## Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides |

Optics Express, Vol. 19, Issue 21, pp. 20172-20181 (2011)

http://dx.doi.org/10.1364/OE.19.020172

Acrobat PDF (1191 KB)

### Abstract

We demonstrate the generation of a supercontinuum in a 2 cm long silicon wire by pumping the wire with mid-infrared picosecond pulses in the anomalous dispersion regime. The supercontinuum extends from 1535 nm up to 2525 nm for a coupled peak power of 12.7 W. It is shown that the supercontinuum originates primarily from the amplification of background noise. A detailed analysis of the spectral components which are generated through phase-matched processes is applied to extract the group velocity dispersion and fourth-order dispersion coefficient of the silicon wire waveguide.

© 2011 OSA

## 1. Introduction

1. C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B **92**(3), 367–378 (2008). [CrossRef]

2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. **26**(9), 608–610 (2001). [CrossRef] [PubMed]

3. S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. **12**(2), 122–147 (2006). [CrossRef]

4. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B **19**(9), 2148–2155 (2002). [CrossRef]

6. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. **87**(20), 203901 (2001). [CrossRef] [PubMed]

7. M. R. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As_{2}S_{3} chalcogenide planar waveguide,” Opt. Express **16**(19), 14938–14944 (2008). [CrossRef] [PubMed]

9. D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express **18**(2), 923–930 (2010). [CrossRef] [PubMed]

10. I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, and Jr., “Supercontinuum generation in silicon photonic wires,” Opt. Express **15**(23), 15242–15249 (2007). [CrossRef] [PubMed]

11. R. M. Osgood, N. C. Jr., J. I. Panoiu, X. Dadap, X. Liu, I.-W. Chen, E. Hsieh, W. M. Dulkeith, 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]

12. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. **80**(3), 416–418 (2002). [CrossRef]

13. 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]

14. X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Jr., Y. A. Assefa, Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express **19**(8), 7778–7789 (2011). [CrossRef] [PubMed]

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

17. S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics **4**(8), 561–564 (2010). [CrossRef]

7. M. R. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As_{2}S_{3} chalcogenide planar waveguide,” Opt. Express **16**(19), 14938–14944 (2008). [CrossRef] [PubMed]

9. D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express **18**(2), 923–930 (2010). [CrossRef] [PubMed]

## 2. Experimental setup

_{Re}= 150 (W·m)

^{−1}[11

11. R. M. Osgood, N. C. Jr., J. I. Panoiu, X. Dadap, X. Liu, I.-W. Chen, E. Hsieh, W. M. Dulkeith, 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]

_{2}of the fundamental TE mode is calculated using a commercial finite element mode solver (RSoft FemSim). As shown in Fig. 1, the wire exhibits anomalous dispersion (β

_{2}< 0) between 1810 nm and 2410 nm.

## 3. Results

19. N. C. Panoiu, X. G. Chen, R. M. Osgood, and Jr., “Modulation Instability in Silicon Photonic Nanowires,” Opt. Lett. **31**(24), 3609–3611 (2006). [CrossRef] [PubMed]

_{2}and β

_{4}are the second- and fourth-order waveguide dispersion respectively, Δω is the detuning of the idler and signal from the pump, γ

_{Re}is the real part of the effective nonlinearity parameter, and

*P*is the peak pump power. The modulation instability sidebands appear where the linear phase mismatch Δk

_{lin}= β

_{2}Δω

^{2}+ (1/12)·β

_{4}Δω

^{4}and the nonlinear phase mismatch Δk

_{nonlin}= 2γ

_{Re}

*P*cancel one another. Finally, Fig. 2 shows that a Raman Stokes peak appears near 2400 nm, red-shifted by ~15.6 THz from the pump as expected [22

22. V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express **15**(22), 14355–14362 (2007). [CrossRef] [PubMed]

23. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**(3), 2602–2607 (1995). [CrossRef] [PubMed]

_{nl}= 500 µm at a coupled peak power of 12.7 W, whereas the soliton fission length is 6.3 cm [5

5. J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys. **78**(4), 1135–1184 (2006). [CrossRef]

24. A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express **12**(13), 2838–2843 (2004). [CrossRef] [PubMed]

25. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express **17**(24), 21497–21508 (2009). [CrossRef] [PubMed]

_{6}, β

_{8}), which become important at large detuning from the pump.

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

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

## 4. Analysis of phase mismatch and waveguide dispersion

_{2}and β

_{4}, is required.

_{lin}, Eq. (1) illustrates that an estimate can be generated using the nonlinear phase mismatch term Δk

_{nonlin}= 2γ

_{Re}

*P*, because the linear and nonlinear phase terms are equal and opposite in sign where efficient MI occurs. Furthermore, the detuning frequencies Δω where Eq. (1) is satisfied for different values of input peak pump power can be read directly from locations of the MI peaks in Fig. 2. The experimental nonlinear phase mismatch values can then plotted versus their respective detunings as shown in Fig. 6 . By fitting this data, an estimate of the linear phase mismatch -Δk

_{lin}around the pump is generated.

