## Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials |

Optics Express, Vol. 20, Issue 24, pp. 26828-26836 (2012)

http://dx.doi.org/10.1364/OE.20.026828

Acrobat PDF (1784 KB)

### Abstract

We present a theoretical investigation of dispersive wave (DW) generation in nonlinear metamaterials (MMs). The role of the anomalous self-steepening (SS) effect, which can be either positive or negative, and the negative SS parameter can have a very large value compared to an ordinary positive-index material, in DW generation is particularly identified. It is demonstrated that the SS effect exerts a great impact on the peak power while has little effect on the frequency shift of DW. For positive third-order dispersion (TOD), the negative SS broadens the pulse spectrum and weakens the DW’s peak power significantly, opposite to the case of positive SS. For negative TOD, however, the negative SS narrows the pulse spectrum and enhances the DW’s peak power, also opposite to the case of positive SS. The results suggest that the DW generation in nonlinear MMs can be manipulated by SS effect to a large extent.

© 2012 OSA

## 1. Introduction

2. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**, 2602–2607 (1995). [CrossRef] [PubMed]

9. S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun. **283**, 3081–3088 (2010). [CrossRef]

2. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**, 2602–2607 (1995). [CrossRef] [PubMed]

6. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A **79**, 023824 (2009). [CrossRef]

7. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett. **34**, 2072–2074 (2009). [CrossRef] [PubMed]

4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy. **78**, 1135–1175 (2006). [CrossRef]

10. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. **88**, 173901 (2002). [CrossRef] [PubMed]

4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy. **78**, 1135–1175 (2006). [CrossRef]

5. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express **12**, 124–135 (2004). [CrossRef] [PubMed]

10. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. **88**, 173901 (2002). [CrossRef] [PubMed]

11. G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express **19**, 6635–6647 (2011). [CrossRef] [PubMed]

6. S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A **79**, 023824 (2009). [CrossRef]

9. S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun. **283**, 3081–3088 (2010). [CrossRef]

9. S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun. **283**, 3081–3088 (2010). [CrossRef]

12. D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol. **27**, 4501–4507 (2009). [CrossRef]

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

15. N. I. Zheludev, “The road ahead for metamaterials,” Science **328**, 582–583 (2010). [CrossRef] [PubMed]

16. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. **85**, 3966–3969 (2000). [CrossRef] [PubMed]

17. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science **308**, 534–537 (2005). [CrossRef] [PubMed]

18. W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B **72**, 193101 (2005). [CrossRef]

19. P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E **72**, 036618 (2005). [CrossRef]

20. N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett. **1**, 10–13 (2002). [CrossRef]

21. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**, 977–980 (2006). [CrossRef] [PubMed]

22. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics **1**, 224–227 (2007). [CrossRef]

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

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

24. 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]

25. A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct. **8**, 228–243 (2010). [CrossRef]

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

29. S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A **75**, 033815 (2007). [CrossRef]

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

29. S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A **75**, 033815 (2007). [CrossRef]

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

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

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

**84**, 033815 (2011). [CrossRef]

## 2. Theoretical model for ultrashort pulse propagation in nonlinear MMs with TOD and Raman delayed response

*β*

_{3}=

*η*

_{3}− 3

*β*

_{2}/

*k*

_{0}

*v*is TOD,

_{g}*S*

_{1}= 1/

*ω*

_{0}+

*γ*

_{1}/

*γ*

_{0}− (

*k*

_{0}

*v*)

_{g}^{−1}is SS coefficient, where

*v*= 2

_{g}*k*

_{0}/(

*F*

_{0}

*G*

_{1}+

*F*

_{1}

*G*

_{0}) is the group velocity,

*η*=

_{m}*m*!

*d*/2

_{m}*k*

_{0},

*F*=

_{m}*∂*

*[*

^{m}*ωε*(

*ω*)]/

*∂ω*|

^{m}_{ω=ω0}, and

*G*=

_{m}*∂*[

^{m}*ωμ*(

*ω*)]/

*∂ω*|

^{m}_{ω=ω0}.

