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

The development of efficient and compact sources of THz-wave is of great interest for applications in various fields such as applied physics, communications, sensing, and life sciences [1]. The difference-frequency generation (DFG) in nonlinear optical crystals is an important technique for coherent THz-wave generation [27]. However, it is difficult to increase the conversion efficiency for DFG based THz-wave generation, because most of nonlinear optical crystals have a large absorption in the THz–wave region. Surface-emitting THz-wave generation can be used to overcome the high absorption loss [811]. Unfortunately, this method requires a specially designed crystal, and the interaction length is limited by the size of the base material [12].

To cope with these difficulties, Suizu 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]. FWM in silicon waveguide had been studied not only theoretically but also experimentally [13, 14]. Compared with conventional fiber, the silicon rib membrane waveguide will be a more viable structure for THz-wave generation via FWM. There are five major inherent advantages. First, the silicon membrane has an absorption loss below 0.23 cm−1 over 1.2-6.9 μm and 25-200 μm [15], while the absorption coefficient of the optical fiber in the THz-wave region is about 5 cm−1. Second, the nonlinear refractive index n2 of silicon is about 200 times larger than that of silica [16]. Third, the refractive index of silicon (around 3.5) is much larger than that of air, which implies a much stronger light confinement. Fourth, the crystalline nature of silicon that makes stimulated Raman scattering (SRS) depend strongly on the waveguide geometry and mode polarization, and SRS cannot occur when an input pulse excites the TM mode [16]. Fifth, the silicon membrane waveguide is also CMOS compatible and enable low-cost large-scale integration [15]. Moreover, the silicon waveguide also have been modified to show second-order nonlinearity at technically relevant levels [17, 18]. Even the THz-wave generation based on DFG has already been experimentally demonstrated in a silicon waveguide by Waechter et al [19]. Despite this progress, there is still a strong motivation to investigate the THz-wave generation based on FWM due to the high third-order nonlinearity of silicon waveguide.

In this paper, we investigate efficient THz-wave generation via FWM in silicon membrane waveguides using Mid-infrared pump and signal waves. The organization of the paper is as follows. In Section 2, we analyze the collinear phase matching condition and phase matching bandwidth with the dispersion relation of silicon membrane waveguides. In section 3, we numerically investigate the conversion efficiency of the THz-wave generation for different pump wavelengths and rib heights of the waveguides. Finally, we summarize this paper in Section 4.

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

We use degenerate FWM to generate THz-wave, which typically involves two pump photons at angular frequency ωp passing their energy to a signal wave at angular frequency ωs and a THz-wave at angular frequency ωTHz. 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]:

2ωpωsωTHz=0,
ks+kTHz2kp+kNL=0,
where kp, ks and kTHz represent the propagation wave number of pump, signal and THz-wave, respectively. kNL is the nonlinear phase mismatch, which induced by self phase modulation (SPM) and cross phase modulation (XPM) [21]. We can also define kL = ks + kTHz-2kp as the linear phase mismatch due to dispersion [22]. Since the signal and THz-wave are located symmetrically around the pump frequency, the linear phase mismatch only depends on even-order dispersion parameters as [20]
kL=β2pΩsp2+2m=2β2mp(2m)!Ωsp2m,
where β2p is the group-velocity dispersion, and β2mp is the even-order dispersion at the pump frequency. Ωsp = ωs-ωp = ωp-ωTHz is the signal-pump (or pump-THz) frequency detuning, which is a large value due to ωTHz<<ωp. Since Ωsp 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 kL can be calculated using the Equation: kL = ks + kTHz-2kp = (nsωs + nTHzωTHz-2npωp)/c, where ns, nTHz, and np represent the fundamental TM mode effective indices of the signal, THz-wave, and pump. c is the speed of light in vacuum.

 

Fig. 1 Schematic of (a) energy-conservation diagram and (b) the phase-matching condition for collinear phase matching.

