## Ultrafast nonlinear optical studies of silicon nanowaveguides |

Optics Express, Vol. 20, Issue 4, pp. 4085-4101 (2012)

http://dx.doi.org/10.1364/OE.20.004085

Acrobat PDF (1894 KB)

### Abstract

Results of a self-consistent ultrafast study of nonlinear optical properties of silicon nanowaveguides using heterodyne pump-probe technique are reported. The two-photon absorption coefficient and free-carrier absorption effective cross-section were determined to be 0.68cm/GW, and 1.9x10^{−17} cm^{2}, respectively and the Kerr coefficient and free-carrier-induced refractive index change 0.32x10^{−13} cm^{2}/W, and −5.5x10^{−21} cm^{3}, respectively. The effects of the proton bombardment on the linear loss and the carrier lifetime of the devices were also studied. Carrier lifetime reduction from 330ps to 33ps with a linear loss of only 14.8dB/cm was achieved using a proton bombardment level of 10^{15}/cm^{2}.

© 2012 OSA

## 1. Introduction

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23. M. A. Popovic, T. Barwicz, M. S. Dahlem, F. W. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in *2008 Conference on Optical Fiber Communication/National Fiber Optic Engineers Conference*, 2296–2298 (2008).

28. T. Barwicz, M. A. Popovi, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, E. P. Ippen, F. X. Kartner, and H. I. Smith, “Reconfigurable silicon photonic circuits for telecommunication applications,” Proc. SPIE **6872**, 68720Z, 68720Z-12 (2008). [CrossRef]

^{2}. At such intensities, the nonlinear optical properties of silicon begin to impose limitations on the maximum data rate that can be carried by such devices. Therefore, they need to be accurately characterized.

29. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics **4**(8), 535–544 (2010). [CrossRef]

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*α*is the linear propagation loss,

_{lin}*β*is the two photon absorption coefficient,

*σf*is the loss incurred due to the interaction of the optical field with the TPA-generated free-carriers of density,

_{α}(N)*N*, and

*I*is the intensity of the optical field. Linear loss,

*α*is due to impurities of the constituent elements, and the surface roughness of the waveguides due to fabrication. The linear loss is independent of the optical power inside the waveguide and is relatively constant over the length of the device so that total loss scales linearly with the length.

_{lin}14. J. Y. Lee, L. H. Yin, G. P. Agrawal, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express **18**(11), 11514–11523 (2010). [CrossRef] [PubMed]

15. A. Martínez, J. Blasco, P. Sanchis, J. V. Galán, J. García-Rupérez, E. Jordana, P. Gautier, Y. Lebour, S. Hernández, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Martí, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Lett. **10**(4), 1506–1511 (2010). [CrossRef] [PubMed]

31. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express **13**(8), 3129–3135 (2005). [CrossRef] [PubMed]

32. M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-voltage, compact, depletion-mode, silicon Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. **16**(1), 159–164 (2010). [CrossRef]

33. 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]

10. F. X. Kärtner, S. Akiyama, G. Barbastathis, T. Barwicz, H. Byun, D. T. Danielson, F. Gan, F. Grawert, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, M. Kim, L. C. Kimerling, J. Liu, J. Michel, O. O. Olubuyide, J. S. Orcutt, M. Park, M. Perrott, M. A. Popovic, P. T. Rackich, R. J. Ram, H. I. Smith, and M. R. Watts, “Electronic photonic integrated circuits for high speed, high resolution, analog to digital conversion,” Proc. SPIE **6125**, 612503, 612503-14 (2006). [CrossRef]

29. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics **4**(8), 535–544 (2010). [CrossRef]

30. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

*n*is the refractive index of the waveguide,

_{0}*n*is the Kerr coefficient,

_{2}*ξf*is the induced phase due to the interaction of the optical field with the TPA-generated free carriers of density

_{ϕ}(N)*N*, and

*I*is the intensity of the optical field.

