Abstract

Four-wave-mixing processes enabled during optical wave-breaking (OWB) are exploited in this paper for supercontinuum generation. Unlike conventional approaches based on OWB, phase-matching is achieved here for these nonlinear interactions, and, consequently, new frequency production becomes more efficient. We take advantage of this kind of pulse propagation to obtain numerically a coherent octave-spanning mid-infrared supercontinuum generation in a silicon waveguide pumping at telecom wavelengths in the normal dispersion regime. This scheme shows a feasible path to overcome limits imposed by two-photon absorption on spectral broadening in silicon waveguides.

© 2015 Optical Society of America

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References

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2015 (1)

2014 (3)

2013 (4)

2012 (6)

2011 (2)

2010 (2)

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

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, “Influence of third-order dispersion on the propagation of incoherent light in optical fibers,” Opt. Lett. 35, 2367–2369 (2010).
[Crossref] [PubMed]

2009 (5)

S. Afshar V. and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures. Part I: Kerr nonlinearity,” Opt Express 17, 2298–2318 (2009).
[Crossref] [PubMed]

J. J. Miret, E. Silvestre, and P. Andrés, “Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers,” Opt. Express 17, 9197–9203 (2009).
[Crossref] [PubMed]

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
[Crossref]

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. Photon. 1, 162–235 (2009).
[Crossref]

B. Barviau, B. Kibler, and A. Picozzi, “Wave-turbulence approach of supercontinuum generation: influence of self-steepening and higher-order dispersion,” Phys. Rev. A 79, 063840 (2009).
[Crossref]

2008 (2)

2007 (8)

2006 (3)

B. Jalali and S. Fathpour, “Silicon Photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
[Crossref]

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

2005 (1)

2004 (1)

2003 (1)

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

2002 (1)

2001 (2)

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

1999 (1)

Y. Takushima and K. Kikuchi, “10-GHz, over 20-channel multiwavelength pulse source by slicing supercontinuum spectrum generated in normal-dispersion-fiber,” IEEE Photon. Technol. Lett. 11, 322–324 (1999).
[Crossref]

1998 (1)

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
[Crossref]

1996 (2)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[Crossref] [PubMed]

1995 (2)

1992 (1)

1989 (2)

J. E. Rothenberg and D. Grischkowsky, “Observation of the formation of an optical intensity shock and wave breaking in the nonlinear propagation of pulses in optical fibers,” Phys. Rev. Lett. 62, 531–534 (1989).
[Crossref] [PubMed]

J. E. Rothenberg, “Femtosecond optical shocks and wave breaking in fiber propagation,” J. Opt. Soc. Am. B 6, 2392–2401 (1989).
[Crossref]

1985 (1)

1984 (1)

1981 (1)

Afshar V., S.

S. Afshar V. and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures. Part I: Kerr nonlinearity,” Opt Express 17, 2298–2318 (2009).
[Crossref] [PubMed]

Agarwal, A.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
[Crossref]

Agarwal, A. M.

Agrawal, G. P.

Ahmed, N.

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–20607 (1995).
[Crossref] [PubMed]

Amiranashvili, Sh.

Sh. Amiranashvili and A. Demircan, “Ultrashort Optical Pulse Propagation in terms of Analytic Signal,” Adv. Opt. Technol. 2011, 989515 (2011).
[Crossref]

Anderson, D.

Andrés, P.

Ania-Castanon, J. D.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
[Crossref]

Bao, C.

Baronio, F.

M. Conforti, F. Baronio, and S. Trillo, “Resonant radiation shed by dispersive shock waves,” Phys. Rev. A 89, 013807 (2014).
[Crossref]

Bartelt, H.

Barviau, B.

B. Barviau, B. Kibler, and A. Picozzi, “Wave-turbulence approach of supercontinuum generation: influence of self-steepening and higher-order dispersion,” Phys. Rev. A 79, 063840 (2009).
[Crossref]

Beausoleil, R. G.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
[Crossref]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20, 1685–1690 (2012).
[Crossref] [PubMed]

Biancalana, F.

Boppart, S. A.

Bosman, G. W.

Boyd, R. W.

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, 021111 (2007).
[Crossref]

Boyraz, O.

Bristow, A. D.

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, 191104 (2007).
[Crossref]

Cao, M.

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
[Crossref]

Castelló-Lurbe, D.

Chen, X.

Chiang, T.-K.

Chou, C.-Y.

