## Efficient terahertz-wave generation via four-wave mixing in silicon membrane waveguides |

Optics Express, Vol. 20, Issue 8, pp. 8920-8928 (2012)

http://dx.doi.org/10.1364/OE.20.008920

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### Abstract

Terahertz (THz) wave generation via four-wave mixing (FWM) in silicon membrane waveguides is theoretically investigated with mid-infrared laser pulses. Compared with the conventional parametric amplification or wavelength conversion based on FWM in silicon waveguides, which needs a pump wavelength located in the anomalous group-velocity dispersion (GVD) regime to realize broad phase matching, the pump wavelength located in the normal GVD regime is required to realize collinear phase matching for the THz-wave generation via FWM. The pump wavelength and rib height of the silicon membrane waveguide can be tuned to obtain a broadband phase matching. Moreover, the conversion efficiency of the THz-wave generation is studied with different pump wavelengths and rib heights of the silicon membrane waveguides, and broadband THz-wave can be obtained with high efficiency exceeding 1%.

© 2012 OSA

## 1. Introduction

1. Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO_{(3)} ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express **15**(22), 14783–14792 (2007). [CrossRef] [PubMed]

2. K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. **80**(2), 195–198 (2002). [CrossRef]

7. Y. J. Ding, “Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry,” Opt. Lett. **35**(2), 262–264 (2010). [CrossRef] [PubMed]

8. Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. **30**(21), 2927–2929 (2005). [CrossRef] [PubMed]

11. Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. **35**(15), 2508–2510 (2010). [CrossRef] [PubMed]

12. K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. **32**(20), 2990–2992 (2007). [CrossRef] [PubMed]

*et al.*proposed a way to generate THz-waves in an optical fiber via FWM process, which is a promising method for realizing a reasonable THz-wave source [12

12. K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. **32**(20), 2990–2992 (2007). [CrossRef] [PubMed]

13. 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**(12), 4629–4637 (2005). [CrossRef] [PubMed]

14. R. L. Espinola, J. I. Dadap, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express **13**(11), 4341–4349 (2005). [CrossRef]

^{−1}over 1.2-6.9 μm and 25-200 μm [15

15. R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. **8**(10), 840 (2006). [CrossRef]

^{−1}. Second, the nonlinear refractive index n

_{2}of silicon is about 200 times larger than that of silica [16

16. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. **32**(4), 391–393 (2007). [CrossRef] [PubMed]

16. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. **32**(4), 391–393 (2007). [CrossRef] [PubMed]

15. R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. **8**(10), 840 (2006). [CrossRef]

17. R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature **441**(7090), 199–202 (2006). [CrossRef] [PubMed]

18. B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express **19**(18), 17212–17219 (2011). [CrossRef] [PubMed]

*et al*[19

19. M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. **97**(16), 161107 (2010). [CrossRef]

## 2. Phase matching condition and phase matching bandwidth for THz-wave generation

*ω*

_{p}passing their energy to a signal wave at angular frequency

*ω*

_{s}and a THz-wave at angular frequency

*ω*

_{THz}. Figure 1 shows the energy conservation diagrams and phase-matching condition for collinear configuration, which ensures that the THz-wave is generated through FWM and grows while copropagating with the pump and signal beam. These relationships can be written as the following equations [20]: where

*k*

_{p},

*k*

_{s}and

*k*

_{THz}represent the propagation wave number of pump, signal and THz-wave, respectively.

*k*

_{NL}is the nonlinear phase mismatch, which induced by self phase modulation (SPM) and cross phase modulation (XPM) [21

21. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

*k*

_{L}=

*k*

_{s}+

*k*

_{THz}-2

*k*

_{p}as the linear phase mismatch due to dispersion [22

22. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express **14**(11), 4786–4799 (2006). [CrossRef] [PubMed]

*β*

_{2p}is the group-velocity dispersion, and

*β*

_{2mp}is the even-order dispersion at the pump frequency. Ω

_{sp}=

*ω*

_{s}-

*ω*

_{p}=

*ω*

_{p}-

*ω*

_{THz}is the signal-pump (or pump-THz) frequency detuning, which is a large value due to

