## Resonance enhanced large third order nonlinear optical response in slow light GaInP photonic-crystal waveguides

Optics Express, Vol. 18, Issue 6, pp. 5746-5753 (2010)

http://dx.doi.org/10.1364/OE.18.005746

Acrobat PDF (180 KB)

### Abstract

We report a large nonlinear response in a 1.3*mm* long GaInP photonic crystal waveguide. The wide band gap of GaInP (1.9 *eV*) ensures that no two photon absorption takes place for photons at 1.55*μm* improving the nonlinear performance. The nonlinearity is enhanced by a resonance effect due to the waveguide end facet reflectivities as well as by the low group velocity exhibited by the waveguide. A low CW input pump power of ≃2*mW* causes a very large change in the nonlinear refractive index coefficient which manifests itself in a large, ≃*π*/3 phase shift in the Fabry Perot fringes. The extracted effective nonlinear coefficient *γ* varies from 3.4 × 10^{5}*W*^{-1}*m*^{-1} at short wavelengths to 2.2 × 10^{6}*W*^{-1}*m*^{-1} near the band edge. These values are several orders of magnitude larger than those obtained in reported nonlinear experiments which exploit the Kerr effect. We postulate therefore that the observed nonlinearity is due to a hybrid phenomenon which combines the Kerr effect and an index change which is induced by local heating that results from the residual linear absorption. The efficient nonlinear phase shift was also exploited in a fast dynamic experiment where we demonstrated wavelength conversion with 100*ps* wide pulses proving the potential for switching functionalities at multi GHz rates. The index change required for this switching experiment can not be obtained, at the power levels used here, with a *γ* value of a few thousands *W*^{-1}*m*^{-1} which is a typical Kerr coefficient in similar waveguides. Hence, we conclude that the hybrid nonlinearity is sufficiently fast to enable switching with a time scale of at least 100*ps*.

© 2010 Optical Society of America

## 1. Introduction

1. Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) **425**, 944–947 (2003)
[CrossRef] [PubMed]

*μm*

^{2}so that the intensities of propagating fields are high and nonlinearities are vastly enhanced. Further enhancement of nonlinearities results from low group velocities which commonly characterize PhC waveguides [2

2. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B **19**, 2052–2059 (2002)
[CrossRef]

3. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express **17**, 2944–2953 (2009)
[CrossRef] [PubMed]

4. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express **17**, 7206–7216 (2009)
[CrossRef] [PubMed]

5. C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express **17**, 22442–22451 (2009) [CrossRef]

6. C. Husko, A. De Rossi, S. Combrié, Q. Vy Tran, F. Raineri, and C. Wei Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. **94**, 021111-1–021111-3 (2009) [CrossRef]

*μ*m telecommunication regime, Silicon and GaAs, the nonlinear losses stem primarily from two photon absorption (TPA) [7

7. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express **13**, 801–820 (2005) [CrossRef] [PubMed]

5. C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express **17**, 22442–22451 (2009) [CrossRef]

*μ*m (whose energy is 0.8

*eV*) are naturally advantageous for nonlinear PhC devices. One such material is GaInP whose bandgap is 1.9

*eV*. PhC waveguides based on GaInP have been recently demonstrated with transmission properties that exhibit nonlinear phase shifts of more than

*π*radians with no apparent saturation for pulse peak powers as large as 2.5

*W*[8

8. S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. **95**, 221108-1–211108-3 (2009) [CrossRef]

*π*/3 phase shift was obtained in a 1.3

*mm*long waveguide with a pump power of ≃2

*mW*. The Fabry Perot fringes characterizing the linear transmission spectrum yield directly the group index

*n*and hence the group velocity. The group velocity decreases with increasing wavelength in particular as the band edge is approached [2

_{g}2. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B **19**, 2052–2059 (2002)
[CrossRef]

*γ*. The extracted values depend quadratically on

*n*, as expected [4

_{g}4. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express **17**, 7206–7216 (2009)
[CrossRef] [PubMed]

5. C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express **17**, 22442–22451 (2009) [CrossRef]

*γ*values are very large at any wavelength across the waveguide transmission band taking on the value of 3.4 × 10