9. H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. **23**(6), 064007 (2008). [CrossRef]

^{−14}cm

^{2}/W to 14.5x10

^{−14}cm

^{2}/W [9

9. H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. **23**(6), 064007 (2008). [CrossRef]

34. K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump - probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. **17**(12), 874–876 (1992). [CrossRef] [PubMed]

35. A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express **18**(4), 3582–3591 (2010). [CrossRef] [PubMed]

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40. A. P. Knights and G. F. Hopper, “Effect of ion implantation induced defects on optical attenuation in silicon waveguides,” Electron. Lett. **39**(23), 1648–1649 (2003). [CrossRef]

41. D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. **87**(26), 261108 (2005). [CrossRef]

## 2. Silicon nanowaveguides

28. T. Barwicz, M. A. Popovi, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, E. P. Ippen, F. X. Kartner, and H. I. Smith, “Reconfigurable silicon photonic circuits for telecommunication applications,” Proc. SPIE **6872**, 68720Z, 68720Z-12 (2008). [CrossRef]

_{2}undercladding and hydrogen silsesquioxane (HSQ) overcladding layers. The waveguides were formed in silicon (n = 3.45), with a height of 106nm and a width of 475nm on a 3μm thick undercladding of SiO

_{2}(n = 1.45). The structures were overcladded with 1μm of HSQ (n = 1.38) on top of which a 100nm thick layer of SiO

_{2}was sputtered for protection. The cross-section of the waveguide and the profile of its fundamental TE mode at 1500nm are shown in Fig. 1(c) and Fig. 1(d), respectively.

## 3. Pulse propagation model

*P(z,t)*is the instantaneous pulse power in the waveguide, and the losses are divided into linear,

*α*and nonlinear

_{lin}*α*components. In this equation, the dispersion broadening can be neglected since the result of cross-correlation of the output pulses show negligible pulse-broadening over a wide range of powers. In addition, the fact that this analysis provides excellent fits to the experimental results as will be demonstrated in Section 5, further supports this assumption. For pulses much shorter than the carrier recovery time, the carrier recombination can be neglected and the nonlinear loss can be modeled bywhere

_{NL}*β*is the TPA coefficient,

*σ*is the FCA effective cross section,

*ħω*is the energy of a photon, and

*I(z,t)*is the instantaneous intensity of the pulse. The first term in this equation describes the instantaneous loss introduced by TPA which is proportional to the optical intensity. The second term describes absorption due to free-carriers, which accumulates in proportion to the square of the optical intensity and recovers with free carrier lifetime.

42. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

*A*and

_{TPA}*A*, are defined as the effective areas of the TPA and FCA, respectively. These effective areas are defined so that the intensities may be defined in terms of a plane-wave mode with the optical power

_{FCA}*P(z,t)*propagating in the optical waveguide. By calculating the overlap of the loss profile as defined by the electric field distribution inside the silicon core with the mode profile, the effective areas are determined. In case of TPA effective area, a rigorous expression was rigorously derived in [42

42. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

*A*. The effective areas,

_{FCA}*A*and

_{TPA}*A*for the silicon waveguides shown in Fig. 1 were determined to be 0.097μm

_{FCA}^{2}and 0.075μm

^{2}, respectively.

## 4. Experimental setup

34. K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump - probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. **17**(12), 874–876 (1992). [CrossRef] [PubMed]

## 5. Results and discussion

### 5.1 Characterization of linear and coupling losses

*P*and

_{in}*P*are the power coupled into the input and output lens-tip fibers, respectively,

_{out}*P*and

_{iw}*P*are the powers inside the waveguide at the input and output facets, and

_{ow}*C*and

_{in}*C*are the coupling losses in dB,

_{out}*α*is the linear loss in dB/cm,

_{lin}*α(Ι)*is the nonlinear loss in dB/cm that varies with intensity of the optical signal inside the waveguide. In Fig. 3, the “input” port is defined to be the port where the pump and probe pulses are coupled into the device, while the “output” port is that end of the device from which the light is collected and directed to the detector.

*α(I)~0*), Eq. (8) describes a line with slope

*α*, and y-intercept point of

_{lin}*C*. Linear loss measurements on five waveguides with differential length of 6.1mm between any two adjacent waveguides were conducted. The differential lengths of the waveguide sections were measured using an interferometric technique where the heterodyne pump-probe setup of Fig. 2 was utilized. In this technique, the pump pulse was blocked, while the probe pulse was coupled into waveguides of different length. To obtain an overlap between the probe and reference pulses, the reference arm path length had to be adjusted. The change in the reference path length was then converted to the path length difference between two adjacent waveguides. Using this data, the total coupling loss of 20.8dB and linear loss of 6.5dB/cm were measured.

