Abstract

On chip high quality and high degree pulse compression is desirable in the realization of integrated ultrashort pulse sources, which are important for nonlinear photonics and spectroscopy. In this paper, we design a simple inversely tapered silicon ridge waveguide with exponentially decreasing dispersion profile along the propagation direction, and numerically investigate self-similar pulse compression of the fundamental soliton within the mid-infrared spectral region. When higher-order dispersion (HOD), higher-order nonlinearity (HON), losses (α), and variation of the Kerr nonlinear coefficient γ(z) are considered in the extended nonlinear Schrödinger equation, a 1 ps input pulse at the wavelength of 2490 nm is successfully compressed to 57.29 fs in only 5.1-cm of propagation, along with a compression factor Fc of 17.46. We demonstrated that the impacts of HOD and HON are minor on the pulse compression process, compared with that of α and variation of γ(z). Our research results provide a promising solution to realize integrated mid-infrared ultrashort pulse sources.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

2016 (1)

2015 (1)

2014 (4)

2013 (3)

2012 (4)

A. C. Peacock, “Mid-IR soliton compression in silicon optical fibers and fiber tapers,” Opt. Lett. 37(5), 818–820 (2012).
[PubMed]

G. Li, J. Yao, H. Thacker, A. Mekis, X. Zheng, I. Shubin, Y. Luo, J.-H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Opt. Express 20(11), 12035–12039 (2012).
[PubMed]

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

2011 (1)

2010 (4)

X. 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).

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).

P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18(14), 14474–14479 (2010).
[PubMed]

Q. Li, J. N. Kutz, and P. K. A. Wai, “Cascaded higher-order soliton for non-adiabatic pulse compression,” J. Opt. Soc. Am. B 27(11), 2180–2189 (2010).

2009 (1)

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. Opt. Photonics 1(1), 162–235 (2009).

2008 (3)

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).

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

J. W. Nicholson, A. D. Yablon, M. F. Yan, P. Wisk, R. Bise, D. J. Trevor, J. Alonzo, T. Stockert, J. Fleming, E. Monberg, F. Dimarcello, and J. Fini, “Coherence of supercontinua generated by ultrashort pulses compressed in optical fibers,” Opt. Lett. 33(18), 2038–2040 (2008).
[PubMed]

2007 (5)

2006 (4)

2005 (3)

M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056619 (2005).
[PubMed]

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

2003 (2)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90(11), 113902 (2003).
[PubMed]

T. Südmeyer, F. Brunner, E. Innerhofer, R. Paschotta, K. Furusawa, J. C. Baggett, T. M. Monro, D. J. Richardson, and U. Keller, “Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber,” Opt. Lett. 28(20), 1951–1953 (2003).
[PubMed]

2002 (1)

I. V. Dzedolik and A. I. Dzedolik, “Soliton formation from a Gaussian pulse in an optical fiber,” Tech. Phys. 47(6), 713–719 (2002).

1998 (1)

D. C. Harris, “Durable 3-5 μm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).

1997 (1)

M. D. Pelusi and H. F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).

1995 (1)

K. C. Chan and H. F. Liu, “Short Pulse Generation by Higher Order Soliton-Effect Comression: Effects of Optical Fiber Characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

1993 (1)

1986 (1)

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Phys. Uspekhi 29(7), 642–647 (1986).

Abdolvand, A.

Agarwal, A. M.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Agrawal, G. P.

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Phys. Uspekhi 29(7), 642–647 (1986).

Alonzo, J.

Asghari, M.

Atanackovic, P.

Baets, R.

Baggett, J. C.

Beausoleil, R. G.

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

Birks, T. A.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Bise, R.

Borselli, M.

Brunner, F.

Buchwald, W.

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

Carruthers, T. F.

Casas-Bedoya, A.

Chan, K. C.

K. C. Chan and H. F. Liu, “Short Pulse Generation by Higher Order Soliton-Effect Comression: Effects of Optical Fiber Characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

Chen, X.

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. Opt. Photonics 1(1), 162–235 (2009).

Chernikov, S. V.