Chudoba, C.

Coen, S.

Cohen, L.

L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).

Conforti, M.

Corless, R. M.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[Crossref]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

Dadap, J. I.

Dave, U.

Demircan, A.

Sh. Amiranashvili and A. Demircan, “Ultrashort Optical Pulse Propagation in terms of Analytic Signal,” Adv. Opt. Technol. 2011, 989515 (2011).
[Crossref]

Desaix, M.

Diddams, S. A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

Dinu, M.

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

Dudley, J.

Dudley, J. M.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
[Crossref]

G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771–1785 (2007).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Dulkeith, E.

Ellingham, T. J.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
[Crossref]

Erkintalo, M.

K. E. Webb, Y. Q. Xu, M. Erkintalo, and S. G. Murdoch, “Generalized dispersive wave emission in nonlinear fibers,” Opt. Lett. 38, 151–153 (2013).
[Crossref] [PubMed]

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
[Crossref]

Faccio, D.

Fathpour, S.

Fauchet, P. M.

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, 021111 (2007).
[Crossref]

Finot, C.

Fontaine, M.

Fujimoto, J. G.

Garcia, H.

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

Genty, G.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
[Crossref]

G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources,” J. Opt. Soc. Am. B 24, 1771–1785 (2007).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Ghanta, R. K.

Godbout, N.

Gonnet, G. H.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
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Grischkowsky, D.

J. E. Rothenberg and D. Grischkowsky, “Observation of the formation of an optical intensity shock and wave breaking in the nonlinear propagation of pulses in optical fibers,” Phys. Rev. Lett. 62, 531–534 (1989).
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D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Hare, D. E. G.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
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Hartl, I.

Hartung, A.

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A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 27, 203901 (2001).
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Huang, N.

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A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 27, 203901 (2001).
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Indukuri, T.

Jalali, B.

Jauslin, H. R.

Jeffrey, D. J.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
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Johnson, A. M.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Kagi, N.

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–20607 (1995).
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Kazovsky, L. G.

Kibler, B.

B. Barviau, B. Kibler, and A. Picozzi, “Wave-turbulence approach of supercontinuum generation: influence of self-steepening and higher-order dispersion,” Phys. Rev. A 79, 063840 (2009).
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C. Finot, B. Kibler, L. Provost, and S. Wabnitz, “Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers,” J. Opt. Soc. Am. B 25, 1938–1948 (2008).
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Kikuchi, K.

Y. Takushima and K. Kikuchi, “10-GHz, over 20-channel multiwavelength pulse source by slicing supercontinuum spectrum generated in normal-dispersion-fiber,” IEEE Photon. Technol. Lett. 11, 322–324 (1999).
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Kimerling, L. C.

C. Bao, Y. Yan, L. Zhang, Y. Yue, N. Ahmed, A. M. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “Increased bandwidth with flattened and low dispersion in a horizontal double-slot silicon waveguide,” J. Opt. Soc. Am. B 32, 26–30 (2015).
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L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
[Crossref]

Knuth, D. E.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
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Ko, T. H.

Kobtsev, S. M.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
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Kockaert, P.

Koonath, P.

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

Kubota, H.

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
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Kukarin, S.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
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Kuyken, B.

Lacroix, S.

Lægsgaard, J.

Leo, F.

Li, X.

Li, X. D.

Lin, Q.

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
[Crossref]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20, 1685–1690 (2012).
[Crossref] [PubMed]

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

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, 021111 (2007).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15, 16604–16644 (2007).
[Crossref] [PubMed]

Lipson, M.

Lisak, M.

Liu, H.

Liu, X.

Liu, Y.

Luo, F.

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
[Crossref]

Marcuse, D.

Marhic, M. E.

Marini, A.

Michel, C.

Michel, J.

C. Bao, Y. Yan, L. Zhang, Y. Yue, N. Ahmed, A. M. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “Increased bandwidth with flattened and low dispersion in a horizontal double-slot silicon waveguide,” J. Opt. Soc. Am. B 32, 26–30 (2015).
[Crossref]

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
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Miret, J. J.

Monro, T. M.

S. Afshar V. and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures. Part I: Kerr nonlinearity,” Opt Express 17, 2298–2318 (2009).
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Murdoch, S. G.

K. E. Webb, Y. Q. Xu, M. Erkintalo, and S. G. Murdoch, “Generalized dispersive wave emission in nonlinear fibers,” Opt. Lett. 38, 151–153 (2013).
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M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
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M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
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Painter, O. J.

