OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 26828–26836
« Show journal navigation

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

Yuanjiang Xiang, Jipeng Wu, Xiaoyu Dai, Shuangchun Wen, Jun Guo, and Qingkai Wang  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 26828-26836 (2012)
http://dx.doi.org/10.1364/OE.20.026828


View Full Text Article

Acrobat PDF (1784 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Optical soliton is the robust balance between dispersion and nonlinearity. In particular, the conventional fundamental optical soliton is the exactly balance between self-phase modulation and anomalous group-velocity dispersion (GVD). However, the high-order dispersion and nonlinearity are ever-present under the realistic condition. These effects disrupt the balance and split the soliton into its components [1

1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).

]. During the fission process, dispersive wave (DW) is generated due to the energy transfer from soliton to narrow resonance in the presence of the high-order dispersions [2

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

9

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]

]. The frequencies of DW are determined by the phase-matching condition between the soliton and DW [2

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

, 6

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

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]

]. DW is of particular importance for supercontinuum generation and broadband light sources [4

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

, 10

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]

]. Recently, the generation of DW in the supercontinuum generation process inside the nonlinear microstructured fiber or photonic crystal fiber is explored under different operational conditions [4

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

, 5

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

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

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]

]. The roles of high-order dispersions in the generation and control of DW are disclosed [6

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

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]

], and the manipulations of DW by the dispersion profile of the specific fiber [9

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]

] or frequency chirp are unfolded [12

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]

]. In this paper, we study the influences of the anomalous SS effect on generating DW based on the numerical simulations.

In the present paper, we show that the DW generation can be manipulated by the anomalous SS effect. The paper is organized as follows. In Sec. II, the theoretical model for ultrashort pulse propagation in nonlinear MMs with TOD and Raman delayed response is introduced. In Sec. III, we discuss the controllable DW generation in the nonlinear MMs, and reveal the roles of the anomalous SS effect in the DW generation. Finally, in Sec. IV, we summarize our results and conclusions.

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

In the GNLSE, β2=η21/k0vg2 is GVD, β3 = η3 − 3β2/k0vg is TOD, S1 = 1/ω0 + γ1/γ0 − (k0vg)−1 is SS coefficient, where vg = 2k0/(F0G1 + F1G0) is the group velocity, ηm = m!dm/2k0, γm=ω0ε0χp(3)Gm/2k0, dm=l=0mFlGml/l!(ml)!, Fm = m[ωε(ω)]/∂ωm|ω=ω0, and Gm = m[ωμ(ω)]/∂ωm|ω=ω0. ε(ω) and μ(ω) are the medium permeability and permeability respectively, k0 is the wave number, ω0 is the carrier frequency, and χp(3) is the third-order electric susceptibility.

3. The controllable DW generation in MMs

To discuss the DW generation in MMs, we employ the standard split-step Fourier method to solve the GNLSE numerically. We have adopted the normalized input pulse in the numerical simulation, 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(β2) = −1) and self-focusing (ϑ = 1) nonlinearity are considered.

3.1. Dispersive wave generation for positive TOD

In the anomalous GVD of MMs described by the Drude dispersive model, the SS coefficient can be positive, zero or negative [32

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

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]

]. Hence, we will discuss the role of the SS effect in the DW generation by the positive and negative SS coefficients, respectively.

Figure 1 demonstrates how the positive SS effect influences the DW generation, here only the positive TOD (δ3 = 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.

Fig. 1 Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = 0, (b)s1 = 0.05, (c)s1 = 0.1 and (d)s1 = 0.2, where δ3 = 0.04.

As the propagating distance increasing, TOD and self-phase modulation induce the fission of the second-order soliton and the radiation emitted by the soliton begins to emerge in the blue-shifted band (see Fig. 1). At 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.

In the absence of SS effect, as shown in Fig. 1(a), the peak of DW occurs near (vvs)Tp = 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 s1 = 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 s1 = 0.2, the peak position of DW shifts to (vvs)Tp = 2.36, and the peak power is about −9dB.

In order to fully understand the roles of the SS effects in the DW generation, in Fig. 2 we have shown the frequency shifts (a) and relative peak power (b) of the DW peak plotted as a function of the positive SS coefficient s1 for δ3 = 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 s1, and the shifts have gradually become saturated when s1 > 0.1. However, the peak power of DW increases as the SS coefficient s1 increases and does not exist saturation phenomenon for 0 < s1 < 0.2. Therefore, we can enhance the peak powers of DW as expected by manipulating the positive SS effect in MMs.

Fig. 2 (a) Frequency shift and (b) relative peak power of the DW peak plotted as a function of SS coefficient s1, where δ3 = 0.04. The square symbols show the results obtained when the Raman effect is neglected, and the circle symbols show the results obtained when the Raman effect is considered.

Next, we turn to the discussion about the role of the negative SS coefficient in DW generation, as shown in Fig. 3. In stark contrast to the results of the positive SS coefficient, as the increasing absolute value of negative SS coefficient, the soliton and DW generation have following characteristics: (1) The spectra of ultrashort pulse become more and more wide, which suggests that the negative SS coefficient and positive TOD coefficient in nonlinear MMs have valuable potentials for supercontinuum generation and broadband source; (2) The peak position of DWs red-shifts and the movement is significant than the positive SS coefficient; (3) The peak powers of DWs are weakened. When s1 = −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 |s1|. The burrs finally lead to the fission of the DW (see Fig. 3(d)).

