## Femtosecond ultrashort pulse generation by addition of positive material dispersion |

Optics Express, Vol. 18, Issue 22, pp. 23088-23094 (2010)

http://dx.doi.org/10.1364/OE.18.023088

Acrobat PDF (964 KB)

### Abstract

We demonstrate femtosecond ultrashort pulse generation by adding further positive group velocity dispersion (GVD) to compensate for the presence of positive GVD. The idea is based on the integer temporal Talbot phenomenon. The broad Raman sidebands with a frequency spacing of 10.6 THz are compressed to form a train of Fourier-transform-limited pulses by passing the sidebands through a device made of dispersive material of variable thickness.

© 2010 OSA

## 1. Introduction

1. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. **9**(5), 150–152 (1984). [CrossRef] [PubMed]

2. E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. **5**(9), 454–458 (1969). [CrossRef]

3. R. Szipocs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. **19**(3), 201–203 (1994). [CrossRef] [PubMed]

4. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. **22**(23), 1793–1795 (1997). [CrossRef]

## 2. Theory

*ω*and a frequency spacing of

_{0}*Δω*. The spectral phase of such spectrum is generally expressed bywhere

*m*is an integer.

*ϕ*indicates higher-order terms. Here, we assume that the second-order term is dominant, and we therefore neglect

^{h}*ϕ*Because the coefficients

^{h}.*ϕ*and

_{0}*ϕ*do not influence the intensity profile of the constructed waveform, we set them at zero. The second-order term gives a GVD, and thereby the Fourier-transform-limited (FTL) condition generally requires the coefficient,

_{1}*ϕ*, to be zero.

_{2}*ϕ*= 0. Equation (2) describes such conditions.where

_{2}*ϕ*=

_{2}*2nπ / Δω*(

^{2}*n*is an integer). When

*n*is even, the spectral phases are equal to integer multiples of 2π. One can immediately find that this also satisfies the FTL condition. Furthermore, when

*n*is odd, the spectral phases alternate between zero and π. This is also equivalent to the FTL condition, but with a group delay of

*ϕ*=

_{1}*π / Δω*against the case where

*n*is even. Therefore, Eq. (2) can give the FTL pulse duration for both even and odd

*n*. This implies the important fact that we can remove the positive GVD of a discrete spectrum by adding, rather than subtracting, positive GVD. A similar idea has been studied in the context of the temporal Talbot effect [6

6. J. Azana and M. A. Muriel, “Temporal Self-Imaging Effects: Theory and Application for Multiplying Pulse Repetition Rates,” IEEE J. Sel. Top. Quantum Electron. **7**(4), 728–744 (2001). [CrossRef]

7. N. K. Berger, B. Levit, A. Bekker, and B. Fischer, “Compression of Periodic Optical Pulses Using Temporal Fractional Talbot Effect,” IEEE Photon. Technol. Lett. **16**(8), 1855–1857 (2004). [CrossRef]

*J*= 2 and 0 in parahydrogen [8

8. M. Katsuragawa, K. Yokoyama, T. Onose, and K. Misawa, “Generation of a 10.6-THz ultrahigh-repetition-rate train by synthesizing phase-coherent Raman-sidebands,” Opt. Express **13**(15), 5628–5634 (2005). [CrossRef] [PubMed]

*n*= –1 (blue), 0 (black), 1 (red), and 2 (green) in Eq. (2). Horizontal dotted lines indicate the values of the spectral phases where spectral lines exist; all the values are integer multiples of ‘π’. The temporal profiles calculated from these four different spectral phases surely provide the same FTL pulse train as that shown in Fig. 1(b). (The time origin for each temporal profile is adjusted accordingly.) Here, the difference in

*ϕ*between the neighboring spectral-phase curves amounts to 1,400 fs

_{2}^{2}. This implies that the FTL condition is recovered every 1,400 fs

^{2}when we add GVDs to the Raman sidebands.

## 3. Numerical experiment

*ϕ*, in addition to the second-order (GVD) term. Figures 2(a) , 2(b), and 2(c) show the peak intensity variations of the constructed waveforms from the spectrum shown in Fig. 1(a) as functions of the thicknesses of the inserted dispersing materials. The initial phase of the spectrum was set to the FTL condition of

^{h}*ϕ*= 0. The FTL pulses were then distorted as the inserted material thickness increased, but they periodically recovered their shapes at specific thicknesses corresponding to the condition of

_{2}*ϕ*=

_{2}*2π/Δω*(

^{2}*n*= 1). For a discrete spectrum with a frequency spacing of 10.6 THz, we found these specific thicknesses for fused quartz, BK7, and sapphire crystal to be 38.5, 31.2, and 24.0 mm, respectively, all of which are experimentally achievable.