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Figure 2 shows the dimension of silicon membrane waveguide, in which the rib is suspended over an air filled cavity comprising the lower cladding, whilst the upper cladding is also air. This waveguide is constructed by etching away the buried-oxide insulating material in silicon on insulator (SOI) locally under the rib [15]. The waveguide should be designed not only confining the THz-wave, but also satisfying the single-mode condition [23]:

WH0.3+r1r2,
where W/H is the ratio of the rib width to overall rib height, and r is the ratio of the slab height (H-h) to overall rib height. Here we set h = H/2 and r = 0.5.

 

Fig. 2 Left: rib silicon membrane waveguide dimension; Right: the TM mode profiles of the silicon membrane waveguide at the wavelength of 35 μm for different rib heights.

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The dimension of the waveguide is optimally designed to realize the collinear phase matching. The rib waveguides with width of 12 μm and rib heights varied from 14 μm up to 17 μm can satisfy the single-mode condition. To determine the performance of these waveguides, we need to simulate the mode profiles at the THz-band using a finite-difference mode solver [24]. There are two assumptions before simulation. The first is that the pump and signal waves are both fundamental TM mode, thus the SRS can be neglected [16]. The second is that the pump and signal waves are Mid-infrared waves and exceed 2.2 μm, leading to a negligible of two-photon absorption (TPA) and free-carrier absorption (FCA) and thus enabling efficient parametric generation [25, 26]. The fundamental TM mode profiles of the silicon membrane waveguide at the wavelength of 35 μm for several rib heights are shown in Fig. 2. It is clear that the designed waveguides can confine THz-wave.

To realize phase matching, we first simulate the dispersion of the waveguides. For the silicon membrane waveguides mentioned above, the fundamental TM mode effective indices neff 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].The dispersion relation is then calculated from β(ω) = neff(ω)ω/c. Higher-order dispersion is finally calculated via numerical differentiation from βn = dnβ/dωn, and the results of the neff 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 β4 and sixth-order dispersion β6 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 Ωsp in the following part.

 

Fig. 3 Plots of computed effective index of refraction (a), and (b) GVD dispersion (c) forth order dispersion (d) sixth order dispersion as a function of pump wavelength for different rib heights.

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In order to determine the effective mode area Aeff, 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 Aeff of the waveguides are 42 μm2, 48 μm2, 54 μm2 and 58 μm2, respectively.

 

Fig. 4 The fundamental TM mode profiles of the waveguides with different rib heights.

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The linear phase mismatch kL as a function of THz wavelength in a waveguide with rib height of 15 μm is shown in Fig. 5 . It is found that the linear phase mismatch is larger for a pump wavelength located in the anomalous GVD regime (6.3 μm) than located in the normal GVD regime (5 μm, 4.5 μm). The Eq. (3) is used to explain this phenomenon. As Ωsp = ωp-ωTHz is large, the second term of Eq. (3) cannot be ignored and must be a large negative figure because β4p and β6p are negative from Fig. 3(c) and Fig. 3(d). If the pump wavelength located in the anomalous GVD regime (β2p<0), the sum (kL) of the first and second term of Eq. (3) must be a larger negative figure. If the pump wavelength located in the normal GVD regime (β2p>0), the negative second term can be counteracted by the positive first term. Therefore, unlike the conventional parametric amplification or wavelength conversion using silicon waveguide, for which a pump wavelength in the anomalous GVD regime is needed to realize broad phase matching [28], proper pump wavelength located in the normal GVD regime can be used to realize a relative small linear phase mismatch for certain THz-waves, which is illustrated in the Fig. 6(a) .

 

Fig. 5 Linear phase mismatch as a function of THz wavelength for different pump wavelengths when the rib height is 15 μm.

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Fig. 6 (a) Linear phase mismatch as a function of THz wavelength for different pump wavelengths, and (b) signal wavelength and related THz-wavelength depend on pump wavelength for collinear phase-matched THz-wave generation when the rib height is 15 μm.

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When the linear phase mismatch kL is compensated by the nonlinear phase mismatch kNL, the phase matching is realized according to Eq. (2). The nonlinear phase mismatch is defined as kNL = 2γPP, where γ = ωn2/cAeff is the effective nonlinearity coefficient of the waveguide, and PP 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−1km−1 with n2 = 5 × 10−18 m2W−1, which is assumed according to [2931]. The nonlinear phase mismatch kNL = 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.

