Abstract

Modulation instability followed by generation of subpicosecond pulses could be obtained with quasi-continuous wave packets propagating in optical fibers with running refractive index wave. We report on comprehensive studies of this process demonstrating that the peak power of the pulses exceeds the power of the pumping radiation by orders of magnitude. Practically, the effect could be implemented through interaction of the surface optical wave with an acoustic wave in a 2 cm cylindrical waveguide in a robust all-fiber format.

© 2019 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2018 (1)

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

2016 (4)

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

I. O. Zolotovskii, D. A. Korobko, V. A. Lapin, and D. I. Sementsov, “Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave,” Opt. Spectrosc. 121, 256–262 (2016).
[Crossref]

I. O. Zolotovskii, V. A. Lapin, and D. I. Sementsov, “Frequency modulation and compression of optical pulses in an optical fibre with a travelling refractive-index wave,” Quantum Electron. 46, 39–44 (2016).
[Crossref]

2015 (2)

2014 (1)

2013 (1)

2011 (1)

2010 (1)

2009 (1)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–548 (2009).
[Crossref]

2006 (1)

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” UFN 176, 175–202 (2006).
[Crossref]

2004 (2)

M. Sumetsky, “Whispering-gallery-bottle microcavities: the three-dimensional etalon,” Opt. Lett. 29, 8–10 (2004).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in low-dimensional Bose-Einstein condensates,” Phys. Rev. A 70, 011601 (2004).
[Crossref]

2003 (2)

V. P. Torchigin and S. V. Torchigin, “Optical solitons appearing during propagation of whispering-gallery waves,” Quantum Electron. 33, 913–918 (2003).
[Crossref]

T. Tanemura and K. Kikuchi, “Unified analysis of modulational instability induced by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 20, 2502–2514 (2003).
[Crossref]

2002 (4)

V. V. Konotop and M. Salerno, “Modulational instability in Bose-Einstein condensates in optical lattices,” Phys. Rev. A65, 021602 (2002).
[Crossref]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105 (2002).
[Crossref]

V. A. Sychugov, V. P. Torchigin, and M. Y. Tsvetkov, “Whispering-gallery waves in optical fibres,” Quantum Electron. 32, 738–742 (2002).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in Bose-Einstein condensates,” Phys. Rev. Lett. 89, 210406 (2002).
[Crossref]

2001 (2)

Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, “Nonlinear modes of a macroscopic quantum oscillator,” Phys. Lett. A 278, 225–230 (2001).
[Crossref]

V. A. Sychugov, L. N. Magdich, and V. P. Torchigin, “Interaction of whispering-gallery electromagnetic waves with acoustic waves in tapered quartz rods,” Quantum Electron. 31, 1089–1094 (2001).
[Crossref]

1997 (1)

1995 (3)

P. Franco, F. Fontana, I. Cristiani, M. Midrio, and M. Romagnoli, “Self-induced modulational-instability laser,” Opt. Lett. 20, 2009–2011 (1995).
[Crossref]

V. P. Torchigin, “Amplification of light pulses in waveguides with a periodically varying refractive index,” Quantum Electron. 25, 484–485 (1995).
[Crossref]

A. N. Buliuk, “Electro-optic modulation and frequency translation of light in a gyrotropic medium,” Quantum Electron. 25, 66–70 (1995).
[Crossref]

1993 (2)

V. P. Torchigin, “Possibility of using the interaction of acoustic and light waves in optical fibers to generate short light pulses,” Quantum Electron. 23, 235–240 (1993).
[Crossref]

V. P. Torchigin, “Possibility of generating coherent light via microwave modulation of the index of refraction of an optical fiber,” Quantum Electron. 23, 241–246 (1993).
[Crossref]

1989 (1)

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “A historical narrative of study of fiber grating solitons,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Springer, 2007).

Alexander, T. J.

Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, “Nonlinear modes of a macroscopic quantum oscillator,” Phys. Lett. A 278, 225–230 (2001).
[Crossref]

Baizakov, B. B.

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105 (2002).
[Crossref]

Buliuk, A. N.

A. N. Buliuk, “Electro-optic modulation and frequency translation of light in a gyrotropic medium,” Quantum Electron. 25, 66–70 (1995).
[Crossref]

Chernikov, S. V.