*ϕ*, because the higher-order dispersions merely accumulate and never subtract the deviations from the conditions of Eq. (2). As seen in Figs. 2(a), 2(b), and 2(c), the peaks of the reconstructed intensity waveforms around the FTL conditions declined as the insertion thicknesses increased (i.e. as

^{h}*n*increased). This is due to the higher-order dispersions. In other words, these higher-order dispersions limit the applicable bandwidth in terms of the number of spectral lines to be phase-dispersion compensated. In this case, where we employed a discrete spectrum with a frequency spacing of 10.6 THz, the shortest pulse duration that could be produced by the dispersion-adding compensation was 15 fs, corresponding to a bandwidth of 30 THz. If we employ different dispersive materials and combine them to compensate for phase dispersion, in principle we can extend this technique to include higher-order dispersion. This will constitute future study.

## 4. Experimental

9. M. Katsuragawa and T. Onose, “Dual-wavelength injection-locked pulsed laser,” Opt. Lett. **30**(18), 2421–2423 (2005). [CrossRef] [PubMed]

10. T. Onose and M. Katsuragawa, “Dual-wavelength injection-locked pulsed laser with highly predictable performance,” Opt. Express **15**(4), 1600–1605 (2007). [CrossRef] [PubMed]

11. S. E. Harris and A. V. Sokolov, “Broadband spectral generation with refractive index control,” Phys. Rev. A **55**(6), R4019–R4022 (1997). [CrossRef]

14. A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Femtosecond light source for phase-controlled multiphoton ionization,” Phys. Rev. Lett. **87**(3), 033402 (2001). [CrossRef] [PubMed]

^{20}cm

^{–3}[8

8. M. Katsuragawa, K. Yokoyama, T. Onose, and K. Misawa, “Generation of a 10.6-THz ultrahigh-repetition-rate train by synthesizing phase-coherent Raman-sidebands,” Opt. Express **13**(15), 5628–5634 (2005). [CrossRef] [PubMed]

8. M. Katsuragawa, K. Yokoyama, T. Onose, and K. Misawa, “Generation of a 10.6-THz ultrahigh-repetition-rate train by synthesizing phase-coherent Raman-sidebands,” Opt. Express **13**(15), 5628–5634 (2005). [CrossRef] [PubMed]

15. T. Suzuki, M. Hirai, and M. Katsuragawa, “Octave-spanning Raman comb with carrier envelope offset control,” Phys. Rev. Lett. **101**(24), 243602 (2008). [CrossRef] [PubMed]

16. T. Suzuki, N. Sawayama, and M. Katsuragawa, “Spectral phase measurements for broad Raman sidebands by using spectral interferometry,” Opt. Lett. **33**(23), 2809–2811 (2008). [CrossRef] [PubMed]

## 5. Results and discussion

*n*= 0, 1, and 2 in Eq. (2), and the observed spectral phases for the device thicknesses every 5 mm from 10 to 40 mm. The initial spectral phase includes both the intrinsic spectral phase aroused in the process of generation of the Raman sidebands and the additional dispersions by the windows of the cell and the cryostat and by the collimating lens. By varying the thickness of the dispersion controller, the spectral phase was continuously changed and nearly matched the FTL conditions twice [Fig. 4(a)]. The pulse shapes in Fig. 4(b) are temporal intensity waveforms corresponding to the spectral phases in Fig. 4(a). The shortest pulse was observed at a thickness of 39 mm, as shown by the black solid curve in Fig. 4(b). The pulse duration was 22 fs at full width at half maximum (FWHM), which matched an FTL duration of 22.05 fs.

## 6. Conclusion

## Acknowledgments

## References and links

1. | R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. |

2. | E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. |

3. | R. Szipocs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. |

4. | D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. |

5. | J. E. Bjorkholm, E. H. Turner, and D. B. Pearson, “Conversion of cw light into a train of subnanosecond pulses using frequency modulation and the dispersion of a near-resonant atomic vapor,” Appl. Phys. Lett. |

6. | J. Azana and M. A. Muriel, “Temporal Self-Imaging Effects: Theory and Application for Multiplying Pulse Repetition Rates,” IEEE J. Sel. Top. Quantum Electron. |

7. | N. K. Berger, B. Levit, A. Bekker, and B. Fischer, “Compression of Periodic Optical Pulses Using Temporal Fractional Talbot Effect,” IEEE Photon. Technol. Lett. |

8. | M. Katsuragawa, K. Yokoyama, T. Onose, and K. Misawa, “Generation of a 10.6-THz ultrahigh-repetition-rate train by synthesizing phase-coherent Raman-sidebands,” Opt. Express |

9. | M. Katsuragawa and T. Onose, “Dual-wavelength injection-locked pulsed laser,” Opt. Lett. |