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Phys. Uspekhi 29(7), 642–647 (1986).

Couny, F.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Cumberland, B. A.

Cunningham, J. E.

Dadap, J. I.

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. Opt. Photonics 1(1), 162–235 (2009).

Dekker, R.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).

Dianov, E. M.

Dimarcello, F.

Dong, P.

Driessen, A.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).

Driscoll, J. B.

Dulkeith, E.

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. Opt. Photonics 1(1), 162–235 (2009).

Duvall, S. G.

Dzedolik, A. I.

I. V. Dzedolik and A. I. Dzedolik, “Soliton formation from a Gaussian pulse in an optical fiber,” Tech. Phys. 47(6), 713–719 (2002).

Dzedolik, I. V.

I. V. Dzedolik and A. I. Dzedolik, “Soliton formation from a Gaussian pulse in an optical fiber,” Tech. Phys. 47(6), 713–719 (2002).

Eggleton, B. J.

Emelett, S. J.

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

Feng, D.

Feng, N.-N.

Fini, J.

Fleming, J.

Fong, J.

Forst, M.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).

Friebele, E. J.

Furusawa, K.

Gaeta, A. L.

George, A. K.

Green, W. M.

Green, W. M. J

X. 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).

Green, W. M. J.

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. Opt. Photonics 1(1), 162–235 (2009).

Griffith, A. G.

Grillet, C.

Grote, R. R.

Harris, D. C.

D. C. Harris, “Durable 3-5 μm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).

Harvey, J. D.

D. Méchin, S. H. Im, V. I. Kruglov, and J. D. Harvey, “Experimental demonstration of similariton pulse compression in a comblike dispersion-decreasing fiber amplifier,” Opt. Lett. 31(14), 2106–2108 (2006).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056619 (2005).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90(11), 113902 (2003).
[PubMed]

He, F.

Horak, P.

Hsieh, I. W.

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. Opt. Photonics 1(1), 162–235 (2009).

Hu, J.

Huang, H.

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

Huang, N.

Hudson, D. D.

Im, S. H.

Innerhofer, E.

Jackson, S. D.

Johnson, T.

Joly, N. Y.

Kang, Z.

Keller, U.

Kim, J.

Kimerling, L. C.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Knight, J. C.

J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt. Express 15(20), 13203–13211 (2007).
[PubMed]

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).

Krishnamoorthy, A. V.

Kruglov, V. I.

D. Méchin, S. H. Im, V. I. Kruglov, and J. D. Harvey, “Experimental demonstration of similariton pulse compression in a comblike dispersion-decreasing fiber amplifier,” Opt. Lett. 31(14), 2106–2108 (2006).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056619 (2005).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90(11), 113902 (2003).
[PubMed]

Kung, C.-C.

Kutz, J. N.

Q. Li, J. N. Kutz, and P. K. A. Wai, “High-degree pulse compression and high-coherence supercontinuum generation in a convex dispersion profile,” Opt. Commun. 301–302, 29–33 (2013).

Q. Li, J. N. Kutz, and P. K. A. Wai, “Cascaded higher-order soliton for non-adiabatic pulse compression,” J. Opt. Soc. Am. B 27(11), 2180–2189 (2010).

Kuyken, B.

Lamont, M. R. E.

Lau, R. K. W.

Lavdas, S.

Lee, J.-H.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).

Li, F.

Li, G.

Li, Q.

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22(22), 27339–27354 (2014).
[PubMed]

Q. Li, J. N. Kutz, and P. K. A. Wai, “High-degree pulse compression and high-coherence supercontinuum generation in a convex dispersion profile,” Opt. Commun. 301–302, 29–33 (2013).

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

Q. Li, J. N. Kutz, and P. K. A. Wai, “Cascaded higher-order soliton for non-adiabatic pulse compression,” J. Opt. Soc. Am. B 27(11), 2180–2189 (2010).

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

Li, X.

Liang, H.

Liao, S.

Lin, Q.

Lipson, M.

Liu, H.

Liu, H. F.

