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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 16735–16745
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Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides

Walid Mathlouthi, Haisheng Rong, and Mario Paniccia  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 16735-16745 (2008)
http://dx.doi.org/10.1364/OE.16.016735


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Abstract

We characterize silicon waveguide based wavelength converters using a commercial semiconductor optical amplifier (SOA) based wavelength converter as a benchmark. Conversion efficiency as high as -5.5 dB can be achieved using a 2.5 cm long sub-micron silicon-on-insulator rib waveguide. Comparison with the SOA reveals that silicon offers broader conversion bandwidth, higher OSNR, and negligible channel crosstalk. The impact of two-photon absorption and free carrier absorption on the conversion efficiency and the dependence of the efficiency on the rib waveguide dimensions are investigated theoretically. Using a nonlinear index coefficient of 4×10-14 cm2/W for silicon, we obtain good agreement between simulations and measurements.

© 2008 Optical Society of America

1. Introduction

2. Device description

Fig. 1. Left: Scanning electron microscope image of the waveguide used in the experiment. Right: mode effective area versus the waveguide width W. Insets are the TE mode profiles of the waveguides with different widths.

The linear optical transmission loss of the waveguides varies from 0.2 dB/cm (W=1µm) to 0.8 dB/cm (W=0.3µm). The loss is measured using a combination of cutback and Fabry-Perot resonance technique [2

2. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004). [CrossRef]

]. The low propagation loss is attributed to improved fabrication process reducing the waveguide sidewall roughness and the shallow rib structure which has much less sidewall area compared to strip waveguides of similar dimensions, further reducing the scattering loss on the waveguide sidewall.

3. Experiment

The experimental setup is depicted in Fig. 2. Two WDM lasers (channel 33 and 34 of the ITU grid), are combined through a WDM multiplexer with a channel spacing of 100 GHz. These two beams are modulated with a pseudorandom binary sequence (PRBS) of length 231-1 at 10 Gb/s. The signals propagate through 8 km of fiber to de-correlate the two data streams. They are combined with a pump laser at 1552.12 nm. In such a configuration, all the spurious non-degenerate mixing products are separated from the converted signals and can be filtered out [5

5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32, 2393–2395 (2007). [CrossRef] [PubMed]

]. The combined beam is coupled into the wavelength conversion device. In this work, we use two different wavelength converters: 1) a commercial multi-quantum well InGaAsP SOA optimized for nonlinear operation; 2) A simple straight silicon rib waveguide fabricated on a silicon-on-insulator substrate. We use lensed fiber to couple light into the silicon waveguide. The coupling loss between the lensed fiber and the waveguides is measured to be 7 dB for all waveguides with the same taper structure.

Fig. 2. Experimental setup: A/D: Add/Drop multiplexer; PC: Polarization Controller; Blue triangle represents EDFA.

The output beam of the waveguide is coupled into another lensed fiber. At this point, an optical spectrum analyzer (OSA) is used to analyze the spectrum of the output light. After the wavelength converter, the pump and the signal are filtered out using a WDM de-multiplexer (channels 29–30) [5

5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32, 2393–2395 (2007). [CrossRef] [PubMed]

]. The converted signals are amplified using an erbium doped fiber amplifier (EDFA), filtered again (using a 100 GHz DWDM filter) to get rid of residual pump as well as additive amplified spontaneous emission (ASE) and finally sent to a photoreceiver. At this point we generate eye diagrams of the converted optical signals using a digital communications analyzer (DCA) and measure bit error rates (BER). In both cases fiber polarization controllers (PCs) are used to align the polarization of the pump and signal beams.

4. Results and discussions

4.1. Performance characterization of the SOI devices

Here, we use a 2.5 cm long silicon waveguide with a rib width W=0.6 µm. Although, we expect to obtain the optimal efficiency for W=0.55 µm, we use W=0.6 µm because of experimental limitations. The linear optical transmission loss of the waveguide is 0.6 dB/cm.

4.1.1. Conversion efficiency and OSNR measurement

Figure 3(a) depicts the spectrum of the output beam from the silicon waveguide when only 1 channel is active. This figure shows a conversion efficiency of -5.5 dB, which is to our knowledge, the highest achieved using a silicon device. The coupled pump power is 25 dBm while the input signal power is 4 dBm. Recall that, for the silicon waveguide case, we follow the definition of wavelength conversion efficiency as the ratio between the peak levels of the converted signal and the original signal in the spectrum.