10. | T. Onose and M. Katsuragawa, “Dual-wavelength injection-locked pulsed laser with highly predictable performance,” Opt. Express |

11. | S. E. Harris and A. V. Sokolov, “Broadband spectral generation with refractive index control,” Phys. Rev. A |

12. | A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. |

13. | J. Q. Liang, M. Katsuragawa, F. L. Kien, and K. Hakuta, “Sideband generation using strongly driven raman coherence in solid hydrogen,” Phys. Rev. Lett. |

14. | A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Femtosecond light source for phase-controlled multiphoton ionization,” Phys. Rev. Lett. |

15. | T. Suzuki, M. Hirai, and M. Katsuragawa, “Octave-spanning Raman comb with carrier envelope offset control,” Phys. Rev. Lett. |

16. | T. Suzuki, N. Sawayama, and M. Katsuragawa, “Spectral phase measurements for broad Raman sidebands by using spectral interferometry,” Opt. Lett. |

**OCIS Codes**

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(190.5650) Nonlinear optics : Raman effect

(320.5520) Ultrafast optics : Pulse compression

(320.7160) Ultrafast optics : Ultrafast technology

(190.4223) Nonlinear optics : Nonlinear wave mixing

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: September 7, 2010

Revised Manuscript: October 10, 2010

Manuscript Accepted: October 13, 2010

Published: October 18, 2010

**Citation**

Takayuki Suzuki and Masayuki Katsuragawa, "Femtosecond ultrashort pulse generation by addition of positive material dispersion," Opt. Express **18**, 23088-23094 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-22-23088

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### References

- R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9(5), 150–152 (1984). [CrossRef] [PubMed]
- E. B. Treacy, “Optical Pulse Compression With Diffraction Gratings,” IEEE J. Quantum Electron. 5(9), 454–458 (1969). [CrossRef]
- R. Szipocs, K. Ferencz, C. Spielmann, and F. Krausz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19(3), 201–203 (1994). [CrossRef] [PubMed]
- D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22(23), 1793–1795 (1997). [CrossRef]
- J. E. Bjorkholm, E. H. Turner, and D. B. Pearson, “Conversion of cw light into a train of subnanosecond pulses using frequency modulation and the dispersion of a near-resonant atomic vapor,” Appl. Phys. Lett. 26(10), 564–566 (1975). [CrossRef]
- J. Azana and M. A. Muriel, “Temporal Self-Imaging Effects: Theory and Application for Multiplying Pulse Repetition Rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001). [CrossRef]
- N. K. Berger, B. Levit, A. Bekker, and B. Fischer, “Compression of Periodic Optical Pulses Using Temporal Fractional Talbot Effect,” IEEE Photon. Technol. Lett. 16(8), 1855–1857 (2004). [CrossRef]
- M. Katsuragawa, K. Yokoyama, T. Onose, and K. Misawa, “Generation of a 10.6-THz ultrahigh-repetition-rate train by synthesizing phase-coherent Raman-sidebands,” Opt. Express 13(15), 5628–5634 (2005). [CrossRef] [PubMed]
- M. Katsuragawa and T. Onose, “Dual-wavelength injection-locked pulsed laser,” Opt. Lett. 30(18), 2421–2423 (2005). [CrossRef] [PubMed]
- T. Onose and M. Katsuragawa, “Dual-wavelength injection-locked pulsed laser with highly predictable performance,” Opt. Express 15(4), 1600–1605 (2007). [CrossRef] [PubMed]
- S. E. Harris and A. V. Sokolov, “Broadband spectral generation with refractive index control,” Phys. Rev. A 55(6), R4019–R4022 (1997). [CrossRef]
- A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Raman generation by phased and antiphased molecular states,” Phys. Rev. Lett. 85(3), 562–565 (2000). [CrossRef] [PubMed]
- J. Q. Liang, M. Katsuragawa, F. L. Kien, and K. Hakuta, “Sideband generation using strongly driven raman coherence in solid hydrogen,” Phys. Rev. Lett. 85(12), 2474–2477 (2000). [CrossRef] [PubMed]
- A. V. Sokolov, D. R. Walker, D. D. Yavuz, G. Y. Yin, and S. E. Harris, “Femtosecond light source for phase-controlled multiphoton ionization,” Phys. Rev. Lett. 87(3), 033402 (2001). [CrossRef] [PubMed]
- T. Suzuki, M. Hirai, and M. Katsuragawa, “Octave-spanning Raman comb with carrier envelope offset control,” Phys. Rev. Lett. 101(24), 243602 (2008). [CrossRef] [PubMed]
- T. Suzuki, N. Sawayama, and M. Katsuragawa, “Spectral phase measurements for broad Raman sidebands by using spectral interferometry,” Opt. Lett. 33(23), 2809–2811 (2008). [CrossRef] [PubMed]

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