^{5}

*W*

^{-1}

*m*

^{-1}at 1530

*nm*and rising to 2.2 × 10

^{6}

*W*

^{-1}

*m*

^{-1}at 1557

*nm*. The observed nonlinear phase change is significantly more efficient than that reported in experiments which are strictly based on the Kerr effect [4

4. K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express **17**, 7206–7216 (2009)
[CrossRef] [PubMed]

6. C. Husko, A. De Rossi, S. Combrié, Q. Vy Tran, F. Raineri, and C. Wei Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. **94**, 021111-1–021111-3 (2009) [CrossRef]

8. S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. **95**, 221108-1–211108-3 (2009) [CrossRef]

*ps*wide pulse was wavelength converted. Tuning the wavelength of the converted signal to either a peak or a valley of a single fringe enables the conversion to be in or out of phase with the pump pulse.

## 2. Experimental results

*μm*wavelength range. They are airbridge W1 type PhC waveguides comprising GaInP slabs patterned with a triangular lattice of air holes. The waveguide is created by omitting a single row of air holes in the ΓK direction and is 1.3

*mm*long. The lattice constant is

*a*= 480

*nm*, the air holes have a radius of

*r*= 0.19

*a*and the semiconductor slab is ≃ 170

*nm*thick [8

8. S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. **95**, 221108-1–211108-3 (2009) [CrossRef]

10. S. Combrié, A. De Rossi, Q. N. V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 mm,” Opt. Lett. **33**, 1908–1910 (2008) [CrossRef] [PubMed]

### 2.1. Static characterization

*μW*) broad band (1525 – 1565

*nm*) probe. Pump and probe are combined by a 50/50 fiber coupler and their polarizations are set to be TE before they are coupled into the PhC waveguide via a lensed fiber. The transmitted light is collected at the waveguide output by a

*NA*= 0.86 microscope objective lens and measured by an optical spectrum analyzer (OSA) with a spectral resolution of 0.01

*nm*. The fiber to waveguide input coupling efficiency was 10% while the waveguide to lens output collection efficiency was 30%.

#### 2.1.1. Linear transmission characterization

*n*=

_{g}*λ*

^{2}/2

*L*Δ

*λ*so that the spectral dependence of

*n*across the transmission spectrum is easily extracted. The two inserts in Fig. 2 (a) highlight the dispersion of

_{g}*n*. The measured

_{g}*n*values are marked by circles in Fig. 2 (b) which shows how

_{g}*n*increases with the wavelength in accordance with the classical dispersive band diagram of W1 type PhC waveguides. The value of

_{g}*n*is larger than that of bulk GaInP (

_{g}*n*= 3.37) all across the transmission spectrum. A quadratic fit to

_{o}*n*is represented by a dashed line in Fig. 2 (b). The accuracy of the fit decreases somewhat near the band edge. Close to the band-edge, a slow mode with a group velocity of about

_{g}*V*=

_{g}*c*/

*n*≃

_{g}*c*/13 is obtained. Since nonlinear effects scale with the square of the slowdown factor

*S*(

*S*=

*n*/

_{g}*n*) [2

_{o}2. M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B **19**, 2052–2059 (2002)
[CrossRef]

*α*were also measured using a tunable single mode laser at specific wavelengths where the experiments were performed (1525

*nm*and 1555

*nm*) and was found to vary between

*α*= 200

*m*

^{-1}to

*α*= 1000

*m*

^{-1}.

#### 2.1.2. Nonlinear static characterization

*λ*= 1537

_{pump}*nm*. The pump powers presented in the legend of Fig. 3 (a), denoted

*P*, are the powers measured at the output facet of the PhC waveguide. The corresponding input powers range from 0 to 2

_{out}*mW*. The pump induces a clear red shift in the phase of the Fabry-Perot fringes, which increases with power. The phase shift

*δφ*is calculated as:

*δφ*= 2

*πϕ*/

*FSR*, where

*ϕ*is the measured shift and

*FSR*is the free spectral range. Figure 3 (b) summarizes the phase shifts as a function of

*P*. The dependence is essentially linear and shows no wiggles or saturation due to the effect of the shifting fringes on the pump. The largest observed phase shift is ≃

_{out}*π*/3 for a power of 600

*μW*. Detailed studies of the induced phase shift revealed two important observations. First, for a fixed pump power and wavelength, the obtained phase shift is the same for all the fringes across the transmission spectrum. Second, a given phase shift, say

*π*/3, is obtained for different pump wavelengths as long as the input pump power is held constant. This is easily understood since both the losses and the group index increase with wavelength so that the nonlinear efficiency remains more or less constant.

