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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7778–7789
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Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge

Xiaoping Liu, Jeffrey B. Driscoll, Jerry I. Dadap, Richard M. Osgood, Jr., Solomon Assefa, Yurii A. Vlasov, and William M. J. Green  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7778-7789 (2011)
http://dx.doi.org/10.1364/OE.19.007778


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Abstract

We report an experimental study of picosecond pulse propagation through a 4-mm-long Si nanophotonic wire with normal dispersion, at excitation wavelengths from 1775 to 2250 nm. This wavelength range crosses the mid-infrared two-photon absorption edge of Si at ~2200 nm. Significant reduction in nonlinear loss due to two-photon absorption is measured as excitation wavelengths approach 2200 nm. At high input power, self-phase modulation is clearly demonstrated by the development of power-dependant spectral fringes. Asymmetry and blue-shift in the appearance of the spectral fringes at 1775 nm versus 2200 nm is further shown to originate from a strong reduction in the intra-pulse density of two-photon absorption-generated free carriers and the associated free-carrier dispersion. Analysis of experimental data and comparison with numerical simulations illustrates that the two-photon absorption coefficient βTPA obtained here from nanophotonic wire measurements is in reasonable agreement with prior measurements of bulk silicon crystals, and that bulk Si values of the nonlinear refractive index n2 can be confidently incorporated in the modeling of pulse propagation in deeply-scaled waveguide structures.

© 2011 OSA

1. Introduction

Research into nonlinear optical propagation within Si nanophotonic wires has recently attracted much interest due to their strong optical confinement and large third-order nonlinear susceptibility χ(3) [1

1. E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

11

11. 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 mu m wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]

]. Particularly striking is the size of the effective nonlinearity parameter γ, as it can be up to five orders of magnitude larger than that of conventional silica glass fibers [12

12. 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]

, 13

13. R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. 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. Opti. Photonics 1(1), 162–235 (2009). [CrossRef]

]. This large nonlinearity facilitates the observation of many nonlinear processes and enables the realization of a wide variety of advanced chip-scale components for performing ultra-fast all-optical signal processing functions, e.g. wavelength conversion [4

4. 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]

, 5

5. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]

, 14

14. H. S. Rong, Y. H. Kuo, A. S. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]

, 15

15. H. Ji, M. Galili, H. Hu, M. H. Pu, L. K. Oxenlowe, K. Yvind, J. M. Hvam, and P. Jeppesen, “1.28-Tb/s Demultiplexing of an OTDM DPSK Data Signal Using a Silicon Waveguide,” IEEE Photon. Technol. Lett. 22(23), 1762–1764 (2010). [CrossRef]

], signal regeneration [16

16. 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,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

, 17

17. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007). [CrossRef] [PubMed]

], switching [18

18. T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express 13(19), 7298–7303 (2005). [CrossRef] [PubMed]

20

20. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41(6), 320–321 (2005). [CrossRef]

], and format conversion [21

21. W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “Conversion of 10 Gb/s NRZ-OOK to RZ-OOK utilizing XPM in a Si nanowire,” Opt. Express 17(15), 12987–12999 (2009). [CrossRef] [PubMed]

, 22

22. W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “All-Optical Format Conversion of NRZ-OOK to RZ-OOK in a Silicon Nanowire Utilizing Either XPM or FWM and Resulting in a Receiver Sensitivity Gain of similar to 2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010). [CrossRef]

].

These recent mid-IR demonstrations make it clear that an important direction for further research is to develop a full understanding of the behavior of the nonlinear refractive index n 2 and the two-photon absorption coefficient β TPA, specifically within the spectral region near and across the TPA edge. Previously, measurements of these quantities have been reported on bulk silicon crystals [26

26. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

28

28. 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(2), 021111–021113 (2007). [CrossRef]

] (telecom-band and mid-IR), and Si nanophotonic wires [1

1. E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

, 8

8. 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]

, 11

11. 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 mu m wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]

] (telecom-band). However, only limited studies have been made of mid-IR pulse propagation in SOI waveguides [23

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

, 24

24. 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]

, 29

29. T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010). [CrossRef] [PubMed]

]. In this paper we study the characteristics of mid-IR picosecond pulse propagation through Si nanophotonic wires, and specifically analyze the observed self-phase modulation (SPM) and nonlinear transmission. In so doing, we obtain valuable insight into the variation of the nonlinear coefficients n 2 and β TPA across the mid-IR TPA threshold near 2200 nm. In addition and in contrast to prior studies of mid-IR four-wave mixing effects in Si nanophotonic wires [23

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

25

25. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]

], we seek to avoid additional contributions from nonlinear Kerr-effect phenomena such as soliton generation [30

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

, 31

31. J. D. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15(12), 7682–7688 (2007). [CrossRef] [PubMed]

], self-steepening [32

32. N. C. Panoiu, X. P. Liu, and R. M. Osgood Jr., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. 34(7), 947–949 (2009). [CrossRef] [PubMed]

], and modulation instability [33

33. N. C. Panoiu, X. F. Chen, and R. M. Osgood Jr., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006). [CrossRef] [PubMed]

], and thus use Si wires designed to have normal dispersion over the spectrum of interest.