_{total}=C_{in}+C_{out}*C*and

_{in}*C*. Therefore, the device was tested in both “forward” and “reverse” directions as demonstrated in Fig. 3. The output power collected by the lens-tip fiber as a function of the power put into the input lens-tip fiber was obtained and the results are shown in Fig. 5(a) . The black and red curves are obtained in the “forward” and “reverse” directions, respectively. The straight line in this plot corresponds to the linear response, hence any variation from this line is deemed to be the nonlinear loss and is a function of the light intensity inside the waveguide. Higher coupling losses result in lower power inside the waveguide, hence smaller nonlinear optical effects and a roll-off at higher input powers. Any two points on the forward and reverse curves that deviate from the linear response by the same amount correspond to having the same powers inside the waveguide. Therefore, the difference between the forward and backward input powers corresponding to any two such points is equal to the difference between the coupled powers. This is graphically shown in Fig. 5(a) where the two vertical arrows indicate a pair of points with identical nonlinear losses in the forward and reverse directions, and the horizontal arrow indicates the difference between the input powers in the forward and reverse directions indicating the difference between the two coupling losses. The deviation of the output power response from the linear response at the input and output ports is calculated and shown in Fig. 5(b). The difference between the input powers corresponding to the same nonlinear loss is plotted in the inset of Fig. 5(b), and as shown, it is 5.6dB.

_{out}*C*= 13.2dB and

_{in}*C*= 7.6dB. The large difference between the input and output coupling losses emphasizes the importance of a careful characterization. This difference is due to fabrication tolerances, both for the curvature of the lensed-tip fiber, as well as the uniformity of the cleave quality of the silicon chip facets.

_{out}### 5.2 TPA and FCA magnitudes

_{1}= 0), followed by a slow recovery time of several hundreds of picoseconds. The amplitude of the instantaneous component is proportional to the intensity of the light inside the waveguide and is caused by two-photon absorption, while the magnitude of the longer-lived response is due to absorption of the probe pulse by the free carriers generated in the TPA process.

*τ*=0 response including the initial fast rise of FCA consistent with Eq. (13). The measured amplitudes of the instantaneous TPA-induced loss and long-lived FCA loss are shown in Fig. 6(b). The TPA loss is shown in blue and consists of a linear section at lower pulse energy levels, while at higher input energy levels the magnitude of this loss saturates as the pump pulse begins to experience loss through its own TPA. The linear section of the curve is dominated by the TPA effect which is proportional to the intensity and the TPA coefficient (

*β*). The instantaneous response due to TPA at low input pulse energy levels can be described by the following equationwhere

*I*and

_{p}*I*are the pump and probe intensities inside the waveguide, respectively. Integrating this equation and solving for a change in

_{s}*I*due to

_{s}*I*

_{p}_{,}we havewhere the new variable

*L*, the effective length of the device, is a function of physical length

_{eff}*L*, and the linear loss

*α*, and

_{lin}*I*is the pump intensity defined as the ratio of the pump power to the TPA effective area. For long waveguides, the effective length reduces to 1

_{p}*/ α*. The silicon waveguides in this study had a dimension of 106nm × 475nm and length equal to 14.9mm.

_{lin}*A*was calculated via an overlap integral of E-field and the nonlinear medium [42

_{TPA,eff}42. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express **15**(10), 5976–5990 (2007). [CrossRef] [PubMed]

^{2}and

*L*was found to be 6mm. From the slope of the TPA loss as shown in Fig. 6(b), we extract the TPA coefficient to be 0.68 cm/GW. This compares with the mid range of values previously published [9

_{eff}9. H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. **23**(6), 064007 (2008). [CrossRef]

*L*is a function of the number of free-carrier pairs and is described by:where

*α*is the total loss due to free-carrier absorption,

_{T,FCA}*N*is the density of carrier pairs per cm

^{3}, and

*N*is the total number of carrier pairs generated. The intensity in this case is calculated by taking into account two effective areas, as in Eq. (5).