*λ*= 1537

_{pump}*nm*, having a group velocity of

*V*≈

_{g}*c*/7, is

*γ*= 3.4 × 10

^{5}

*W*

^{-1}

*m*

^{-1}. The effect of the slowdown factor is demonstrated by calculating 7 values for various pump wavelengths. Figure 4 shows the wavelength dependence of

*γ*, together with a fit (dashed curve) representing the quadratic dependence of the group index on wavelength. The upper axis shows the group index as obtained from Fig. 2 (b). Each point in Fig. 4 was obtained by choosing a pump wavelength which coincides with a fringe peak, measuring the obtained phase shift and calculating

*γ*. Near the band-edge,

*γ*of the slow guided mode (

*V*≈

_{g}*c*/15) reaches the high value of

*γ*= 2.2 × 10

^{6}

*W*

^{-1}

*m*

^{-1}.

### 2.2. Dynamic behavior

*ps*wide pulses. The experimental set-up is illustrated in Fig. 5. Here, the pump signal is externally modulated by a Mach Zender modulator driven by a fast pulse generator and the probe is a tunable CW signal. The pulsed pump comprised 100

*ps*pulses at a duty cycle of 1 : 16 with a maximum input peak power of 25

*mW*. The probe input power was 1 – 2

*mW*. The probe signal is filtered at the waveguide output and detected by a preamplified wide band receiver whose output is observed on a fast sampling oscilloscope.

## 3. Discussion

*γ*value due to the Kerr effect was measured in similar waveguides [8

**95**, 221108-1–211108-3 (2009) [CrossRef]

*W*

^{-1}

*m*

^{-1}. It follows that at the power levels used in the dynamic experiment (100

*ps*pulses with a peak power of ≈ 25

*mW*), such a

*γ*value would result in a minuscule phase shift of less than 10

^{-2}radians with which the switching experiment would be impossible. The hybrid nonlinear effect must therefore be sufficiently fast to respond on the 100

*ps*time scale.

## 4. Conclusions

*μ*m further enhance the nonlinear response. Static measurements reveal a very large phase shift of ≃

*π*/3 in the Fabry Perot fringes for an input power of 2

*mW*. The dynamic nonlinear response of the waveguide was demonstrated in a wavelength conversion experiment with 100

*ps*wide pump pulses with a ≈ 25

*mW*peak power which are imprinted on a CW probe signal. The converted signal can follow the pump pulse or take on its complimentary version depending on wether the probe wavelength coincides with a valley or a peak of a single fringe. The fast response suggests that such nonlinear waveguides hold the promise for compact switching devices operating at multi

*GHz*rates.

## Acknowledgment

## References and links

1. | Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) |

2. | M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B |

3. | C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express |

4. | K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, “Enhanced third-order nonlinear effects in slow-light photonic-crystal slab waveguides of line-defect,” Opt. Express |

5. | C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express |

6. | C. Husko, A. De Rossi, S. Combrié, Q. Vy Tran, F. Raineri, and C. Wei Wong, “Ultrafast all-optical modulation in GaAs photonic crystal cavities,” Appl. Phys. Lett. |

7. | P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express |

8. | S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. |

9. | E. Inbar and A. Arie, “High-sensitivity measurements of the Kerr constant in gases using a Fabry Perot-based ellipsometer,” Appl. Phys. B |

10. | S. Combrié, A. De Rossi, Q. N. V. Tran, and H. Benisty, “GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 mm,” Opt. Lett. |

11. | A. Yariv, |

12. | R. W. Boyd, |

13. | A. E. Siegman, |

14. | N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, A. Sato, H. Yokoyama, K. Yamada, T. Watanabe, T. Tsuchizawa, H. Fukuda, S. Itabashi, and K. Edamatsu, “All-optical phase modulations in a silicon wire waveguide at ultralow light levels,” Appl. Phys. Lett. |