2. Waveguide dispersion and effective nonlinearity

Figures 1(a) and 1(b) show the calculated electric field E x profiles of the quasi-TE00 mode using a finite-element (FEM) solver at wavelengths of 1550 nm and 2200 nm, respectively. This Si nanophotonic wire has a power confinement κ of 92% at 1550 nm, and, since the mode expands at longer wavelengths, the power confinement drops to 75% at 2200 nm. The wavelength-dependent second-order dispersion β 2 and effective nonlinearity parameter γ for the quasi-TE00 mode are shown in Fig. 1(c). The effective nonlinearity is derived using the expression γ = 3ωRe(Γ)/(4ε 0 A 0 v g 2), where ω is the angular frequency, ε 0 is the vacuum permittivity, A 0 is the area of the Si core, v g is the group velocity of the quasi-TE00 mode, and the quantity Γ is the complex effective waveguide susceptibility determined by the weighted integral of the third-order susceptibility χ(3) of bulk silicon over the waveguide mode [36

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

, 37

37. X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006). [CrossRef]

]. The effective nonlinearity of the Si nanophotonic wire (blue curve) decreases substantially as the wavelength increases, i.e. from ~300 W−1m−1 at 1750 nm to ~75 W−1m−1 at 2450 nm. This is largely due to decreasing mode confinement within the Si wire core, as seen in Figs. 1(a) and 1(b). The reduced effective nonlinearity could be mitigated by choosing slightly larger Si core dimensions for improved optical confinement, when optimizing Si nanophotonic wires for operation in the mid-IR near ~2200 nm. The waveguide dispersion information, calculated using a FEM mode solver with the same method as described in [36

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

], is shown in the black curve of Fig, 1(c). Normal dispersion prevails over the wavelength range from 1775 to 2450 nm due to the reduced contribution of waveguide dispersion, again due to weaker optical confinement within the Si core. The worst-case dispersion (|β 2| < 20 ps2/m) yields a dispersion length of L D = T 0 2/β 2 > 200 mm, where T 0 (~2 ps) is the FWHM of the picosecond pulses used in this work. This dispersion length is much larger than the length of the Si nanophotonic wire (~4 mm), and therefore dispersion is expected to have minimal impact upon pulse propagation.

3. Experiments

3.1 Measurement configuration

The experimental setup for the measurement of both the linear and nonlinear mid-IR propagation characteristics of the nanophotonic wires is shown in Fig. 2(a)
Fig. 2 (a) Schematic of the experimental setup. (b) Si nanophotonic wire propagation loss across the telecommunication bands and the mid-IR region, and coupling loss between lensed fiber and SiOxNy mode converter in the mid-IR region.
. A pulse train of ~2 ps FWHM pulses is generated by a Ti:sapphire-pumped tunable optical parametric oscillator (OPO) system (Coherent Mira-OPO), and then fiber coupled using an objective lens. The pulse repetition rate is 76 MHz. The pump power coupled into the fiber is controlled using a neutral density (ND) filter. The center wavelength of the pump is tuned over the spectral range 1700-2300 nm by changing the cavity length of the OPO system, and is monitored along with its time-average power by a mid-IR optical spectrum analyzer (OSA; Yokogawa AQ6375). The pulse train is coupled into and out-of the Si nanophotonic wire chip via tapered lensed fibers, while the polarization of the pulses is aligned to excite the quasi-TE00 mode using an in-line fiber polarization controller. The transmitted pulse at the nanophotonic wire output is then directed to the OSA for analysis.

The peak pump power P P at the nanophotonic wire input is calculated using the expression P P = P avg/(). Here, P avg is the time-average input power integrated over the input pump spectrum, scaled by the wavelength-dependent fiber coupling loss (Fig. 2(b), explained further in section 3.2), F is the repetition rate of the OPO, and τ is the pulse duration.