We can also tailor the rib height to tune the THz-wave bandwidth for a fixed pump, which is illustrated by Fig. 7(a) . It is shown that the phase matching is changed for different rib heights, which means that THz-wave with different wavelength can be generated by changing rib heights. The corresponding relationship of rib height, signal and THz-wave wavelength for the phase matching point is described in Fig. 7(b). It is clear that the phase matching bandwidth of THz-wave ranging from 7.7 THz to 10 THz (or from 30 μm to 39 μm) can be achieved by tailoring the rib height from 14 μm to 17 μm when the pump wavelength is 4.3 μm. If the rib height H>17 μm, phase matching for THz-wave with much longer wavelength can be realized as the trend shown in Fig. 7. However, larger rib height means larger mode areas Aeff, which will lead to lower nonlinearity coefficient γ and reduce the efficiency of THz-wave generation.

 

Fig. 7 (a) Linear phase mismatch as a function of THz wavelength for different rib heights, and (b) signal wavelength and related THz-wavelength depend on rib heights for collinear phase-matched THz-wave generation when the pump wavelength is 4.3 μm.

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3. The efficiency of THz-wave generation

The FWM process can be described by the following coupling equations [29]:

dApdz=αp2Ap+iγp|Ap|2Ap+2iγps|As|2Ap+2iγpt|At|2Ap+2iγpAsAtAp*exp(ikLz),
dAsdz=αs2As+iγs|As|2As+2iγsp|Ap|2As+2iγst|At|2As+iγsAp2At*exp(ikLz),
dAtdz=αt2At+iγt|At|2At+2iγtp|Ap|2At+2iγts|As|2At+iγtAp2As*exp(ikLz),
where Ap, As and At represent the slowly varying amplitude of the pump, signal and THz-waves, and z is the propagation distance. The parameters αp, αs and αt represent the linear propagation losses of the pump, signal and THz-wave, which are assumed as 0.138 cm−1, 0.092 cm−1 and 0.23 cm−1, respectively [15, 32]. The nonlinearity coefficient γxy (xy = ps, st, pt) can be calculated with the averaged frequency, ωxy = (ωx + ωy)/2 [29]. Here, we assume n2=5×10−18 m2W−1 for the pump and THz-wave [2931]. Despite the n2 for the signal wave is predicted to be about 8×10−18 m2W−1 [30], for simplicity, we also use n2=5×10−18 m2W−1 for the signal in the simulation. Moreover, the value of n2 used to calculate γxy is also assumed as 5×10−18 m2W−1.

The THz-wave generation via FWM is numerically studied by simultaneously injecting pump pulses and signal pulses in the Mid-infrared band [33]. The pump and signal pulses are taken to be hyperbolic-secant pulses with same pulse width of 12 ns and same repetition rate [33]. Here, we assume the signal peak power is half of the pump peak power. The multi-photon absorption can be neglected in this paper, which does not presents a significant obstacle for practical applications [26].

Figure 8(a) depicts the peak power of the THz-wave along the waveguide for several pump peak powers, when the pump wavelength is 4.3 μm and the rib height is 15 μm. The input signal wavelength can be obtained from Fig. 6(b). The peak power of the THz-wave is increasing with the increase of the distance until the max. is attained, then the peak power of the THz wave drops to zero as a period of FWM completes and next period occurs. When the pump peak power is 2000 W, the maximum peak power (25 W) of THz-wave can be obtained in a 6-mm-long waveguide due to phase matching. The output spectra centered at 9.2304 THz for several pump peak powers are shown in Fig. 8(b). Furthermore, the maximum conversion efficiency 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:

 

Fig. 8 (a) The THz-wave peak power depends on distance for different pump peak powers; (b) The output spectra of THz-wave with different pump peak powers when the distance is 6 mm.

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η=PTHzout/Ppumpin

For simplicity, we assume the waveguide length is 6 mm and the pump peak power is 2000 W in the following part.

