Abstract

Nonlinear silicon photonics will play an important role in future integrated opto-electronic circuits. Here we report temporal pulse broadening induced by the dynamic interplay of nonlinear free-carrier dispersion coupled with group-velocity dispersion in nanostructured silicon waveguides for the first time, to the best of our knowledge. Further, we demonstrate that the nonlinear temporal dynamics are supported or countered by third-order dispersion, depending on the sign. Our time-domain measurements of the subpicojoule pulse dynamics are supported by strong agreement with numerical modeling. In addition to the fundamental nonlinear optical processes unveiled here, these results highlight dispersion engineering as a powerful tool for controlling free-carrier temporal effects.

© 2014 Optical Society of America

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2014 (5)

C. Monat, C. Grillet, M. Collins, A. Clark, J. Schroeder, C. Xiong, J. Li, L. O’Faolain, T. F. Krauss, B. J. Eggleton, D. J. Moss, “Integrated optical auto-correlator based on third harmonic generation in a silicon photonic crystal waveguide,” Nat. Commun. 5, 3246 (2014).
[Crossref]

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[Crossref]

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M.-S. Rouifed, S. Cecchi, P. Crozat, G. Isella, L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
[Crossref]

F. D. Ros, D. Vukovic, A. Gajda, K. Dalgaard, L. Zimmermann, B. Tillack, M. Galili, K. Petermann, C. Peucheret, “Phase regeneration of DPSK signals in a silicon waveguide with reverse-biased p-i-n junction,” Opt. Express 22, 5029–5036 (2014).
[Crossref]

D. Vukovic, Y. Ding, H. Hu, H. Ou, L. K. Oxenlø we, C. Peucheret, “Polarization-insensitive wavelength conversion of 40  Gb/s NRZ-DPSK signals in a silicon polarization diversity circuit,” Opt. Express 22, 12467–12474 (2014).
[Crossref]

2013 (5)

J. Liao, M. Marko, X. Li, H. Jia, J. Liu, Y. Tan, J. Yang, Y. Zhang, W. Tang, M. Yu, G.-Q. Lo, D.-L. Kwong, C. W. Wong, “Cross-correlation frequency-resolved optical gating and dynamics of temporal solitons in silicon nanowire waveguides,” Opt. Lett. 38, 4401–4404 (2013).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

C. A. Husko, S. Combrié, P. Colman, J. Zheng, A. De Rossi, C. W. Wong, “Soliton dynamics in the multiphoton plasma regime,” Sci. Rep. 3, 1100 (2013).

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref]

F. Raineri, T. J. Karle, V. Roppo, P. Monnier, R. Raj, “Time-domain mapping of nonlinear pulse propagation in photonic-crystal slow-light waveguides,” Phys. Rev. A 87, 041802 (2013).
[Crossref]

2012 (1)

T. Baehr-Jones, T. Pinguet, P. L. Guo-Qiang, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[Crossref]

2011 (4)

2010 (7)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

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

D. T. H. Tan, P. C. Sun, Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat. Commun. 1, 116 (2010).
[Crossref]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[Crossref]

G. T. Reed, G. Mashanovich, F. Gardes, D. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

A. D. Ellis, J. Zhao, D. Cotter, “Approaching the non-linear Shannon limit,” J. Lightwave Technol. 28, 423–433 (2010).
[Crossref]

W. Ding, A. V. Gorbach, W. J. Wadswarth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, R. M. D. L. Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[Crossref]

2009 (4)

2008 (1)

2007 (5)

2006 (1)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref]

2005 (3)

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914–1916 (2005).

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

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

2004 (2)

M. Soljacic, J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3, 211–219 (2004).
[Crossref]

V. Raghunathan, R. Claps, D. Dimitropoulos, B. Jalali, “Wavelength conversion in silicon using Raman induced four-wave mixing,” Appl. Phys. Lett. 85, 34–36 (2004).
[Crossref]

2003 (1)

D. V. Skryabin, F. Luan, J. C. Knight, P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).
[Crossref]

2002 (1)

2001 (2)

S. Johnson, J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref]

N. A. R. Bhat, J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001).
[Crossref]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[Crossref]

1987 (1)

R. A. Soref, B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Agrawal, G. P.

Asano, T.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref]

Baba, T.

Baehr-Jones, T.

T. Baehr-Jones, T. Pinguet, P. L. Guo-Qiang, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[Crossref]

Baets, R. G.

Bennett, B. R.

R. A. Soref, B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Bhat, N. A. R.

N. A. R. Bhat, J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001).
[Crossref]

Blanco-Redondo, A.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat. Commun. 5, 3160 (2014).
[Crossref]

Bogaerts, W.

Bolten, J.

Boyd, R. W.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200  nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Cecchi, S.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M.-S. Rouifed, S. Cecchi, P. Crozat, G. Isella, L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
[Crossref]

Chaisakul, P.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M.-S. Rouifed, S. Cecchi, P. Crozat, G. Isella, L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
[Crossref]

Chen, L.

Chen, X.

Chihara, M.

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498, 470–474 (2013).
[Crossref]

Chou, C.-Y.

Chrastina, D.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M.-S. Rouifed, S. Cecchi, P. Crozat, G. Isella, L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
[Crossref]

Claps, R.

V. Raghunathan, R. Claps, D. Dimitropoulos, B. Jalali, “Wavelength conversion in silicon using Raman induced four-wave mixing,” Appl. Phys. Lett. 85, 34–36 (2004).
[Crossref]

Clark, A.