Figure 3(b) shows the optical spectrum obtained at the output of the silicon (blue) and SOA (red) based wavelength converters when both channels are turned on. The pump power is 9.5 dBm and the input signal power is 3.4 dBm/channel for the SOA. When comparing the spectra, we see that the OSNR is about 20 dB higher for silicon device than for the SOA which suffers from the ASE generated by the amplifier. The bit error rate (BER) performance of the converted signals will be limited by the signal-to-spontaneous beat noise [14

14. N. A. Olsson, “Lightwave systems with optical amplifiers,” IEEE J. Lightwave Technol. 7, 1071–1082 (1989). [CrossRef]

].

4.1.2. Conversion bandwidth measurement

The conversion efficiency is also measured as a function of Δλ, the wavelength detuning of the signal from the pump. In the SOA case, due to the additional signal gain, the ratio of the converted signal at the output over the original signal at the input is used. As shown in Fig. 4, the 3 dB bandwidth of the silicon device is larger compared to SOA (20 nm vs. 1.6 nm).

Fig. 3. (a) Spectrum of the output beam from a 2.5 cm long waveguide. Coupled pump power is 25 dBm, and the conversion efficiency is -5.5 dB. (b) Spectra at output of the SOI device (blue) and the SOA (red) for the 2 active channels case.

In this experiment, a peak efficiency of about -10 dB was obtained for the SOA at a pump power of 9.5 dBm. Further increasing the pump power did not significantly improve the efficiency due to the gain saturation.

Fig. 4. Conversion efficiency as function of the detuning; (▪) for SOA and (∙) for silicon.

4. 1.3. Bit error rate

To compare the ability of each device to convert high speed optical data, we measure the bit error rate for both converters. In Fig. 5, we present BER results with 1) only one channel; and 2) both channels. This will give us an insight into the power penalty introduced by channel crosstalk. Figure 5(a) shows results for the SOA. No significant power penalty is observed for the single channel case. However, when both channels are on, each of the channels suffer about 2 dB power penalty due to the channel crosstalk. This is mainly due to cross gain modulation (XGM) in the SOA. XGM could be reduced by operating the SOA in the linear regime (less saturation). However, this will result in lower FWM efficiency. The XGM induced penalty is expected to increase with the number of channels. Figure 5(b) shows the BER results for the silicon converter. No significant power penalty is observed when both channels are on. This a major advantage for multi-channel wavelength conversion and dispersion compensation [5

5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32, 2393–2395 (2007). [CrossRef] [PubMed]

]. The eye diagrams as insets in the figures further illustrate the crosstalk effects. Significant noise increase is seen when using the SOA.

Fig. 5. (a) BER using SOA and (b) using silicon: (▪) are for back to back, (∙) are for Ch. 29 when only one channel is active, (▾) and (▴) are for Ch.30 and Ch. 29 respectively when both channels are on.

4.2. Performance dependence on the waveguide dimensions

In the following, we compare the performance of the silicon wavelength converters using silicon rib waveguides with four different widths W=0.3, 0.6, 0.8 and 1µm. The propagation loss for each waveguide is measured to be 0.8, 0.6, 0.4 and 0.2 dB/cm, respectively.

4.2.1. Conversion efficiency

An important parameter of the silicon waveguides is the free carrier lifetime. Two-photon absorption generates free carriers in the waveguides [17

17. H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85, 2196–2198 (2004). [CrossRef]

]. In the TPA process, two photons are absorbed simultaneously and an electron-hole pair is created in the silicon waveguide. These generated carriers cause additional optical loss. In order to determine the carriers lifetime for the different waveguides, we measure the waveguide transmission versus input optical power. We use the same procedure as in [18

18. R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005). [CrossRef] [PubMed]

] to determine the carrier lifetime τ. Figure 6(a) shows the output optical power as a function of the coupled input power for a 2.5 cm long silicon waveguides. Dashed lines represent curve fitting based on simulation. In the modeling, we use the measured linear absorption coefficient for each waveguide and the calculated corresponding effective area Aeff. A TPA coefficient of βTPA=0.5 cm/GW and FCA cross section of σ=1.45×10-17 cm2 are used as in [18

18. R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005). [CrossRef] [PubMed]

], and τ is a fitting parameter. As shown in Fig. 6(a), the modeled and measured nonlinear transmission agree well when using τ=3, 2.25, 2.5 and 3.3 ns for each silicon waveguide respectively. Recall that this carrier lifetime could be further reduced by adding a reverse biased p-i-n diode in the waveguide [18

18. R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005). [CrossRef] [PubMed]

].