M. D. Pelusi and H. F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).

K. C. Chan and H. F. Liu, “Short Pulse Generation by Higher Order Soliton-Effect Comression: Effects of Optical Fiber Characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

Liu, X.

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[PubMed]

X. 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).

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. Opt. Photonics 1(1), 162–235 (2009).

Lu, C.

Luo, Y.

Luther-Davies, B.

Madden, S.

Mak, K. F.

Mangan, B. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Marks, B. S.

Méchin, D.

Mei, C.

Mekis, A.

Menyuk, C. R.

Michel, J.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Monberg, E.

Monro, T. M.

Moss, D. J.

Nakkeeran, K.

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

Nicholson, J. W.

Okawachi, Y.

Osgood, R. M.

S. Lavdas, J. B. Driscoll, R. R. Grote, R. M. Osgood, and N. C. Panoiu, “Pulse compression in adiabatically tapered silicon photonic wires,” Opt. Express 22(6), 6296–6312 (2014).
[PubMed]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[PubMed]

X. 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).

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. Opt. Photonics 1(1), 162–235 (2009).

Painter, O.

Painter, O. J.

Palomba, S.

Panoiu, N. C.

S. Lavdas, J. B. Driscoll, R. R. Grote, R. M. Osgood, and N. C. Panoiu, “Pulse compression in adiabatically tapered silicon photonic wires,” Opt. Express 22(6), 6296–6312 (2014).
[PubMed]

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. Opt. Photonics 1(1), 162–235 (2009).

Paschotta, R.

Payne, D. N.

Peacock, A. C.

A. C. Peacock, “Mid-IR soliton compression in silicon optical fibers and fiber tapers,” Opt. Lett. 37(5), 818–820 (2012).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056619 (2005).
[PubMed]

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90(11), 113902 (2003).
[PubMed]

Pearl, S.

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).

Pelusi, M. D.

M. D. Pelusi and H. F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).

Poletti, F.

Popov, S. V.

Price, J. H. V.

Qian, W.

Raj, K.

Read, A.

Richardson, D. J.

Roberts, P. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Roelkens, G.

Rotenberg, N.

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).

Rulkov, A. B.

Russell, P. S. J.

Russell, P. St. J.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Sabert, H.

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Sang, X. Z.

Senthilnathan, K.

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

Shafiiha, R.

Shubin, I.

Singh, N.

Soref, R.

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

Stockert, T.

Stone, J. M.

Südmeyer, T.

Sun, Q.

Tam, H. Y.

Taunay, T. F.

Taylor, J. R.

Thacker, H.

Travers, J. C.

Trevor, D. J.

Tse, M. L. V.

Usechak, N.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).

van Driel, H. M.

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).

Vlasov, Y. A.

X. 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).

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. Opt. Photonics 1(1), 162–235 (2009).

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Phys. Uspekhi 29(7), 642–647 (1986).

Wai, P. K. A.

J. H. Yuan, Z. Kang, F. Li, X. T. Zhang, X. Z. Sang, Q. Wu, B. B. Yan, K. R. Wang, X. Zhou, K. P. Zhong, G. Y. Zhou, C. X. Yu, C. Lu, H. Y. Tam, and P. K. A. Wai, “Mid-infrared octave-spanning supercontinuum and frequency comb generation in a suspended germanium-membrane ridge waveguide,” J. Lightwave Technol. 35(14), 2994–3002 (2017).

C. Mei, F. Li, J. H. Yuan, Z. Kang, X. T. Zhang, K. R. Wang, X. Z. Sang, Q. Wu, B. B. Yan, X. Zhou, L. Wang, C. X. Yu, and P. K. A. Wai, “High degree picosecond pulse compression in chalcogenide-silicon slot waveguide taper,” J. Lightwave Technol. 34(16), 3843–3852 (2016).

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22(22), 27339–27354 (2014).
[PubMed]

Q. Li, J. N. Kutz, and P. K. A. Wai, “High-degree pulse compression and high-coherence supercontinuum generation in a convex dispersion profile,” Opt. Commun. 301–302, 29–33 (2013).

