A. Kumar and A. K. Mishra, “Anomalous self-steepening, temporal pulse splitting and ring formation in a left-handed metamaterial with cubic nonlinearity,” J. Opt. Soc. Am. B 29, 1330–1337 (2012).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

A. K. Sarma and M. Saha, “Modulational instability of coupled nonlinear field equations for pulse propagation in a negative index material embedded into a Kerr medium,” J. Opt. Soc. Am. B 28, 944–948 (2011).

[CrossRef]

A. Joseph and K. Porsezian, “Stability criterion for Gaussian pulse propagation through negative index materials,” Phys. Rev. A 81, 023805 (2010).

[CrossRef]

P. Li, R. Yang, and Z. Xu, “Gray solitary-wave solutions in nonlinear negative-index materials,” Phys. Rev. A 82, 046603 (2010).

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81, 023808 (2010).

[CrossRef]

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

Y. Hu and H. Zhuo, “Investigation of quasi-steady-state self-focusing in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 26, B68–B73 (2009).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Ultraslow light pulses in a nonlinear metamaterial,” J. Opt. Soc. Am. B 25, 1236–1241 (2008).

[CrossRef]

S. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100, 063901 (2008).

[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

A. Couairon and A. Mysrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).

[CrossRef]

A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. 31, 2169–2171 (2006).

[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006).

[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23, 529–534 (2006).

[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005).

[CrossRef]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005).

[CrossRef]

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13, 4922–4930 (2005).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85, 1451–1453 (2004).

[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).

[CrossRef]

A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003).

[CrossRef]

S. Champeaux and L. Bergé, “Femtosecond pulse compression in pressure-gas cells filled with argon,” Phys. Rev. E 68, 066603 (2003).

[CrossRef]

H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90, 053901 (2003).

[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).

[CrossRef]

J. K. Ranka and A. L. Gaeta, “Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses,” Opt. Lett. 23, 534–536 (1998).

[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).

[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).

[CrossRef]

M. Trippenbach and Y. B. Band, “Dynamics of short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).

[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).

[CrossRef]

M. Trippenbach and Y. B. Band, “Dynamics of short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90, 053901 (2003).

[CrossRef]

S. Champeaux and L. Bergé, “Femtosecond pulse compression in pressure-gas cells filled with argon,” Phys. Rev. E 68, 066603 (2003).

[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Ultraslow light pulses in a nonlinear metamaterial,” J. Opt. Soc. Am. B 25, 1236–1241 (2008).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).

[CrossRef]

S. Champeaux and L. Bergé, “Femtosecond pulse compression in pressure-gas cells filled with argon,” Phys. Rev. E 68, 066603 (2003).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).

[CrossRef]

A. Couairon and A. Mysrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).

[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Ultraslow light pulses in a nonlinear metamaterial,” J. Opt. Soc. Am. B 25, 1236–1241 (2008).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).

[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006).

[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85, 1451–1453 (2004).

[CrossRef]

S. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100, 063901 (2008).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).

[CrossRef]

J. K. Ranka and A. L. Gaeta, “Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses,” Opt. Lett. 23, 534–536 (1998).

[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).

[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

S. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100, 063901 (2008).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

Y. Hu and H. Zhuo, “Investigation of quasi-steady-state self-focusing in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 26, B68–B73 (2009).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

A. Joseph and K. Porsezian, “Stability criterion for Gaussian pulse propagation through negative index materials,” Phys. Rev. A 81, 023805 (2010).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81, 023808 (2010).

[CrossRef]

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).

[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23, 529–534 (2006).

[CrossRef]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85, 1451–1453 (2004).

[CrossRef]

A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003).

[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005).

[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).

[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).

[CrossRef]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).

[CrossRef]

P. Li, R. Yang, and Z. Xu, “Gray solitary-wave solutions in nonlinear negative-index materials,” Phys. Rev. A 82, 046603 (2010).

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006).