C. Monat, C. Grillet, M. Collins, A. Clark, J. Schroeder, C. Xiong, J. Li, L. O’Faolain, T. F. Krauss, B. J. Eggleton, D. J. Moss, “Integrated optical auto-correlator based on third harmonic generation in a silicon photonic crystal waveguide,” Nat. Commun. 5, 3246 (2014).
[Crossref]

Clark, A. S.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

Clemmen, S.

Coen, S.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
[Crossref]

Cohen, O.

Collins, M.

C. Monat, C. Grillet, M. Collins, A. Clark, J. Schroeder, C. Xiong, J. Li, L. O’Faolain, T. F. Krauss, B. J. Eggleton, D. J. Moss, “Integrated optical auto-correlator based on third harmonic generation in a silicon photonic crystal waveguide,” Nat. Commun. 5, 3246 (2014).
[Crossref]

Collins, M. J.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

Colman, P.

C. A. Husko, S. Combrié, P. Colman, J. Zheng, A. De Rossi, C. W. Wong, “Soliton dynamics in the multiphoton plasma regime,” Sci. Rep. 3, 1100 (2013).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[Crossref]

Combrie, S.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
[Crossref]

Combrié, S.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

C. A. Husko, S. Combrié, P. Colman, J. Zheng, A. De Rossi, C. W. Wong, “Soliton dynamics in the multiphoton plasma regime,” Sci. Rep. 3, 1100 (2013).

Corcoran, B.

Cotter, D.

Crozat, P.

P. Chaisakul, D. Marris-Morini, J. Frigerio, D. Chrastina, M.-S. Rouifed, S. Cecchi, P. Crozat, G. Isella, L. Vivien, “Integrated germanium optical interconnects on silicon substrates,” Nat. Photonics 8, 482–488 (2014).
[Crossref]

Dadap, J. I.

Dalgaard, K.

Danziger, S.

T. Baehr-Jones, T. Pinguet, P. L. Guo-Qiang, S. Danziger, D. Prather, M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6, 206–208 (2012).
[Crossref]

De Rossi, A.

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,” Sci. Rep. 3, 3087 (2013).

C. A. Husko, S. Combrié, P. Colman, J. Zheng, A. De Rossi, C. W. Wong, “Soliton dynamics in the multiphoton plasma regime,” Sci. Rep. 3, 1100 (2013).

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4, 862–868 (2010).
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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Sample parameters and temporal characterization setup. (a) Measured group index (blue line), and second-order (red line) and third-order (green line) dispersion of the photonic crystal waveguide. The markers represent the values for the measured wavelengths. (b) Experimental FREG setup, consisting of the following: MML, mode-locked laser; WS, pulse shaper; PhC-wg, photonic crystal waveguide; τ variable delay; PD, fast photodiode; MZM, Mach–Zehnder modulator; OSA, optical spectrum analyzer. The inset shows a scanning electron micrograph of our silicon PhC-wg device.
Fig. 2.
Fig. 2. Frequency-resolved electrical gating (FREG) measurements. (a) Experimental spectrograms at the input (waveguide bypassed) and output for three different coupled peak powers at 1543 nm. The cross-correlation delay is τ. (b) Measured pulse durations as a function of coupled peak power for three different wavelengths. Color-shaded regions indicate the dominant effect: dispersive broadening (GVD, red), Kerr-induced narrowing (SPM, yellow), and free-carrier dispersion broadening (FCD, blue).
Fig. 3.
Fig. 3. Ratios of key physical length scales in silicon waveguides for the 1543 nm case. As LFCD and LNL are power dependent, we show the relative balance of the characteristic length scales as a function of coupled power. The other wavelengths exhibit similar behavior.
Fig. 4.
Fig. 4. Temporal and spectral pulse profiles: experiment and model. (a),(b) Normalized intensity in the time and frequency domains for (a) 1543 nm and (b) 1545 nm. The red lines represent the experiment and the solid blue lines the GNLSE simulations. Color-shaded regions indicate the dominant effect: dispersive broadening (GVD, red), Kerr-induced narrowing (SPM, yellow), and free-carrier dispersion broadening (FCD, blue).
Fig. 5.
Fig. 5. Nonlinear temporal dynamics in the silicon waveguide FCD-GVD regime. (a)–(c) Pulse duration as a function of coupled peak power for (a) 1545 nm, (b) 1541 nm, and (c) 1543 nm cases. The color markers represent the experimental FREG measurements, the solid black lines represent the full GNLSE simulation, the dashed black lines neglect the free-carrier effects, the purple dotted lines neglect TOD, the red dotted–dashed line neglects GVD and TOD, and the blue dotted line neglects all effects except for SPM.
Fig. 6.
Fig. 6. Pulse acceleration for the 1545 nm case. We show the experimental FREG measurements (colored markers), the full GNLSE simulation (solid black line), free-carrier effects off (dashed black line), TOD off (purple dotted line), and positive β2 with the remaining parameters from the full simulation (turquoise dot-dashed line).

Tables (1)

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Table 1. Measured Parameters and Ratios for the Wavelengths Studieda

Equations (4)

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S(ω,τ)=|+E(t)R(tτ)exp(iωt)dt|2.
Az=αl2Aiβ222At2+β363At3+(iγγTPA2)|A|2A+(ik0nFCσ2)NcA.
Nct=ρFC|A|4Ncτc.
LFCD=1k0|nFC|ρFCP02T0,

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