_{total}*ΔE*is the deviation of the output energy due to nonlinearity as demonstrated in Fig. 7,

*α*is the linear loss, and

_{lin}*L*is the physical length of the device. The result of the calculation using Eq. (15) is shown in Fig. 9 with (+) markers, which demonstrates a quadratic dependence on the input pulse energy.

^{2}/sec [44] and redistribute evenly across the waveguide cross within a few picoseconds. Therefore, an effective area for the overlap of the E-field of the propagating mode with this rectangular cross section is calculated and is equal to 0.075μm

^{2}. In the regime that linear loss still dominates over nonlinear loss, these carriers are distributed along the length of the device over the FCA effective length,

*L*given by:where the factor of two in the denominator is due to the dependence of free-carrier density on the square of the optical intensity. The total FCA loss is determined from the heterodyne pump-probe experimental results by measuring the transmission loss at time delays larger than 5ps, which is approximately how long it takes for the carriers to diffuse to a uniform transverse distribution. The magnitude of this loss as a function of the input pulse energy is calculated from the pump-probe traces of Fig. 6(a), and shown in Fig. 6(b). The fit to the measured data is accomplished using the carrier density calculated using Eq. (13) and Eq. (15) with the FCA effective cross section

_{FCA,eff}*σ*= 1.9x10

^{−17}cm

^{2}. The summary of the extracted parameters described in this section is given in Table 1 .

### 5.3 Comparison of simulation and experimental results

### 5.4 Optical Kerr effect and free-carrier index changes

*L*as well. Using the total number of carriers, we define the refractive index change as a function of carrier density as:where

_{FCA,eff}*Δn*is the total change in the refractive index due to free-carriers,

_{FCA}*ξ*is a proportionality constant,

*N*is the total number of carrier pairs generated over the waveguide length [30

_{total}30. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express **15**(25), 16604–16644 (2007). [CrossRef] [PubMed]

*ξ*= −5.5 × 10

^{−21}cm

^{3}. The results obtained in this section are summarized in Table 2 .

### 5.5 Carrier recovery time and proton bombardment

35. A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express **18**(4), 3582–3591 (2010). [CrossRef] [PubMed]

45. N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, and G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” in *Group IV Photonics, 2008 5th IEEE International Conference on*, 122–124 (2008).

46. J. K. Doylend, P. E. Jessop, and A. P. Knights, “Optical attenuation in ion-implanted silicon waveguide racetrack resonators,” Opt. Express **19**(16), 14913–14918 (2011). [CrossRef] [PubMed]

^{12}to 10

^{15}/cm

^{2}. It was necessary to determine the energy level of protons that would penetrate different layers of the structure. These layers are illustrated in Fig. 1(c). In order for the protons to reach the silicon waveguides, they must penetrate through 100nm layer of SiO

_{2}, 1μm of HSQ, and get implanted in the 100nm-thick silicon waveguide. To determine the proper energy levels, the SRIM program was utilized (www.srim.org). Based on Monte-Carlo analysis, the SRIM program simulates the penetration depth of protons of different energy accounting for scattering, energy loss, and non-uniformity of proton energy levels. Each device was proton-bombarded using a combination of three different proton energies of 80, 90, and 100KeV to account for variations in the density of HSQ layer, which is highly dependent on the fabrication process, and to still create the desired distribution of defect states in the silicon waveguides. As shown in Fig. 1(c), the silicon waveguides start at the depth of 1100nm and extend to 1206nm where the largest number of defect states is created.

^{15}/cm

^{2}. This combination of recovery time reduction and degradation in linear loss seems to be the best thus far reported for the proton bombardment technique [39

39. P. J. Foster, J. K. Doylend, P. Mascher, A. P. Knights, and P. G. Coleman, “Optical attenuation in defect-engineered silicon rib waveguides,” J. Appl. Phys. **99**(7), 073101 (2006). [CrossRef]

## 6. Conclusion

^{−17}cm

^{2}, respectively and the Kerr coefficient and free-carrier-induced refractive index change 0.32x10

^{−13}cm

^{2}/W, and −5.5x10

^{−21}cm

^{3}, respectively. The parameters extracted were applied to a model predicting the output power response of the waveguides as a function of the input power. This model was utilized to predict the limitations imposed by the nonlinearity on the transmission of pulsewidths of different duration [47

47. A. R. Motamedi, J. J. Plant, J. P. Donnelly, P. W. Juodawlkis, and E. P. Ippen, “Ultrafast nonlinearities and gain dynamics in high-power semiconductor amplifiers,” Appl. Phys. Lett. **93**(25), 251106 (2008). [CrossRef]

^{15}/cm

^{2}with an increase of linear loss to 14.8dB/cm was achieved.