Panoiu, N. C.

Picozzi, A.

C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, “Influence of third-order dispersion on the propagation of incoherent light in optical fibers,” Opt. Lett. 35, 2367–2369 (2010).
[Crossref] [PubMed]

B. Barviau, B. Kibler, and A. Picozzi, “Wave-turbulence approach of supercontinuum generation: influence of self-steepening and higher-order dispersion,” Phys. Rev. A 79, 063840 (2009).
[Crossref]

Piredda, G.

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, 021111 (2007).
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Provost, L.

Quiroga-Teixeiro, M. L.

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954 (2003).
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Ranka, J. K.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an airsilica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Roelkens, G.

Rohwer, E. G.

Rotenberg, N.

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, 191104 (2007).
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Rothenberg, J. E.

J. E. Rothenberg and D. Grischkowsky, “Observation of the formation of an optical intensity shock and wave breaking in the nonlinear propagation of pulses in optical fibers,” Phys. Rev. Lett. 62, 531–534 (1989).
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J. E. Rothenberg, “Femtosecond optical shocks and wave breaking in fiber propagation,” J. Opt. Soc. Am. B 6, 2392–2401 (1989).
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Safioui, J.

Schwoerer, H.

Silvestre, E.

Smirnov, S.V.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
[Crossref]

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]

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

Stolen, R. H.

Sun, Q.

Suret, P.

Takushima, Y.

Y. Takushima and K. Kikuchi, “10-GHz, over 20-channel multiwavelength pulse source by slicing supercontinuum spectrum generated in normal-dispersion-fiber,” IEEE Photon. Technol. Lett. 11, 322–324 (1999).
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Tamura, K.

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
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Tatian, B.

Tomlinson, W. J.

Torres-Company, V.

Tran, T. X.

Trillo, S.

M. Conforti, F. Baronio, and S. Trillo, “Resonant radiation shed by dispersive shock waves,” Phys. Rev. A 89, 013807 (2014).
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M. Conforti and S. Trillo, “Dispersive wave emission from wave breaking,” Opt. Lett. 38, 3815–3818 (2013).
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Tu, H.

Turitsyn, S. K.

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
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Tzolov, V. P.

van Driel, H. M.

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, 191104 (2007).
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Vlasov, Y. A.

Wabnitz, S.

Wang, Z.

Webb, K. E.

Wen, J.

Willner, A. E.

Windeler, R. S.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an airsilica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001).
[Crossref]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
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Wu, J.

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
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Xia, F.

Xu, Y. Q.

K. E. Webb, Y. Q. Xu, M. Erkintalo, and S. G. Murdoch, “Generalized dispersive wave emission in nonlinear fibers,” Opt. Lett. 38, 151–153 (2013).
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M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
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Yan, Y.

Yin, L.

Yoshida, E.

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
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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, 021111 (2007).
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Zhang, Q.

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
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Adv. Comput. Math. (1)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
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Adv. Opt. Photon. (1)

Adv. Opt. Technol. (1)

Sh. Amiranashvili and A. Demircan, “Ultrashort Optical Pulse Propagation in terms of Analytic Signal,” Adv. Opt. Technol. 2011, 989515 (2011).
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Appl. Opt. (2)

Appl. Phys. Lett. (4)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82, 2954 (2003).
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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, 021111 (2007).
[Crossref]

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, 191104 (2007).
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P. Koonath, D. R. Solli, and B. Jalali, “Limiting nature of continuum generation in silicon,” Appl. Phys. Lett. 93, 091114 (2008).
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IEEE J. Sel. Topics Quantum Electron. (1)

L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, A. Agarwal, L. C. Kimerling, J. Michel, and A. E. Willner, “On-chip octave-spanning supercontinuum in nanostructured silicon waveguides using ultralow pulse energy,” IEEE J. Sel. Topics Quantum Electron. 18, 1799–1806 (2012).
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IEEE Photon. Technol. Lett. (1)

Y. Takushima and K. Kikuchi, “10-GHz, over 20-channel multiwavelength pulse source by slicing supercontinuum spectrum generated in normal-dispersion-fiber,” IEEE Photon. Technol. Lett. 11, 322–324 (1999).
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J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (6)

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S. Afshar V. and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures. Part I: Kerr nonlinearity,” Opt Express 17, 2298–2318 (2009).
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Opt. Express (10)

