Abstract

In this paper we numerically study supercontinuum generation by pumping a silicon nitride waveguide, with two zero-dispersion wavelengths, with femtosecond pulses. The waveguide dispersion is designed so that the pump pulse is in the normal-dispersion regime. We show that because of self-phase modulation, the initial pulse broadens into the anomalous-dispersion regime, which is sandwiched between the two normal-dispersion regimes, and here a soliton is formed. The interaction of the soliton and the broadened pulse in the normal-dispersion regime causes additional spectral broadening through formation of dispersive waves by non-degenerate four-wave mixing and cross-phase modulation. This broadening occurs mainly towards the second normal-dispersion regime. We show that pumping in either normal-dispersion regime allows broadening towards the other normal-dispersion regime. This ability to steer the continuum extension towards the direction of the other normal-dispersion regime beyond the sandwiched anomalous-dispersion regime underlies the directional supercontinuum notation. We numerically confirm the approach in a standard silica microstructured fiber geometry with two zero-dispersion wavelengths.

© 2019 Optical Society of America

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2018 (3)

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

2017 (5)

2016 (1)

2015 (3)

2014 (2)

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref]

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

2013 (2)

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref]

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

2011 (3)

2010 (2)

2009 (1)

2008 (2)

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).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

2007 (2)

2006 (2)

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (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 (3)

2004 (6)

2003 (1)

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

1995 (1)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref]

1989 (1)

1988 (1)

Agrawal, G. P.

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref]

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Andersen, T.

Andersen, T. V.

Andrekson, P. A.

Asahi, H.

Bache, M.

Bang, O.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

C. R. Petersen, R. D. Engelsholm, C. Markos, L. Brilland, C. Caillaud, J. Trolès, and O. Bang, “Increased mid-infrared supercontinuum bandwidth and average power by tapering large-mode-area chalcogenide photonic crystal fibers,” Opt. Express 25, 15336–15348 (2017).
[Crossref]

Bengtsson, J.

Bhadra, S. K.

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref]

Brilland, L.

Broderick, N. G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

Caillaud, C.

Cardenas, J.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Y. Okawachi, M. Yu, J. Cardenas, X. Ji, M. Lipson, and A. L. Gaeta, “Coherent, directional supercontinuum generation,” Opt. Lett. 42, 4466–4469 (2017).
[Crossref]

Coen, S.

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

Couairon, A.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
[Crossref]

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Di Trapani, P.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
[Crossref]

Dubietis, A.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
[Crossref]

Dudley, J. M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

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

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).

Dutt, A.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Efimov, A.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Engelsholm, R. D.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

C. R. Petersen, R. D. Engelsholm, C. Markos, L. Brilland, C. Caillaud, J. Trolès, and O. Bang, “Increased mid-infrared supercontinuum bandwidth and average power by tapering large-mode-area chalcogenide photonic crystal fibers,” Opt. Express 25, 15336–15348 (2017).
[Crossref]

Erkintalo, M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

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

Faccio, D.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
[Crossref]

Finot, C.

Freude, W.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Fülöp, A.

Gaeta, A. L.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Y. Okawachi, M. Yu, J. Cardenas, X. Ji, M. Lipson, and A. L. Gaeta, “Coherent, directional supercontinuum generation,” Opt. Lett. 42, 4466–4469 (2017).
[Crossref]

Gaižauskas, E.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
[Crossref]

Ganin, D.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Genty, G.

Gonzalo, I. B.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

Gordon, J. P.

Gris-Sánchez, I.

Gu, J.

Guo, H.

Hansen, K. P.

Haus, H. A.

Heidt, A. M.

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Hilligsøe, K. M.

Hult, J.

Jaskorzynska, B.

Ji, X.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Y. Okawachi, M. Yu, J. Cardenas, X. Ji, M. Lipson, and A. L. Gaeta, “Coherent, directional supercontinuum generation,” Opt. Lett. 42, 4466–4469 (2017).
[Crossref]

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Joshi, C.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Kaivola, M.

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[Crossref]

Karpov, M.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Kartashov, Y.