Having estimated the carrier lifetime for the different waveguides, we can evaluate the impact of this parameter on the maximal achievable efficiency. To describe the nonlinear optical interaction of the pump, signal and converted signal generated by FWM in the waveguide, we use the formulism described in [19

19. G. P. Agrawal, Nonlinear Fiber Optics, 3nd edition (Academic Press, New York, 2001).

] and take into account the effect of TPA and FCA induced propagation loss. Denoting the pump, the input and converted signals amplitudes (optical power being the square of the amplitude) Ap, As, and Ac, respectively, the equations that govern the evolution of the different waves read as

dAp(z)dz=[αp2βTPA2Aeff(Ap2(z)+2As2(z)+2Ac2(z))σp2βTPAτ2hpcAeff2(λpAp4(z)+λsAs4(z)+λcAc4(z))]Ap(z)+
2πλp2n2AeffAp(z)As(z)Ac(z)
(1)
dAs(z)dz=[αs2βTPA2Aeff(2Ap2(z)+As2(z)+2Ac2(z))σs2βTPAτ2hpcAeff2(λpAp4(z)+λsAs4(z)+λcAc4(z))]As(z)+
2πλs2n2AeffAp2(z)Ac(z)
(2)
dAc(z)dz=[αc2βTPA2Aeff(2Ap2(z)+2Ap2(z)+Ac2(z))σc2βTPAτ2hpcAeff2(λpAp4(z)+λsAs4(z)+λcAc4(z))]Ac(z)+
2πλc2n2AeffAp2(z)As(z)
(3)

where α is the linear propagation loss, n2 is the silicon nonlinear index coefficient, hp is Planck’s constant and c is the speed of light. Note that we neglected the phase mismatch between the different signals here since we are only interested in the maximal achievable conversion efficiency for signals close to the pump wavelength and for which the conversion efficiency is flat for the considered range of wavelengths. The above coupled equations are solved using a 4th order Runge-Kutta solver. Before discussing the effect of the various parameters on the conversion efficiency, we compare simulated and experimental efficiency as a function of the pump power for our four waveguides. Figure 6(b) shows the results.

Fig. 6. Experimental and simulation fits (dashed lines) of (a) the pump transmission for 4 different waveguides. (b) conversion efficiency as a function of the coupled pump power.

Figure 6(b) also shows that the highest efficiency occurs for a waveguide width around W=0.6 µm. Further decreasing the width reduces the efficiency because of the increased linear propagation loss and effective mode area Aeff. Figure 7 gives a better insight on the dependence of the maximal efficiency on the waveguide width. On this figure, the pump power is set at 380 mW. Note that the maximum on this figure is obtained for W=0.51 µm which agrees well with the experimental observations.

Fig. 7. Simulated maximal conversion efficiency as a function of the waveguide width. Coupled pump power is 380 mW. Signal power is 5 mW.

Now, having established the model to simulate the experimental observations, we investigate the effect of the carrier lifetime on the conversion efficiency. The waveguide width is fixed at W=0.5 µm. Figure 8 depicts the conversion efficiency versus the carrier lifetime for different pump powers. As expected, the efficiency drops as the carrier lifetime increases. For strong pump powers, this effect is more pronounced. Note that, with a pump power of 1 W and short carrier lifetime, the conversion efficiency approaches 0 dB. By incorporating a reverse biased p-i-n diode structure in the silicon rib waveguide one can sweep out the carriers from the waveguide hence reducing the effective carrier lifetime.

Fig. 8. Efficiency versus the effective carrier lifetime for various pump powers.

4.2.2. Conversion bandwidth

In today’s optical networks, a desirable feature for wavelength converters is broader bandwidth. For this purpose, we measure the efficiency as a function of the wavelength for the various waveguides under investigation. The results are depicted in Fig. 9. Figure 9(a) shows the experimental normalized conversion as a function of the wavelength detuning Δλ for different waveguide widths. The curves are symmetric around Δλ=0, so only the Δλ>0 half is plotted. As expected, these curves have sinc2 function shape. In Fig. 9(b) we can see the bandwidth versus the waveguide width where the bandwidth is defined as the position of the first minimum in the efficiency curve. Note that the bandwidth varies with W. The bandwidth increases from 15 nm to 22 nm when the width is varied from 0.3 µm to 1 µm. This is due to the different group velocity dispersion and phase matching condition of the different waveguides.

Fig. 9. (a) Measured conversion efficiency versus signal and pump detuning for 4 waveguide widths. (b) Measured and simulated (using eq. 4) conversion bandwidth versus waveguide width. Coupled pump power: 380 mW; signal power: 5 mW.