3.2 Linear propagation loss

The propagation loss of the quasi-TE00 mode for the Si nanophotonic wire is measured using the cut-back method (comparing relative transmission through 4 mm-long and 20 mm-long wires) at several discrete input wavelengths across the TPA edge of Si. To avoid nonlinear loss, measurements are performed with the input peak power attenuated to less than 0.25 mW. The measured loss is shown as a black dashed line through square black data points in Fig. 2(b), and ranges from 4.5 dB/cm to 7 dB/cm. For comparison, the propagation loss across the telecommunication bands is also shown in Fig. 2(b) (solid black curve, measured with 1500-1700 nm broadband LED source). This data shows that within the mid-IR wavelength region < 2100 nm the linear propagation loss of this wire is significantly less than that in the telecommunication bands. The propagation loss decreases with increasing wavelength, approximately following the expected behavior for Rayleigh scattering in such a waveguide [38

38. G. T. Reed, and A. P. Knights, Silicon Photonics: An Introduction (Wiley, West Sussex, 2004).

]. However, this loss also shows a perceptible increase when the wavelength approaches 2200 nm, most likely due to a) absorption loss from the outer cladding of the nanophotonic wire, i.e., SiO2 [39

39. R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006). [CrossRef]

], or b) mode leakage into the Si substrate. Such losses could be mitigated by using low-loss conformal spacer layers, e.g. air [40

40. R. Shankar, I. Bulu, R. Leijssen, and M. Loncar, “Silicon-Based Mid-Infrared Photonic Crystal Cavities,” PECS-IX (2010).

], Al2O3 [29

29. T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010). [CrossRef] [PubMed]

], Si3N4 [39

39. R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006). [CrossRef]

, 41

41. Y. Yue, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Ultrabroadband Low Dispersion Silicon-on-Nitride Waveguide in Mid-Infrared Region,” Integrated Photonics Research, IWH4 (2010).

], etc., and/or by increasing the BOX layer thickness [23

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

, 39

39. R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006). [CrossRef]

]

Also shown in Fig. 2(b) is the wavelength-dependent facet coupling loss between lensed fiber and the SiOxNy mode-converter, as illustrated by the blue dashed line through blue circle data points. While the loss is measured to be ~5 dB/facet at 1800 nm, the loss becomes larger than 12 dB for wavelengths ≥ 2200 nm. Facet coupling loss is larger at long wavelengths because the SiOxNy mode-converter used here was of a design previously optimized for operation at 1550 nm [34

34. J. Van Campenhout, W. M. J. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2x2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17(26), 24020–24029 (2009). [CrossRef]

, 35

35. S. Assefa, C. Jahnes, and Y. Vlasov, “CMOS compatible integrated dielectric optical waveguide coupler and fabrication,” US Patent US7738753B2 (2010).

].

3.3 Self-phase modulation versus input wavelength

As discussed in the introduction, it is important to characterize the optical parameters describing nonlinear wave propagation in Si nanophotonic wires. Here we utilize a series of SPM experiments to assess both the nonlinear refractive index n 2 and the two-photon absorption coefficient β TPA as a function of wavelength. The behavior of SPM is characterized at four different pump wavelengths. The measured power-dependent transmission spectra at the center wavelengths 1775 nm, 1988 nm, 2200 nm, and 2250 nm are shown in Figs. 3(a)
Fig. 3 Experimental power-dependent transmission spectra as a function of pump center wavelength: (a) 1775 nm, (b) 1988 nm, (c) 2200 nm, (d) 2250 nm. Center wavelengths of the input pulse are indicated by the dashed line. The power levels indicated by the labels within each panel refer to the peak power at the input of the Si nanophotonic wire. Spectra have been vertically offset relative to each other by 10 dB for clarity.
3(d), respectively. For each input wavelength, output transmission spectra are recorded at several values of input peak power; these wavelengths are designated by the color-coding shown in the upper-right corner of each panel.

To ensure that any observed nonlinearity originates solely from transmission through the Si nanophotonic wire, reference measurements with the nanophotonic wire removed from the optical path are performed, by directly coupling the tips of the tapered input/output fibers. Even at the highest input power levels used across all wavelengths in the above measurements, there is no observable SPM or nonlinear absorption. Therefore, the nonlinear contribution from all passive fiber components within the setup is found to be negligible.

4. Discussion

4.1 Self-limiting of transmission and mid-IR nonlinear loss

The power-dependent transmission spectra in Fig. 3 are analyzed in greater detail to characterize the Si nanophotonic wire’s nonlinear loss as a function of input wavelength. For each set of input conditions, the output peak power is calculated as described in section 3.3 above, using the integrated time-averaged power within the Si nanophotonic wire output spectrum. Figure 4(a)
Fig. 4 Characteristics of the nonlinear power transmission through the Si nanophotonic wire at four different input wavelengths. (a) Output peak power versus input peak power. (b) Reciprocal transmission coefficient versus input peak power.
shows the nonlinear transmission response of the Si nanophotonic wire for wavelengths between 1775 and 2250 nm, obtained by plotting the output peak power versus the input peak power. The error bars in the figure reflect the power fluctuations (~1 dB) measured at the waveguide output. Note that the effects of inter-pulse free-carrier accumulation are negligible, since the 13.1 ns period between pump pulses is much larger than the free-carrier recombination lifetime (approximately 0.5-1 ns) in our sub-micrometer Si nanophotonic wires [44

44. Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

, 45

45. J. Van Campenhout, W. M. J. Green, X. P. Liu, S. Assefa, R. M. Osgood, and Y. A. Vlasov, “Silicon-nitride surface passivation of submicrometer silicon waveguides for low-power optical switches,” Opt. Lett. 34(10), 1534–1536 (2009). [CrossRef] [PubMed]

].