Keiding, S.

Kibler, B.

Kippenberg, T. J.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Klintberg, T.

Knight, J.

I. Gris-Sánchez, B. Mangan, and J. Knight, “Reducing spectral attenuation in small-core photonic crystal fibers,” Opt. Mater. Express 1, 179–184 (2011).
[Crossref]

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

Knight, J. C.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Kolesik, M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear x waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92, 253901 (2004).
[Crossref]

König, F.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Koos, C.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Kordts, A.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Koshiba, M.

Kristiansen, R.

Krockenberger, J.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Krückel, C. J.

Kudlinski, A.

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Laegsgaard, J.

Larsen, J. J.

Lehtonen, M.

Leonhardt, U.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Li, P.

Limpert, J.

Lipson, M.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Y. Okawachi, M. Yu, J. Cardenas, X. Ji, M. Lipson, and A. L. Gaeta, “Coherent, directional supercontinuum generation,” Opt. Lett. 42, 4466–4469 (2017).
[Crossref]

Liu, X.

Liu, Z.

Luan, F.

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

Ludvigsen, H.

Luke, K.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Mangan, B.

Marest, T.

Marin-Palomo, P.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Markos, C.

Milián, C.

Misawa, H.

Mølmer, K.

Moloney, J. V.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear x waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92, 253901 (2004).
[Crossref]

Monro, T. M.

Morgner, U.

Moselund, P. M.

P. M. Moselund, “Long-pulse supercontinuum light sources,” Ph.D. thesis (DTU Fotonik, Technical University of Denmark, 2009).

Murazawa, N.

Murdoch, S. G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

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

Nielsen, C. K.

Nishijima, Y.

Okawachi, Y.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Y. Okawachi, M. Yu, J. Cardenas, X. Ji, M. Lipson, and A. L. Gaeta, “Coherent, directional supercontinuum generation,” Opt. Lett. 42, 4466–4469 (2017).
[Crossref]

Omenetto, F. G.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Paulsen, H. N.

Petersen, C. R.

Pfeiffer, M. H. P.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Provost, L.

Pu, M.

Randel, S.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Robertson, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

Roy, S.

Russell, P. St.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Russell, P. St. J.

A. Yulin, D. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett. 29, 2411–2413 (2004).
[Crossref]

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

Saitoh, K.

Schadt, D.

Schimpf, D.

Schreiber, T.

Shahraam Afshar, V.

Shi, K.

Skryabin, D.

Skryabin, D. V.

C. Milián, T. Marest, A. Kudlinski, and D. V. Skryabin, “Spectral wings of the fiber supercontinuum and the dark-bright soliton interaction,” Opt. Express 25, 10494–10499 (2017).
[Crossref]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Sørensen, M. P.

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[Crossref]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

Stolen, R. H.

Sun, Q.

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Taylor, J. R.

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).

Tomlinson, W. J.

Torres-Company, V.

Trocha, P.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Trolès, J.

Tünnermann, A.

Ueno, K.

Wabnitz, S.

Wang, S.

Webb, K. E.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

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

Weimann, C.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Wolf, S.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

Wright, E. M.

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear x waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92, 253901 (2004).
[Crossref]

Xu, Y.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

Xu, Y. Q.

Ye, Z.

Yin, S.

Yu, M.

Yulin, A.

Yulin, A. V.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

Zeng, X.

Zhou, B.

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Nat. Commun. (1)

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5, 4969 (2014).
[Crossref]

Opt. Express (16)

