## Direct measurement of group delay dispersion in metamagnetics for ultrafast pulse shaping |

Optics Express, Vol. 20, Issue 21, pp. 23082-23087 (2012)

http://dx.doi.org/10.1364/OE.20.023082

Acrobat PDF (1413 KB)

### Abstract

In this paper, we explore the use of magnetic resonant metamaterials, so called metamagnetics, as dispersive elements for optical pulse shaping. We measure both positive and negative group delay dispersion (GDD) values in a metamagnetic material using the multiphoton interference phase scan (MIIPS) technique and show pulse temporal profiles numerically. The results are compared with finite element models. These GDD properties of metamagnetics, along with previously shown tunability and loss control with gain media, enable their use in ultrashort pulse optical applications.

© 2012 OSA

## 1. Introduction

5. S. G. Rautian, “Reflection and refraction at the boundary of a medium with negative group velocity,” Physics-Uspekhi **51**(10), 981–988 (2008). [CrossRef]

6. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. **95**(3), 033115 (2009). [CrossRef]

7. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature **466**(7307), 735–738 (2010). [CrossRef] [PubMed]

8. S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics **4**(11), 760–766 (2010). [CrossRef]

9. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. **23**(10), 792–794 (1998). [CrossRef] [PubMed]

11. V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. **29**(7), 775–777 (2004). [CrossRef] [PubMed]

12. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature **418**(6897), 512–514 (2002). [CrossRef] [PubMed]

13. Y. Silberberg, “Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy,” Annu. Rev. Phys. Chem. **60**(1), 277–292 (2009). [CrossRef] [PubMed]

4. M. Mojahedi and G. V. Eleftheriades, “Dispersion engineering: the use of abnormal velocities and negative index of refraction to control dispersive effects,” in *Negative refraction metamaterials: fundamental properties and applications*, G. V. Eleftheriades and K. G. Balmain, eds. (Wiley & Sons, 2005), Chap. 10.

14. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. **9**(9), 707–715 (2010). [CrossRef] [PubMed]

15. M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. **88**(6), 067402 (2002). [CrossRef] [PubMed]

17. R. U. Tok and K. Sendur, “Femtosecond pulse shaping using plasmonic snowflake nanoantennas,” Phys. Rev. A **84**(3), 033847 (2011). [CrossRef]

*n*is the effective refractive index of the material, and

## 2. Experimental setup

20. B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B **23**(4), 750–759 (2006). [CrossRef]

21. W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with Rainbow Colors,” Opt. Express **15**(6), 3333–3341 (2007). [CrossRef] [PubMed]

22. Z. T. Liu, K. P. Chen, X. J. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B **27**(12), 2465–2470 (2010). [CrossRef]

*n*= 1,

*k*= 0), glass (

*n*= 1.52,

*k*= 0), Al

_{2}O

_{3}(dispersion from [23]), and Ag (Drude-Lorentz model with a loss factor of 3 from [24

24. V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. S. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express **16**(2), 1186–1195 (2008). [CrossRef] [PubMed]

25. K. P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. **10**(3), 916–922 (2010). [CrossRef] [PubMed]

20. B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B **23**(4), 750–759 (2006). [CrossRef]

^{2}, and the derived GDD from ellipsometry was 429 ± 2 fs

^{2}. This agrees well with a Cauchy model using data from Schott that gives a GDD of 429 fs

^{2}at 800 nm. The GVD using the ellipsometry and Schott value is 134 fs

^{2}/mm.

## 3. Results and discussion

^{2}and crosses zero near 801 nm. The level of agreement between simulation and experiment reflects a possible difference between the simulation design and the real geometry. It includes inhomogeneous size distribution over the sample, roughness, and asymmetry in the trapezoidal shape, which are taken into account only in average. Each point of the representative measured spectrum is a moving-average over 12 consequent experimental points corresponding to 4 nm of spectral interval. The error bars in Fig. 2 (c) show an estimate of the root-mean-square deviation from the averaged values.

_{2}O

_{3}|30-nm-Ag|40-nm-Al

_{2}O

_{3}|30-nm-Ag|10-nm-Al

_{2}O

_{3}layers (here Ag permittivity is modeled with a loss factor of 1), and the center wavelength of a 10-fs pulse was 774 nm.

6. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. **95**(3), 033115 (2009). [CrossRef]

7. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature **466**(7307), 735–738 (2010). [CrossRef] [PubMed]

## 4. Conclusions

14. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. **9**(9), 707–715 (2010). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | P. W. Milonni, |

2. | R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

3. | 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 |

4. | M. Mojahedi and G. V. Eleftheriades, “Dispersion engineering: the use of abnormal velocities and negative index of refraction to control dispersive effects,” in |

5. | S. G. Rautian, “Reflection and refraction at the boundary of a medium with negative group velocity,” Physics-Uspekhi |

6. | S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. |

7. | S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature |

8. | S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics |

9. | C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. |

10. | D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Müller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. |

11. | V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett. |

12. | N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature |

13. | Y. Silberberg, “Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy,” Annu. Rev. Phys. Chem. |

14. | B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. |

15. | M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. |

16. | D. Brinks, R. Hildner, F. D. Stefani, and N. F. van Hulst, “Beating spatio-temporal coupling: implications for pulse shaping and coherent control experiments,” Opt. Express |

17. | R. U. Tok and K. Sendur, “Femtosecond pulse shaping using plasmonic snowflake nanoantennas,” Phys. Rev. A |

18. | J.-C. Diels and W. Rudolph, |

19. | A. M. Weiner, |

20. | B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B |

21. | W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with Rainbow Colors,” Opt. Express |

22. | Z. T. Liu, K. P. Chen, X. J. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B |

23. | X. Ni, Z. Liu, and A. V. Kildishev, |

24. | V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. S. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express |

25. | K. P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. |

**OCIS Codes**

(320.5540) Ultrafast optics : Pulse shaping

(320.7100) Ultrafast optics : Ultrafast measurements

(160.3918) Materials : Metamaterials

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: July 24, 2012

Revised Manuscript: September 15, 2012

Manuscript Accepted: September 17, 2012

Published: September 24, 2012

**Citation**

Dean P. Brown, Mark A. Walker, Augustine M. Urbas, Alexander V. Kildishev, Shumin Xiao, and Vladimir P. Drachev, "Direct measurement of group delay dispersion in metamagnetics for ultrafast pulse shaping," Opt. Express **20**, 23082-23087 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23082

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### References

- P. W. Milonni, Fast Light, slow light and left-handed light (IOP Publishing Ltd., 2005).
- R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(5), 056625 (2001). [CrossRef] [PubMed]
- 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(16), 165112 (2004). [CrossRef]
- M. Mojahedi and G. V. Eleftheriades, “Dispersion engineering: the use of abnormal velocities and negative index of refraction to control dispersive effects,” in Negative refraction metamaterials: fundamental properties and applications, G. V. Eleftheriades and K. G. Balmain, eds. (Wiley & Sons, 2005), Chap. 10.
- S. G. Rautian, “Reflection and refraction at the boundary of a medium with negative group velocity,” Physics-Uspekhi51(10), 981–988 (2008). [CrossRef]
- S. Xiao, U. K. Chettiar, A. V. Kildishev, V. P. Drachev, C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett.95(3), 033115 (2009). [CrossRef]
- S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature466(7307), 735–738 (2010). [CrossRef] [PubMed]
- S. T. Cundiff and A. M. Weiner, “Optical arbitrary waveform generation,” Nat. Photonics4(11), 760–766 (2010). [CrossRef]
- C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett.23(10), 792–794 (1998). [CrossRef] [PubMed]
- D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Müller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett.23(13), 1046–1048 (1998). [CrossRef] [PubMed]
- V. V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation,” Opt. Lett.29(7), 775–777 (2004). [CrossRef] [PubMed]
- N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature418(6897), 512–514 (2002). [CrossRef] [PubMed]
- Y. Silberberg, “Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy,” Annu. Rev. Phys. Chem.60(1), 277–292 (2009). [CrossRef] [PubMed]
- B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater.9(9), 707–715 (2010). [CrossRef] [PubMed]
- M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett.88(6), 067402 (2002). [CrossRef] [PubMed]
- D. Brinks, R. Hildner, F. D. Stefani, and N. F. van Hulst, “Beating spatio-temporal coupling: implications for pulse shaping and coherent control experiments,” Opt. Express19(27), 26486–26499 (2011). [CrossRef] [PubMed]
- R. U. Tok and K. Sendur, “Femtosecond pulse shaping using plasmonic snowflake nanoantennas,” Phys. Rev. A84(3), 033847 (2011). [CrossRef]
- J.-C. Diels and W. Rudolph, Ultrafast Laser Pulse Phenomena (Academic Press, 2006).
- A. M. Weiner, Ultrafast Optics (Wiley & Sons, 2009).
- B. Xu, J. M. Gunn, J. M. D. Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond laser pulses,” J. Opt. Soc. Am. B23(4), 750–759 (2006). [CrossRef]
- W. Cai, U. K. Chettiar, H.-K. Yuan, V. C. de Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with Rainbow Colors,” Opt. Express15(6), 3333–3341 (2007). [CrossRef] [PubMed]
- Z. T. Liu, K. P. Chen, X. J. Ni, V. P. Drachev, V. M. Shalaev, and A. V. Kildishev, “Experimental verification of two-dimensional spatial harmonic analysis at oblique light incidence,” J. Opt. Soc. Am. B27(12), 2465–2470 (2010). [CrossRef]
- X. Ni, Z. Liu, and A. V. Kildishev, PhotonicsDB: Optical Constants, DOI: 10254/nanohub-r3692.10 (2010).
- V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. S. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express16(2), 1186–1195 (2008). [CrossRef] [PubMed]
- K. P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett.10(3), 916–922 (2010). [CrossRef] [PubMed]

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