Churkin, D. V.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

Conforti, M.

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

Copie, F.

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

Cristiani, I.

de Valcarcel, G. J.

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in low-dimensional Bose-Einstein condensates,” Phys. Rev. A 70, 011601 (2004).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in Bose-Einstein condensates,” Phys. Rev. Lett. 89, 210406 (2002).
[Crossref]

Dianov, E. M.

Fedoruk, M. P.

Feng, L.

Fontana, F.

Franco, P.

Goutzoulis, A. P.

A. P. Goutzoulis and D. R. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Gulyaev, Y. V.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” UFN 176, 175–202 (2006).
[Crossref]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “A historical narrative of study of fiber grating solitons,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref]

Ivanov, O. V.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” UFN 176, 175–202 (2006).
[Crossref]

Kikuchi, K.

Kivshar, Y. S.

Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, “Nonlinear modes of a macroscopic quantum oscillator,” Phys. Lett. A 278, 225–230 (2001).
[Crossref]

Konotop, V. V.

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105 (2002).
[Crossref]

V. V. Konotop and M. Salerno, “Modulational instability in Bose-Einstein condensates in optical lattices,” Phys. Rev. A65, 021602 (2002).
[Crossref]

Korobko, D. A.

Kudlinski, A.

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

Lapin, V. A.

I. O. Zolotovskii, D. A. Korobko, V. A. Lapin, and D. I. Sementsov, “Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave,” Opt. Spectrosc. 121, 256–262 (2016).
[Crossref]

I. O. Zolotovskii, V. A. Lapin, and D. I. Sementsov, “Frequency modulation and compression of optical pulses in an optical fibre with a travelling refractive-index wave,” Quantum Electron. 46, 39–44 (2016).
[Crossref]

Li, Q.

Longhi, S.

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in low-dimensional Bose-Einstein condensates,” Phys. Rev. A 70, 011601 (2004).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in Bose-Einstein condensates,” Phys. Rev. Lett. 89, 210406 (2002).
[Crossref]

Love, J.

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

Magdich, L. N.

V. A. Sychugov, L. N. Magdich, and V. P. Torchigin, “Interaction of whispering-gallery electromagnetic waves with acoustic waves in tapered quartz rods,” Quantum Electron. 31, 1089–1094 (2001).
[Crossref]

Malomed, B. A.

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Mamyshev, P. V.

Midrio, M.

Moiseev, S. G.

Mussot, A.

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

Nakazawa, M.

Nakkeeran, K.

Nikitov, S. A.

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” UFN 176, 175–202 (2006).
[Crossref]

Okhotnikov, O. G.

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–548 (2009).
[Crossref]

Pape, D. R.

A. P. Goutzoulis and D. R. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Perego, A. M.

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

Prokhorov, A. M.

Pu, X.-Y.

Romagnoli, M.

Rubenchik, A. M.

Salerno, M.

V. V. Konotop and M. Salerno, “Modulational instability in Bose-Einstein condensates in optical lattices,” Phys. Rev. A65, 021602 (2002).
[Crossref]

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105 (2002).
[Crossref]

Sementsov, D. I.

I. O. Zolotovskii, V. A. Lapin, and D. I. Sementsov, “Frequency modulation and compression of optical pulses in an optical fibre with a travelling refractive-index wave,” Quantum Electron. 46, 39–44 (2016).
[Crossref]

I. O. Zolotovskii, D. A. Korobko, V. A. Lapin, and D. I. Sementsov, “Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave,” Opt. Spectrosc. 121, 256–262 (2016).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

Staliunas, K.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in low-dimensional Bose-Einstein condensates,” Phys. Rev. A 70, 011601 (2004).
[Crossref]

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in Bose-Einstein condensates,” Phys. Rev. Lett. 89, 210406 (2002).
[Crossref]

Suchkov, S. V.

Sukhorukov, A. A.

Sumetsky, M.

Sychugov, V. A.

