Abstract

We analytically and experimentally investigate cross-phase modulation (XPM) in silicon waveguides. In contrast to the well known result in pure Kerr media, the spectral broadening ratio of XPM to self-phase modulation is not two in the presence of either two-photon absorption (TPA) or free carriers. The physical origin of this change is different for each effect. In the case of TPA, this nonlinear absorption attenuates and slightly modifies the pulse shape due to differential absorption in the pulse peak and wings. When free carriers are present two different mechanisms modify the dynamics. First, free-carrier absorption performs a similar role to TPA, but is additionally asymmetric due to the delayed free-carrier response. Second, free-carrier dispersion induces an asymmetric blue phase shift which competes directly with the symmetric Kerr-induced XPM red shift. We confirm this analysis with pump-probe experiments in a silicon photonic crystal waveguide.

© 2016 Optical Society of America

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References

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2015 (1)

2014 (1)

2013 (3)

2012 (1)

2011 (1)

2010 (6)

2009 (1)

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

2008 (1)

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
[Crossref]

2007 (2)

2006 (1)

2004 (1)

1999 (1)

1998 (1)

1991 (1)

1985 (1)

Agrawal, G. P.

Andersen, J. D.

Andrés, P.

Boyraz, O.

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

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

Cartaxo, A. V.

Castelló-Lurbe, D.

Chen, X.

Colman, P.

Combrié, S.

Corcoran, B.

Cotter, D.

Dadap, J. I.

Dalgaard, K.

De Rossi, A.

Dekker, R.

Densmore, A.

Dimitropoulos, D.

D. Dimitropoulos and B. Jalali, “Optical information capacity of silicon,” OFC, 2–25 (2015).

Driessen, A.

Eggleton, B. J.

Ellis, A. D.

Essiambre, R.-J.

Feng, K.-M.

Fermann, M. E.

Forchhammer, S.

Först, M.

Foschini, G. J.

Foster, M. A.

Freude, W.

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

Gaeta, A. L.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nature Photon. 7, 138–141 (2013).
[Crossref]

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

Galili, M.

Goebel, B.

Haberl, F.

Haus, H.

Hofer, M.

Hsieh, H.-S.

Hsieh, I.-W.

Hu, H.

Huang, N.

Husko, C.

Indukuri, T.

Ippen, E.

Jalali, B.

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
[Crossref]

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

D. Dimitropoulos and B. Jalali, “Optical information capacity of silicon,” OFC, 2–25 (2015).

Janz, S.

Koonath, P.

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
[Crossref]

Koos, C.

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

Kramer, G.

Krauss, T. F.

Larsen, K. J.

Lee, M.-C. M.

Lefrancois, S.

Leuthold, J.

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

Levy, J. S.

Li, X.

Lipson, M.

Liu, H.

Ma, R.

Margalit, M.

McNab, S. J.

Monat, C.

Moormann, C.

Moss, D. J.

Niehusmann, J.

Ober, M.

Osgood, R. M.

Oxenløwe, L. K.

Panoiu, N. C.

Pelusi, M. D.

Pinault, S. C.

Poitras, C. B.

Potasek, M.

Pu, M.

Qing, F.

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

Rasmussen, A.

Rey, I. H.

Saha, K.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nature Photon. 7, 138–141 (2013).
[Crossref]

Salem, R.

Sang, X.-Z.

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

Schmidt, A.

Schröder, J.

Silvestre, E.

Solli, D. R.

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
[Crossref]

Song, Q.

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

Sørensen, B. M.

Sun, Q.

Tien, E.-K.

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

Turner-Foster, A. C.

Venkataraman, V.

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nature Photon. 7, 138–141 (2013).
[Crossref]

Vlasov, Y. A.

Vo, T. D.

Wahlbrink, T.

Wang, Z.

Wen, J.

Winzer, P. J.

Wong, C. W.

Xu, D.-X.

Yin, L.

Yu, C.

Yvind, K.

Zhang, Y.

Zhao, J.