THz-wave generation based on FWM is also a discrete wavelength conversion. Figure 9 shows the conversion efficiency of the generated THz-wave when the signal wavelength is tuned from 2299.8 nm to 2304.9 nm for a fixed pump located at 4.3 μm. It is shown that the maximum conversion efficiency occurs at the THz-wavelength of 32.5μm when the signal is tuned to satisfy the phase-matching condition. For this discrete wavelength conversion, the bandwidth of the generated THz-wave is about 1 μm, while the corresponding bandwidth of the signal is only 5.1 nm.

 

Fig. 9 The conversion efficiency as a function of THz-wavelength when the signal wavelength is tuned from 2299.8 nm to 2304.9 nm for a fixed pump located at 4.3 μm.

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The output peak power and related wavelength of the THz-wave as a function of pump wavelength are shown in Fig. 10(a) . With the increase of the pump wavelength, the frequency and peak power of the THz-wave increase, which is illustrated in Fig. 10(b). This can be explained that the THz-wave with relative high frequency can obtain more energy from the pump according to Eq. (1). The maximum conversion efficiency η is 1.39% at 9.8684 THz when the pump wavelength is 4.4 μm, and the minimal conversion efficiency η is 1.12% at 8.6455 THz when the pump wavelength is 4.2 μm.

 

Fig. 10 (a) The peak power and related wavelength of THz-wave as a function of pump wavelength and (b) the corresponding output spectra of THz-wave when the rib height is 15 μm.

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When the pump wavelength is located at a fixed value such as 4.3 μm, we can also tailor the rib height to turn the bandwidth of the THz-wave. Figure 11(a) shows the peak power and related wavelength of THz-wave as a function of rib height. It is clear that the peak power of THz-wave decreases as the rib height increases due to the increase of the effective mode area Aeff, which leads to a low nonlinearity coefficient γ. The frequency of the THz-wave decreases with the increase of the rib height, and the THz-wave with relative low frequency obtains less energy from the pump, which is also a reason for the low peak power of the low frequency THz-wave as shown in Fig. 11(b). The maximum conversion efficiency η is 1.71% at 10.1 THz when the rib height is 14 μm, and the minimal conversion efficiency η is 0.63% at 7.7 THz when the rib height is 17 μm.

 

Fig. 11 (a) The THz-wave peak power and related THz-wavelength as a function of rib height and (b) the corresponding output spectra of THz-wave when the pump wavelength is 4.3 μm.

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4. Conclusion

We have presented a theoretical study of THz-wave generation using Mid-infrared pump and signal waves in silicon membrane waveguides. The simulation model allows us to show the importance of the pump wavelength to the collinear phase matching, which can be realized only when the pump wavelength locates in the normal GVD regime. Moreover, broadband phase matching can be achieved by tuning the pump wavelength and the rib height. Finally, we numerically discuss the conversion efficiency of the THz-wave generation in the silicon membrane waveguides. This method and results show a promising way to realize an efficient and compact THz-wave source.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 61078029.

References and links

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]  

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. 30(24), 3392–3394 (2005). [CrossRef]   [PubMed]  

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. 31(7), 978–980 (2006). [CrossRef]   [PubMed]  

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 16(9), 6471–6478 (2008). [CrossRef]   [PubMed]  

6. 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]  

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]  

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. 31(7), 957–959 (2006). [CrossRef]   [PubMed]  

10. T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006). [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]  

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]  

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]  

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]  

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]  

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]  

20. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

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]  

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]  

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]  

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 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]  

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]  

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 19(24), 24730–24737 (2011). [CrossRef]   [PubMed]  

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]  

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]  

31. N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011). [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]  

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

References

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  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]
  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. 30(24), 3392–3394 (2005).
    [CrossRef] [PubMed]
  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. 31(7), 978–980 (2006).
    [CrossRef] [PubMed]
  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 16(9), 6471–6478 (2008).
    [CrossRef] [PubMed]
  6. 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]
  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]
  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. 31(7), 957–959 (2006).
    [CrossRef] [PubMed]
  10. T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
    [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]
  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, S. J. McNab, and Y. A. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
    [CrossRef]
  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]
  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]
  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]
  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]
  20. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).
  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]
  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]
  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]
  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 16(14), 10596–10610 (2008).
    [CrossRef] [PubMed]
  26. X. Liu, R. M. Osgood, 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]
  27. R. M. Osgood, 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]
  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 19(24), 24730–24737 (2011).
    [CrossRef] [PubMed]
  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]
  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]
  31. N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
    [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]
  33. http://www.nature.com/nphoton/journal/v4/n8/full/nphoton.2010.173.html .

