Abstract

We analyzed the amplification effect of orthogonally polarized pulse trapping in birefringent fibers both experimentally and numerically. Trapped pulses were amplified over a wide wavelength range of 1650-1800 nm accompanying the red-shift. The maximum effective gain was 26 dB for a 140 m-long low birefringent fiber. It was clarified that this amplification effect is caused by stimulated Raman scattering between orthogonally polarized pulses.

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
  2. J. C. Knight and D. V. Skryabin, “Nonlinear waveguide optics and photonic crystal fibers,” Opt. Express 15(23), 15365–15376 (2007).
    [CrossRef] [PubMed]
  3. N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009).
    [CrossRef]
  4. N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulse Generation Using Optical Fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999).
    [CrossRef]
  5. J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
    [CrossRef]
  6. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25(19), 1415–1417 (2000).
    [CrossRef]
  7. N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L365–L367 (2001).
    [CrossRef]
  8. X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26(6), 358–360 (2001).
    [CrossRef]
  9. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).
  10. M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14(18), 1011–1013 (1989).
    [CrossRef] [PubMed]
  11. N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27(3), 152–154 (2002).
    [CrossRef]
  12. N. Nishizawa and T. Goto, “Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,” Opt. Express 10(21), 1151–1160 (2002).
    [PubMed]
  13. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibers,” Nat. Photonics 1(11), 653–657 (2007).
    [CrossRef]
  14. J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008).
    [CrossRef] [PubMed]
  15. J. C. Travers, A. B. Rulkov, B. A. Cumberland, S. V. Popov, and J. R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400 W continuous wave fiber laser,” Opt. Express 16(19), 14435–14447 (2008).
    [CrossRef] [PubMed]
  16. J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34(2), 115–117 (2009).
    [CrossRef] [PubMed]
  17. S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17(16), 13588–13600 (2009).
    [CrossRef] [PubMed]
  18. N. Nishizawa and T. Goto, “Ultrafast all optical switching by use of pulse trapping across zero-dispersion wavelength,” Opt. Express 11(4), 359–365 (2003).
    [CrossRef] [PubMed]
  19. N. Nishizawa and K. Itoh, “Control of optical pulse at visible region using pulse trapping by soliton pulse in photonic crystal fibers,” Appl. Phys. Express 2, 062501 (2009).
    [CrossRef]
  20. N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002).
    [PubMed]
  21. N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express 13(20), 8128–8135 (2005).
    [CrossRef] [PubMed]
  22. C. R. Menyuk, M. N. Islam, and J. P. Gordon, “Raman effect in birefringent optical fibers,” Opt. Lett. 16(8), 566–568 (1991).
    [CrossRef] [PubMed]
  23. C.-J. Chen, C. R. Menyuk, M. N. Islam, and R. H. Stolen, “Numerical study of the Raman effect and its impact on soliton-dragging logic gates,” Opt. Lett. 16(21), 1647–1649 (1991).
    [CrossRef] [PubMed]
  24. N. Nishizawa, A. Muto, and T. Goto, “Measurement of chromatic dispersion of optical fibers using wavlength-tunable soliton pulses,” Jpn. J. Appl. Phys. 39(Part 1, No. 8), 4990–4992 (2000).
    [CrossRef]
  25. Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31(21), 3086–3088 (2006).
    [CrossRef] [PubMed]

2009 (4)

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009).
[CrossRef]

J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34(2), 115–117 (2009).
[CrossRef] [PubMed]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17(16), 13588–13600 (2009).
[CrossRef] [PubMed]

N. Nishizawa and K. Itoh, “Control of optical pulse at visible region using pulse trapping by soliton pulse in photonic crystal fibers,” Appl. Phys. Express 2, 062501 (2009).
[CrossRef]

2008 (2)

2007 (2)

J. C. Knight and D. V. Skryabin, “Nonlinear waveguide optics and photonic crystal fibers,” Opt. Express 15(23), 15365–15376 (2007).
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibers,” Nat. Photonics 1(11), 653–657 (2007).
[CrossRef]

2006 (1)

2005 (1)

2003 (1)

2002 (3)

2001 (2)

N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L365–L367 (2001).
[CrossRef]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26(6), 358–360 (2001).
[CrossRef]

2000 (3)

1999 (1)

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulse Generation Using Optical Fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999).
[CrossRef]

1991 (2)

1989 (1)

Agrawal, G. P.

Birks, T. A.

Chandalia, J. K.

Chen, C.-J.

Cumberland, B. A.

Eggleton, B. J.

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibers,” Nat. Photonics 1(11), 653–657 (2007).
[CrossRef]

Gordon, J. P.

Goto, T.