*ω*

_{THz}<<

*ω*

_{p}. Since Ω

_{sp}is so large, the higher-order dispersions become important for the phase-matching [20]. However, the higher-order dispersions cannot be accurately calculated using numerical method. Therefore, Eq. (3) can’t be used to calculate the linear phase mismatch, and we use it only to explain the influence of the higher-order dispersions on the linear phase mismatch in the following part of the paper. The linear phase mismatch

*k*

_{L}can be calculated using the Equation:

*k*

_{L}=

*k*

_{s}+

*k*

_{THz}-2

*k*

_{p}= (

*n*+

_{s}ω_{s}*n*-2

_{THz}ω_{THz}*n*)/

_{p}ω_{p}*c,*where

*n*,

_{s}*n*, and

_{THz}*n*represent the fundamental TM mode effective indices of the signal, THz-wave, and pump.

_{p}*c*is the speed of light in vacuum.

15. R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. **8**(10), 840 (2006). [CrossRef]

23. G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. **23**(6), 064002 (2008). [CrossRef]

*r*is the ratio of the slab height (H-h) to overall rib height. Here we set h = H/2 and r = 0.5.

24. T. E. Murphy, software available at http://www.photonics.umd.edu.

16. L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. **32**(4), 391–393 (2007). [CrossRef] [PubMed]

25. Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express **16**(14), 10596–10610 (2008). [CrossRef] [PubMed]

26. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophtonic waveguides,” Nat. Photonics **4**(8), 557–560 (2010). [CrossRef]

*n*as a function of pump wavelength are numerically determined using the finite-difference mode solver. Note that in the calculations, the material dispersion of the silicon is determined by a Sellmeier equation mentioned in [27

_{eff}27. R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photon. **1**(1), 162–235 (2009). [CrossRef]

*β(ω) = n*. Higher-order dispersion is finally calculated via numerical differentiation from

_{eff}(ω)ω/c*β*, and the results of the

_{n}= d^{n}β/dω^{n}*n*and even-order dispersion are shown in Fig. 3 . The zero dispersion wavelengths of the four waveguides are 6 μm, 6.1 μm, 6.2 μm, and 6.3 μm, respectively. The fourth-order dispersion

_{eff}*β*

_{4}and sixth-order dispersion

*β*

_{6}are all negative for the pump wavelength ranging from 4 μm to 7 μm. In the calculation process, the initial errors would be amplified when taking so many derivatives of discrete date and the curves of higher-order dispersion will be distorted for a high spectral resolution. As we only concern the sign of higher-order dispersions other than precision, we can decrease spectral resolution to obtain smooth curves as shown in Fig. 3. Despite the value of higher-order dispersions can’t be accurately calculated, we can distinguish the sign of higher-order dispersions, which will be used to explain the change of linear phase mismatch with different pump wavelengths for a large signal-pump frequency detuning Ω

_{sp}in the following part.

*A*

_{eff}, we calculate the mode profiles at wavelength from 2 μm to 7 μm. Figure 4 shows the fundamental TM mode profiles of the waveguides with different heights. Because of the little variation of the mode profiles for the Mid-infrared waves, we use 4.3 μm as the operation wavelength to simulate the mode profiles and calculate the effective mode areas. The effective mode areas

*A*

_{eff}of the waveguides are 42 μm

^{2}, 48 μm

^{2}, 54 μm

^{2}and 58 μm

^{2}, respectively.

*k*

_{L}is compensated by the nonlinear phase mismatch

*k*

_{NL}, the phase matching is realized according to Eq. (2). The nonlinear phase mismatch is defined as

*k*

_{NL}= 2

*γP*

_{P}, where

*γ = ωn*

_{2}

*/cA*

_{eff}is the effective nonlinearity coefficient of the waveguide, and

*P*

_{P}represents the pump peak power. If we assumed the pump wavelength is 4.3 μm and the rib height is 15 μm, the nonlinearity coefficient

