Abstract

We experimentally and numerically investigate femtosecond pulse propagation in a microstructured optical fiber consisting of a silica core surrounded by air holes which are filled with a high index fluid. Such fibers have discrete transmission bands which exhibit strong dispersion arising from the scattering resonances of the high index cylinders. We focus on nonlinear propagation near the zero dispersion point of one of these transmission bands. As expected from theory, we observe propagation of a red-shifted soliton which radiates dispersive waves. Using frequency resolved optical gating, we measure the pulse evolution in the time and frequency domains as a function of both fiber length and input power. Experimental data are compared with numerical simulations.

© 2005 Optical Society of America

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  1. 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, 25-27 (2000).
    [CrossRef]
  2. F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth and P. St. J. Russell, "Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber," Opt. Lett. 26, 1158-1160 (2001).
    [CrossRef]
  3. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
    [CrossRef] [PubMed]
  4. S. O. Konorov, A. B. Fedotov and A. M. Zheltikov, "Enhanced four-wave mixing in a hollow-core photonic crystal fiber," Opt. Lett. 28, 1448-1450 (2003).
    [CrossRef] [PubMed]
  5. F. Benabid, J. C. Knight, G. Antonopoulos and P. St. J. Russell, "Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber," Science 298, 399-402 (2002).
    [CrossRef] [PubMed]
  6. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch and A. L. Gaeta, "Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers," Science 301, 1702-1704 (2003).
    [CrossRef] [PubMed]
  7. D. V. Skryabin, F. Luan, J. C. Knight and P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. P. Steinvurzel, B. T. Kuhlmey, T. P. White, M. J. Steel, C. M. de Sterke and B. J. Eggleton, "Long wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424</a>.
    [CrossRef] [PubMed]
  13. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
    [CrossRef] [PubMed]
  14. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. B. Cordeiro, F. Luan and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309</a>.
    [CrossRef] [PubMed]
  15. N. M. Litchinitser, A. K. Abeeluck, C. Headley and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
    [CrossRef]
  16. T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
    [CrossRef]
  17. M. A. Duguay, Y. Kokubun, T. L. Koch and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
    [CrossRef]
  18. C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks and P. St. J. Russell, "Octave supercontinuum generated in tapered conventional fibres by a nanosecond 1064 nm laser," presented at Conference on Lasers and Electro-Optics (San Francisco, 2004) paper CThC2.
  19. R. Zhang, J. Teipel, X. Zhang, D. Nau and H. Giessen, "Group velocity dispersion of tapered fibers immersed in different liquids," Opt. Express 12, 1700-1707 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1700">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1700</a>.
    [CrossRef] [PubMed]
  20. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen and B. J. Eggleton, "Nonlinear propagation effects in anti-resonant high-index inclusion photonic crystal fibers," Opt. Lett. (to be published).
    [PubMed]
  21. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Amer. B 19, 2322-2330 (2002).
    [CrossRef]
  22. P. K. A. Wai, C. R. Menyuk, H. H. Chen and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a single mode fiber," Opt. Lett. 12, 628-630 (1987).
    [CrossRef] [PubMed]
  23. A. S. Gouveia-Neto, M. E. Faldon and J. R. Taylor, "Solitons in the region of the minimum group-velocity dispersion of single-mode optical fibers," Opt. Lett. 13, 770-772 (1988).
    [CrossRef] [PubMed]
  24. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, San Diego, 1995).
  25. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana and P. St. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.</a>
    [CrossRef] [PubMed]
  26. N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995).
    [CrossRef] [PubMed]
  27. A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
    [CrossRef] [PubMed]
  28. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, (Kluwer Academic Publishers, Boston, 2002).
    [CrossRef]
  29. I. Cristiani, R. Tediosi, L. Tartara and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124</a>.
    [CrossRef] [PubMed]

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch and L. Pfeiffer, "Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures," Appl. Phys. Lett. 49, 13-15 (1986).
[CrossRef]

Conference on Lasers and Electro-Optics (1)

C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks and P. St. J. Russell, "Octave supercontinuum generated in tapered conventional fibres by a nanosecond 1064 nm laser," presented at Conference on Lasers and Electro-Optics (San Francisco, 2004) paper CThC2.

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Amer. B (1)

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Amer. B 19, 2322-2330 (2002).
[CrossRef]

Nature (1)

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Opt. Express (7)

T. T. Larsen, A. Bjarklev, D. S. Hermann and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2589">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2589</a>.
[CrossRef] [PubMed]

I. Cristiani, R. Tediosi, L. Tartara and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-124</a>.
[CrossRef] [PubMed]

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana and P. St. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-299.</a>
[CrossRef] [PubMed]

R. Zhang, J. Teipel, X. Zhang, D. Nau and H. Giessen, "Group velocity dispersion of tapered fibers immersed in different liquids," Opt. Express 12, 1700-1707 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1700">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1700</a>.
[CrossRef] [PubMed]

P. Steinvurzel, B. T. Kuhlmey, T. P. White, M. J. Steel, C. M. de Sterke and B. J. Eggleton, "Long wavelength anti-resonant guidance in high index inclusion microstructured fibers," Opt. Express 12, 5424-5433 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5424</a>.
[CrossRef] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. B. Cordeiro, F. Luan and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-309</a>.
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight and P. S. J. Russell, "Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modeling," Opt. Express 12, 6498-6507 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-26-6498">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-26-6498</a>.
[CrossRef] [PubMed]