I-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, and R. M. Osgood, “Supercontinuum generation in silicon photonic wires,” Opt. Express 15, 15242–15249 (2007).
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D. Castelló-Lurbe, P. Andrés, and E. Silvestre, “Dispersion-to-spectrum mapping in nonlinear fibers based on optical wave-breaking,” Opt. Express 21, 28550–28558 (2013).
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M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, “Interaction between optical fields and their conjugates in nonlinear media,” Opt. Express 21, 31239–31252 (2013).
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M. Zhu, H. Liu, X. Li, N. Huang, Q. Sun, J. Wen, and Z. Wang, “Ultrabroadband flat dispersion tailoring of dual-slot silicon waveguides,” Opt. Express 20, 15899–15907 (2012).
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J. J. Miret, E. Silvestre, and P. Andrés, “Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers,” Opt. Express 17, 9197–9203 (2009).
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A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19, 3775–3787 (2011).
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L. Zhang, Q. Lin, Y. Yue, Y. Yan, R. G. Beausoleil, and A. E. Willner, “Silicon waveguide with four zero-dispersion wavelengths and its application in on-chip octave-spanning supercontinuum generation,” Opt. Express 20, 1685–1690 (2012).
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Opt. Fiber Technol. (2)

S.V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12, 122–147 (2006).
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M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, “Coherence degradation in the process of supercontinuum generation in an optical fiber,” Opt. Fiber Technol. 4, 215–223 (1998).
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Opt. Laser Technol. (1)

J. Wu, F. Luo, Q. Zhang, and M. Cao, “Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides,” Opt. Laser Technol. 41, 360–364 (2009).
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J. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002).
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C. Michel, P. Suret, S. Randoux, H. R. Jauslin, and A. Picozzi, “Influence of third-order dispersion on the propagation of incoherent light in optical fibers,” Opt. Lett. 35, 2367–2369 (2010).
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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, 2031–2033 (2007).
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D. Castelló-Lurbe, E. Silvestre, P. Andrés, and V. Torres-Company, “Spectral broadening enhancement in silicon waveguides through pulse shaping,” Opt. Lett. 37, 2757–2759 (2012).
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K. E. Webb, Y. Q. Xu, M. Erkintalo, and S. G. Murdoch, “Generalized dispersive wave emission in nonlinear fibers,” Opt. Lett. 38, 151–153 (2013).
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M. Conforti and S. Trillo, “Dispersive wave emission from wave breaking,” Opt. Lett. 38, 3815–3818 (2013).
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F. Leo, S. Gorza, J. Safioui, P. Kockaert, S. Coen, U. Dave, B. Kuyken, and G. Roelkens, “Dispersive wave emission and supercontinuum generation in a silicon wire waveguide pumped around the 1550 nm telecommunication wavelength,” Opt. Lett. 39, 3623–3625 (2014).
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Phys. Rev. A (3)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–20607 (1995).
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M. Conforti, F. Baronio, and S. Trillo, “Resonant radiation shed by dispersive shock waves,” Phys. Rev. A 89, 013807 (2014).
[Crossref]

B. Barviau, B. Kibler, and A. Picozzi, “Wave-turbulence approach of supercontinuum generation: influence of self-steepening and higher-order dispersion,” Phys. Rev. A 79, 063840 (2009).
[Crossref]

Phys. Rev. Lett. (3)

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, “Cascaded phase matching and nonlinear symmetry breaking in fiber frequency combs,” Phys. Rev. Lett. 109, 223904 (2012).
[Crossref]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 27, 203901 (2001).
[Crossref]

J. E. Rothenberg and D. Grischkowsky, “Observation of the formation of an optical intensity shock and wave breaking in the nonlinear propagation of pulses in optical fibers,” Phys. Rev. Lett. 62, 531–534 (1989).
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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[Crossref]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288, 635–639 (2000).
[Crossref] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 4th ed., 2007).

L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).