V. A. Sychugov, V. P. Torchigin, and M. Y. Tsvetkov, “Whispering-gallery waves in optical fibres,” Quantum Electron. 32, 738–742 (2002).
[Crossref]

V. A. Sychugov, L. N. Magdich, and V. P. Torchigin, “Interaction of whispering-gallery electromagnetic waves with acoustic waves in tapered quartz rods,” Quantum Electron. 31, 1089–1094 (2001).
[Crossref]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “A historical narrative of study of fiber grating solitons,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref]

Tanemura, T.

Tarasov, N.

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “A historical narrative of study of fiber grating solitons,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref]

Torchigin, S. V.

V. P. Torchigin and S. V. Torchigin, “Optical solitons appearing during propagation of whispering-gallery waves,” Quantum Electron. 33, 913–918 (2003).
[Crossref]

Torchigin, V. P.

V. P. Torchigin and S. V. Torchigin, “Optical solitons appearing during propagation of whispering-gallery waves,” Quantum Electron. 33, 913–918 (2003).
[Crossref]

V. A. Sychugov, V. P. Torchigin, and M. Y. Tsvetkov, “Whispering-gallery waves in optical fibres,” Quantum Electron. 32, 738–742 (2002).
[Crossref]

V. A. Sychugov, L. N. Magdich, and V. P. Torchigin, “Interaction of whispering-gallery electromagnetic waves with acoustic waves in tapered quartz rods,” Quantum Electron. 31, 1089–1094 (2001).
[Crossref]

V. P. Torchigin, “Amplification of light pulses in waveguides with a periodically varying refractive index,” Quantum Electron. 25, 484–485 (1995).
[Crossref]

V. P. Torchigin, “Possibility of generating coherent light via microwave modulation of the index of refraction of an optical fiber,” Quantum Electron. 23, 241–246 (1993).
[Crossref]

V. P. Torchigin, “Possibility of using the interaction of acoustic and light waves in optical fibers to generate short light pulses,” Quantum Electron. 23, 235–240 (1993).
[Crossref]

Trillo, S.

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

Tsvetkov, M. Y.

V. A. Sychugov, V. P. Torchigin, and M. Y. Tsvetkov, “Whispering-gallery waves in optical fibres,” Quantum Electron. 32, 738–742 (2002).
[Crossref]

Turitsyn, S. K.

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

A. M. Rubenchik, S. K. Turitsyn, and M. P. Fedoruk, “Modulation instability in high power laser amplifiers,” Opt. Express 18, 1380–1388 (2010).
[Crossref]

Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, “Nonlinear modes of a macroscopic quantum oscillator,” Phys. Lett. A 278, 225–230 (2001).
[Crossref]

Wai, P. K. A.

Yoshida, E.

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–548 (2009).
[Crossref]

Zhang, Y.-X.

Zhu, K.

Zolotovskii, I. O.

I. O. Zolotovskii, V. A. Lapin, and D. I. Sementsov, “Frequency modulation and compression of optical pulses in an optical fibre with a travelling refractive-index wave,” Quantum Electron. 46, 39–44 (2016).
[Crossref]

I. O. Zolotovskii, D. A. Korobko, V. A. Lapin, and D. I. Sementsov, “Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave,” Opt. Spectrosc. 121, 256–262 (2016).
[Crossref]

D. A. Korobko, S. G. Moiseev, and I. O. Zolotovskii, “Induced modulation instability of surface plasmon polaritons,” Opt. Lett. 40,4619–4622 (2015).
[Crossref]

D. A. Korobko, O. G. Okhotnikov, and I. O. Zolotovskii, “High-repetition-rate pulse generation and compression in dispersion decreasing fibers,” J. Opt. Soc. Am. B 30, 2377–2386 (2013).
[Crossref]

Adv. Opt. Photonics (1)

A. Mussot, M. Conforti, S. Trillo, F. Copie, and A. Kudlinski, “Modulation instability in dispersion oscillating fibers,” Adv. Opt. Photonics 10, 1–42 (2018).
[Crossref]

J. Opt. Soc. Am. B (4)

J. Phys. B (1)

B. B. Baizakov, V. V. Konotop, and M. Salerno, “Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability,” J. Phys. B 35, 5105 (2002).
[Crossref]

Nat. Commun. (1)