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

Q. Li, J. N. Kutz, and P. K. A. Wai, “Cascaded higher-order soliton for non-adiabatic pulse compression,” J. Opt. Soc. Am. B 27(11), 2180–2189 (2010).

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

Wang, K. R.

Wang, L.

Wang, Z.

Wen, J.

Willner, A. E.

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

Wisk, P.

Wright, B. M.

Wu, Q.

Yablon, A. D.

Yan, B. B.

Yan, M. F.

Yao, J.

Yin, L.

Yu, C. X.

Yu, Y.

Yuan, J.

Yuan, J. H.

Yue, Y.

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

Zhang, L.

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

Zhang, X. T.

Zheng, X.

Zhong, K. P.

Zhou, G. Y.

Zhou, X.

Adv. Opt. Photonics (1)

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. Opt. Photonics 1(1), 162–235 (2009).

Appl. Phys. Lett. (1)

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).

IEEE J. Quantum Electron. (2)

K. C. Chan and H. F. Liu, “Short Pulse Generation by Higher Order Soliton-Effect Comression: Effects of Optical Fiber Characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

M. D. Pelusi and H. F. Liu, “Higher order soliton pulse compression in dispersion-decreasing optical fibers,” IEEE J. Quantum Electron. 33, 1430–1439 (1997).

IEEE Photonics J. (1)

Y. Yue, L. Zhang, H. Huang, R. G. Beausoleil, and A. E. Willner, “Silicon-on-nitride waveguide with ultralow dispersion over an octave-spanning mid-infrared wavelength range,” IEEE Photonics J. 4(1), 126–132 (2012).

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D. C. Harris, “Durable 3-5 μm transmitting infrared window materials,” Infrared Phys. Technol. 39(4), 185–201 (1998).

J. Lightwave Technol. (2)

J. Opt. A, Pure Appl. Opt. (1)

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

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

J. Phys. D Appl. Phys. (1)

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).

Nanophotonics (1)

L. Zhang, A. M. Agarwal, L. C. Kimerling, and J. Michel, “Nonlinear Group IV photonics based on silicon and germanium: from near-infrared to mid-infrared,” Nanophotonics 3(4–5), 247–268 (2014).

Nat. Photonics (2)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).

X. 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).

Opt. Commun. (2)

K. Senthilnathan, K. Nakkeeran, Q. Li, and P. K. A. Wai, “Pedestal free pulse compression of chirped optical solitons,” Opt. Commun. 285(6), 1449–1455 (2012).

Q. Li, J. N. Kutz, and P. K. A. Wai, “High-degree pulse compression and high-coherence supercontinuum generation in a convex dispersion profile,” Opt. Commun. 301–302, 29–33 (2013).

Opt. Express (10)

M. Borselli, T. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005).
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J. Hu, B. S. Marks, C. R. Menyuk, J. Kim, T. F. Carruthers, B. M. Wright, T. F. Taunay, and E. J. Friebele, “Pulse compression using a tapered microstructure optical fiber,” Opt. Express 14(9), 4026–4036 (2006).
[PubMed]

B. Kuyken, X. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[PubMed]

P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18(14), 14474–14479 (2010).
[PubMed]

J. C. Travers, J. M. Stone, A. B. Rulkov, B. A. Cumberland, A. K. George, S. V. Popov, J. C. Knight, and J. R. Taylor, “Optical pulse compression in dispersion decreasing photonic crystal fiber,” Opt. Express 15(20), 13203–13211 (2007).
[PubMed]

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).
[PubMed]

F. Li, Q. Li, J. Yuan, and P. K. A. Wai, “Highly coherent supercontinuum generation with picosecond pulses by using self-similar compression,” Opt. Express 22(22), 27339–27354 (2014).
[PubMed]

G. Li, J. Yao, H. Thacker, A. Mekis, X. Zheng, I. Shubin, Y. Luo, J.-H. Lee, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-loss, high-density SOI optical waveguide routing for macrochip interconnects,” Opt. Express 20(11), 12035–12039 (2012).
[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(2), 1840–1848 (2013).
[PubMed]

S. Lavdas, J. B. Driscoll, R. R. Grote, R. M. Osgood, and N. C. Panoiu, “Pulse compression in adiabatically tapered silicon photonic wires,” Opt. Express 22(6), 6296–6312 (2014).
[PubMed]

Opt. Fiber Commun. Rep. (1)

P. J. Roberts, B. J. Mangan, H. Sabert, F. Couny, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Control of dispersion in photonic crystal fibers,” Opt. Fiber Commun. Rep. 2(5), 435–461 (2005).

