays the characteristic surface-wave profile taken at X = 0 , with interfaces marked by solid (LHM-air) and dashed (air-glass) curves. Data are as follows: (a) μ = 0.29 and ϵ = 5.81 ; (b) μ = 1.2800 , and ϵ = 0.6963 , 45° beam angle with air gap of 30 spatial cells; and (c) μ = 0.29 and ϵ = 5.81 , (a) and (c) 30° beam angle with air gap of 10 spatial cell. x and y are measured in units of cell λ 33 .

Fig. 4
Fig. 4

Time-averaged electric field amplitude over the time step T = 10000 . LHM–air interface is at Y = 300 , air–linear glass ( n = 1.53 ) interface is at Y = 310 . Dashed curve indicates expected position of beam in non resonant case. μ = 0.5000 and ϵ = 2.5605 , beam angle to 40°; x and y are measured in units of cell λ 33 .

Fig. 5
Fig. 5

Time-averaged electric field amplitude over the time step T = 19000 . Glass–LHM interface is at Y = 300 . Inset displays the characteristic surface-wave profile taken at X = 2600 with the interface marked by a solid curve. μ = 1 and ϵ = 2.25 , beam angle 5°; x and y are measured in units of cell λ 33 .

Fig. 6
Fig. 6

Time-averaged electric field amplitude over the time step T = 25000 . Glass–LHM interface is at Y = 300 . μ = 1 and ϵ = 2.25 , beam angle 5°; x and y are measured in units of cell λ 33 .

Fig. 7
Fig. 7

Top, profiles extracted along the glass–LHM interface at Y = 300 from time-averaged electric field amplitudes for time-step T = 19000 (dotted curve) and T = 25000 (solid curve). Bottom, Zoomed time average of the electric field for the time steps 25000 (right) and 19000 (left). μ = 1 and ϵ = 2.25 beam angle 5°; x and y are measured in units of cell λ 33 .

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ϵ ( ω ) ϵ b > 0 , k 2 = ω 2 c 2 { ϵ b ϵ ( ω ) ϵ b + ϵ ( ω ) } .
( k 2 ω 2 c 2 ϵ b ) 1 2 + [ k 2 ω 2 c 2 ϵ ( ω ) ] 1 2 = 0 ,
ϵ ( ω ) = 1 ω pe 2 ω ( ω + i Γ e ) , μ ( ω ) = 1 ω pm 2 ω ( ω + i Γ m ) ,
κ b = ( k 2 ϵ b ω 2 c 2 ) 1 2 , κ = [ k 2 ϵ ( ω ) μ ( ω ) ω 2 c 2 ] 1 2 .
D ( ω , k ) = κ b + κ μ = 0 .
D ω δ ω + D k x δ k x = 0 v g = ω k x = D k x D ω .
v g = k ( 1 κ b + 1 μ κ ) ω c 2 ( ϵ b κ b + 1 μ κ ) ω pm 2 ω 3 μ κ c 2 ( ω pe 2 2 κ c 2 μ ) .
E MAX = ( N λ N 0 n 0 n 2 E ) 1 2 ,
E Z ( X = 0 , Y ) = ξ 1 k w 1 ( n 0 n 2 E ) 1 2 sech ( Y Y 0 w ) ,

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