## Acknowledgments

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8. | R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. |

9. | H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. |

10. | F. X. Kärtner, S. Akiyama, G. Barbastathis, T. Barwicz, H. Byun, D. T. Danielson, F. Gan, F. Grawert, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, M. Kim, L. C. Kimerling, J. Liu, J. Michel, O. O. Olubuyide, J. S. Orcutt, M. Park, M. Perrott, M. A. Popovic, P. T. Rackich, R. J. Ram, H. I. Smith, and M. R. Watts, “Electronic photonic integrated circuits for high speed, high resolution, analog to digital conversion,” Proc. SPIE |

11. | A. Alduino, L. Liao, R. Jones, M. Morse, B. Kim, W.-Z. Lo, J. Basak, B. Koch, H.-F. Liu, H. Rong, M. Sysak, C. Krause, R. Saba, D. Lazar, L. Horwitz, R. Bar, S. Litski, A. Liu, K. Sullivan, O. Dosunmu, N. Na, T. Yin, F. Haubensack, I. W. Hsieh, J. Heck, R. Beatty, H. Park, J. Bovington, S. Lee, H. Nguyen, H. Au, K. Nguyen, P. Merani, M. Hakami, and M. Paniccia, “Demonstration of a high speed 4-channel integrated silicon photonics WDM link with hybrid silicon lasers,” in |

12. | D. A. B. Miller, “Optical interconnects to electronic chips,” Appl. Opt. |

13. | M. Khorasaninejad and S. S. Saini, “All-optical logic gates using nonlinear effects in silicon-on-insulator waveguides,” Appl. Opt. |

14. | J. Y. Lee, L. H. Yin, G. P. Agrawal, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express |

15. | A. Martínez, J. Blasco, P. Sanchis, J. V. Galán, J. García-Rupérez, E. Jordana, P. Gautier, Y. Lebour, S. Hernández, R. Spano, R. Guider, N. Daldosso, B. Garrido, J. M. Fedeli, L. Pavesi, and J. Martí, “Ultrafast all-optical switching in a silicon-nanocrystal-based silicon slot waveguide at telecom wavelengths,” Nano Lett. |

16. | 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 |

17. | Q. F. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express |

18. | P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J. L. Wasserman, F. J. O'Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microw. Theory Tech. |

19. | G. C. Valley, “Photonic analog-to-digital converters,” Opt. Express |

20. | F. X. Kartner, R. Amatya, M. Araghchini, J. Birge, H. Byun, J. Chen, M. Dahlem, N. A. DiLello, F. Gan, C. W. Holzwarth, J. L. Hoyt, E. P. Ippen, A. Khilo, J. Kim, M. Kim, A. Motamedi, J. S. Orcutt, M. Park, M. Perrott, M. A. Popovi, R. J. Ram, H. I. Smith, G. R. Zhou, S. J. Spector, T. M. Lyszczarz, M. W. Geis, D. M. Lennon, J. U. Yoon, M. E. Grein, and R. T. Schulein, “Photonic analog-to-digital conversion with electronic-photonic integrated circuits,” Proc. SPIE |

21. | A. H. Nejadmalayeri, M. Grein, A. Khilo, J. P. Wang, M. Y. Sander, M. Peng, C. M. Sorace, E. P. Ippen, and F. X. Kärtner, “A 16-fs aperture-jitter photonic ADC: 7.0 ENOB at 40 GHz,” in |

22. | M. E. Grein, S. J. Spector, A. Khilo, A. H. Najadmalayeri, M. Y. Sander, M. Peng, J. Wang, C. M. Sorace, M. W. Geis, M. M. Willis, D. M. Lennon, T. M. Lyszczarz, E. P. Ippen, and F. X. Kärtner, “Demonstration of a 10 GHz CMOS-compatible integrated photonic analog-to-digital converter,” in |

