Abstract

We demonstrate the evolution of picosecond pulses in silicon nanowire waveguides by sum frequency generation cross-correlation frequency-resolved optical gating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. Due to the unambiguous temporal direction and ultrahigh sensitivity of the SFG-XFROG, which enable observation of the pulse accelerations, the captured pulses’ temporal and spectral characteristics showed remarkable agreement with NLSE predictions. The temporal intensity redistribution of the pulses through the silicon nanowire waveguide for various input pulse energies is analyzed experimentally and numerically to demonstrate the nonlinear contributions of self-phase modulation, two-photon absorption, and free carriers. It indicates that free carrier absorption dominates the pulse acceleration. The model for pulse evolution during propagation through arbitrary lengths of silicon nanowire waveguides is established by NLSE, in support of chip-scale optical interconnects and signal processing.

© 2013 Optical Society of America

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2013 (3)

A. V. Velasco, P. Cheben, P. J. Bock, A. Delâge, J. H. Schmid, J. Lapointe, S. Janz, M. L. Calvo, D. Xu, M. A. F. Czyk, and M. Vachon, Opt. Lett. 38, 706 (2013).
[CrossRef]

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

2012 (3)

2011 (3)

2010 (5)

2009 (3)

2008 (2)

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, Opt. Express 16, 1300 (2008).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

2007 (2)

2005 (2)

2004 (2)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[CrossRef]

O. Boyraz, T. Indukuri, and B. Jalali, Opt. Express 12, 829 (2004).
[CrossRef]

2003 (1)

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

2002 (1)

Aden, Y.

Agrawal, A.

Agrawal, G.

Agrawal, G. P.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[CrossRef]

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[CrossRef]

Bergman, K.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Bock, P. J.

Bowers, J. E.

Boyraz, O.

Calvo, M. L.

Cao, Q.

Cheben, P.

Coen, S.

Colman, P.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

Combrie, S.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Combrié, S.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

Czyk, M. A. F.

Dadap, J. I.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Dai, D.

De Rossi, A.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

C. A. Husko, A. De Rossi, and C. W. Wong, Opt. Lett. 36, 2239 (2011).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Delâge, A.

Dissanayake, C.

Driscoll, J. B.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Dudley, J. M.

Efimov, A.

Fainman, Y.

D. T. H. Tan, P. C. Sun, and Y. Fainman, Nat. Commun. 1, 116 (2010).
[CrossRef]

Fauchet, P. M.

Foster, A. C.

Foster, M. A.

Freude, W.

Gaeta, A. L.

Galili, M.

Grattan, K. T. V.

Grote, R. R.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Gu, X.

Hattori, T.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Hikosaka, K.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Hu, H.

Husko, C.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

Husko, C. A.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

C. A. Husko, A. De Rossi, and C. W. Wong, Opt. Lett. 36, 2239 (2011).
[CrossRef]

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Hvam, J. M.

Indukuri, T.

Jacome, K. L.

Jalali, B.

Janz, S.

Jeppesen, P.

Ji, H.

Kejalakshmy, N.

Kimmel, M.

Kwong, D.-L.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Opt. Express 18, 15484 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Lapointe, J.

Leung, D. M. H.

Leuthold, J.

Li, X.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

Liao, J.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

Lipson, M.

Liu, K.

Lo, G.-Q.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

Marko, M. D.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

McMillan, J. F.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Opt. Express 18, 15484 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Mulvad, H. C. H.

O’Shea, P.

Ogura, M.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Ophir, N.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Osgood, R. M.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Oxenløwe, L. K.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[CrossRef]

Panoiu, N. C.

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, Opt. Express 20, 9277 (2012).

Petrillo, K. G.

Peucheret, C.

Poulton, C.

Premaratne, M.

Pu, M.

Rahman, B. M. A.

Raineri, F.

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Rukhlenko, I. D.

Sagnes, I.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

Salem, R.

Schmid, J. H.

Sun, P. C.

D. T. H. Tan, P. C. Sun, and Y. Fainman, Nat. Commun. 1, 116 (2010).
[CrossRef]

Tan, D. T. H.