*γ =*152.2 W

^{−1}km

^{−1}with

*n*

_{2}= 5 × 10

^{−18}m

^{2}W

^{−1}, which is assumed according to [29

29. E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express **18**(21), 21981–21989 (2010). [CrossRef] [PubMed]

31. N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si_{1-x}Ge_{x} in the midwave and longwave infrared,” J. Appl. Phys. **110**(1), 011301 (2011). [CrossRef]

*k*

_{NL}= 6.08 cm

^{−1}when the pump peak power is set to be 2000 W. Thus, the phase matching is realized when the linear phase mismatch is about −6 cm

^{−1}as shown in Fig. 6(a), and the points of intersection are the phase matching point. The corresponding relationship of pump, signal and THz-wave wavelength for the phase matching point is described in Fig. 6(b). Therefore, phase matching for a widely tunable THz-wave ranging from 8.57 THz to 10 THz (or from 30 μm to 35 μm) can be realized by tuning the pump wavelength from 4.2 μm to 4.4 μm in the silicon membrane waveguide with rib height of 15 μm. If the pump wavelength is less than 4.2 μm, much broader THz-wave bandwidth can be achieved as the trend shown in Fig. 6. However, the corresponding signal wavelength satisfying the phase matching will be reduced less than 2.2 μm and the efficiency for THz-wave generation will be decreased due to TPA.

## 3. The efficiency of THz-wave generation

29. E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express **18**(21), 21981–21989 (2010). [CrossRef] [PubMed]

*A*,

_{p}*A*and

_{s}*A*represent the slowly varying amplitude of the pump, signal and THz-waves, and

_{t}*z*is the propagation distance. The parameters α

*α*

_{p,}*and α*

_{s}*represent the linear propagation losses of the pump, signal and THz-wave, which are assumed as 0.138 cm*

_{t}^{−1}, 0.092 cm

^{−1}and 0.23 cm

^{−1}, respectively [15

**8**(10), 840 (2006). [CrossRef]

32. G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express **19**(8), 7112–7119 (2011). [CrossRef] [PubMed]

*γ*(

_{xy}*xy*=

*ps*,

*st*,

*pt*) can be calculated with the averaged frequency,

*ω*(

_{xy}=*ω*)/2 [29

_{x}+ ω_{y}29. E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express **18**(21), 21981–21989 (2010). [CrossRef] [PubMed]

*n*

_{2}=5×10

^{−18}m

^{2}W

^{−1}for the pump and THz-wave [29

**18**(21), 21981–21989 (2010). [CrossRef] [PubMed]

31. N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si_{1-x}Ge_{x} in the midwave and longwave infrared,” J. Appl. Phys. **110**(1), 011301 (2011). [CrossRef]

_{2}for the signal wave is predicted to be about 8×10

^{−18}m

^{2}W

^{−1}[30

30. A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. **90**(19), 191104 (2007). [CrossRef]

*n*

_{2}=5×10

^{−18}m

^{2}W

^{−1}for the signal in the simulation. Moreover, the value of n

_{2}used to calculate

*γ*is also assumed as 5×10

_{xy}^{−18}m

^{2}W

^{−1}.

26. X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophtonic waveguides,” Nat. Photonics **4**(8), 557–560 (2010). [CrossRef]

*η*= 25/2000 = 1.25% in this case, which is calculated as the ratio of output THz-power with respect to the input pump peak:

## 4. Conclusion

## Acknowledgments

## References and links

1. | Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO |

2. | K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett. |

3. | A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett. |

4. | X. Xie, J. Xu, and X.-C. Zhang, “Terahertz wave generation and detection from a cdte crystal characterized by different excitation wavelengths,” Opt. Lett. |

5. | T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express |

6. | K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. |

7. | Y. J. Ding, “Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry,” Opt. Lett. |

8. | Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. |

9. | K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. |

10. | T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express |

11. | Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. |

12. | K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett. |

13. | 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 |

14. | R. L. Espinola, J. I. Dadap, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express |

15. | R. A. Soref, S. J. Emelett, and W. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. |

16. | L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. |

17. | R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature |

18. | B. Chmielak, M. Waldow, C. Matheisen, C. Ripperda, J. Bolten, T. Wahlbrink, M. Nagel, F. Merget, and H. Kurz, “Pockels effect based fully integrated, strained silicon electro-optic modulator,” Opt. Express |