N. Tarasov, A. M. Perego, D. V. Churkin, K. Staliunas, and S. K. Turitsyn, “Mode-locking via dissipative Faraday instability,” Nat. Commun. 7, 12441 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Opt. Spectrosc. (1)

I. O. Zolotovskii, D. A. Korobko, V. A. Lapin, and D. I. Sementsov, “Modulation instability of pulsed radiation in an optical waveguide in the presence of the traveling refractive index wave,” Opt. Spectrosc. 121, 256–262 (2016).
[Crossref]

Phys. D (1)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Phys. D 238, 540–548 (2009).
[Crossref]

Phys. Lett. A (1)

Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, “Nonlinear modes of a macroscopic quantum oscillator,” Phys. Lett. A 278, 225–230 (2001).
[Crossref]

Phys. Rev. (1)

V. V. Konotop and M. Salerno, “Modulational instability in Bose-Einstein condensates in optical lattices,” Phys. Rev. A65, 021602 (2002).
[Crossref]

Phys. Rev. A (1)

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in low-dimensional Bose-Einstein condensates,” Phys. Rev. A 70, 011601 (2004).
[Crossref]

Phys. Rev. Lett. (3)

K. Staliunas, S. Longhi, and G. J. de Valcarcel, “Faraday patterns in Bose-Einstein condensates,” Phys. Rev. Lett. 89, 210406 (2002).
[Crossref]

A. M. Perego, N. Tarasov, D. V. Churkin, S. K. Turitsyn, and K. Staliunas, “Pattern generation by dissipative parametric instability,” Phys. Rev. Lett. 116, 028701 (2016).
[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “A historical narrative of study of fiber grating solitons,” Phys. Rev. Lett. 56, 135–138 (1986).
[Crossref]

Quantum Electron. (8)

V. P. Torchigin, “Possibility of using the interaction of acoustic and light waves in optical fibers to generate short light pulses,” Quantum Electron. 23, 235–240 (1993).
[Crossref]

V. P. Torchigin, “Amplification of light pulses in waveguides with a periodically varying refractive index,” Quantum Electron. 25, 484–485 (1995).
[Crossref]

V. P. Torchigin, “Possibility of generating coherent light via microwave modulation of the index of refraction of an optical fiber,” Quantum Electron. 23, 241–246 (1993).
[Crossref]

A. N. Buliuk, “Electro-optic modulation and frequency translation of light in a gyrotropic medium,” Quantum Electron. 25, 66–70 (1995).
[Crossref]

I. O. Zolotovskii, V. A. Lapin, and D. I. Sementsov, “Frequency modulation and compression of optical pulses in an optical fibre with a travelling refractive-index wave,” Quantum Electron. 46, 39–44 (2016).
[Crossref]

V. A. Sychugov, L. N. Magdich, and V. P. Torchigin, “Interaction of whispering-gallery electromagnetic waves with acoustic waves in tapered quartz rods,” Quantum Electron. 31, 1089–1094 (2001).
[Crossref]

V. A. Sychugov, V. P. Torchigin, and M. Y. Tsvetkov, “Whispering-gallery waves in optical fibres,” Quantum Electron. 32, 738–742 (2002).
[Crossref]

V. P. Torchigin and S. V. Torchigin, “Optical solitons appearing during propagation of whispering-gallery waves,” Quantum Electron. 33, 913–918 (2003).
[Crossref]

UFN (1)

O. V. Ivanov, S. A. Nikitov, and Y. V. Gulyaev, “Cladding modes of optical fibers: properties and applications,” UFN 176, 175–202 (2006).
[Crossref]

Other (4)

A. P. Goutzoulis and D. R. Pape, Design and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

G. Agrawal, Nonlinear Fiber Optics, 4th ed. (Springer, 2007).

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

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Figures (6)