_{Re}

*P*, it is important to account for the fact that the pump power decreases along the length of the waveguide, due to both linear and nonlinear loss from residual two-photon absorption (TPA). As a result, the nonlinear MI process will get weaker with propagation length. The majority of the observable MI (and nonlinear phase shift) will in fact originate near the input end of the waveguide. For this reason, the nonlinear phasematch is estimated using an “average” value of the peak pump power calculated along the entrance portion of the waveguide, where the power remains larger than 1/

*e*of the coupled power

*P*

_{0}at the input facet. The average power

*P*

_{avg}_{1/}

*is calculated by solving Eq. (2) and Eq. (3) below. Here,*

_{e}*α*is the linear loss of the waveguide (0.58/cm), γ

_{Im}(6.3 (W·m)

^{−1}) is the imaginary part of the waveguide’s effective nonlinear response from two-photon absorption, and z

_{1/}

*the length after which the power has dropped by 1/*

_{e}*e*. Due to the short duration of the pump pulses and the small TPA coefficient, the effect of TPA-induced free carrier absorption is miniscule and can be neglected.

*P*

_{avg}_{1/}

*versus the detuning Δω for MI bands on the red side of the pump. The uncertainty in the magnitude of the nonlinear phase shift (vertical error bar) is derived from a 1 dB uncertainty in the determination of the input coupling loss, and therefore increases with increasing pump power. The uncertainty in the detuning (horizontal error bar) is derived from the −1 dB bandwidth of the modulation instability peaks in Fig. 2. As the experimental data points in Fig. 6 correspond to spectral positions at which the linear and nonlinear phase mismatch are equal and opposite in sign, a fit curve drawn through the data following the form of Eq. (1) will therefore yield -Δk*

_{e}_{lin}(Δω), and can thus be used to obtain an experimental estimate of β

_{2}and β

_{4}. The solid black line in Fig. 6 depicts the fit for -Δk

_{lin}(Δω) obtained by using a regression technique to minimize the left hand side of Eq. (1). The shaded region illustrates the bounds on the fitted detuning curve resulting from the error on the dispersion coefficients.

_{2}and β

_{4}(and their associated standard deviations) from the fit are listed in Table 1 . The fit results in a value of −0.43 ± 0.07 ps

^{2}/m for β

_{2}, and 2.3 ± 0.4 x 10

^{−4}ps

^{4}/m for β

_{4}. The fitted dispersion coefficients are also compared to values obtained from numerical mode-solver simulations (Fig. 1). The fitted value for β

_{2}agrees within error to the value of −0.47 ps

^{2}/m predicted by simulations. However, the simulated value for β

_{4}of 3.2 x 10

^{−5}ps

^{4}/m is approximately a factor of 7 smaller than the fitted value. Unfortunately, small variations in β

_{4}have a large impact in terms of predicting the conditions for phase matching, particularly because the β

_{4}dependence in Eq. (1) varies as the fourth power of the detuning Δω. For example, substituting the simulated β

_{2}and β

_{4}values into Eq. (1) would suggest that the MI(2) band at the red edge of the supercontinuum in Fig. 3 should appear approximately near 3900 nm, which is inconsistent with the experimental observations.

_{4}is computed by taking four derivatives of the frequency-dependent modal propagation constant β

_{0}(ω), with numerical uncertainty accumulating at each derivative. However, even if the numerical precision of the mode solver calculations were improved, there will remain more fundamental sources of uncertainty associated with small local variations in the dimensions of the wire waveguide. While the dimensions of a simulated waveguide are assumed to remain constant along its entire length, in practice, the height and width of the core can vary locally due to very small manufacturing variations in the thickness of the SOI layer, lithographic tolerances, and reactive ion etch loading and bias [26, 27

27. W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express **18**(23), 23598–23607 (2010). [CrossRef] [PubMed]

28. E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express **14**(9), 3853–3863 (2006). [CrossRef] [PubMed]

31. X. Liu, W. M. J. Green, X. Chen, I.-W. Hsieh, J. I. Dadap, Y. A. Vlasov, R. M. Osgood, and Jr., “Conformal dielectric overlayers for engineering dispersion and effective nonlinearity of silicon nanophotonic wires,” Opt. Lett. **33**(24), 2889–2891 (2008). [CrossRef] [PubMed]

27. W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express **18**(23), 23598–23607 (2010). [CrossRef] [PubMed]

_{4}. Thus, it is important to note that the β

_{2}and β

_{4}values derived from the experimental data in fact represent an “average” waveguide dispersion, which takes into account the inevitable manufacturing-dependent local dispersion variations seen by the pump pulses propagating along the 2 cm long waveguide. Moreover, given the difficulty of achieving perfectly uniform dispersion throughout a silicon photonic wire, it is likely that an experimental approach for extracting “average” dispersion values, such as the method outlined above, will be required in combination with numerical simulations to produce a sufficiently accurate design and analysis methodology for broadband highly nonlinear silicon photonic wire devices.