19. | M. Wächter, C. Matheisen, M. Waldow, T. Wahlbrink, J. Bolten, M. Nagel, and H. Kurz, “Optical generation of terahertz and second-harmonic light in plasma-activated silicon nanophotonic structures,” Appl. Phys. Lett. |

20. | G. P. Agrawal, |

21. | M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature |

22. | Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express |

23. | G. Z. Mashanovich, M. Milosevic, P. Matavulj, S. Stankovic, B. Timotijevic, P. Y. Yang, E. J. Teo, M. B. H. Breese, A. A. Bettiol, and G. T. Reed, “Silicon photonic waveguides for different wavelength regions,” Semicond. Sci. Technol. |

24. | T. E. Murphy, software available at http://www.photonics.umd.edu. |

25. | Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express |

26. | X. Liu, R. M. Osgood Jr, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophtonic waveguides,” Nat. Photonics |

27. | R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. Hsieh, E. Dulkeith, W. M. J. Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photon. |

28. | Z. Wang, H. Liu, N. Huang, Q. Sun, and J. Wen, “Impact of dispersion profiles of silicon waveguides on optical parametric amplification in the femtosecond regime,” Opt. Express |

29. | E. K. Tien, Y. Huang, S. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express |

30. | A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm,” Appl. Phys. Lett. |

31. | N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si |

32. | G. Z. Mashanovich, M. M. Milošević, M. Nedeljkovic, N. Owens, B. Xiong, E. J. Teo, and Y. Hu, “Low loss silicon waveguides for the mid-infrared,” Opt. Express |

33. | http://www.nature.com/nphoton/journal/v4/n8/full/nphoton.2010.173.html. |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(230.7370) Optical devices : Waveguides

(310.2790) Thin films : Guided waves

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: February 16, 2012

Revised Manuscript: March 17, 2012

Manuscript Accepted: March 20, 2012

Published: April 2, 2012

**Citation**

Zhaolu Wang, Hongjun Liu, Nan Huang, Qibing Sun, and Jin Wen, "Efficient terahertz-wave generation via four-wave mixing in silicon membrane waveguides," Opt. Express **20**, 8920-8928 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-8920

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### References

- Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO(3) ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express15(22), 14783–14792 (2007). [CrossRef] [PubMed]
- K. Kawase, H. Minamide, K. Imai, J. Shikata, and H. Ito, “Injection-seeded terahertz-wave parametric generator with wide tenability,” Appl. Phys. Lett.80(2), 195–198 (2002). [CrossRef]
- A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett.30(24), 3392–3394 (2005). [CrossRef] [PubMed]
- X. Xie, J. Xu, and X.-C. Zhang, “Terahertz wave generation and detection from a cdte crystal characterized by different excitation wavelengths,” Opt. Lett.31(7), 978–980 (2006). [CrossRef] [PubMed]
- T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express16(9), 6471–6478 (2008). [CrossRef] [PubMed]
- K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett.33(20), 2314–2316 (2008). [CrossRef] [PubMed]
- Y. J. Ding, “Efficient generation of high-frequency terahertz waves from highly lossy second-order nonlinear medium at polariton resonance under transverse-pumping geometry,” Opt. Lett.35(2), 262–264 (2010). [CrossRef] [PubMed]
- Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett.30(21), 2927–2929 (2005). [CrossRef] [PubMed]
- K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett.31(7), 957–959 (2006). [CrossRef] [PubMed]
- T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express14(4), 1604–1610 (2006). [CrossRef] [PubMed]
- Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett.35(15), 2508–2510 (2010). [CrossRef] [PubMed]
- K. Suizu and K. Kawase, “Terahertz-wave generation in a conventional optical fiber,” Opt. Lett.32(20), 2990–2992 (2007). [CrossRef] [PubMed]
- 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. Express13(12), 4629–4637 (2005). [CrossRef] [PubMed]
- R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express13(11), 4341–4349 (2005). [CrossRef]
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