N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express 13(20), 8128–8135 (2005).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Ultrafast all optical switching by use of pulse trapping across zero-dispersion wavelength,” Opt. Express 11(4), 359–365 (2003).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,” Opt. Express 10(21), 1151–1160 (2002).
[PubMed]

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002).
[PubMed]

N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27(3), 152–154 (2002).
[CrossRef]

N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L365–L367 (2001).
[CrossRef]

N. Nishizawa, A. Muto, and T. Goto, “Measurement of chromatic dispersion of optical fibers using wavlength-tunable soliton pulses,” Jpn. J. Appl. Phys. 39(Part 1, No. 8), 4990–4992 (2000).
[CrossRef]

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulse Generation Using Optical Fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999).
[CrossRef]

Hill, S.

Islam, M. N.

Itoh, K.

N. Nishizawa and K. Itoh, “Control of optical pulse at visible region using pulse trapping by soliton pulse in photonic crystal fibers,” Appl. Phys. Express 2, 062501 (2009).
[CrossRef]

Knight, J. C.

Knox, W. H.

König, F.

Kosinski, S. G.

Kuklewicz, C. E.

Leonhardt, U.

Lin, Q.

Liu, X.

Menyuk, C. R.

Muto, A.

N. Nishizawa, A. Muto, and T. Goto, “Measurement of chromatic dispersion of optical fibers using wavlength-tunable soliton pulses,” Jpn. J. Appl. Phys. 39(Part 1, No. 8), 4990–4992 (2000).
[CrossRef]

Nishizawa, N.

N. Nishizawa and K. Itoh, “Control of optical pulse at visible region using pulse trapping by soliton pulse in photonic crystal fibers,” Appl. Phys. Express 2, 062501 (2009).
[CrossRef]

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009).
[CrossRef]

N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express 13(20), 8128–8135 (2005).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Ultrafast all optical switching by use of pulse trapping across zero-dispersion wavelength,” Opt. Express 11(4), 359–365 (2003).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002).
[PubMed]

N. Nishizawa and T. Goto, “Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,” Opt. Express 10(21), 1151–1160 (2002).
[PubMed]

N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27(3), 152–154 (2002).
[CrossRef]

N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L365–L367 (2001).
[CrossRef]

N. Nishizawa, A. Muto, and T. Goto, “Measurement of chromatic dispersion of optical fibers using wavlength-tunable soliton pulses,” Jpn. J. Appl. Phys. 39(Part 1, No. 8), 4990–4992 (2000).
[CrossRef]

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulse Generation Using Optical Fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999).
[CrossRef]

Poole, C. D.

Popov, S. V.

Ranka, J. K.

Rulkov, A. B.

Russell, P. St. J.

Skryabin, D. V.

J. C. Knight and D. V. Skryabin, “Nonlinear waveguide optics and photonic crystal fibers,” Opt. Express 15(23), 15365–15376 (2007).
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibers,” Nat. Photonics 1(11), 653–657 (2007).
[CrossRef]

Stentz, A. J.

Stolen, R. H.

Stone, J. M.

Taylor, J. R.

Travers, J. C.

Ukai, Y.

Wadsworth, W. J.

Windeler, R. S.

Xu, C.

Appl. Phys. Express (1)

N. Nishizawa and K. Itoh, “Control of optical pulse at visible region using pulse trapping by soliton pulse in photonic crystal fibers,” Appl. Phys. Express 2, 062501 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Nishizawa and T. Goto, “Compact System of Wavelength-Tunable Femtosecond Soliton Pulse Generation Using Optical Fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999).
[CrossRef]

Jpn. J. Appl. Phys. (2)

N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L365–L367 (2001).
[CrossRef]

N. Nishizawa, A. Muto, and T. Goto, “Measurement of chromatic dispersion of optical fibers using wavlength-tunable soliton pulses,” Jpn. J. Appl. Phys. 39(Part 1, No. 8), 4990–4992 (2000).
[CrossRef]

Nat. Photonics (1)

A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibers,” Nat. Photonics 1(11), 653–657 (2007).
[CrossRef]

Opt. Express (8)

J. M. Stone and J. C. Knight, “Visibly “white” light generation in uniform photonic crystal fiber using a microchip laser,” Opt. Express 16(4), 2670–2675 (2008).
[CrossRef] [PubMed]

J. C. Travers, A. B. Rulkov, B. A. Cumberland, S. V. Popov, and J. R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400 W continuous wave fiber laser,” Opt. Express 16(19), 14435–14447 (2008).
[CrossRef] [PubMed]

S. Hill, C. E. Kuklewicz, U. Leonhardt, and F. König, “Evolution of light trapped by a soliton in a microstructured fiber,” Opt. Express 17(16), 13588–13600 (2009).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Ultrafast all optical switching by use of pulse trapping across zero-dispersion wavelength,” Opt. Express 11(4), 359–365 (2003).
[CrossRef] [PubMed]