In general, the β TPA values reported in Table 1 are in reasonable agreement with those measured previously in bulk Si crystals using the z-scan technique [27

27. 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]

, 28

28. 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(2), 021111–021113 (2007). [CrossRef]

]. Quantitatively, these β TPA values are approximately a factor of 1.5 × larger than those reported in [27

27. 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]

], and about a factor of 5 × larger than reported in [28

28. 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(2), 021111–021113 (2007). [CrossRef]

]. One potential source of discrepancies with comparison to bulk Si may originate from the fact that the fabrication processes used to define the Si nanophotonic wires (i.e., reactive ion etching, oxidation, deposition of cladding films by plasma-enhanced chemical vapor deposition, etc.) can create crystal damage at the surfaces and within the bulk of the wire. It is known that surface states [48

48. T. Baehr-Jones, M. Hochberg, and A. Scherer, “Photodetection in silicon beyond the band edge with surface states,” Opt. Express 16(3), 1659–1668 (2008). [CrossRef] [PubMed]

] and bulk states from vacancies and/or interstitials [49

49. M. W. Geis, S. J. Spector, M. E. Grein, R. J. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Käertner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15(25), 16886–16895 (2007). [CrossRef] [PubMed]

] in silicon are capable of producing linear absorption at wavelengths longer than the bandedge wavelength of silicon. It is therefore possible to envision that such damage-induced bulk and surface states present in our Si nanophotonic wires may also contribute to nonlinear absorption at wavelengths near 2200 nm which would otherwise be free of TPA in bulk silicon crystals. Note that even in the case of the C-band, where the β TPA and n 2 nonlinear coefficients have been studied more extensively [1

1. E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

, 26

26. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

28

28. 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(2), 021111–021113 (2007). [CrossRef]

, 50

50. O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12(5), 829–834 (2004). [CrossRef] [PubMed]

], experimental uncertainties make definitive statements about the sources of different behavior between bulk Si and Si nanophotonic wires difficult without further study. Despite measurement uncertainties, the values of β TPA in Table 1 provide useful experimental quantities for the design and modeling of future Si nanophotonic wire-based mid-IR nonlinear optical devices. In analyzing our measured value of the β TPA coefficient, note that it is not possible to relate this value via the Kramers-Kronig relation to the n 2 coefficient, due to the presence of other nearby-lying nonlinear processes [27

27. 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]

], and the fact that our measurements extend over only a limited frequency range.

It is worthwhile to note that three photon absorption (3PA) has recently been revealed as the leading-order source of nonlinear loss for sufficiently high peak power (tens of Watts) pulse propagation experiments in Si near λ = 2200 nm [23

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

, 51

51. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93(13), 131102 (2008). [CrossRef]

]. However, given the magnitude of the 3PA coefficient (γ3PA ~0.025 cm3/GW2 at λ = 2170 nm), 3PA is not expected to contribute significantly to nonlinear loss at peak input power levels < 6 W and wavelengths > 2200 nm in the present experiments. An upper limit of nonlinear loss due to 3PA (in dB units) can be estimated by α = 10·log(exp(γ 3PA(κP P/A 0)2 L)), where γ 3PA is the 3PA coefficient, κ is power confinement factor, P P is peak power in the Si nanophotonic wire, A 0 is the area of the silicon core, and L is the length of the Si nanophotonic wire. This estimation predicts a maximum nonlinear loss of 0.5 dB from 3PA within the 4 mm-long Si nanophotonic wire.

4.2 Free-carrier dispersion-induced spectral asymmetry

The SPM spectra in Fig. 3 also reveal additional qualitative characteristics of nonlinear pulse transmission through the nanophotonic wire as the input wavelength is scanned across the TPA threshold of silicon. For example, at the lower values of input power shown in Fig. 3(a)3(d), the spectral fringes appear symmetrically on both sides of the pump spectrum for all input wavelengths. At higher input powers, the total number of fringes increases, as expected due to the increasing nonlinear phase accumulated across the pump spectrum. However, the fringes become distributed asymmetrically, i.e. the fringes on the red side of the spectrum become spaced more closely together than those on the blue side. This effect is most particularly pronounced for input wavelengths below the TPA edge of silicon, i.e. 1775 nm and 1988 nm. Moreover, these same spectra show a significant spectral blue-shift at high input peak power levels, in contrast to the spectra at 2200 nm and 2250 nm.