Opt. Lett. (10)

J. W. Nicholson, A. D. Yablon, M. F. Yan, P. Wisk, R. Bise, D. J. Trevor, J. Alonzo, T. Stockert, J. Fleming, E. Monberg, F. Dimarcello, and J. Fini, “Coherence of supercontinua generated by ultrashort pulses compressed in optical fibers,” Opt. Lett. 33(18), 2038–2040 (2008).
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T. Südmeyer, F. Brunner, E. Innerhofer, R. Paschotta, K. Furusawa, J. C. Baggett, T. M. Monro, D. J. Richardson, and U. Keller, “Nonlinear femtosecond pulse compression at high average power levels by use of a large-mode-area holey fiber,” Opt. Lett. 28(20), 1951–1953 (2003).
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A. C. Peacock, “Mid-IR soliton compression in silicon optical fibers and fiber tapers,” Opt. Lett. 37(5), 818–820 (2012).
[PubMed]

D. Méchin, S. H. Im, V. I. Kruglov, and J. D. Harvey, “Experimental demonstration of similariton pulse compression in a comblike dispersion-decreasing fiber amplifier,” Opt. Lett. 31(14), 2106–2108 (2006).
[PubMed]

M. L. V. Tse, P. Horak, J. H. V. Price, F. Poletti, F. He, and D. J. Richardson, “Pulse compression at 1.06 µm in dispersion-decreasing holey fibers,” Opt. Lett. 31(23), 3504–3506 (2006).
[PubMed]

L. Yin, Q. Lin, and G. P. Agrawal, “Soliton fission and supercontinuum generation in silicon waveguides,” Opt. Lett. 32(4), 391–393 (2007).
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L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32(14), 2031–2033 (2007).
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R. K. W. Lau, M. R. E. Lamont, A. G. Griffith, Y. Okawachi, M. Lipson, and A. L. Gaeta, “Octave-spanning mid-infrared supercontinuum generation in silicon nanowaveguides,” Opt. Lett. 39(15), 4518–4521 (2014).
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K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. S. J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38(18), 3592–3595 (2013).
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Optica (1)

Phys. Rev. A (1)

K. Senthilnathan, Q. Li, K. Nakkeeran, and P. K. A. Wai, “Robust pedestal-free pulse compression in cubic-quintic nonlinear media,” Phys. Rev. A 78, 033835 (2008).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71(5 Pt 2), 056619 (2005).
[PubMed]

Phys. Rev. Lett. (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90(11), 113902 (2003).
[PubMed]

Phys. Uspekhi (1)

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, “Self-action of wave packets in a nonlinear medium and femtosecond laser pulse generation,” Phys. Uspekhi 29(7), 642–647 (1986).

Tech. Phys. (1)

I. V. Dzedolik and A. I. Dzedolik, “Soliton formation from a Gaussian pulse in an optical fiber,” Tech. Phys. 47(6), 713–719 (2002).

Other (3)

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Elsevier, 2007).

Yu. S. Kivshar and G. P. Agraval, Optical solitons: from fibers to photonic crystals, (Academic, 2003).