Appl. Phys. Lett. (2)

P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
[Crossref]

E.-K. Tien, X.-Z. Sang, F. Qing, Q. Song, and O. Boyraz, “Ultrafast pulse characterization using cross phase modulation in silicon,” Appl. Phys. Lett. 95, 051101 (2009).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Nature Photon. (2)

V. Venkataraman, K. Saha, and A. L. Gaeta, “Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing,” Nature Photon. 7, 138–141 (2013).
[Crossref]

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

Opt. Express (10)

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

I.-W. Hsieh, X. 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, 1135–1146 (2007).
[Crossref] [PubMed]

B. Corcoran, T. D. Vo, M. D. Pelusi, C. Monat, D.-X. Xu, A. Densmore, R. Ma, S. Janz, D. J. Moss, and B. J. Eggleton, “Silicon nanowire based radio-frequency spectrum analyzer,” Opt. Express 18, 20190–20200 (2010).
[Crossref] [PubMed]

M. Margalit, C. Yu, E. Ippen, and H. Haus, “Cross phase modulation squeezing in optical fibers,” Opt. Express 2, 72–76 (1998).
[Crossref] [PubMed]

H. Hu, J. D. Andersen, A. Rasmussen, B. M. Sørensen, K. Dalgaard, M. Galili, M. Pu, K. Yvind, K. J. Larsen, S. Forchhammer, and L. K. Oxenløwe, “Forward error correction supported 150 Gbit/s error-free wavelength conversion based on cross phase modulation in silicon,” Opt. Express 21, 3152–3160 (2013).
[Crossref] [PubMed]

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

H.-S. Hsieh, K.-M. Feng, and M.-C. M. Lee, “Study of cross-phase modulation and free-carrier dispersion in silicon photonic wires for Mamyshev signal regenerators,” Opt. Express 18, 9613–9621 (2010).
[Crossref] [PubMed]

Y. Zhang, C. Husko, S. Lefrancois, I. H. Rey, T. F. Krauss, J. Schröder, and B. J. Eggleton, “Nondegenerate two-photon absorption in silicon waveguides: analytical and experimental study,” Opt. Express 23, 17101–17110 (2015).
[Crossref] [PubMed]

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

Z. Wang, H. Liu, N. Huang, Q. Sun, J. Wen, and X. Li, “Influence of three-photon absorption on mid-infrared cross-phase modulation in silicon-on-sapphire waveguides,” Opt. Express 21, 1840–1848 (2013).
[Crossref] [PubMed]

Opt. Lett. (5)

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Springer, 2000).

D. Dimitropoulos and B. Jalali, “Optical information capacity of silicon,” OFC, 2–25 (2015).

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Figures (4)

Fig. 1
Fig. 1 (a) Output pulse shapes of the pump and probe with TPA-only calculated from analytic solution Eq. (1) at the input power of 2 W (left) and 10 W (right). (b) Spectral broadening factor obtained from ( 1 + 0.77 ϕ max 2 ) 1 / 2 and numerical calculation (NLSE) with and without free carriers (FC).
Fig. 2
Fig. 2 (a) Numerically calculated ρ υ = Δ υ XPM Δ υ SPM with various nonlinear effects. (b) Chirp rates of pump (solid) and probe (dashed) under different conditions at an input power of 10 W.
Fig. 3
Fig. 3 (a) Output probe spectrum as a function of delay at an input peak pump power of 3.8 W. The arrows indicate the regions of free carriers (FC) and TPA. (b) Probe spectral width as a function of time at different pump power levels.
Fig. 4
Fig. 4 (a) Comparison of spectral broadening ratio of XPM and SPM (ρυ) obtained from experimental results and numerical modelling (NLSE) with and without chirp. (b) Experimental and simulated spectra at three input pump powers.

Equations (8)

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P 1 ( z , t ) = P 1 , in ( t ) e α z 1 + P 1 , in ( t ) z eff γ TPA ,
P 2 ( z , t ) = P 2 , in ( t ) e α z ( 1 + P 1 , in ( t ) z eff γ TPA ) 2 ,
ϕ 1 ( z , t ) = γ γ TPA ln [ 1 + γ TPA P 1 , in ( t ) z eff ] ,
ϕ 2 ( z , t ) = 2 ϕ 1 = 2 γ γ TPA ln [ 1 + γ TPA P 1 , in ( t ) z eff ] ,
P 1 ( z , t ) = P 1 , in e α z e γ TPA P 1 d z e σ N c d z ,
P 2 ( z , t ) = P 2 , in e α z e 2 γ TPA P 1 d z e σ N c d z ,
ϕ 1 ( z , t ) = γ P 1 ( z , t ) d z + k 0 n FC N c ( z , t ) d z ,
ϕ 2 ( z , t ) = 2 γ P 1 ( z , t ) d z + k 0 n FC N c ( z , t ) d z ,

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