These wavelength-dependent SPM fringe asymmetries and spectral blue-shift characteristics are highlighted in Fig. 5(a)
Fig. 5 Comparison of SPM fringe asymmetry and spectral blue-shift between 1775 nm and 2200 nm input wavelengths, using experimental and simulated data. (a) Experimental spectrum at 1775 nm wavelength with coupled peak power of 15.2 W. (b) Experimental spectrum at 2200 nm wavelength with peak coupled power of 5.7 W. (c) Simulated spectrum corresponding to conditions at 1775 nm. (d) Simulated spectrum corresponding to conditions at 2200 nm. The additional black dashed spectrum is a simulation performed for an input peak power condition of 15.2 W (not accessible in the experiments), in order to contrast the symmetric output at 2200 nm against that at 1775 nm in (c).
and 5(b), through a comparison of the experimental output spectra at wavelengths of 1775 nm (P p = 15.2 W) and 2200 nm (P p = 5.7 W). The notable difference in SPM spectral evolution correlates with the input wavelength being situated far below or near the TPA threshold of silicon. In fact, the observed fringe asymmetry and spectral blue-shift are consistent with the presence of intra-pulse free-carrier dispersion (FCD) effects [1

1. E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

, 8

8. 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]

, 9

9. J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]

], originating from TPA-generated free carriers.

In order to further confirm our understanding of the characteristic spectral differences observed across the TPA threshold, we use a perturbed nonlinear Schrödinger equation (NSE) to numerically simulate picosecond pulse propagation in the Si nanophotonic wires [9

9. J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]

, 13

13. R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. 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. Opti. Photonics 1(1), 162–235 (2009). [CrossRef]

]. The numerical model captures the negative linear chirp of the input pump pulses, the value of which is determined by fitting to the measured input pump spectral width. The wavelength-dependent dispersion and effective nonlinearity parameter in Fig. 1(c) are incorporated into the model, as well as the values of β TPA determined from the self-limiting measurements (Section 4.1 and Table 1). Finally, the model also uses the values of n 2 taken from measurements on bulk silicon [27

27. 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]

, 28

28. 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(2), 021111–021113 (2007). [CrossRef]

]. The important parameters used in the simulations are all summarized in Table 2

Table 2. Parameters Used in Pulse Propagation Simulations at Wavelengths of 1775 nm and 2200 nm

table-icon
View This Table
| View All Tables
.

Figures 5(c) and 5(d) contain the simulated output transmission spectra calculated using the same values of input peak power as in the experimental data of Fig. 5(a) and 5(b) (solid lines). As illustrated by comparison with Figs. 5(a) and 5(b), the simulated spectra for both 1775 nm and 2200 nm input wavelengths agree qualitatively well with the spectra obtained from experiment. Moreover, although the maximum experimentally accessible peak pump powers were lower at 2200 nm as compared to 1775 nm, a simulated spectrum for which the pump power is increased to 15.2 W (black dashed curve in Fig. 5(d)) confirms that spectral symmetry (i.e., symmetric SPM fringes and absence of blue-shift) is preserved at 2200 nm for pump power conditions comparable with those at 1775 nm. This result is consistent with the negligible impact of TPA-induced free-carrier generation and dispersion expected near and above the ~2200 nm TPA threshold. In fact, our model shows that the peak intra-pulse free-carrier density at the beginning of the Si nanophotonic wire is reduced by a factor of 60, from 6x1018 cm−3 at the wavelength 1775 nm to 1x1017 cm−3 at the wavelength of 2200 nm, when using the same coupled peak power value of 15.2 W.

The measurements and simulations of pulse propagation and SPM presented here do not permit reliable extraction of silicon’s nonlinear parameter n 2, primarily due to uncertainty in the input pulse’s chirp, which is itself a fitting parameter as stated above. Nevertheless the agreement between the experiments and simulations in Fig. 5 gives confidence that the values of the nonlinear parameters n 2 (based upon bulk Si measurements) and β TPA (extracted from self-limiting transmission experiments above) used as simulation inputs, in fact provide an accurate description of the mid-IR nonlinear characteristics of the Si nanophotonic wires. Moreover, we can also infer that the numerical tools used to compute the spatial mode distribution and waveguide dispersion are appropriate for precise mid-IR modeling.