In order to gain more understanding on the upper limit of the efficiency that could be achieved with our devices, we calculate the group velocity dispersion GVD parameter β2=d2 β/2. The material dispersion of both silicon and silica is included using the Sellmeier relations. The TE mode effective indices are numerically determined using the effective index method. 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/n.

Figure 10 shows the GVD parameter as a function of the wavelength and the waveguide width. Note that a minimum of β2=0.7 ps2/m is obtained around 1550 nm for a waveguide width W=1 µm. For each waveguide, we use the corresponding GVD at the pump wavelength to calculate the normalized efficiency as a function of the detuning given by [26

26. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Shmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–962 (2006). [CrossRef] [PubMed]

27

27. J. Hansryd, A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002). [CrossRef]

]

η=[2πn2PpumpλAeffsinh(gL)g]2
(4)

where

g=[2πn2PpumpλpAeffβ2(Δω)2(β2(Δω)22)2]12
(5)

is the gain parameter. A good fit of the experimental results is obtained for all the waveguides using (4) and (5) with n2=4×10-14 cm2/W, as seen in Fig. 9(b). However, simulations also show that none of the waveguides exhibit anomalous dispersion (β2>0 for all wavelengths and widths) making it impossible to have conversion gain. In order to have anomalous group velocity dispersion near the pump wavelength, one possible solution could be to increase the etch depth so that hH while keeping the rib structure. This could provide parametric gain as well as larger conversion bandwidth [26

26. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Shmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–962 (2006). [CrossRef] [PubMed]

]. Note that such a rib waveguide structure still allows sweeping out the TPA generated carriers by integrating a p-i-n diode.

Fig. 10. Group velocity dispersionβ2 versus wavelength and waveguide width. H=340 nm and h=130 nm.

5. Conclusion

In conclusion, we have achieved -5.5 dB conversion efficiency in a 2.5 cm long submicron silicon waveguide via FWM process. Experimental results show that our device can achieve higher conversion efficiency as well as larger bandwidth than commercially available SOA. We showed that, for WDM application, our device does not suffer channel crosstalk. BER curves were measured for two ITU-DWDM channels at 10 Gb/s. No power penalty was observed for the converted signals when using our silicon device, whereas a 2 dB power penalty was measured for SOA based converter. We also investigated the impact of carrier lifetime on the maximal achievable conversion. We note that reducing the carrier lifetime by implementing a p-i-n diode along the waveguide could further improve the efficiency. We studied the effect of the silicon waveguide dimensions on the FWM efficiency. We show that the conversion bandwidth varies with the width of the waveguide. Numerical simulations show that an optimum width of 0.51 µm gives the maximal efficiency. Using a value of n2=4×10-14 cm2/W, our simulations fitted measurements under several conditions. Finally, further tailoring the dispersion of the waveguide via setting the optimal dimensions will enable parametric gain and high bandwidth wavelength conversion using silicon rib waveguides which allow integration of a p-i-n structure to minimize FCA. Using resonant structures such as ring resonators, the FWM effect can be further enhanced if the phase matching condition is fulfilled [28

28. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16, 4881–4887 (2008). [CrossRef] [PubMed]

].

Acknowledgments

The authors thank M. Lee, and S. Xu for help in the experimental setup; Y.-W. Shin, H. Nguyen, and A. Liu for helpful discussions; E. Eitan, D. Rubin, A. Alduino, K. Callegari, J. C. Jimenez, and J. Ngo for assistance in device fabrication and sample preparation.

References and Links

1.

L. Pavesi and D. J. Lockwood, Silicon Photonics (Spronger-Verlag, New York, 2004).

2.

G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004). [CrossRef]

3.

Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721 (2006). [CrossRef] [PubMed]

4.

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14, 1182–1188 (2006). [CrossRef] [PubMed]

5.

S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, “Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator,” Opt. Lett. 32, 2393–2395 (2007). [CrossRef] [PubMed]

6.

S. Ayotte, S. Xu, H. Rong, and M. J. Paniccia, “Dispersion compensation by optical phase conjugation in silicon waveguide,” Electron. Lett. 43, 1037–1039 (2007). [CrossRef]

7.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nature Photonics 2, 35–38 (2008). [CrossRef]

8.

D. Nesset, T. Kelly, and D. Marcenac, “All-optical wavelength conversion using SOA nonlinearities,” IEEE Commun. Mag. 36, 56–61 (1998). [CrossRef]

9.

C. Q. Xu, H. Okayama, and M. Kawahara, “1.5 µm band efficient broadband wavelength conversion by difference frequency generation in a periodically domain-inverted LiNbO3 channel waveguide,” Appl. Phys. Lett. 63, 3559–3561 (1993). [CrossRef]

10.