2011 (4)

2010 (5)

2009 (1)

2008 (4)

2007 (4)

2006 (7)

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]

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]

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]

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[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]

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]

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]

2005 (4)

2002 (1)

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]

Agrawal, G. P.

Andersen, K. N.

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]

Avetisyan, Y.

Avetisyan, Y. H.

Bettiol, A. A.

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]

Bjarklev, A.

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]

Bolten, J.

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]

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]

Borel, P. I.

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]

Boyraz, O.

Breese, M. B. H.

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]

Bristow, A. D.

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]

Buchwald, W. R.

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]

Chen, X.

Chen, Y. H.

Chiang, A. C.

Chmielak, B.

Chung, Y. C.

Dadap, J. I.

Ding, Y. J.

Dulkeith, E.

Emelett, S. J.

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]

Espinola, R. L.

Fage-Pedersen, J.

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]

Fauchet, P. M.

Foster, M. A.

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]

Frandsen, L. H.

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]

Fukuda, H.

Gaeta, A. L.

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]

Gao, S.

Green, W. M. J.

Hansen, O.

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]

Hon, N. K.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Hsieh, I.

Hu, Y.

Huang, N.

Huang, Y.

Huang, Y. C.

Ikari, T.

Imai, K.

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]

Itabashi, S.

Ito, H.

Jacobsen, R. S.

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]

Jalali, B.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Johnson, T. J.

Kalyoncu, S. K.

Kawase, K.

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

Kristensen, M.

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]

Kurz, H.

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]

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]

Lavrinenko, A. V.

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]

Lee, H. H.

Lin, Q.

Lin, S. T.

Lin, Y. Y.

Lipson, M.

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]

Liu, H.

Liu, X.

Mashanovich, G. Z.

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]

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]

Matavulj, P.

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]

Matheisen, C.

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]

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]

McNab, S. J.

Merget, F.

Michael, C. P.

Milosevic, M.

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]

Miloševic, M. M.

Minamide, H.

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[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]

Moulin, G.

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]

Nagel, M.

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]

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]

Nedeljkovic, M.

Osgood, R. M.

Ou, H.

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]

Owens, N.

Painter, O. J.

Panoiu, N. C.

Perahia, R.

Peucheret, C.

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]

Qian, F.

Reed, G. T.

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]

Ripperda, C.

Rotenberg, N.

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]

Sasaki, Y.

Schmidt, B. S.

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]

Sharping, J. E.

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]

Shikata, J.

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]

Shin, S. Y.

Shoji, T.

Song, Q.

Soref, R.

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

Soref, R. A.

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]

Stankovic, S.

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]

Suizu, K.

Sun, Q.

Suzuki, Y.

Takahashi, J.

Takahashi, M.

Takushima, Y.

Teo, E. J.

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]

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]

Tien, E. K.

Timotijevic, B.

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]

Tsuchizawa, T.

Turner, A. C.

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]

van Driel, H. M.

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]

Vlasov, Y. A.

Vodopyanov, K. L.

Wächter, M.

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]

Wahlbrink, T.

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]

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]

Waldow, M.

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]

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]

Wang, T. D.

Wang, Z.

Watanabe, T.

Wen, J.

Xie, X.

Xiong, B.

Xu, J.

Yamada, K.

Yang, P. Y.

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]

Yin, L.

Yokoyama, H.

Zhang, J.

Zhang, X.

Zhang, X.-C.

Zsigri, B.