K. M. Hilligsøe, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Mølmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, “Supercontinuum generation in a photonic crystal fiber with two zero dispersion wavelengths,” Opt. Express 12, 1045–1054 (2004).
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K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12, 2096–2101 (2004).
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G. Genty, M. Lehtonen, H. Ludvigsen, and M. Kaivola, “Enhanced bandwidth of supercontinuum generated in microstructured fibers,” Opt. Express 12, 3471–3480 (2004).
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G. Genty, M. Lehtonen, and H. Ludvigsen, “Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30  fs pulses,” Opt. Express 12, 4614–4624 (2004).
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Q. Sun, H. Asahi, Y. Nishijima, N. Murazawa, K. Ueno, and H. Misawa, “Pulse duration dependent nonlinear propagation of a focused femtosecond laser pulse in fused silica,” Opt. Express 18, 24495–24503 (2010).
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V. Shahraam Afshar 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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S. Roy, S. K. Bhadra, K. Saitoh, M. Koshiba, and G. P. Agrawal, “Dynamics of Raman soliton during supercontinuum generation near the zero-dispersion wavelength of optical fibers,” Opt. Express 19, 10443–10455 (2011).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, U. Morgner, and G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express 22, 3866–3879 (2014).
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T. Schreiber, T. Andersen, D. Schimpf, J. Limpert, and A. Tünnermann, “Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths,” Opt. Express 13, 9556–9569 (2005).
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J. Laegsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007).
[Crossref]

C. Milián, T. Marest, A. Kudlinski, and D. V. Skryabin, “Spectral wings of the fiber supercontinuum and the dark-bright soliton interaction,” Opt. Express 25, 10494–10499 (2017).
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C. R. Petersen, R. D. Engelsholm, C. Markos, L. Brilland, C. Caillaud, J. Trolès, and O. Bang, “Increased mid-infrared supercontinuum bandwidth and average power by tapering large-mode-area chalcogenide photonic crystal fibers,” Opt. Express 25, 15336–15348 (2017).
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C. J. Krückel, A. Fülöp, Z. Ye, P. A. Andrekson, and V. Torres-Company, “Optical bandgap engineering in nonlinear silicon nitride waveguides,” Opt. Express 25, 15370–15380 (2017).
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D. Skryabin and Y. Kartashov, “Self-locking of the frequency comb repetition rate in microring resonators with higher order dispersions,” Opt. Express 25, 27442–27451 (2017).
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J. Gu, H. Guo, S. Wang, and X. Zeng, “Probe-controlled soliton frequency shift in the regime of optical event horizon,” Opt. Express 23, 22285–22290 (2015).
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C. J. Krückel, A. Fülöp, T. Klintberg, J. Bengtsson, P. A. Andrekson, and V. Torres-Company, “Linear and nonlinear characterization of low-stress high-confinement silicon-rich nitride waveguides,” Opt. Express 23, 25827–25837 (2015).
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Phys. Rev. E (1)

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear x-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73, 016608 (2006).
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Phys. Rev. Lett. (4)

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[Crossref]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Dynamic nonlinear x waves for femtosecond pulse propagation in water,” Phys. Rev. Lett. 92, 253901 (2004).
[Crossref]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. St. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110, 233901 (2013).
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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).
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Sci. Adv. (1)

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Sci. Rep. (1)

I. B. Gonzalo, R. D. Engelsholm, M. P. Sørensen, and O. Bang, “Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation,” Sci. Rep. 8, 6579 (2018).
[Crossref]

Science (3)

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

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

Other (3)

P. M. Moselund, “Long-pulse supercontinuum light sources,” Ph.D. thesis (DTU Fotonik, Technical University of Denmark, 2009).

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers (Cambridge University, 2010).

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Figures (9)

