## Spectral shift of femtosecond pulses in nonlinear quadratic PPSLT Crystals

Optics Express, Vol. 14, Issue 11, pp. 4774-4779 (2006)

http://dx.doi.org/10.1364/OE.14.004774

Acrobat PDF (195 KB)

### Abstract

Spectral blue- and red-shifts in a range of 100 nm are achieved by propagating 40 fs pulses with a 70 nm spectrum centered at 1450 nm in a 25-mm-long periodically poled stoichiometric lithium tantalate crystal. We show experimentally that these shifts, originating from a phase-mismatched second harmonic generation process under conditions of strong group-velocity mismatch, can be efficiently controlled by acting on pulse intensity and phase-mismatch.

© 2006 Optical Society of America

## 1. Introduction

2. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum **74**, 1–18 (2003). [CrossRef]

3. J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express **11**, 818–823 (2003). [CrossRef] [PubMed]

4. F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. **164**, 312–323 (1967). [CrossRef]

9. P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. **21**, 659–661 (1996). [CrossRef] [PubMed]

10. R. DeSalvo, D. Hagan, M. Sheik-Bahae, G. Stegeman, E. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. **17**, 28–30 (1992) [CrossRef] [PubMed]

11. C. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to *χ*^{(2)}: *χ*^{(2)} cascading,” J. Opt. Soc. Am. B **11**, 2434–2443 (1994). [CrossRef]

12. J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. **29**, 757–776 (1997). [CrossRef]

13. P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO_{3} waveguides,” Opt. Lett. **27**, 2182–2184 (2002). [CrossRef]

14. F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B **6**, S182–S189 (2004). [CrossRef]

15. F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B **21**, 376–383 (2004). [CrossRef]

## 2. Theoretical analysis

16. C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. **78**, 4749–4752 (1997). [CrossRef]

_{FF}-β’

_{SH}; Δk=2β

_{FF}- β

_{SH}+2π/Λ is the effective wavevector-mismatch, where Λ is the QPM period; χ

_{FF}=2χ

^{(2)}/λn

_{FF}and χ

_{SH}=2χ

^{(2)}/λn

_{SH}, where χ

^{(2)}is the nonlinear coefficient, n is the refractive index, λ the FF wavelength. We consider the usual case where only the FF light is incident on the quadratic medium. In the limit of large phase-mismatch, an equation of motion for the FF field can be derived from (1) [11

11. C. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to *χ*^{(2)}: *χ*^{(2)} cascading,” J. Opt. Soc. Am. B **11**, 2434–2443 (1994). [CrossRef]

12. J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. **29**, 757–776 (1997). [CrossRef]

4. F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. **164**, 312–323 (1967). [CrossRef]

9. P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. **21**, 659–661 (1996). [CrossRef] [PubMed]

8. A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A **52**, 3231–3238 (1995). [CrossRef] [PubMed]

^{2}is the initial pulse shape, g(t) is the initial phase distribution, γ=2δχ

_{FFχSH}/Δk

^{2}and κ=χ

_{FFχSH}/Δk.

*γ*<0 (the usual case since the SH wave is slower than the FF one), both positive and negative mismatch conditions lead to a steepening of the trailing edge of the FF pulse, due to the dragging by the slower SH wave. This effect is directly proportional to the parameter δ because of increased dragging for larger GVM; it is inversely proportional to Δk

^{2}, due the lower amount of SH and less efficient dragging for increasing phase-mismatch, and it increases with the FF pulse intensity. The group velocity reduction caused by self-steepening was recently demonstrated experimentally [18

18. M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. **31**, 534–536 (2006). [CrossRef] [PubMed]

*γ*<0 the trailing edge of the pulse is steeper than the leading one and produces the strongest shift, towards the blue for Δk<0, and towards the red for Δk>0, the magnitude of such shift being larger for shorter input pulse-widths. It is worth noting that the relationship between group velocity modification and spectral shift of the FF pulse is quite different with respect to the linear case since the reduction of the FF group velocity occurring for

*γ*<0 can be accompanied either by blue-shift [15

15. F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B **21**, 376–383 (2004). [CrossRef]

18. M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. **31**, 534–536 (2006). [CrossRef] [PubMed]

13. P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO_{3} waveguides,” Opt. Lett. **27**, 2182–2184 (2002). [CrossRef]