15. | P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. |

16. | H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express |

17. | K. Suzuki, Y. Hamachi, and T. Baba, “Fabrication and characterization of chalcogenide glass photonic crystal waveguides,” Opt. Express |

18. | A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzetti, L. C. Andreani, F. Romanato, L. Businaro, E. Di Fabrizio, A. Passaseo, and M. De Vittorio, “Resonant second-harmonic generation in a GaAs photonic crystal waveguide,” Phys. Rev. B |

**OCIS Codes**

(190.3270) Nonlinear optics : Kerr effect

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(130.5296) Integrated optics : Photonic crystal waveguides

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 9, 2009

Revised Manuscript: January 19, 2010

Manuscript Accepted: January 19, 2010

Published: March 8, 2010

**Citation**

I. Cestier, V. Eckhouse, G. Eisenstein, S. Combrié, P. Colman, and A. De Rossi, "Resonance enhanced large third order nonlinear optical response in slow light GaInP photonic-crystal waveguides," Opt. Express **18**, 5746-5753 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5746

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### References

- Y. Akahane, T. Asano, B. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425,944-947 (2003). [CrossRef] [PubMed]
- M. Soljacic, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, "Photonic-crystal slow-light enhancement of nonlinear phase sensitivity," J. Opt. Soc. Am. B 19,2052-2059 (2002). [CrossRef]
- C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, "Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides," Opt. Express 17,2944-2953 (2009). [CrossRef] [PubMed]
- K. Inoue, H. Oda, N. Ikeda, and K. Asakawa, "Enhanced third-order nonlinear effects in slow-light photoniccrystal slab waveguides of line-defect," Opt. Express 17,7206-7216 (2009). [CrossRef] [PubMed]
- C. Husko, S. Combrié, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, "Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides," Opt. Express 17,22442-22451 (2009). [CrossRef]
- C. Husko, A. De Rossi, S. Combrié, Q. Vy Tran, F. Raineri, and C. W. Wong, "Ultrafast all-optical modulation in GaAs photonic crystal cavities," Appl. Phys. Lett. 94, 021111-1-021111-3 (2009). [CrossRef]
- P. E. Barclay, K. Srinivasan, and O. Painter, "Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper," Opt. Express 13,801-820 (2005). [CrossRef] [PubMed]
- S. Combrié, Q. Vy Tran, C. Husko, P. Colman, and A. De Rossi, "High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption," Appl. Phys. Lett. 95, 221108-1-211108-3 (2009). [CrossRef]
- E. Inbar and A. Arie, "High-sensitivity measurements of the Kerr constant in gases using a Fabry Perot-based ellipsometer," Appl. Phys. B 70,849-852 (2000).
- S. Combrié, A. De Rossi, Q. N. V. Tran, and H. Benisty, "GaAs photonic crystal cavity with ultrahigh Q: microwatt nonlinearity at 1.55 ?m," Opt. Lett. 33,1908-1910 (2008). [CrossRef] [PubMed]
- A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997).
- R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
- A. E. Siegman, Lasers (University Science Books, 1986).
- N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, A. Sato, H. Yokoyama, K. Yamada, T. Watanabe, T. Tsuchizawa, H. Fukuda, S. Itabashi, and K. Edamatsu, "All-optical phase modulations in a silicon wire waveguide at ultralow light levels," Appl. Phys. Lett.95, 171110-1-171110-3 (2009). [CrossRef]
- P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, "Wavelength conversion in GaAs micro-ring resonators," Opt. Lett. 25,554-556 (2000). [CrossRef]
- H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13,4629-4637 (2005). [CrossRef] [PubMed]
- K. Suzuki, Y. Hamachi, and T. Baba, "Fabrication and characterization of chalcogenide glass photonic crystal waveguides," Opt. Express 17,22393-22400 (2009). [CrossRef]
- A. M. Malvezzi, G. Vecchi, M. Patrini, G. Guizzetti, L. C. Andreani, F. Romanato, L. Businaro, E. Di Fabrizio, A. Passaseo, and M. De Vittorio, "Resonant second-harmonic generation in a GaAs photonic crystal waveguide," Phys. Rev. B 68, 161306-1-161306-4 (2003). [CrossRef]

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