Fig. 3 Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = −0.02, (b)s1 = −0.04, (c)s1 = −0.06 and (d)s1 = −0.08, where δ3 = 0.04.

To get a thorough understanding of the influence of the negative SS coefficient on the DW generation, Fig. 4 indicates the frequency shift (Square symbol line) and relative peak power (Circle symbol line) of the DW peak plotted as a function of negative SS coefficient. With the increasing |s1|, the peak position of DWs shifts to lower frequency. At s1 = −0.08, the peak position has shifted to (vvs)Tp = 1.85, however, the peak powers of DWs weaken as SS coefficient |s1| 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 |s1|.

Fig. 4 Frequency shift (Square symbol line) and relative peak power (Circle symbol line) of the DW peak plotted as a function of negative SS coefficient s1, where δ3 = 0.04.

Fig. 5 (a) Frequency shift and (b) relative peak power of the DW peak plotted as a function of TOD coefficient δ3, where s1 = −0.06 (triangle symbol line), 0 (square symbol line) and 0.2 (circus symbol line).

3.2. Dispersive wave generation for negative TOD

The former section just considers the role of the positive TOD parameter in the DW generation. Actually, we can also obtain the negative value of TOD parameter if we control the composite materials and the structure parameters of the each unit in MMs. Next, we consider the influence of the negative TOD parameter and abnormal SS effect together on the DW generation. Fig. 6(a)–(c) show the contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients for δ3 = −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 s1 = 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 s1 < −0.1. Hence, we can enhance or suppress the DW generation in MMs by controlling the SS effect for the negative TOD parameter.

Fig. 6 Contour and output spectra of a second-order soliton (N = 2) at the different SS coefficients, (a)s1 = −0.1, (b)s1 = 0, (c)s1 = 0.06, where δ3 = −0.04. (d) Frequency shift and relative peak power of the DW peak plotted as a function of SS coefficient s1.

3.3. Influence of Raman effect on DW generation in MMs

The Raman scattering effect has been neglected in the above researches. Now we investigate the influence of the Raman scattering effect on the DW generation, as shown in Fig. 2, here the circle symbols show the results obtained when the Raman effect is considered (τR = 0.05). Compared with the results without considering the Raman effect (τR = 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 s1 = 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 s1 = 0.

4. Conclusion

We identified the combined effect of anomalous SS effect and TOD on DW generation in nonlinear MMs. Our results show that DW generation can be controlled by the anomalous SS effect in nonlinear MMs depending on the sign of SS coefficient and TOD parameter. For the positive value of TOD parameter, the amplitude of the DW peak increases rapidly with positive SS coefficient, and decreases with negative SS coefficient. However, the results are just opposite to the case of negative value of TOD parameter: the amplitude of the DW peak decreases rapidly with positive SS coefficient, and increases with negative SS coefficient. These results suggest that the DW generation can be manipulated as required in nonlinear MMs and nonlinear MMs are valuable candidates for applications in which a supercontinuum source is required.

Acknowledgments

This work is supported by the National Basic Research Program (973 Program) of China (Grant No. 2012CB315701), the National Natural Science Foundation of China (Grant No. 61025024, 11004053, and 10974049), the China Postdoctoral Science Foundation (Grant No. 2012M511365), the Hunan Provincial Natural Science Foundation of China (Grant No. 11JJB001 and 12JJ7005), and the Young Teacher Development Plan of Hunan University.

References and links

1.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).

2.

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

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. 95, 213902 (2005). [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]

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]

8.

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]

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]

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]

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]

14.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

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]

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]

26.

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

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 schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett. 95, 013902 (2005). [CrossRef] [PubMed]

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 69, 165112 (2004). [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]

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]

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 26, 564–571 (2009). [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]

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


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (San Diego, Academic, 2001).
  2. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995). [CrossRef] [PubMed]
  3. 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]
  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. Express12, 124–135 (2004). [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. A79, 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]
  8. 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]
  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]
  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. Express19, 6635–6647 (2011). [CrossRef] [PubMed]
  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. Photonics1, 41–48 (2007). [CrossRef]
  14. C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).
  15. N. I. Zheludev, “The road ahead for metamaterials,” Science328, 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,” Science308, 534–537 (2005). [CrossRef] [PubMed]
  18. W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B72, 193101 (2005). [CrossRef]
  19. P. A. Belov and C. R. Simovski, “Subwavelength metallic waveguides loaded by uniaxial resonant scatterers,” Phys. Rev. E72, 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,” Science314, 977–980 (2006). [CrossRef] [PubMed]
  22. W. S. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics1, 224–227 (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. E67, 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]
  26. I. Kourakis and P. K. Shukla, “Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials,” Phys. Rev. E72, 016626 (2005). [CrossRef]
  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 schrödinger equation for dispersive susceptibility and permeability: application to negative index materials,” Phys. Rev. Lett.95, 013902 (2005). [CrossRef] [PubMed]
  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. B69, 165112 (2004). [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. A75, 033815 (2007). [CrossRef]
  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. Express14, 1568–1575 (2006). [CrossRef] [PubMed]
  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. B26, 564–571 (2009). [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. B24, 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. A84, 033815 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited