Abstract

Optimization of the compression of input N-solitons into robust ultra-narrow fundamental solitons, with a tunable up- or downshifted frequency, is proposed in photonic crystal fibers free of the Raman effect. Due to the absence of the Raman self-frequency shift, these fundamental solitons continue propagation, maintaining the acquired frequency, once separated from the input N soliton’s temporal slot. A universal optimal value of the relative strength of the third-order dispersion is found, providing the strongest compression of the fundamental soliton is found. It depends only on the order of the injected N-soliton. The largest compression degree significantly exceeds the analytical prediction supplied by the Satsuma–Yajima formula. The mechanism behind this effect, which remains valid in the presence of the self-steepening, is explained.

© 2013 Optical Society of America

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2013 (4)

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).
[CrossRef]

G. Yang, L. Li, S. Jia, and D. Mihalache, Rom. Rep. Phys. 65, 391 (2013).

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, Opt. Express 21, 14481 (2013).
[CrossRef]

R. Driben, A. V. Yulin, A. Efimov, and B. A. Malomed, Opt. Express 21, 19091 (2013).
[CrossRef]

2012 (3)

W. Liu, L. Pang, X. Lin, R. Gao, and X. Song, Appl. Opt. 51, 8095 (2012).
[CrossRef]

R. Driben and I. Babushkin, Opt. Lett. 37, 5157 (2012).
[CrossRef]

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

2011 (1)

2010 (2)

R. Driben, F. Mitschke, and N. Zhavoronkov, Opt. Express 18, 25993 (2010).
[CrossRef]

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

2008 (1)

J. H. Lee, J. V. Howe, C. Xu, and X. Liu, IEEE J. Sel. Top. Quantum Electron. 14, 713 (2008).
[CrossRef]

2007 (1)

S. Kivisto, T. Hakulinen, M. Guina, and O. G. Okhotnikov, IEEE Photon. Technol. Lett. 19, 934 (2007).
[CrossRef]

2006 (2)

J. M. Dudley, G. Gentry, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

M. H. Frosz, O. Bang, and A. Bjarklev, Opt. Express 14, 9391 (2006).
[CrossRef]

2005 (2)

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

2003 (3)

J. Yang and T. R. Akylas, Stud. Appl. Math. 111, 359 (2003).
[CrossRef]

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

2002 (1)

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

2001 (1)

R. Driben and B. A. Malomed, Opt. Commun. 197, 481 (2001).
[CrossRef]

1991 (1)

B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
[CrossRef]

1989 (1)

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

1987 (1)

Y. Kodama and A. Hasegawa, IEEE Photon. Technol. Lett. QE-23, 510 (1987).

1986 (1)

1985 (1)

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, JETP Lett. 42, 74 (1985).

1983 (1)

1974 (1)

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Akylas, T. R.

J. Yang and T. R. Akylas, Stud. Appl. Math. 111, 359 (2003).
[CrossRef]

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

Amiranashvili, Sh.

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Babushkin, I.

Bang, O.

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Bjarklev, A.

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Chang, W.

Coen, S.

J. M. Dudley, G. Gentry, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Crasovan, L. C.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Dianov, E. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, JETP Lett. 42, 74 (1985).

Driben, R.

Dudley, J. M.

J. M. Dudley, G. Gentry, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Efimov, A.

R. Driben, A. V. Yulin, A. Efimov, and B. A. Malomed, Opt. Express 21, 19091 (2013).
[CrossRef]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Frosz, M. H.

Gao, R.

Gentry, G.

J. M. Dudley, G. Gentry, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Golovchenko, E. A.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, JETP Lett. 42, 74 (1985).

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Guina, M.

S. Kivisto, T. Hakulinen, M. Guina, and O. G. Okhotnikov, IEEE Photon. Technol. Lett. 19, 934 (2007).
[CrossRef]

Hakulinen, T.

S. Kivisto, T. Hakulinen, M. Guina, and O. G. Okhotnikov, IEEE Photon. Technol. Lett. 19, 934 (2007).
[CrossRef]

Hasegawa, A.

Y. Kodama and A. Hasegawa, IEEE Photon. Technol. Lett. QE-23, 510 (1987).

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Howe, J. V.

J. H. Lee, J. V. Howe, C. Xu, and X. Liu, IEEE J. Sel. Top. Quantum Electron. 14, 713 (2008).
[CrossRef]

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Jia, S.

G. Yang, L. Li, S. Jia, and D. Mihalache, Rom. Rep. Phys. 65, 391 (2013).

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

Joly, N. Y.

Kartashov, Y. V.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Kivisto, S.

S. Kivisto, T. Hakulinen, M. Guina, and O. G. Okhotnikov, IEEE Photon. Technol. Lett. 19, 934 (2007).
[CrossRef]

Kivshar, Y. S.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[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. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Kodama, Y.

Y. Kodama and A. Hasegawa, IEEE Photon. Technol. Lett. QE-23, 510 (1987).

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Lee, J. H.