5. Conclusion

In this paper we report an experimental and numerical study of mid-IR linear and nonlinear picosecond pulse propagation through a normally dispersive 4 mm-long Si nanophotonic wire. Using a set of input wavelengths which cross the silicon TPA threshold at ~2200 nm, we demonstrate characteristics of SPM and self-limiting transmission having markedly different behavior at longer versus shorter mid-IR wavelengths. We interpret both quantitative and qualitative aspects of these experimental characteristics in the context of fundamental TPA and TPA-induced free-carrier generation/dispersion. Through analysis of the experimental data as well as comparison with numerical simulations, we illustrate that the nonlinear refractive index n 2 and the two-photon absorption coefficient β TPA derived from measurements of bulk silicon can be used to model the mid-IR nonlinear transmission characteristics of Si nanophotonic wires with reasonably good accuracy. This appears to be the case even for deeply scaled waveguide structures in which the (non-ideal, damaged) patterned silicon surfaces are in close interacting proximity with the highly-confined optical mode.

Acknowledgement

The authors are grateful for the assistance of the staff at the IBM Microelectronics Research Laboratory where the Si nanophotonic wires are fabricated. The authors also wish to acknowledge IBM Summer Internship support of Xiaoping Liu, as well as partial support under the Columbia University portion of DARPA program #CU08-7741.

References and links

1.

E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood Jr., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]

2.

I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express 14(25), 12380–12387 (2006). [CrossRef] [PubMed]

3.

I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood Jr, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15(3), 1135–1146 (2007). [CrossRef] [PubMed]

4.

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]

5.

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]

6.

H. S. Rong, A. S. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 292–294 (2005). [CrossRef] [PubMed]

7.

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004). [CrossRef] [PubMed]

8.

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]

9.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood Jr., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]

10.

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

11.

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 mu m wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]

12.

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]

13.

R. M. Osgood Jr, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. 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. Opti. Photonics 1(1), 162–235 (2009). [CrossRef]

14.

H. S. Rong, Y. H. Kuo, A. S. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]

15.

H. Ji, M. Galili, H. Hu, M. H. Pu, L. K. Oxenlowe, K. Yvind, J. M. Hvam, and P. Jeppesen, “1.28-Tb/s Demultiplexing of an OTDM DPSK Data Signal Using a Silicon Waveguide,” IEEE Photon. Technol. Lett. 22(23), 1762–1764 (2010). [CrossRef]

16.

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,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]

17.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007). [CrossRef] [PubMed]

18.

T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express 13(19), 7298–7303 (2005). [CrossRef] [PubMed]

19.

R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Forst, “Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mum femtosecond pulses,” Opt. Express 14(18), 8336–8346 (2006). [CrossRef] [PubMed]

20.

D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41(6), 320–321 (2005). [CrossRef]

21.

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “Conversion of 10 Gb/s NRZ-OOK to RZ-OOK utilizing XPM in a Si nanowire,” Opt. Express 17(15), 12987–12999 (2009). [CrossRef] [PubMed]

22.

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “All-Optical Format Conversion of NRZ-OOK to RZ-OOK in a Silicon Nanowire Utilizing Either XPM or FWM and Resulting in a Receiver Sensitivity Gain of similar to 2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010). [CrossRef]

23.

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

24.

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]

25.

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]

26.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

27.

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]

28.

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(2), 021111–021113 (2007). [CrossRef]

29.

T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010). [CrossRef] [PubMed]

30.

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

31.

J. D. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15(12), 7682–7688 (2007). [CrossRef] [PubMed]

32.

N. C. Panoiu, X. P. Liu, and R. M. Osgood Jr., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. 34(7), 947–949 (2009). [CrossRef] [PubMed]

33.

N. C. Panoiu, X. F. Chen, and R. M. Osgood Jr., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006). [CrossRef] [PubMed]

34.

J. Van Campenhout, W. M. J. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2x2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17(26), 24020–24029 (2009). [CrossRef]

35.

S. Assefa, C. Jahnes, and Y. Vlasov, “CMOS compatible integrated dielectric optical waveguide coupler and fabrication,” US Patent US7738753B2 (2010).

36.

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

37.

X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006). [CrossRef]

38.

G. T. Reed, and A. P. Knights, Silicon Photonics: An Introduction (Wiley, West Sussex, 2004).

39.

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006). [CrossRef]

40.

R. Shankar, I. Bulu, R. Leijssen, and M. Loncar, “Silicon-Based Mid-Infrared Photonic Crystal Cavities,” PECS-IX (2010).

41.

Y. Yue, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Ultrabroadband Low Dispersion Silicon-on-Nitride Waveguide in Mid-Infrared Region,” Integrated Photonics Research, IWH4 (2010).

42.

B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25(7), 445–447 (2000). [CrossRef]

43.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 2001).

44.

Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]

45.