K. Bergman, L. P. Carloni, A. Biberman, J. Chan, and G. Hendry, Photonic Network-on-chip Design (Springer, 2014).

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic diagram of the designed inversely tapered silicon ridge waveguide. (b) Dispersion curves of the fundamental mode in the designed waveguide with width (W) varying from 800 to 1390 nm. The red vertical line indicates the pump wavelength of 2490 nm and the light green region has normal dispersion. (c) The variation of β2 at 2490 nm versus W. The insets show the mode patterns at the input and output ports of the waveguide taper.
Fig. 2
Fig. 2 (a) The profile of W(z) along the propagation direction z. (b) The variations of the nonlinearity coefficient γ(z) (blue solid curve) and dispersion β2 (red dashed curve) along z.
Fig. 3
Fig. 3 The evolutions of the (a) temporal waveform and (b) normalized spectrum of the pulse along the propagation distance in the waveguide in the ideal case, where the variation of γ(z), α0, 3PA, HON, and HOD are all neglected.
Fig. 4
Fig. 4 The evolutions of the (a) temporal profile and (b) normalized spectrum of the pulse along the propagation distance in the waveguide when the variation of γ(z), α0, 3PA, HON, and HOD are all considered.
Fig. 5
Fig. 5 Comparison of (a) the temporal profiles and (b) normalized spectra of the output pulses when the variation of γ(z) (orange short dashed curves), α including α0 and 3PA (cyan dashed curves), HON (green dash dotted curves) which means the self-steepening, and HOD (blue short dash dotted curves) are considered, respectively. The output pulse of the ideal case (NLSE, black solid curves) and realistic case with all effects included (red solid curves) are also plotted for comparison. The inset in (b) shows the detail of the peaks in the curves of NLSE, HON, HOD, and α.
Fig. 6
Fig. 6 The variations of different order dispersion lengths LDk (k = 2, 3, 4 and 5, red, navy, yellow, and green solid curves, respectively), and the ratio LD2/LD3 (black dash dotted curve) along the propagation distance. The black dashed vertical lines indicate the locations with zero β4 and β5.
Fig. 7
Fig. 7 The evolutions of (a) TFWHM and (b) the peak power of the pulse along the propagation in the waveguide taper in the ideal case (NLSE, black solid curves), with the variation of γ(z) (blue dashed curves), HOD (orange dash dotted curves), HON (green dash dot doted curves), α including α0 and 3PA (cyan short dash dotted curves), and all effects (red solid curves), respectively.
Fig. 8
Fig. 8 The evolutions of the second-order dispersion length LD2 (red solid curves) and nonlinear length LNL (blue solid curves) in logarithmic scale along the propagation in the waveguide taper when (a) only the variation of γ(z) and (b) all effects are considered. The black dotted lines are the chirp length LC. The green dashed curves represent LD2 and LNL in the ideal case (NLSE) for comparison. (c) The relative deviations δL/L = 2(LD2LNL)/(LD2 + LNL) in the cases with γ(z) or all effects included.
Fig. 9
Fig. 9 The evolutions of (a) TFWHM and (b) peak power of the pulses along the propagation in the waveguide taper with α0 = 0.026 (red dashed curves), 0.1 (blue short dashed curves), 0.274 (orange dash dotted curves), and 1 dB/cm (green dash dot dotted curves), respectively. The curves for α0 = 0 (black solid curves) are also plotted for comparison.

Tables (1)

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Table 1 TFWHM, peak power, and Fc of the output pulse for different α0 and a 1-ps input pulse.

Equations (9)

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A z = m2 i m+1 β m (z) m! m A t m +iγ(z)( 1+i τ s t ) | A | 2 A 1 2 α 0 A γ 3PA 3 A eff 2 (z) | A | 4 A,
γ= ω c n 2 (x,y) | F(x,y) | 4 dxdy ( | F(x,y) | 2 dxdy ) 2 ,
A z = i β 2 (z) 2 2 A t 2 +iγ(z) | A | 2 A,
β 2 (z) = β 2 (0)exp(σz),
A(z,t)= ( P 0 e σz ) 1/2 sech[ (t t 0 ) e σz T 0 ]exp[ i 2 ξ (t t 0 ) 2 e σz ],
P 0 = | β 2 (0) |/ [ γ(0) T 0 2 ] ,
F c = T FWHM_i / T FWHM_o ,
Q c = P out / ( P in F c ) ,
L Dk (z)= T 0 k (z)/ | β k (z) | ,

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