J. C. Knight and D. V. Skryabin, “Nonlinear waveguide optics and photonic crystal fibers,” Opt. Express 15(23), 15365–15376 (2007).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Characteristics of pulse trapping by ultrashort soliton pulse in optical fibers across zerodispersion wavelength,” Opt. Express 10(21), 1151–1160 (2002).
[PubMed]

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002).
[PubMed]

N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express 13(20), 8128–8135 (2005).
[CrossRef] [PubMed]

Opt. Lett. (9)

C. R. Menyuk, M. N. Islam, and J. P. Gordon, “Raman effect in birefringent optical fibers,” Opt. Lett. 16(8), 566–568 (1991).
[CrossRef] [PubMed]

C.-J. Chen, C. R. Menyuk, M. N. Islam, and R. H. Stolen, “Numerical study of the Raman effect and its impact on soliton-dragging logic gates,” Opt. Lett. 16(21), 1647–1649 (1991).
[CrossRef] [PubMed]

Q. Lin and G. P. Agrawal, “Raman response function for silica fibers,” Opt. Lett. 31(21), 3086–3088 (2006).
[CrossRef] [PubMed]

X. Liu, C. Xu, W. H. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, “Soliton self-frequency shift in a short tapered air-silica microstructure fiber,” Opt. Lett. 26(6), 358–360 (2001).
[CrossRef]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25(1), 25–27 (2000).
[CrossRef]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25(19), 1415–1417 (2000).
[CrossRef]

M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14(18), 1011–1013 (1989).
[CrossRef] [PubMed]

N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27(3), 152–154 (2002).
[CrossRef]

J. C. Travers and J. R. Taylor, “Soliton trapping of dispersive waves in tapered optical fibers,” Opt. Lett. 34(2), 115–117 (2009).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).

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

Supplementary Material (2)

» Media 1: MOV (1480 KB)     
» Media 2: MOV (1023 KB)     

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for pulse trapping. HWP, half wave plate; WC-PMF, wavelength conversion PMF; PBS, polarizing beam splitter; DL, delay line.

Fig. 2
Fig. 2

Numerical results of evolutions of the control (blue line) and the signal pulses (red line) in the propagation along a 200 m PMF: (a) spectra (Media 1), (b) temporal waveforms (Media 2). The input energies of the control and the signal pulses are 250 pJ and 4 pJ, respectively. The group velocity matching condition is satisfied. The zero position of the time scales is always adjusted to the peak point of the control pulse.

Fig. 3
Fig. 3

Representative output spectra from the fast axis of PMF. The solid line shows the trapped and the non-trapped signal pulse when the control and signal pulse is coupled into the PMF. The broken line shows the signal pulse when only the signal pulse is present, which corresponds to the original signal pulse. The dotted line on the trapped signal pulse is the sech2 fit. Inset shows a magnified view. The difference component between the original signal and the non-trapped signal pulses corresponds to the effective signal pulse.

Fig. 4
Fig. 4

(a) Effective gain Geff as a function of energy of effective signal pulses in PMF1-3. The filled symbols and the dashed lines are the experimental and the numerical results, respectively: circles, PMF1; squares, PMF2; triangles, PMF3. (b) Raman gain spectra for a silica fiber [25] at a pump wavelength of 1.65 μm when two pulses (pump and Stokes pulses) are co-polarized (g //) and orthogonally polarized (g ). The filled circular, square, and triangular symbols are the obtained Raman gain coefficients used in the numerical analyses for PMF1-3, respectively.

Fig. 5
Fig. 5

(a) Relative delay time of PMF1 as a function of wavelength. Wavelength relations (i)-(iv), which are used for the experimental analyses, satisfy the group velocity (the group delay) matching conditions. (b) Wideband amplification characteristics of pulse trapping; the symbols show the input-output gain GIO for small signal pulses under the wavelength relations (i)-(iv). The energies of control pulses are 205-250 pJ at the output. The dashed lines show the numerical results for a variety of input energies of the control pulses, Eic .

Tables (2)

Tables Icon

Table 1 Parameters of sample PMFs at a wavelength of 1550 nm

Tables Icon

Table 2 Conditions of the input pulses

Equations (4)

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E ( z , t ) = 1 2 x ^ A exp [ i β 0 A z ω 0 A t ] + 1 2 y ^ B exp [ i β 0 B z ω 0 B t ] ,
A z + i β 2 A 2 2 A T 2 β 3 A 6 3 A T 3 + α A 2 A = i γ A ( | A | 2 A + 2 3 | B | 2 A + i ω 0 A T ( | A | 2 A ) T R | A | 2 T A ) g A 2 | B | 2 A ,
B z d B T + i β 2 B 2 2 B T 2 β 3 B 6 3 B T 3 + α B 2 B = i γ B ( | B | 2 B + 2 3 | A | 2 B + i ω 0 B T ( | B | 2 B ) T R | B | 2 T B ) + g B 2 | A | 2 B ,
g A = ω 0 A ω 0 B g B = g R A e f f ,

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