J. Van Campenhout, W. M. J. Green, X. P. Liu, S. Assefa, R. M. Osgood, and Y. A. Vlasov, “Silicon-nitride surface passivation of submicrometer silicon waveguides for low-power optical switches,” Opt. Lett. 34(10), 1534–1536 (2009). [CrossRef] [PubMed]

46.

V. Raghunathan, R. Shori, O. M. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” Physica. Status. Solidi. a-Applications. and Materials Science 203, 38–40 (2006). [CrossRef]

47.

H. K. Tsang, R. V. Penty, I. H. White, R. S. Grant, W. Sibbett, J. B. D. Soole, H. P. Leblanc, N. C. Andreadakis, R. Bhat, and M. A. Koza, “two-photon absorption and self-phase modulation in InGaAsP/InP multi-quantum-well wave-guides,” J. Appl. Phys. 70(7), 3992–3994 (1991). [CrossRef]

48.

T. Baehr-Jones, M. Hochberg, and A. Scherer, “Photodetection in silicon beyond the band edge with surface states,” Opt. Express 16(3), 1659–1668 (2008). [CrossRef] [PubMed]

49.

M. W. Geis, S. J. Spector, M. E. Grein, R. J. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Käertner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15(25), 16886–16895 (2007). [CrossRef] [PubMed]

50.

O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12(5), 829–834 (2004). [CrossRef] [PubMed]

51.

S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93(13), 131102 (2008). [CrossRef]

OCIS Codes
(060.5060) Fiber optics and optical communications : Phase modulation
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: December 8, 2010
Revised Manuscript: February 16, 2011
Manuscript Accepted: February 28, 2011
Published: April 7, 2011

Citation
Xiaoping Liu, Jeffrey B. Driscoll, Jerry I. Dadap, Richard M. Osgood, Solomon Assefa, Yurii A. Vlasov, and William M. J. Green, "Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge," Opt. Express 19, 7778-7789 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7778