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]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (3)

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]

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]

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]

J. Appl. Phys. (1)

N. K. Hon, R. Soref, and B. Jalali, “The third-order nonlinear optical coefficients of Si, Ge, and Si1-xGex in the midwave and longwave infrared,” J. Appl. Phys. 110(1), 011301 (2011).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

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]

Nat. Photonics (1)

X. Liu, R. M. Osgood, 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]

Nature (2)

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]

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]

Opt. Express (11)

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. Express 13(11), 4341–4349 (2005).
[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(12), 4629–4637 (2005).
[CrossRef] [PubMed]

T. Ikari, X. Zhang, H. Minamide, and H. Ito, “THz-wave parametric oscillator with a surface-emitted configuration,” Opt. Express 14(4), 1604–1610 (2006).
[CrossRef] [PubMed]

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]

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]

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 16(9), 6471–6478 (2008).
[CrossRef] [PubMed]

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]

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]

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]

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]

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 19(24), 24730–24737 (2011).
[CrossRef] [PubMed]

Opt. Lett. (9)

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

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]

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

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]

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]

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]

Semicond. Sci. Technol. (1)

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]

Other (3)

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

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

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Figures (11)

Fig. 1
Fig. 1

Schematic of (a) energy-conservation diagram and (b) the phase-matching condition for collinear phase matching.

Fig. 2
Fig. 2

Left: rib silicon membrane waveguide dimension; Right: the TM mode profiles of the silicon membrane waveguide at the wavelength of 35 μm for different rib heights.

Fig. 3
Fig. 3

Plots of computed effective index of refraction (a), and (b) GVD dispersion (c) forth order dispersion (d) sixth order dispersion as a function of pump wavelength for different rib heights.

Fig. 4
Fig. 4

The fundamental TM mode profiles of the waveguides with different rib heights.

Fig. 5
Fig. 5

Linear phase mismatch as a function of THz wavelength for different pump wavelengths when the rib height is 15 μm.

Fig. 6
Fig. 6

(a) Linear phase mismatch as a function of THz wavelength for different pump wavelengths, and (b) signal wavelength and related THz-wavelength depend on pump wavelength for collinear phase-matched THz-wave generation when the rib height is 15 μm.

Fig. 7
Fig. 7

(a) Linear phase mismatch as a function of THz wavelength for different rib heights, and (b) signal wavelength and related THz-wavelength depend on rib heights for collinear phase-matched THz-wave generation when the pump wavelength is 4.3 μm.

Fig. 8
Fig. 8

(a) The THz-wave peak power depends on distance for different pump peak powers; (b) The output spectra of THz-wave with different pump peak powers when the distance is 6 mm.

Fig. 9
Fig. 9

The conversion efficiency as a function of THz-wavelength when the signal wavelength is tuned from 2299.8 nm to 2304.9 nm for a fixed pump located at 4.3 μm.

Fig. 10
Fig. 10

(a) The peak power and related wavelength of THz-wave as a function of pump wavelength and (b) the corresponding output spectra of THz-wave when the rib height is 15 μm.

Fig. 11
Fig. 11

(a) The THz-wave peak power and related THz-wavelength as a function of rib height and (b) the corresponding output spectra of THz-wave when the pump wavelength is 4.3 μm.

Equations (8)

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2 ω p ω s ω THz =0,
k s + k THz 2 k p + k NL =0,
k L = β 2p Ω sp 2 +2 m=2 β 2mp (2m)! Ω sp 2m ,
W H 0.3+ r 1 r 2 ,
d A p dz = α p 2 A p +i γ p | A p | 2 A p +2i γ ps | A s | 2 A p +2i γ pt | A t | 2 A p +2i γ p A s A t A p * exp( i k L z ),
d A s dz = α s 2 A s +i γ s | A s | 2 A s +2i γ sp | A p | 2 A s +2i γ st | A t | 2 A s +i γ s A p 2 A t * exp( i k L z ),
d A t dz = α t 2 A t +i γ t | A t | 2 A t +2i γ tp | A p | 2 A t +2i γ ts | A s | 2 A t +i γ t A p 2 A s * exp( i k L z ),
η= P THz out / P pump in

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