[CrossRef]

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Ultraslow light pulses in a nonlinear metamaterial,” J. Opt. Soc. Am. B 25, 1236–1241 (2008).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).

[CrossRef]

A. Couairon and A. Mysrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

A. Joseph and K. Porsezian, “Stability criterion for Gaussian pulse propagation through negative index materials,” Phys. Rev. A 81, 023805 (2010).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23, 529–534 (2006).

[CrossRef]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85, 1451–1453 (2004).

[CrossRef]

A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003).

[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

[CrossRef]

A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. 31, 2169–2171 (2006).

[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005).

[CrossRef]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005).

[CrossRef]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).

[CrossRef]

M. Trippenbach and Y. B. Band, “Dynamics of short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

[CrossRef]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90, 053901 (2003).

[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

P. Li, R. Yang, and Z. Xu, “Gray solitary-wave solutions in nonlinear negative-index materials,” Phys. Rev. A 82, 046603 (2010).

P. Li, R. Yang, and Z. Xu, “Gray solitary-wave solutions in nonlinear negative-index materials,” Phys. Rev. A 82, 046603 (2010).

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

Y. Hu and H. Zhuo, “Investigation of quasi-steady-state self-focusing in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 26, B68–B73 (2009).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).

[CrossRef]

M. W. Feise, I. V. Shadrivov, and Y. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. 85, 1451–1453 (2004).

[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 23, 529–534 (2006).

[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Ultraslow light pulses in a nonlinear metamaterial,” J. Opt. Soc. Am. B 25, 1236–1241 (2008).

[CrossRef]

Y. Xiang, S. Wen, X. Dai, Z. Tang, W. Su, and D. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B 24, 3058–3063 (2007).

[CrossRef]

A. K. Sarma and M. Saha, “Modulational instability of coupled nonlinear field equations for pulse propagation in a negative index material embedded into a Kerr medium,” J. Opt. Soc. Am. B 28, 944–948 (2011).

[CrossRef]

A. Kumar and A. K. Mishra, “Anomalous self-steepening, temporal pulse splitting and ring formation in a left-handed metamaterial with cubic nonlinearity,” J. Opt. Soc. Am. B 29, 1330–1337 (2012).

[CrossRef]

Y. Hu and H. Zhuo, “Investigation of quasi-steady-state self-focusing in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B 26, B68–B73 (2009).

[CrossRef]

A. D. Boardman, N. King, R. C. Mitchell-Thomas, V. Malnev, and V. G. Rapoport, “Gain control and diffraction-managed solitons in metamaterials,” Metamaterials 2, 145–154 (2008).

[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

[CrossRef]

Y. Hu, S. Wen, Y. Wang, and D. Fan, “Propagation of Gaussian beams in negative-index metamaterials with cubic nonlinearity,” Opt. Commun. 281, 2663–2669 (2008).

[CrossRef]

Y. Hu, S. Wen, H. Zhuo, K. You, and D. Fan, “Focusing properties of Gaussian beams by a slab of Kerr-type left-handed metamaterial,” Opt. Express 16, 4774–4784 (2008).

[CrossRef]

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13, 4922–4930 (2005).

[CrossRef]

Y. Xiang, J. Wu, X. Dai, S. Wen, J. Guo, and Q. Wang, “Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials,” Opt. Express 20, 26828–26836 (2012).

[CrossRef]

S. Wen, Y. Xiang, W. Su, Y. Hu, X. Fu, and D. Fan, “Role of the anomalous self steepening in modulation instability in negative-index material,” Opt. Express 14, 1568–1575 (2006).

[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006).

[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005).

[CrossRef]

Y. Silberberg, “Collapse of optical beams,” Opt. Lett. 15, 1282–1284 (1990).

[CrossRef]

J. E. Rothenberg, “Pulse splitting during self-focusing in normally dispersive media,” Opt. Lett. 17, 583–585 (1992).

[CrossRef]

J. E. Rothenberg, “Space–time focusing: breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses,” Opt. Lett. 17, 1340–1342 (1992).