Fig. 1.
Fig. 1. GVD (β2) for the SiRN waveguide. The circles mark the pump wavelengths used in the paper. The inset represents the Comsol simulation of the waveguide and the mode obtained.
Fig. 2.
Fig. 2. Directional SCG in the SiRN waveguide pumped at 1.56 μm with 0.58 kW peak power. (a) The power-spectral density (PSD) at the beginning (dashed) and end of the SiRN waveguide (full). (b) The spectral evolution in the waveguide as a function of propagation distance, along with the phase-matched wavelengths from Eq. (5) after 22 mm of propagation in the waveguide, marked as downward pointing triangles (J=1), empty circles (J=0), and triangles pointing upwards (J=1). (c) Dispersion relation of the waveguide in the soliton’s group-velocity frame (full). The dashed lines are the wavenumbers for the J=1, 0, 1 cases as labeled. The dotted lines in all the figures are the ZDWs. (d) Temporal evolution in the waveguide. Key spectral regions are marked.
Fig. 3.
Fig. 3. Spectrogram at 22 mm calculated with a 16 fs gating pulse. The full black line shows the accumulated dispersion delay.
Fig. 4.
Fig. 4. Two-pulse model where the SiRN waveguide is pumped at 1.56 μm with 125 fs 140 W peak power and a soliton state is injected at 1.25 μm with 55 fs 40 W peak power. (a) Spectrum at the output of the SiRN waveguide (full) and the input (dashed). (b) Simulation of spectral evolution of a fundamental soliton colliding with a pulse in the NDR II. The vertical dotted lines mark the ZDWs in both the figures.
Fig. 5.
Fig. 5. Directional SCG in the SiRN waveguide pumped at 0.94 μm with 0.7 kW peak power. (a) Spectrum at the end of the waveguide (full) and the pump (dashed). (b) The spectrum evolution in the waveguide as a function of propagation distance for the waveguide pumped at 0.94 μm. The vertical dashed lines mark the ZDWs in both the figures. For this pump wavelength the nonlinear coefficient is γ=7.2W1m1.
Fig. 6.
Fig. 6. GVD (β2) of the MSF as a function of wavelength. The dashed horizontal line is the ZDW, and the dotted vertical line marks the pump wavelength at 1.56 μm. The inset represents the Comsol simulation of the fiber and the mode obtained.
Fig. 7.
Fig. 7. Directional SCG in an MSF pumped at 1.56 μm with 9 kW peak power. (a) The PSD at the beginning (dashed) and end of the fiber (full). (b) Spectral evolution along the length of the fiber. The empty circles at 0.876 μm and 1.999 μm are the calculated wavelength at which the DWs are generated from the phase-matching condition for the soliton at 1.20 μm alone after 0.5 m of propagation in the fiber. The downward pointing triangle at 0.819 μm is the calculated wavelength with the J=1 condition in Eq. (5), at which DWs are generated from the non-degenerate FWM of the part of the pump at 1.649 μm in NDR II and the soliton after 0.5 m of the fiber. The triangles pointing upwards at 1.649 μm and 1.765 μm are the calculated wavelength with the J=1 condition in Eq. (5), at which DW are generated after 0.5 m of the fiber. (c) Dispersion relation of the waveguide in the soliton’s group-velocity frame after 0.5 m of propagation in the fiber (full). The dashed lines are the wavenumbers for the J=1, 0, 1 cases as labeled. The intersection points between the full line and the dashed lines are calculated phase-matching wavelengths for the generation of DWs. The dotted vertical lines in all three figures are the ZDWs.
Fig. 8.
Fig. 8. Directional SCG in an MSF pumped at 1.56 μm with 20 kW peak power. (a) The PSD at the beginning (dashed) and end of the MSF (full). (b) Spectral evolution along 1 m of the fiber. The vertical dotted lines in both the figures are the ZDWs.
Fig. 9.
Fig. 9. Spectrograms for an input peak power of 20 kW calculated with a gating function of 20 fs: (a) at z=0.122m, showing the soliton in ADR I and the co-propagating pulse in NDR II; (b) at z=0.167m, showing the soliton being pushed into the NDR I. (c) Spectrogram numerically bandpass filtered from 1.1 to 1.5 μm to show the spectral and temporal profile in ADR I at z=0.122m.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

C˜zi{β(ω)[β(ω0)+β1(ω0)(ωω0)]}C˜+α(ω)2C˜=iγ¯(ω)[1+ωω0ω0]F{CR(T)|C(TT)|2dT}.
γ¯(ω)=n2n0ω0cneff(ω)Aeff(ω)Aeff(ω0),
Aeff(ω)=(+|F(x,y,ω)|2dxdy)2+|F(x,y,ω)|4dxdy.
ω(T)γ1LπT|A2(L,T)|2,
βlin(ωd)=J[βlin(ωp)βsol(ωp)]+βsol(ωd);forJ=1,0,1,
βsol(ω)=βlin(ωs)+β1(ωs)[ωωs]+qsol.

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