*ε*(

*ω*) and

*μ*(

*ω*) are the medium permeability and permeability respectively,

*k*

_{0}is the wave number,

*ω*

_{0}is the carrier frequency, and

**84**, 033815 (2011). [CrossRef]

*β*

_{2},

*δ*

_{3}and

*s*

_{1}are determined by basic electromagnetic characteristic of MMs, especially the dispersive permittivity

*ε*(

*ω*) and magnetic permeability

*μ*(

*ω*). For the Drude dispersive model for both

*ε*(

*ω*) and

*μ*(

*ω*), it has been indicated that in the anomalous GVD region,

*s*

_{1}has a very large value compared to an ordinary positive-index material and can be either positive or negative determined by the structure parameters of MMs [30

30. S. C. Wen, Y. J. Xiang, W. H. Su, H. Y. Hu, X. Q. Fu, and D. Y. Fan, “Role of the anomalous self-steepening effect in modulation instability in negative-index material,” Opt. Express **14**, 1568–1575 (2006). [CrossRef] [PubMed]

**84**, 033815 (2011). [CrossRef]

*δ*

_{3}is always positive [33

**84**, 033815 (2011). [CrossRef]

## 3. The controllable DW generation in MMs

*U*(0,

*τ*) =

*sech*(

*τ*). We only consider the DW generation of the second-order soliton (

*N*= 2), and the qualitative behavior of the higher-order soliton (

*N*> 2) is similar. To gain a physical understanding of the effects, the loss of MMs is neglected. If no otherwise specified, only the anomalous GVD (

*sgn*(

*β*

_{2}) = −1) and self-focusing (

*ϑ*= 1) nonlinearity are considered.

### 3.1. Dispersive wave generation for positive TOD

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

**84**, 033815 (2011). [CrossRef]

*δ*

_{3}= 0.04) is considered and the Raman effect is neglected. In each figure, the upper one is the contour maps of the pulse evolution, and the lower one is the input pulse (dotted line) and output pulse (solid line) spectra at

*ξ*= 4.0. In the following analyses, the lowest limit relative power level of −80 dB is assumed for the formation of the DW peak in the output spectrum, hence the relative power level litter than −80 dB has been neglected.

*ξ*= 4.0, a distinct peak generated through DW is observed in the high frequency range. As the distance increases, the peak position of DW is fixed, however the output spectrum is widened. As a consequence, the output pulse spectra are widened significantly at the joint action of generating DW and broadening soliton spectra.

*v*−

*v*)

_{s}*T*= 2.23, and the peak power of the DW is about −21dB. Comparing Fig. 1(a)–(d), it is observed that the SS effect is important for the DW generation. With the increase of the positive SS coefficients, the evolutions of the output spectra have the following characteristics: (1) The pulse spectra become narrow. When the SS coefficient increases from zero to 0.1, the output spectra become narrow obviously, this is disadvantage to the supercontinuum generation. But the spectra broaden again due to a new sidelobe with lower power generation in the soliton fission for

_{p}*s*

_{1}= 0.2 (Fig. 1(d)); (2) The peak positions of DW move toward the blue side of pulse spectra. But the shifting is not remarkable, which indicates that the influences of the SS effect on the frequency shifts of DW are less important than TOD; (3) The peak power of DW is enhanced, and the positive SS coefficient enhances the peak power of DW for positive TOD coefficient. For

*s*

_{1}= 0.2, the peak position of DW shifts to (

*v*−

*v*)

_{s}*T*= 2.36, and the peak power is about −9dB.

_{p}*s*

_{1}for

*δ*

_{3}= 0.04. The square symbols show the results obtained without considering the Raman effect. It can be seen that the peak position shifts slowly to higher frequency with the increasing SS coefficient

*s*

_{1}, and the shifts have gradually become saturated when

*s*

_{1}> 0.1. However, the peak power of DW increases as the SS coefficient

*s*

_{1}increases and does not exist saturation phenomenon for 0 <

*s*

_{1}< 0.2. Therefore, we can enhance the peak powers of DW as expected by manipulating the positive SS effect in MMs.