Opt. Lett. (10)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D. M. Bird, J. C. Knight and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen and B. J. Eggleton, "Nonlinear propagation effects in anti-resonant high-index inclusion photonic crystal fibers," Opt. Lett. (to be published).
[PubMed]

S. O. Konorov, A. B. Fedotov and A. M. Zheltikov, "Enhanced four-wave mixing in a hollow-core photonic crystal fiber," Opt. Lett. 28, 1448-1450 (2003).
[CrossRef] [PubMed]

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, 25-27 (2000).
[CrossRef]

P. K. A. Wai, C. R. Menyuk, H. H. Chen and Y. C. Lee, "Soliton at the zero-group-dispersion wavelength of a single mode fiber," Opt. Lett. 12, 628-630 (1987).
[CrossRef] [PubMed]

A. S. Gouveia-Neto, M. E. Faldon and J. R. Taylor, "Solitons in the region of the minimum group-velocity dispersion of single-mode optical fibers," Opt. Lett. 13, 770-772 (1988).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996).
[CrossRef] [PubMed]

F. G. Omenetto, A. J. Taylor, M. D. Moores, J. Arriaga, J. C. Knight, W. J. Wadsworth and P. St. J. Russell, "Simultaneous generation of spectrally distinct third harmonics in a photonic crystal fiber," Opt. Lett. 26, 1158-1160 (2001).
[CrossRef]

N. M. Litchinitser, A. K. Abeeluck, C. Headley and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, "Cherenkov radiation emitted by solitons in optical fibers," Phys. Rev. A 51, 2602-2607 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. V. Husakou and J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers," Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef] [PubMed]

Science (3)

F. Benabid, J. C. Knight, G. Antonopoulos and P. St. J. Russell, "Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber," Science 298, 399-402 (2002).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch and A. L. Gaeta, "Generation of Megawatt Optical Solitons in Hollow-Core Photonic Band-Gap Fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight and P. St. J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic Press, San Diego, 1995).

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, (Kluwer Academic Publishers, Boston, 2002).
[CrossRef]

Supplementary Material (2)

» Media 1: MPG (370 KB)     
» Media 2: MPG (334 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic of ARROW-PCF geometry (b) measured (black) and simulated (red) transmission through ARROW-PCF sample and corresponding simulated β2, and (c) electron microscope image of PCF used in experiment.

Fig. 2.
Fig. 2.

(a) Experimental setup for dispersion measurement, with a microchip Nd:YAG laser pumping the PCF supercontinuum source. MO=microscope objective, BS=beam splitter, R=retroreflector, M=mirror, and SMF=single mode fiber. The retroreflector is mounted to a motorized stage so that the reference arm path length can be adjusted to optimize the interference fringe spacing. (b) Left axis: relative delay (squares) measured from interference pattern and 4th order polynomial fit (black line). Right axis: β2 derived from group delay measurement (blue line) and from multipole simulations (red line).

Fig. 3.
Fig. 3.

Experimental Setup. MO: Microscope Objective; AL: Achromatic Lens

Fig. 4.
Fig. 4.

Movie of the evolution of the FROG Trace with (a) increasing fiber length (0–350 mm) and fixed average power (30mW) (370 kB) and (b) fixed fiber length (180 mm) and increasing average power (0–70 mW) (334 kB).

Fig. 5.
Fig. 5.

(a) Spectral and (b) temporal evolution of the pulses as they propagate inside the ARROW-PCF. The average input power is fixed at 30 mW. Left pictures: Results obtained from NLSE simulations. Right pictures: Data retrieved from the measured FROG-Traces.

Fig. 6.
Fig. 6.

(a) Spectral and (b) temporal intensity and phase of the ultrashort laser pulses after propagation in a 250 mm long ARROW-PCF. Red line: Direct measurement of the spectral intensity. Blue lines: Retrieved from the measured FROG-Trace. Black lines: Results of the NLSE simulations.

Fig. 7.
Fig. 7.

(a) Spectral and (b) temporal evolution of the pulses in the ARROW-PCF as a function of input power. The fiber length is fixed at 180 mm. Left pictures: Results obtained from NLSE simulations. Right pictures: Data retrieved from the measured FROG traces.

Fig. 8.
Fig. 8.

(a) Black line: Expected soliton frequency shift after Eq. (4). Blue line: Extracted from the NLSE simulations. Red dots: Measured. (b) Phase difference between a soliton centered at λs=783 nm and radiation at wavelength λ and corresponding measured spectrum. Dotted line: Phase difference without including the nonlinear term.

Equations (6)

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

L NL = 1 γ · P ̂ and L D = τ 0 2 β 2
N = L D L NL
L D = τ 0 3 β 3 and N = L D L NL
Δ ω = 1 β 3 [ τ 0 2 γ P ̂ 2 · 1.5 2 + sgn ( β 3 ) β 2 ]
Δ Φ = β NSR β S ( ω NSR ω S ) v s γ · P ̂ .
Δ Φ = n = 2 1 n ! β n ( ω NSR ω S ) n γ · P ̂ .

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