D. T. H. Tan, P. C. Sun, and Y. Fainman, Nat. Commun. 1, 116 (2010).
[CrossRef]

Taylor, A. J.

Tran, Q. V.

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Trebino, R.

Tsurumachi, N.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Turner, A. C.

Turner-Foster, A. C.

Vachon, M.

Velasco, A. V.

Wang, K. Y.

Wang, X.-L.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Watanabe, N.

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Windeler, R. S.

Wong, C. W.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

C. A. Husko, A. De Rossi, and C. W. Wong, Opt. Lett. 36, 2239 (2011).
[CrossRef]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Opt. Express 18, 15484 (2010).
[CrossRef]

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Xu, D.

Xu, L.

Xu, W.

Ye, W. M.

Yin, L.

Yu, M.

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Opt. Express 18, 15484 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Yuan, X. D.

Yvind, K.

Zeek, E.

Zeng, C.

Zhang, J.

Zheng, J.

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

Zhu, Z. H.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

C. A. Husko, A. De Rossi, S. Combrie, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

M. D. Marko, X. Li, J. Zheng, J. Liao, M. Yu, G.-Q. Lo, D.-L. Kwong, C. A. Husko, and C. W. Wong, Appl. Phys. Lett. 103, 021103 (2013).
[CrossRef]

J. Appl. Phys. (1)

N. Tsurumachi, K. Hikosaka, X.-L. Wang, M. Ogura, N. Watanabe, and T. Hattori, J. Appl. Phys. 94, 2616 (2003).
[CrossRef]

Nat. Commun. (1)

D. T. H. Tan, P. C. Sun, and Y. Fainman, Nat. Commun. 1, 116 (2010).
[CrossRef]

Nat. Photonics (1)

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, Nat. Photonics 4, 862 (2010).
[CrossRef]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, Nature 431, 1081 (2004).
[CrossRef]

Opt. Express (11)

Opt. Lett. (6)

Sci. Rep. (1)

C. A. Husko, S. Combrie, P. Colman, J. Zheng, A. De Rossi, and C. W. Wong, Sci. Rep. 3, 1100 (2013).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Single-mode SPNW and experimental setup. (a) Scanning electron micrograph of the SPNW and (b) experimental setup with SFG-XFROG. MLL, mode-locked fiber laser; HWP, half-wave plate; C, optical collimator; BS, beam splitter; P, polarizer; FL, focus lens; FM, flip mirror; OSA, optical spectrum analyzer; RF, reflector; DM, D-shaped mirror; LMS, linear motorized stage; CL, bi-convex lens; BBO, barium borate crystal; SM, spectrometer with CCD.

Fig. 2.
Fig. 2.

Temporal intensity profile, phase distribution, and spectrum of the output pulses at 25 pJ input pulse energy. (a), (b) 1555 nm; (c), (d) 1560 nm. Red curves are experimental results, and blue curves are simulation results. The green-dotted line is the phase distribution retrieved from SFG-XFROG; the green solid line is the numerically predicted phase distribution. Insets in (b) and (d) are SFG-XFROG retrieved traces.

Fig. 3.
Fig. 3.

Temporal and spectral intensity profiles of the output pulses for increasing coupled pulse energies from 170 fJ to 98.2 pJ. (a) Results retrieved from SFG-XFROG measurements and (b) numerically predicted results from NLSE mode simulations. Input pulse profiles are also shown in black at the figure bottom. The central labels denote the input pulse energies.

Fig. 4.
Fig. 4.

Measured and simulation pulse accelerations. (a) Temporal centroid of output pulses versus input pulse energy. SFG-XFROG measurement in data points; NLSE simulations in solid lines. (b) Simulation extracted temporal centroids at 1550 nm for various cases. G, GVD; S, SPM; T, TPA.

Fig. 5.
Fig. 5.

Pulse properties. (a) Pulse duration, (b) temporal centroid, and (c) spectral centroid versus waveguide length up to 500 mm for 25 pJ input pulse energy. Insets: zoom-in of the initial saturation region with the same coordinate labels as the main figure. (d) Pulse duration, (e) temporal centroid, and (f) spectral centroid versus input pulse energy up to 400 pJ for 4 mm waveguide length. Wavelength assignment throughout is as shown in key in (a).

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