*s*

_{1}= −0.08, the peak powers of DW have less than −30dB. Therefore, we can suppress the peak powers of DW as expected by manipulating the negative SS effect in MMs. Furthermore, it is observed that some burrs occur in the DW’s spectra for larger |

*s*

_{1}|. The burrs finally lead to the fission of the DW (see Fig. 3(d)).

*s*

_{1}|, the peak position of DWs shifts to lower frequency. At

*s*

_{1}= −0.08, the peak position has shifted to (

*v*−

*v*)

_{s}*T*= 1.85, however, the peak powers of DWs weaken as SS coefficient |

_{p}*s*

_{1}| increases. These results demonstrate that the peak power of DW can be suppressed by the negative SS coefficient and the peak position can be shifted slightly to red side by increasing |

*s*

_{1}|.

*δ*

_{3}increases. Moreover, both the peak position and the peak power of DW become saturated gradually. In Fig. 5, we also show the influence of SS coefficient on DWs. For

*δ*

_{3}< 0.05, the influence of the positive SS coefficient (

*s*

_{1}= 0.2) on the peak position of DWs is significant; however, in the range 0.05 <

*δ*

_{3}< 0.1, the influence of the positive SS coefficient on the peak position of DWs can be neglected. When the negative SS effect (

*s*

_{1}= −0.06) is considered, it is obvious that frequency shifts are firstly increased and then decreased. The peak power of DWs is influenced by the SS effect distinctly, especially when the TOD coefficient is small. With these analysis results, we stress that the positive SS effect enhances the DWs generation and the negative SS effect weakens the DWs generation for positive TOD. When

*δ*

_{3}= 0.01, the peak power is about −45dB if SS effect is neglected; however, it can be enhanced by the positive SS coefficient to −10dB at

*s*

_{1}= 0.2 and it can be weakened by the negative SS coefficient to −94dB at

*s*

_{1}= −0.06.

### 3.2. Dispersive wave generation for negative TOD

*N*= 2) at the different SS coefficients for

*δ*

_{3}= −0.04, and Fig. 6(d) indicates the frequency shift and relative peak power of the DW peak plotted as a function of SS coefficient. Obviously, the DWs occur in the red side of the spectra (low frequency) for negative TOD, and the negative SS coefficient narrows the pulse spectra. But for

*s*

_{1}= 0.06, the positive SS coefficient play a leading role in the fission of the DW’s spectrum. With the increase of SS coefficient from negative to positive, the peak position of DW has a blue shift to higher frequency and the peak power weakens continuously. Moreover, it is found that the frequency shift of DW is sharply for the positive SS coefficient and it becomes slow for

*s*

_{1}< −0.1. Hence, we can enhance or suppress the DW generation in MMs by controlling the SS effect for the negative TOD parameter.

### 3.3. Influence of Raman effect on DW generation in MMs

*τ*= 0.05). Compared with the results without considering the Raman effect (

_{R}*τ*= 0), we observe that the peak positions of DW’s spectra have a tiny red shift, and the frequency shift difference induced by Raman effect may exceed 0.1 at

_{R}*s*

_{1}= 0.2. Moreover, the peak powers of DW’s spectra are suppressed greatly by the Raman effect, and the reduced peak powers may exceed a factor of 8dB at

*s*

_{1}= 0.

## 4. Conclusion

## Acknowledgments

## References and links

1. | G. P. Agrawal, |

2. | N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A |

3. | A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor 1, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. |

4. | J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy. |

5. | I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express |

6. | S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A |

7. | S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett. |

8. | S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun. |

9. | S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun. |

10. | J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. |

11. | G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express |

12. | D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol. |

13. | V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics |

14. | C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics |

15. | N. I. Zheludev, “The road ahead for metamaterials,” Science |

16. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

17. | N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science |

18. | W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B |

19. | P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E |

20. | N. Engheta, “An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability,” IEEE Antennas Wireless Propagat. Lett. |

21. | D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science |

22. | W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics |

23. | A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. |

24. | M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E |

25. | A. D. Boardman, O. Hess, R. C. Mitchell-Thomas, Y. G. Rapoport, and L. Velasco, “Temporal solitons in magnetooptic and metamaterial waveguides,” Photonics Nanostruct. |