## 5. Conclusions

_{2}and β

_{4}. This method is general and can be applied to characterize the dispersion characteristics of various highly-nonlinear optical devices, based upon silicon or other high-index contrast materials. Comparison of the extracted dispersion values with those obtained through numerical simulations illustrates that the experimental analysis approach can be more accurate, particularly for higher orders of dispersion. In practice, a combination of the experimental and simulation techniques will likely be required for sufficiently accurate silicon nonlinear waveguide device design.

## Acknowledgments

## References and links

1. | C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B |

2. | I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. |

3. | S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. |

4. | W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B |

5. | J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys. |

6. | A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. |

7. | M. R. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As |

8. | R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, A. L. Gaeta, “Octave spanning supercontinuum generation in CMOS compatible silicon nitride waveguides,” in CLEO, PDPA6 (2011). |

9. | D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express |

10. | I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, and Jr., “Supercontinuum generation in silicon photonic wires,” Opt. Express |

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

12. | H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. |

13. | 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. |

14. | X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Jr., Y. A. Assefa, Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express |

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

16. | R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. |

17. | S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics |

18. | G. Crowder, “Infrared methods for gas detection,” in |

19. | N. C. Panoiu, X. G. Chen, R. M. Osgood, and Jr., “Modulation Instability in Silicon Photonic Nanowires,” Opt. Lett. |

20. | X. Liu, B. Kuyken, G. Roelkens, R. Baets, Y. Vlasov, R. M. Osgood Jr., W. M. J. Green, “Mid-infrared broadband modulation instability and 50dB Raman assisted parametric gain in silicon photonic wires,” in CLEO, CTuS2.pdf (2011). |

21. | B. Kuyken, X. Liu, R. M. Osgood Jr., Y. Vlasov, G. Roelkens, R. Baets, and W. M. J. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” Optical Fiber Communication Conference, OThU4 (2011). |

22. | V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express |

23. | N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A |

24. | A. Mussot, E. Lantz, H. Maillotte, T. Sylvestre, C. Finot, and S. Pitois, “Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers,” Opt. Express |

25. | J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express |

26. | S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. |

27. | W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express |

28. | E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express |

29. | A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express |

30. | R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. |

31. | X. Liu, W. M. J. Green, X. Chen, I.-W. Hsieh, J. I. Dadap, Y. A. Vlasov, R. M. Osgood, and Jr., “Conformal dielectric overlayers for engineering dispersion and effective nonlinearity of silicon nanophotonic wires,” Opt. Lett. |

**OCIS Codes**

(130.4310) Integrated optics : Nonlinear

(320.6629) Ultrafast optics : Supercontinuum generation

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: May 23, 2011

Revised Manuscript: September 19, 2011

Manuscript Accepted: September 25, 2011

Published: September 30, 2011

**Citation**

Bart Kuyken, Xiaoping Liu, Richard M. Osgood Jr., Roel Baets, Günther Roelkens, and William M. J. Green, "Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides," Opt. Express **19**, 20172-20181 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20172

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### References

- C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B92(3), 367–378 (2008). [CrossRef]
- I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett.26(9), 608–610 (2001). [CrossRef] [PubMed]
- S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol.12(2), 122–147 (2006). [CrossRef]
- W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B19(9), 2148–2155 (2002). [CrossRef]
- J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys.78(4), 1135–1184 (2006). [CrossRef]
- A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett.87(20), 203901 (2001). [CrossRef] [PubMed]
- M. R. Lamont, B. Luther-Davies, D. Y. Choi, S. Madden, and B. J. Eggleton, “Supercontinuum generation in dispersion engineered highly nonlinear (γ = 10 /W/m) As2S3 chalcogenide planar waveguide,” Opt. Express16(19), 14938–14944 (2008). [CrossRef] [PubMed]
- R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, A. L. Gaeta, “Octave spanning supercontinuum generation in CMOS compatible silicon nitride waveguides,” in CLEO, PDPA6 (2011).
- D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express18(2), 923–930 (2010). [CrossRef] [PubMed]
- I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, and Jr., “Supercontinuum generation in silicon photonic wires,” Opt. Express15(23), 15242–15249 (2007). [CrossRef] [PubMed]
- R. M. Osgood, N. C. Jr., J. I. Panoiu, X. Dadap, X. Liu, I.-W. Chen, E. Hsieh, W. M. Dulkeith, 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]
- H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett.80(3), 416–418 (2002). [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]
- X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Jr., Y. A. Assefa, Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express19(8), 7778–7789 (2011). [CrossRef] [PubMed]
- X. Liu, R. M. Osgood, Y. A. Jr., Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics4(8), 557–560 (2010). [CrossRef]
- R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett.36(7), 1263–1265 (2011). [CrossRef] [PubMed]
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