14. F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B **6**, S182–S189 (2004). [CrossRef]

## 3. Experimental results

2. G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum **74**, 1–18 (2003). [CrossRef]

^{2}), independently of phase-mismatch, the FF output pulse spectrum is indistinguishable from the input one. At negative phase-mismatch values, corresponding to a self-defocusing cascaded nonlinearity, at high enough intensity, spectral blue-shifts of the injected pulses are observed. Typical experimental results obtained injecting FF pulses at 1450 nm with ΔkL=-80π are shown in Fig. 1(a). The blue-shift was observed to increase with the injected power, with a maximum value of about 40 nm at an intensity of 20 GW/cm

^{2}. Under these conditions a spectral narrowing of ~20% also occurs. The experimental spectra can not be quantitatively fit using the above described analytical model due to the non-negligible role of dispersion, but they are nicely reproduced by full numerical simulations solving Eqs. (1), as shown in Fig 1 (b). The inset shows the evolution of the FF spectrum during propagation in the nonlinear crystal, demonstrating that the effect saturates after short propagation. A method for circumventing this limitation, based on engineered aperiodically poled crystals, was recently proposed [19

19. K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. **29**, 763–765 (2004). [CrossRef] [PubMed]

^{2}, and a group-delay shift induced by self-steepening takes place (see Ref. 18 for details). It is worth noting that in the non-poled region of the crystal, even at high intensity, no spectral modification was observed, thus indicating a negligible contribution by third order susceptibility. The spectral shift is thus a pure self-effect of quadratic interactions.

^{2}a pronounced red-shift of 40 nm is observed, which is well reproduced by numerical simulations. At higher intensity (20 GW/cm

^{2}) an even stronger red-shift occurs (~90 nm), which can not be quantitatively reproduced by the numerical model due to the onset of self-focusing (spatial break-up instabilities) leading to an increase of the local intensity. Moreover, in the time domain the combined effect of positive dispersion and self-focusing cascaded nonlinearity gives rise to pulse broadening and also to pulse break-up at high intensities. These effects need to be considered in applications requiring good temporal quality of femtosecond pulses.

15. F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B **21**, 376–383 (2004). [CrossRef]

13. P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO_{3} waveguides,” Opt. Lett. **27**, 2182–2184 (2002). [CrossRef]

14. F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B **6**, S182–S189 (2004). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

1. | Y. S. Kivshar and G. P. Agrawal, |

2. | G. Cerullo and S. De Silvestri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum |

3. | J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, “High-power air-clad large-mode-area photonic crystal fiber laser,” Opt. Express |

4. | F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, “Self-Steepening of Light Pulses,” Phys. Rev. |

5. | T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, “Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments,” Phys. Rev. |

6. | D. Grischkowsky, M. Loy, and P. Liao, “Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation,” Phys. Rev. A |

7. | D. Anderson and M. Lisak, “Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides,” Phys. Rev. A |

8. | A.S. Rodrigues, M. Santagiustina, and E.M. Wright, “Nonlinear pulse propagation in the vicinity of a two-photon resonance,” Phys. Rev. A |

9. | P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, “Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide,” Opt. Lett. |

10. | R. DeSalvo, D. Hagan, M. Sheik-Bahae, G. Stegeman, E. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. |

11. | C. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to |

12. | J.P. Torres and L. Torner, “Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media,” Opt. Quantum Electron. |

13. | P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, “Spatial trapping of short pulses in Ti-indiffused LiNbO |

14. | F. Baronio, A. Barthélémy, S. Carrasco, V. Couderc, C. De Angelis, L. Lefort, Y. Min, P. H Pioger, V. Quiring, L. Torner, and W. Sohler, “Generation of quadratic spatially trapped beams with short pulsed light,” J. Opt. B |

15. | F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B |

16. | C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, “Spatial Solitons and Induced Kerr Effects in Quasi-Phase-Matched Quadratic Media,” Phys. Rev. Lett. |

17. | In literature, the fourth term in Eq. (2) is usually referred as the self-steepening term (see for example Ref. [4–9]). |

18. | M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, “Groupvelocity control by quadratic nonlinear interactions,” Opt. Lett. |

19. | K. Beckwitt, F. Ilday, and F. Wise, “Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials,” Opt. Lett. |

**OCIS Codes**

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.5530) Nonlinear optics : Pulse propagation and temporal solitons