[CrossRef]

J. K. Ranka and A. L. Gaeta, “Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses,” Opt. Lett. 23, 534–536 (1998).

[CrossRef]

A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. 31, 2169–2171 (2006).

[CrossRef]

G. D’Aguanno, N. Akozbek, N. Mattiucci, M. Scalora, M. J. Bloemer, and A. M. Zheltikov, “Dispersion-free pulse propagation in a negative-index material,” Opt. Lett. 30, 1998–2000 (2005).

[CrossRef]

A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photon. Nanostr. Fundam. Appl. 8, 228–243 (2010).

[CrossRef]

A. Couairon and A. Mysrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).

[CrossRef]

M. Trippenbach and Y. B. Band, “Effects of self-steepening and self-frequency shifting on short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 57, 4791–4803 (1998).

[CrossRef]

M. Trippenbach and Y. B. Band, “Dynamics of short-pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

[CrossRef]

A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).

[CrossRef]

A. Joseph and K. Porsezian, “Stability criterion for Gaussian pulse propagation through negative index materials,” Phys. Rev. A 81, 023805 (2010).

[CrossRef]

Y. Xiang, X. Dai, S. Wen, J. Guo, and D. Fang, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A 84, 033815 (2011).

[CrossRef]

P. Li, R. Yang, and Z. Xu, “Gray solitary-wave solutions in nonlinear negative-index materials,” Phys. Rev. A 82, 046603 (2010).

J. Zhang, S. Wen, Y. Xiang, Y. Wang, and H. Luo, “Spatiotemporal electromagnetic soliton and spatial formation in nonlinear metamaterials,” Phys. Rev. A 81, 023829 (2010).

[CrossRef]

S. Wen, Y. Xiang, X. Dai, Z. Tang, W. Su, and D. Fan, “Theoretical models for ultrashort electromagnetic beam propagation in nonlinear metamaterials,” Phys. Rev. A 75, 033815 (2007).

[CrossRef]

P. Kinsler, “Unidirectional optical pulse propagation equation for materials with both electric and magnetic responses,” Phys. Rev. A 81, 023808 (2010).

[CrossRef]

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).

[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, “Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials,” Phys. Rev. B 69, 241101 (2004).

[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E 67, 065601 (2003).

[CrossRef]

I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E 72, 016626 (2005).

[CrossRef]

N. L. Tsitsas, N. Rompotis, I. Kourakis, P. G. Kevrekidis, and D. J. Frantzeskakis, “Higher-order effects and ultrashort solitons in left-handed metamaterials,” Phys. Rev. E 79, 037601 (2009).

[CrossRef]

S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E 73, 036617 (2006).

[CrossRef]

N. Lazarides and G. P. Tsironis, “Coupled nonlinear Schrödinger field equations for electromagnetic wave propagation in nonlinear left-handed materials,” Phys. Rev. E 71, 036614 (2005).

[CrossRef]

S. Champeaux and L. Bergé, “Femtosecond pulse compression in pressure-gas cells filled with argon,” Phys. Rev. E 68, 066603 (2003).

[CrossRef]

H. Ward and L. Bergé, “Temporal shaping of femtosecond solitary pulses in photoionized media,” Phys. Rev. Lett. 90, 053901 (2003).

[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).

[CrossRef]

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).

[CrossRef]

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).

[CrossRef]

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of pulse splitting in nonlinear dispersive media,” Phys. Rev. Lett. 77, 3783–3786 (1996).

[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).

[CrossRef]

M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005).

[CrossRef]

S. Feng and K. Halterman, “Parametrically shielding electromagnetic fields by nonlinear metamaterials,” Phys. Rev. Lett. 100, 063901 (2008).

[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).

[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).

[CrossRef]

A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. 91, 037401 (2003).

[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J. P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).

[CrossRef]

J. B. Pendry, D. Shurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).

[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).

[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).