Fig. 1.
Fig. 1. (a) Quasi-linear and (b), (c) nonlinear dynamics of a Gaussian pulse simulated for the following parameters: (a) ${\tau _p} = {10^{ - 10}}\,\,{\rm{s}}$ , $ {P_0} = 0.1\,\,{\rm{W}} $ , $ {d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}} $ , $ {d_3} = {10^{ - 40}}\,\,{{\rm{s}}^3}/{\rm{m}} $ , $ R = {10^{ - 3}}\,\,{( {{\rm{W}} \cdot {\rm{m}}} )^{ - 1}} $ ; (b) ${\tau _p} = {10^{ - 9}}\,\,{\rm{s}}$ , $ {P_0} = 10\,\,{\rm{W}} $ , $ {d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}} $ $ {d_3} = 0 $ , $ R = {10^{ - 3}}\,\,{( {{\rm{W}} \cdot {\rm{m}}} )^{ - 1}} $ ; (c) ${\tau _p} = {10^{ - 9}}\,\,{\rm{s}}$ , ${\tau _R} = {10^{ - 14}}\,\,{\rm{s}}$ , $ {P_0} = 10\,\,{\rm{W}} $ , $ {d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}} $ , $ {d_3} = {10^{ - 41}}\,\,{{\rm{s}}^3}/{\rm{m}} $ , $ R = {10^{ - 3}}\,\,{( {{\rm{W}} \cdot {\rm{m}}} )^{ - 1}} $ , $ \Omega = {10^9}\,\,{{\rm{s}}^{ - 1}} $ , $ \beta = {10^7}\,\,{{\rm{m}}^{ - 1}} $ , $ \Delta n = {10^{ - 4}} $ .
Fig. 2.
Fig. 2. (a)–(c) Transformation of a quasi-continuous wave into ultrashort pulse train for different waveguide lengths: $ {d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}} $ , $ {d_3} = 0 $ , $ R = {10^{ - 3}}\,\,{( {{\rm{W}} \cdot {\rm{m}}} )^{ - 1}} $ , $ {P_0} = 0.1\,\,{\rm{W}} $ , $ \Omega = {10^9}\,\,{{\rm{s}}^{ - 1}} $ , $ \beta = {10^7}\,\,{{\rm{m}}^{ - 1}} $ , $ \Delta n = {10^{ - 4}} $ , $ {\Omega _{mod}} = {10^{12}}\,\,{{\rm{s}}^{ - 1}},\,\zeta = {10^{ - 3}} $ , ${\tau _R} = 5 \cdot {10^{ - 15}}{\rm{s}}$ .
Fig. 3.
Fig. 3. (a)–(c) Ultrashort pulse train generation at $ {d_2} = $ $- {10^{ - 26}}\,{{\rm{s}}^2}/{\rm{m}} \,\,{d_3} = {10^{ - 40}}\,{{\rm{s}}^3}/{\rm{m}}, R = ({10^{ - 3}},{10^{ - 2}},{10^{ - 1}})({\rm{W}} \cdot{\rm{m}})^{ - 1} $ , ${\tau _R} = 5 \cdot 10^{ - 15}\,\,{\rm{s}}$ ; other parameters are the same as in Fig. 2.
Fig. 4.
Fig. 4. (a), (b) Temporal dependence of superpulse power simulated for the lengths $ z \approx {z_s} = 497\,\,{\rm{m}} $ : (a) ${d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}}$ , $ {P_0} = 0.1\,\,{\rm{W}} $ , $ \Omega = {10^9}\,\,{{\rm{s}}^{ - 1}} $ , $ \beta = {10^7}\,\,{{\rm{m}}^{ - 1}} $ , $ \Delta n = {10^{ - 4}} $ , $ {d_3} = 0 $ , $ {\tau _R} = {510^{ - 15}} \,\,{\rm{s}} $ ; (b) $ {d_3} = {10^{ - 40}}\,\,{{\rm{s}}^3}/{\rm{m}} $ , $ R = {10^{ - 2}},\,\,{10^{ - 3}}\,\,( {{\rm{W}} \cdot {{\rm{m}}} )^{ - 1}} $ , ${\tau _R} = 5 \cdot {10^{ - 15}}\,\,{\rm{s}}$ (1, solid line; 2, dashed line).
Fig. 5.
Fig. 5. (a), (b) Evolution of the superpulse formation: $ {P_0} = 1\,\,{\rm{W}} $ , ${d_2} = - {10^{ - 26}}\,\,{{\rm{s}}^2}/{\rm{m}}$ , $ \Omega = {10^9}\,\,{{\rm{s}}^{ - 1}} $ , $ \beta = {10^7}\,\,{{\rm{m}}^{ - 1}} $ , $ \Delta n = {10^{ - 4}},\, {d_3} = $ $ {10^{ - 41}}\,\,{{\rm{s}}^3}/{\rm{m}} $ , $\varsigma = {10^{ - 3}}$ , ${\Omega_{\!\bmod }} = {10^{12}}\,\,{{\rm{s}}^{ - 1}}$ , $R = {10^{ - 3}}\,\,{( {{\rm{W}} \cdot {\rm{m}}} )^{ - 1}}$ ; (a) ${\tau _R} = 5 \cdot {10^{ - 15}}\,\,{\rm{s}}$ ; (b) ${\tau _R} = 5 \cdot {10^{ - 14}}\,\,{\rm{s}}$ .
Fig. 6.
Fig. 6. Propagation of the tunneling wave synchronized with RRIW over the cylinder surface.