26. | I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E |

27. | M. Scalora, M. S. Syrchin, N. Akozbek, E. Y. Poliakov, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, and A. M. Zheltikov, “Generalized nonlinear schr |

28. | V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A.A. Zakhidov, “Linear and nonlinear wave propagation in negative refraction metamaterials,” Phys. Rev. B |

29. | S. C. Wen, Y. J. Xiang, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials,” Phys. Rev. A |

30. | S. C. Wen, Y. J. Xiang, W. H. Su, H. Y. Hu, X. Q. Fu, and D. Y. Fan, “Role of the anomalous self-steepening effect in modulation instability in negative-index material,” Opt. Express |

31. | X. Y. Dai, Y. J. Xiang, S. C. Wen, and D. Y. Fan, “Modulation instability of copropagating light beams in nonlinear metamaterials,” J. Opt. Soc. Am. B |

32. | Y. J. Xiang, S. C. Wen, X. Y. Dai, Z. X. Tang, W. H. Su, and D. Y. Fan, “Modulation instability induced by nonlinear dispersion in nonlinear metamaterials,” J. Opt. Soc. Am. B |

33. | Y. J. Xiang, X. Y. Dai, S. C. Wen, J. Guo, and D. Y. Fan, “Controllable Raman soliton self-frequency shift in nonlinear metamaterials,” Phys. Rev. A |

**OCIS Codes**

(190.4400) Nonlinear optics : Nonlinear optics, materials

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: July 10, 2012

Revised Manuscript: November 1, 2012

Manuscript Accepted: November 6, 2012

Published: November 13, 2012

**Citation**

Yuanjiang Xiang, Jipeng Wu, Xiaoyu Dai, Shuangchun Wen, Jun Guo, and Qingkai Wang, "Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials," Opt. Express **20**, 26828-26836 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-26828

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### References

- G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).
- N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995). [CrossRef] [PubMed]
- A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett.95, 213902 (2005). [CrossRef] [PubMed]
- J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phy.78, 1135–1175 (2006). [CrossRef]
- I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express12, 124–135 (2004). [CrossRef] [PubMed]
- S. Roy, S. K. Bhadra, and G. P. Agrawal, “Dispersive waves emitted by solitons perturbed by third-order dispersion inside optical fibers,” Phys. Rev. A79, 023824 (2009). [CrossRef]
- S. Roy, S. K. Bhadra, and G. P. Agrawal, “Effects of higher-order dispersion on resonant dispersive waves emitted by solitons,” Opt. Lett.34, 2072–2074 (2009). [CrossRef] [PubMed]
- S. Roy, S. K. Bhadra, and G. P. Agrawal, “Perturbation of higher-order solitons by fourth-order dispersion in optical fibers,” Opt. Commun.282, 3798–3803 (2009). [CrossRef]
- S. Roy, D. Ghosh, S. K. Bhadra, and G. P. Agrawal, “Role of dispersion profile in controlling emission of dispersive waves by solitons in supercontinuum generation,” Opt. Commun.283, 3081–3088 (2010). [CrossRef]
- J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, “Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett.88, 173901 (2002). [CrossRef] [PubMed]
- G. Q. Chang, L. J. Chen, and F. X. Kärtner, “Fiber-optic Cherenkov radiation in the few-cycle regime,” Opt. Express19, 6635–6647 (2011). [CrossRef] [PubMed]
- D. J. Lei, H. Dong, S. C. Wen, and H. Yang, “Manipulating dispersive wave generation by frequency chirp in photonic crystal fibers,” J. Lightwave. Technol.27, 4501–4507 (2009). [CrossRef]
- V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007). [CrossRef]
- C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).
- N. I. Zheludev, “The road ahead for metamaterials,” Science328, 582–583 (2010). [CrossRef] [PubMed]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [CrossRef] [PubMed]
- N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffaction-limited optical imaging with a silver superlens,” Science308, 534–537 (2005). [CrossRef] [PubMed]
- W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005). [CrossRef]
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