S. L. Jansen, D. van den Borne, P. M. Krummrich, S. Spalter, G. D. Khoe, and H. de Waardt, “Long-Haul DWDM Transmission Systems Employing Optical Phase Conjugation,” IEEE J. Lightwave Technol. 12, 505–520 (2006).

11.

A. Mecozzi, G. Contestabile, L. Graziani, F. Martelli, A. D’Ottavi, P. Spano, R. Dall’Ara, and J. Eckner, “Polarization-insensitive four-wave mixing in a semiconductor optical amplifier,” Appl. Phys. Lett. 72, 2651–2653 (1998). [CrossRef]

12.

T. Borghesani, “Semiconductor optical amplifiers for advanced optical applications,” ICTON, paper Tu.C1.3, (2006).

13.

Details are available at http://www.photond.com.

14.

N. A. Olsson, “Lightwave systems with optical amplifiers,” IEEE J. Lightwave Technol. 7, 1071–1082 (1989). [CrossRef]

15.

F. Girardin, J. Eckner, G. Guekos, R. Dall’Ara, A. Mecozzi, A. D’Ottavi, F. Martelli, S. Scotti, and P. Spano, “Low-noise and very high efficiency four-wavemixing in 1.5-mm-long semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9, 746–748 (1997). [CrossRef]

16.

T. Akiyama, H. Kuatsuka, N. Hatori, Y. Nakata, H. Ebe, and M. Sugawara, “Symmetric highly efficient (~0 dB) wavelength conversion based on Four-wave mixing in quantum dot optical amplifiers,” IEEE Photon. Technol. Lett. 14, 1139–1141 (2002). [CrossRef]

17.

H. Rong, A. Liu, R. Nicolaescu, M. Paniccia, O. Cohen, and D. Hak, “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” Appl. Phys. Lett. 85, 2196–2198 (2004). [CrossRef]

18.

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak, and O. Cohen, “Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering,” Opt. Express 13, 519–525 (2005). [CrossRef] [PubMed]

19.

G. P. Agrawal, Nonlinear Fiber Optics, 3nd edition (Academic Press, New York, 2001).

20.

O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12, 829–834 (2004). [CrossRef] [PubMed]

21.

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]

22.

R. Salem, G. E. Tudury, T. U. Horton, G. M. Carter, and T. E. Murphy, “Polarization-insensitive optical clock recovery at 80 Gb/s using a silicon photodiode,” IEEE Photon. Technol. Lett. 17, 1968–1970 (2005). [CrossRef]

23.

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14, 5524–5534 (2006). [CrossRef] [PubMed]

24.

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, 191104 (2007). [CrossRef]

25.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91, 21111 (2007). [CrossRef]

26.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Shmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–962 (2006). [CrossRef] [PubMed]

27.

J. Hansryd, A. Andrekson, M. Westlund, J. Li, and P. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506 (2002). [CrossRef]

28.

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16, 4881–4887 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(230.4320) Optical devices : Nonlinear optical devices
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Nonlinear Optics

History
Original Manuscript: August 11, 2008
Revised Manuscript: September 29, 2008
Manuscript Accepted: September 29, 2008
Published: October 6, 2008

Citation
Walid Mathlouthi, Haisheng Rong, and Mario Paniccia, "Characterization of efficient wavelength conversion by four-wave mixing in sub-micron silicon waveguides," Opt. Express 16, 16735-16745 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16735


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References

  1. L. Pavesi and D. J. Lockwood, Silicon Photonics (Spronger-Verlag, New York, 2004).
  2. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004). [CrossRef]
  3. S. Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, "Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides," Opt. Express 14, 11721 (2006). [CrossRef] [PubMed]
  4. H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006). [CrossRef] [PubMed]
  5. S. Ayotte, H. Rong, S. Xu, O. Cohen, and M. Paniccia, "Multichannel dispersion compensation using a silicon waveguide-based optical phase conjugator," Opt. Lett. 32, 2393-2395 (2007). [CrossRef] [PubMed]
  6. S. Ayotte, S. Xu, H. Rong, and M. J. Paniccia, "Dispersion compensation by optical phase conjugation in silicon waveguide," Electron. Lett. 43, 1037-1039 (2007). [CrossRef]
  7. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, "Signal regeneration using low-power four-wave mixing on silicon chip," Nature Photonics 2, 35-38 (2008). [CrossRef]
  8. D. Nesset, T. Kelly, and D. Marcenac, "All-optical wavelength conversion using SOA nonlinearities," IEEE Commun. Mag. 36, 56-61 (1998). [CrossRef]
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