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References

  1. E. Dulkeith, Y. A. Vlasov, X. G. Chen, N. C. Panoiu, and R. M. Osgood., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006). [CrossRef] [PubMed]
  2. I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Ultrafast-pulse self-phase modulation and third-order dispersion in Si photonic wire-waveguides,” Opt. Express 14(25), 12380–12387 (2006). [CrossRef] [PubMed]
  3. I. W. Hsieh, X. G. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15(3), 1135–1146 (2007). [CrossRef] [PubMed]
  4. 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]
  5. M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007). [CrossRef] [PubMed]
  6. H. S. Rong, A. S. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, “An all-silicon Raman laser,” Nature 433(7023), 292–294 (2005). [CrossRef] [PubMed]
  7. O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12(21), 5269–5273 (2004). [CrossRef] [PubMed]
  8. 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]
  9. J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008). [CrossRef] [PubMed]
  10. I. W. Hsieh, X. G. Chen, X. P. Liu, J. I. Dadap, N. C. Panoiu, C. Y. Chou, F. N. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007). [CrossRef] [PubMed]
  11. 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 mu m wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002). [CrossRef]
  12. 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]
  13. R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. 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. Opti. Photonics 1(1), 162–235 (2009). [CrossRef]
  14. H. S. Rong, Y. H. Kuo, A. S. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006). [CrossRef] [PubMed]
  15. H. Ji, M. Galili, H. Hu, M. H. Pu, L. K. Oxenlowe, K. Yvind, J. M. Hvam, and P. Jeppesen, “1.28-Tb/s Demultiplexing of an OTDM DPSK Data Signal Using a Silicon Waveguide,” IEEE Photon. Technol. Lett. 22(23), 1762–1764 (2010). [CrossRef]
  16. 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,” Nat. Photonics 2(1), 35–38 (2008). [CrossRef]
  17. R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “All-optical regeneration on a silicon chip,” Opt. Express 15(12), 7802–7809 (2007). [CrossRef] [PubMed]
  18. T. K. Liang, L. R. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. R. A. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. K. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express 13(19), 7298–7303 (2005). [CrossRef] [PubMed]
  19. R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, and M. Forst, “Ultrafast Kerr-induced all-optical wavelength conversion in silicon waveguides using 1.55 mum femtosecond pulses,” Opt. Express 14(18), 8336–8346 (2006). [CrossRef] [PubMed]
  20. D. J. Moss, L. Fu, I. Littler, and B. J. Eggleton, “Ultrafast all-optical modulation via two-photon absorption in silicon-insulator waveguides,” Electron. Lett. 41(6), 320–321 (2005). [CrossRef]
  21. W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “Conversion of 10 Gb/s NRZ-OOK to RZ-OOK utilizing XPM in a Si nanowire,” Opt. Express 17(15), 12987–12999 (2009). [CrossRef] [PubMed]
  22. W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood, “All-Optical Format Conversion of NRZ-OOK to RZ-OOK in a Silicon Nanowire Utilizing Either XPM or FWM and Resulting in a Receiver Sensitivity Gain of similar to 2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010). [CrossRef]
  23. X. P. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010). [CrossRef]
  24. 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]
  25. A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010). [CrossRef] [PubMed]
  26. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]
  27. 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]
  28. 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(2), 021111–021113 (2007). [CrossRef]
  29. T. Baehr-Jones, A. Spott, R. Ilic, A. Spott, B. Penkov, W. Asher, and M. Hochberg, “Silicon-on-sapphire integrated waveguides for the mid-infrared,” Opt. Express 18(12), 12127–12135 (2010). [CrossRef] [PubMed]
  30. L. H. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007). [CrossRef] [PubMed]
  31. J. D. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, “Optical solitons in a silicon waveguide,” Opt. Express 15(12), 7682–7688 (2007). [CrossRef] [PubMed]
  32. N. C. Panoiu, X. P. Liu, and R. M. Osgood., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. 34(7), 947–949 (2009). [CrossRef] [PubMed]
  33. N. C. Panoiu, X. F. Chen, and R. M. Osgood., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006). [CrossRef] [PubMed]
  34. J. Van Campenhout, W. M. J. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2x2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17(26), 24020–24029 (2009). [CrossRef]
  35. S. Assefa, C. Jahnes, and Y. Vlasov, “CMOS compatible integrated dielectric optical waveguide coupler and fabrication,” US Patent US7738753B2 (2010).
  36. X. P. Liu, W. M. J. Green, X. G. Chen, I. W. Hsieh, J. I. Dadap, Y. A. Vlasov, and R. M. Osgood., “Conformal dielectric overlayers for engineering dispersion and effective nonlinearity of silicon nanophotonic wires,” Opt. Lett. 33(24), 2889–2891 (2008). [CrossRef] [PubMed]
  37. X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006). [CrossRef]
  38. G. T. Reed, and A. P. Knights, Silicon Photonics: An Introduction (Wiley, West Sussex, 2004).
  39. R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006). [CrossRef]
  40. R. Shankar, I. Bulu, R. Leijssen, and M. Loncar, “Silicon-Based Mid-Infrared Photonic Crystal Cavities,” PECS-IX (2010).
  41. Y. Yue, L. Zhang, R. G. Beausoleil, and A. E. Willner, “Ultrabroadband Low Dispersion Silicon-on-Nitride Waveguide in Mid-Infrared Region,” Integrated Photonics Research, IWH4 (2010).
  42. B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25(7), 445–447 (2000). [CrossRef]
  43. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 2001).
  44. Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]
  45. J. Van Campenhout, W. M. J. Green, X. P. Liu, S. Assefa, R. M. Osgood, and Y. A. Vlasov, “Silicon-nitride surface passivation of submicrometer silicon waveguides for low-power optical switches,” Opt. Lett. 34(10), 1534–1536 (2009). [CrossRef] [PubMed]
  46. V. Raghunathan, R. Shori, O. M. Stafsudd, and B. Jalali, “Nonlinear absorption in silicon and the prospects of mid-infrared silicon Raman lasers,” Physica. Status. Solidi. a-Applications. and Materials Science 203, 38–40 (2006). [CrossRef]
  47. H. K. Tsang, R. V. Penty, I. H. White, R. S. Grant, W. Sibbett, J. B. D. Soole, H. P. Leblanc, N. C. Andreadakis, R. Bhat, and M. A. Koza, “two-photon absorption and self-phase modulation in InGaAsP/InP multi-quantum-well wave-guides,” J. Appl. Phys. 70(7), 3992–3994 (1991). [CrossRef]
  48. T. Baehr-Jones, M. Hochberg, and A. Scherer, “Photodetection in silicon beyond the band edge with surface states,” Opt. Express 16(3), 1659–1668 (2008). [CrossRef] [PubMed]
  49. M. W. Geis, S. J. Spector, M. E. Grein, R. J. Schulein, J. U. Yoon, D. M. Lennon, C. M. Wynn, S. T. Palmacci, F. Gan, F. X. Käertner, and T. M. Lyszczarz, “All silicon infrared photodiodes: photo response and effects of processing temperature,” Opt. Express 15(25), 16886–16895 (2007). [CrossRef] [PubMed]
  50. O. Boyraz, T. Indukuri, and B. Jalali, “Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12(5), 829–834 (2004). [CrossRef] [PubMed]
  51. S. Pearl, N. Rotenberg, and H. M. van Driel, “Three photon absorption in silicon for 2300-3300 nm,” Appl. Phys. Lett. 93(13), 131102 (2008). [CrossRef]

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