J. H. Lee, J. V. Howe, C. Xu, and X. Liu, IEEE J. Sel. Top. Quantum Electron. 14, 713 (2008).
[CrossRef]

Li, L.

G. Yang, L. Li, S. Jia, and D. Mihalache, Rom. Rep. Phys. 65, 391 (2013).

Lin, X.

Liu, W.

Liu, X.

J. H. Lee, J. V. Howe, C. Xu, and X. Liu, IEEE J. Sel. Top. Quantum Electron. 14, 713 (2008).
[CrossRef]

Mahnke, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Malomed, B. A.

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, Opt. Express 21, 14481 (2013).
[CrossRef]

R. Driben, A. V. Yulin, A. Efimov, and B. A. Malomed, Opt. Express 21, 19091 (2013).
[CrossRef]

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).
[CrossRef]

R. Driben and B. A. Malomed, Opt. Commun. 197, 481 (2001).
[CrossRef]

B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

Mihalache, D.

G. Yang, L. Li, S. Jia, and D. Mihalache, Rom. Rep. Phys. 65, 391 (2013).

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Mitschke, F.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

R. Driben, F. Mitschke, and N. Zhavoronkov, Opt. Express 18, 25993 (2010).
[CrossRef]

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Nold, J.

Okhotnikov, O. G.

S. Kivisto, T. Hakulinen, M. Guina, and O. G. Okhotnikov, IEEE Photon. Technol. Lett. 19, 934 (2007).
[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. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

Ominetto, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Pagel, T.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

Pang, L.

Pérez-García, V. M.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Prokhorov, A. M.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, JETP Lett. 42, 74 (1985).

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Russell, P.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

Russell, P. St. J.

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St. J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Satsuma, J.

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Serkin, V. N.

E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, JETP Lett. 42, 74 (1985).

Skryabin, D. V.

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, Opt. Express 21, 14481 (2013).
[CrossRef]

R. Driben, B. A. Malomed, A. V. Yulin, and D. V. Skryabin, Phys. Rev. A 87, 063808 (2013).
[CrossRef]

D. V. Skryabin and A. V. Gorbach, Rev. Mod. Phys. 82, 1287 (2010).
[CrossRef]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Song, X.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Sci. Rep. 2, 850 (2012).
[CrossRef]

A. Demircan, Sh. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, Appl. Phys. B, doi: 10.1007/s00340-013-5609-9 (2013).
[CrossRef]

Stolen, R. H.

Stratmann, M.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902 (2005).
[CrossRef]

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef]

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. Ominetto, A. Efimov, and A. J. Taylor, Nature 424, 511 (2003).
[CrossRef]

Tomlinson, W. J.

Torner, L.

L. C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, Phys. Rev. E 67, 046610 (2003).
[CrossRef]

Travers, J. C.

Wadsworth, W. J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn, Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef]

Xu, C.

J. H. Lee, J. V. Howe, C. Xu, and X. Liu, IEEE J. Sel. Top. Quantum Electron. 14, 713 (2008).
[CrossRef]

Yajima, N.

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Yang, G.

G. Yang, L. Li, S. Jia, and D. Mihalache, Rom. Rep. Phys. 65, 391 (2013).

Yang, J.

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Figures (5)

Fig. 1.
Fig. 1.

Generation of frequency-shifted fundamental solitons from the 10-soliton input with T0=0.05ps at four different values of δ3. The blue curve corresponds to the analytical SY prediction [2].

Fig. 2.
Fig. 2.

Generation of frequency-shifted fundamental solitons from the 10-soliton input with T0=0.05ps at the optimal value of δ3=0.0045. The dynamics are presented in the (a) temporal and (b) spectral domains. The red vertical line represents the strongest soliton’s evolution with the acquired constant wavelength of 948 nm, once it escapes the parental N-soliton temporal slot at z=0.3m.

Fig. 3.
Fig. 3.

(a) Optimal value δ3β3/(6β2T0) as a function of the input soliton’s order (the blue solid curve). The red dashed curve shows the best fit to const·N1; see the text. (b) The blue (upper) curve shows the ratio between the largest fundamental soliton’s peak power and the input peak power for both signs of δ3. The black dashed (lower) curve corresponds to the analytical result (3). The optimal values of δ3 are taken from panel (a). (c) Wavelength upshift and downshifts of the tallest generated fundamental soliton relative to the input wavelength of 800 nm. The upshift for δ3>0 and downshift for δ3<0 are represented, respectively, by the solid red and dashed blue (top and bottom) curves.

Fig. 4.
Fig. 4.

Simulations of the 10 soliton with T0=0.05ps, using Eq. (1) with s=0: (a) δ3=0, (b) δ3=0.0012, and (c) δ3=0.0025.

Fig. 5.
Fig. 5.

Simulations of the 10 soliton with T0=0.05ps, using Eq. (1) with the shock term included (s=0.0085). (a) δ3=0.0025. (b) δ3=0.0012.

Equations (2)

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iuz+(1/2)uTT+|u|2u=iδ3uTTTis(|u|2u)T,
Pj=2(2N2j+1)/N2

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