Equations (25)

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n ( t , z ) = n 0 [ 1 m cos ( Ω t q z ) ] ,
A ( t , z = 0 ) = A 0 exp ( ( τ 0 2 + i α 0 ) t 2 / 2 ) ,
A z + v g 1 A t i d 2 2 2 A t 2 + d 3 6 3 A t 3 + i R ( | A | 2 τ R | A | 2 τ ) A = i Δ β A ,
Δ β = n 0 k 0 m cos ( Ω t q z )
A z i d 2 2 2 A τ 2 + d 3 6 3 A τ 3 + i R | A | 2 A = i β m cos [ Ω ( τ δ τ ) ] A ,
τ δ τ = τ ( ν m 1 ν g 1 ) z
cos [ Ω ( τ δ τ ) ] 1 Ω 2 ( τ δ τ ) 2 / 2
A z i d 2 2 2 A τ 2 + d 3 6 3 A τ 3 + i R ( | A | 2 τ R | A | 2 τ ) A = i ( S 1 + S 2 τ + S 3 τ 2 ) A ,
S 1 = m β ( 1 Ω 2 δ τ 2 / 2 ) , S 2 = m β Ω 2 δ τ , S 3 = m β Ω 2 / 2.
A ( z ) = a ( z ) exp [ i ( φ ( z ) + b ( z ) τ + α ( z ) τ 2 ) ] .
a z + d 2 ( b + 2 α τ ) a τ i d 2 2 2 a τ 2 + d 3 6 3 a τ 3 + i R ( | a | 2 τ R | a | 2 τ ) a = γ ( z ) a ,
b z + 2 α b d 2 = S 2 ,
α z + 2 d 2 α 2 = S 3 ,
γ ( z ) = i ( S 1 φ z b 2 d 2 + i α d 2 ) ,
a = a ¯ exp [ γ ( z ) d z ] .
a ¯ z + d 2 ( b + 2 α τ ) a ¯ τ i d 2 2 2 a ¯ τ 2 + d 3 6 3 a ¯ τ 3 + i R e f ( | a ¯ | 2 τ R | a ¯ | 2 τ ) a ¯ = 0 ,
f ( z ) = 1 cos ( | Ω | d 2 m β z ) .
z z s = π 2 | Ω | m β d 2 .
τ ( z ) = f ( z ) τ d 2 f ( z ) b ( z ) d z ,
a ¯ z i d 2 e f 2 2 a ¯ τ 2 + d 3 e f 6 3 a ¯ τ 3 + i R e f | a ¯ | 2 a ¯ = 0 ,
A ( 0 , τ ) = P 0 [ 1 + ζ cos ( Ω mod τ ) ] ,
g ( z , ω ) = 2 | Δ Ω d 2 e f | 2 R e f P 0 / | d 2 e f | Δ Ω 2 ,
E ( z , r , t , φ ) = A ( z , t ) Φ ( r , z , φ ) exp ( i ω t i 0 z k z ( z ) d z ) ,
A ξ i d 2 2 2 A τ 2 + d 3 6 3 A τ 3 + i R m | A | 2 A = i β m cos [ Ω ( τ δ τ ) ] A .
ξ ( ν g / ν m ) z ( c / n ν m ) z γ 1 z ,

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