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Figures (4)

Fig. 1
Fig. 1 (a) Evolution of the generalized lengths, −1, in the OWB regime. It corresponds to the pulse propagation of (b–c). (b) Output spectrum for a femtosecond pulse in a waveguide. λ0 indicates the pumping wavelength, λZD points out the zero-dispersion wavelength [note it is the pump wave considered in Eq. (7)], and λ DW th refers to the theoretical wavelengths of the dispersive wave (i.e. the idler wave). (c) Output pulse corresponding to (b). (d) Output spectrum for a picosecond pulse in a fiber. (See text for details.)
Fig. 2
Fig. 2 Sketch for the interpretation of the FWM processes considered in this paper. We assume that the schematic plots of the instantaneous frequency, δω(t) — continuous lines —, and instantaneous power, P(t) — dashed lines —, correspond to the distance zOWB given by Eq. (5). Thick lines highlight the blue-shifted and red-shifted frequencies that overlap after zOWB. The process described by Eq. (7) and the time shifting induced by dispersion are also represented.
Fig. 3
Fig. 3 (a) Output spectra produced by OWB and SPM in the presence of TPA (see details in the text). (b) Output pulse corresponding to the solid curve spectrum in (a).
Fig. 4
Fig. 4 (a) Dispersion curve of a strip silicon waveguide with a slot of SiO2 [47] (included as an inset). (b) Complex nonlinear coefficient. (c) Output spectrum spanning an octave after a propagation distance of 3 mm. (d) Modulus of the complex degree of first order coherence corresponding to (c).

Tables (1)

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Table 1 Cauchy parameters for the Kerr index and the two-photon absorption coefficient.

Equations (19)

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z A ˜ ( z , ω ω 0 ) = i β p ( ω ) A ˜ ( z , ω ω 0 ) + i γ 0 ω 0 [ | A ( z , t ) | 2 A ( z , t ) ] ,
˜ ( x , ω ) = A ˜ ( z , ω ω 0 ) e ( x t ) ( S d S z ^ ( e t × h t ) / 2 ) 1 / 2 e i ( β 0 + β 1 ( ω ω 0 ) ) z ,
NL 1 ( z ) = γ 0 d t | A ( z , t ) | 4 2 d t | A ( z , t ) | 2 ,
D 1 ( z ) = d ω β p ( ω ) | A ( z , ω ω 0 ) | 2 d ω | A ( z , ω ω 0 ) | 2 .
z OWB L D L NL ϰ 2 σ 2 ,
δ ω ( z OWB , t ) ϰ γ 0 t | A ( 0 , t ) | 2 z OWB .
2 ( ω 0 + δ ω min ) ω 0 + ω DW .
β 3 = σ 2 ϒ 2 β 2 3 L NL ,
ω DW ω 0 = 2 β 2 β 3 .
min t { δ ω TPA ( t , z ^ OWB ) } = min t ^ { δ ω ^ ( t ^ , z ^ OWB ) } , min t { Re ( γ 0 ) t | A ( 0 , t ) | 2 z ^ OWB 1 + 2 Im ( γ 0 ) | A ( 0 , t ) | 2 z ^ OWB } = γ ^ 0 min t ^ { t ^ | A ( 0 , t ^ ) | 2 } z ^ OWB ,
W 2 2 ζ 2 W ζ 2 = 0 ,
Re ( γ 0 ) γ ^ 0 = 4 3 3 1 x x 2 ,
z A ˜ = α 2 A ˜ + i β p ( ω ) A ˜ + i γ ( ω ) ω 0 [ | A | 2 A ] σ 2 ( 1 + i μ ) ω 0 [ N c ( z , t ) A ] ,
N c ( z , t ) = 2 π [ Im ( γ 0 ) ] 2 h ω 0 β TPA ( ω 0 ) t e t t τ c | A ( z , t ) | 4 d t ,
γ ( ω ) = ε 0 μ 0 ( S ( e t × h t ) z ^ d S ) 2 S d S [ ω n 2 c + i β TPA 2 ] ρ n 2 [ ( e t e t ) 2 + 2 3 e t e t | e z | 2 + | e z | 4 ] ,
μ k = d ω ( ω ω 0 ) k | A ˜ ( ω ω 0 ) | 2 d ω | A ˜ ( ω ω 0 ) | 2 = d t A * ( t ) ( i t ) k A ( t ) d t | A ( t ) | 2 d t [ φ ( t ) ] k | A ( t ) | 2 d t | A ( t ) | 2 ,
| A ( z , t ) | 2 = a ( z ) | A ( 0 , t 1 + α z 2 ) | 2 .
δ ω ( z OWB , t ) = t φ ( z OWB , t ) γ 0 0 z OWB d z t | A ( z , t ) | 2 ϰ γ 0 t | A ( 0 , t ) | 2 z OWB ,
k = 2 ( 1 ) k k ! L NL L D ( k ) ( ϰ z OWB L NL ) k σ k = 1 2 ,

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