(190.5940) Nonlinear optics : Self-action effects

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: February 14, 2006

Revised Manuscript: April 27, 2006

Manuscript Accepted: April 29, 2006

Published: May 29, 2006

**Citation**

F. Baronio, C. De Angelis, M. Marangoni, C. Manzoni, R. Ramponi, and G. Cerullo, "Spectral shift of femtosecond pulses in nonlinear quadratic PPSLT Crystals," Opt. Express **14**, 4774-4779 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-11-4774

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### References

- Y. S. Kivshar and G. P. Agrawal, Optical solitons (Academic press, San Diego, 2003).
- G. Cerullo and S. De Silvestri, "Ultrafast optical parametric amplifiers," Rev. Sci. Instrum 74, 1-18 (2003). [CrossRef]
- J. Limpert, T. Schreiber, S. Nolte, H. Zellmer, T. Tunnermann, R. Iliew, F. Lederer, J. Broeng, G. Vienne, A. Petersson, and C. Jakobsen, "High-power air-clad large-mode-area photonic crystal fiber laser," Opt. Express 11, 818-823 (2003). [CrossRef] [PubMed]
- F. De Martini, C.H. Townes, T.K. Gustafson, and P.L. Kelley, "Self-steepening of Light Pulses," Phys. Rev. 164, 312-323 (1967). [CrossRef]
- T.K. Gustafson, J.P. Taran, H.A. Haus, J.R. Lifsitz, and P.L. Kelley, "Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments," Phys. Rev. 177, 306-313 (1969). [CrossRef]
- D. Grischkowsky, M. Loy, and P. Liao, "Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation," Phys. Rev. A 12, 2514-2533 (1975). [CrossRef]
- D. Anderson and M. Lisak, "Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides," Phys. Rev. A 27, 1393-1398 (1983). [CrossRef]
- A.S. Rodrigues, M. Santagiustina, and E.M. Wright, "Nonlinear pulse propagation in the vicinity of a two-photon resonance," Phys. Rev. A 52, 3231-3238 (1995). [CrossRef] [PubMed]
- P. Guerreiro, S. Lee, A. Rodrigues, Y. Hu, E. Wright, S. Najafi, J. Mackenzie, and N. Peyghambarian, "Femtosecond pulse propagation near a two-photon transition in a semiconductor quantum-dot waveguide," Opt. Lett. 21, 659-661 (1996). [CrossRef] [PubMed]
- R. DeSalvo, D. Hagan, M. Sheik-Bahae, G. Stegeman, E. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded second-order effects in KTP," Opt. Lett. 17, 28-30 (1992) [CrossRef] [PubMed]
- C. Menyuk, R. Schiek, and L. Torner, "Solitary waves due to χ(2): χ(2) cascading," J. Opt. Soc. Am. B 11, 2434-2443 (1994). [CrossRef]
- J.P. Torres and L. Torner, "Self-splitting of beams into spatial solitons in planar waveguides made of quadratic nonlinear media," Opt. Quantum Electron. 29, 757-776 (1997). [CrossRef]
- P. Pioger, V. Couderc, L. Lefort, A. Barthelemy, F. Baronio, C. De Angelis, Y. Min, V. Quiring, and W. Sohler, "Spatial trapping of short pulses in Ti-indiffused LiNbO3 waveguides, " Opt. Lett. 27, 2182-2184 (2002). [CrossRef]
- F. Ilday, K. Beckwitt, Y. Chen, H. Lim, and F. Wise, "Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes, " J. Opt. Soc. Am. B 21, 376-383 (2004). [CrossRef]
- C. Balslev Clausen, O. Bang, and Yu. S. Kivshar, "Spatial solitons and induced Kerr effects in quasi-phase-matched Quadratic Media," Phys. Rev. Lett. 78, 4749-4752 (1997). [CrossRef]
- In literature, the fourth term in Eq. (2) is usually referred as the self-steepening term (see for example Ref. [4-9]). [CrossRef]
- M. Marangoni, C. Manzoni, R. Ramponi, G. Cerullo, F. Baronio, C. De Angelis, and K. Kitamura, "Group-velocity control by quadratic nonlinear interactions, " Opt. Lett. 31, 534-536 (2006).
- K. Beckwitt, F. Ilday, and F. Wise, "Frequency shifting with local nonlinearity management in nonuniformly poled quadratic nonlinear materials," Opt. Lett. 29, 763-765 (2004). [CrossRef] [PubMed]

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