23. | M. A. Popovic, T. Barwicz, M. S. Dahlem, F. W. Gan, C. W. Holzwarth, P. T. Rakich, M. R. Watts, H. I. Smith, F. X. Kärtner, and E. P. Ippen, “Hitless-reconfigurable and bandwidth-scalable silicon photonic circuits for telecom and interconnect applications,” in |

24. | J. S. Orcutt, A. Khilo, M. A. Popovic, C. W. Holzwarth, H. Li, J. Sun, B. Moss, M. S. Dahlem, E. P. Ippen, J. L. Hoyt, V. Stojanovic, F. X. Kärtner, H. I. Smith, and R. J. Ram, “Photonic integration in a commercial scaled bulk-CMOS process,” in |

25. | C. W. Holzwarth, A. Khilo, M. Dahlem, M. A. Popovic, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Device architecture and precision nanofabrication of microring-resonator filter banks for integrated photonic systems,” J. Nanosci. Nanotechnol. |

26. | A. Khilo, M. A. Popović, M. Araghchini, and F. X. Kärtner, “Efficient planar fiber-to-chip coupler based on two-stage adiabatic evolution,” Opt. Express |

27. | C. R. Doerr, P. J. Winzer, Y.-K. Chen, S. Chandrasekhar, M. S. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. |

28. | T. Barwicz, M. A. Popovi, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, E. P. Ippen, F. X. Kartner, and H. I. Smith, “Reconfigurable silicon photonic circuits for telecommunication applications,” Proc. SPIE |

29. | J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics |

30. | Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express |

31. | L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express |

32. | M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, “Low-voltage, compact, depletion-mode, silicon Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. |

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

34. | K. L. Hall, G. Lenz, E. P. Ippen, and G. Raybon, “Heterodyne pump - probe technique for time-domain studies of optical nonlinearities in waveguides,” Opt. Lett. |

35. | A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express |

36. | P. Apiratikul, A. M. Rossi, and T. E. Murphy, “Nonlinearities in porous silicon optical waveguides at 1550 nm,” Opt. Express |

37. | K. Preston, P. Dong, B. Schmidt, and M. Lipson, “High-speed all-optical modulation using polycrystalline silicon microring resonators,” Appl. Phys. Lett. |

38. | P. G. Coleman, C. P. Burrows, and A. P. Knights, “Simple expression for vacancy concentrations at half ion range following MeV ion implantation of silicon,” Appl. Phys. Lett. |

39. | P. J. Foster, J. K. Doylend, P. Mascher, A. P. Knights, and P. G. Coleman, “Optical attenuation in defect-engineered silicon rib waveguides,” J. Appl. Phys. |

40. | A. P. Knights and G. F. Hopper, “Effect of ion implantation induced defects on optical attenuation in silicon waveguides,” Electron. Lett. |

41. | D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. |

42. | C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express |

43. | M. Popovic, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in OSA Trends in Optics and Photonics (Optical Society of America, 2003), ITuD4 (2003). |

44. | S. M. Sze and K. K. Ng, |

45. | N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, and G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” in |

46. | J. K. Doylend, P. E. Jessop, and A. P. Knights, “Optical attenuation in ion-implanted silicon waveguide racetrack resonators,” Opt. Express |

47. | A. R. Motamedi, J. J. Plant, J. P. Donnelly, P. W. Juodawlkis, and E. P. Ippen, “Ultrafast nonlinearities and gain dynamics in high-power semiconductor amplifiers,” Appl. Phys. Lett. |

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.4360) Nonlinear optics : Nonlinear optics, devices

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(190.4400) Nonlinear optics : Nonlinear optics, materials

(320.7100) Ultrafast optics : Ultrafast measurements

(320.7110) Ultrafast optics : Ultrafast nonlinear optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: December 13, 2011

Revised Manuscript: January 26, 2012

Manuscript Accepted: January 27, 2012

Published: February 2, 2012

**Citation**

Ali R. Motamedi, Amir H. Nejadmalayeri, Anatol Khilo, Franz X. Kärtner, and Erich P. Ippen, "Ultrafast nonlinear optical studies of silicon nanowaveguides," Opt. Express **20**, 4085-4101 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4085

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