Abstract

It is possible to modify pulse propagation and nonlinear interactions in microstructured fibers using phase-tailored ultrashort laser pulses. We experimentally investigate how pre-shaping of the input laser pulse can be used to alter its evolution and subsequent output characteristics. We also demonstrate how adaptive pulse shaping can be used to control the output properties of the pulse spectrum. Numerical simulations based on the nonlinear Schrodinger equation predict the output spectral profiles of the propagated pulse in good agreement with experimental results, and elucidate the relevant processes producing the optimal output.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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IEEE J. Quantum Electron. (2)

K. J. Blow and D. Wood, "Theoretical description of transient stimulated raman-scattering in optical fibers,�?? IEEE J. Quantum Electron. 25, 2665-2673 (1989).
[CrossRef]

M. Stern, J. P. Heritage and E. W. Chase, "Grating compensation of third-order fiber dispersion,�?? IEEE J. Quantum Electron. 28, 2742-2748 (1992).
[CrossRef]

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

J. Opt. Soc. B (3)

K. M. Hilligsoe, H. N. Paulsen, J. Thogersen, S. R. Keiding SR, and J. J. Larsen, "Initial steps of supercontinuum generation in photonic crystal fibers,�?? J. Opt. Soc. B 20, 1887�??1893 (2003).
[CrossRef]

A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, "Spectral shaping of supercontinuum in a cobweb photonic-crystal fiber with sub-20-fs pulses,�?? J. Opt. Soc. B 19, 2165�??2170 (2002).
[CrossRef]

A. Rundquist, A. Efimov, and D. H. Reitze, "Rapid mask synthesis using the Gerchberg-Saxton algorithm for femtosecond pulse shaping,�?? J. Opt. Soc. B 19, 2468-2478 (2002).
[CrossRef]

Nature (1)

R. A. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov , M. M. Murnane, and H. C. Kapteyn, "Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays,�?? Nature 406, 164-166 (2000).
[CrossRef] [PubMed]

Opt. Lett. (11)

D. H. Reitze, S. Kazamias, F. Weihe, G. Mullot, D. Douillet, F. Aug, O. Albert, V. Ramanathan, J. P. Chambaret, D. Hulin, and P. Balcou, "Enhancement of high order harmonic generation at tuned wavelengths via adaptive control,�?? Opt. Lett. 29, 86-88 (2004).
[CrossRef] [PubMed]

Fiorenzo G. Omenetto, Antoinette J. Taylor, Mark D. Moores, and D. H. Reitze, "Adaptive control of nonlinear femtosecond pulse propagation in optical fibers,�?? Opt. Lett. 26, 938-940 (2001).
[CrossRef]

A. Efimov, A. J. Taylor, F. G. Omenetto, E. Vanin, "Adaptive control of femtosecond soliton self-frequency shift in fibers,�?? Opt. Lett. 29, 271-273 (2004).
[CrossRef] [PubMed]

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,�?? Opt. Lett. 26, 608�??610 (2001).
[CrossRef]

A. J. Gaeta, "Nonlinear propagation and continuum generation in microstructured optical fibers,�?? Opt. Lett. 27, 924�??926 (2002).
[CrossRef]

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O�??Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, "Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,�?? Opt. Lett. 27, 1174�??1176 (2002).
[CrossRef]

Jinendra K. Ranka, Robert S. Windeler, and Andrew J. Stentz, �??Visible continuum generation in airsilica microstructure optical fibers with anomalous dispersion at 800 nm,�?? Opt. Lett. 25, 25�??27 (1999).
[CrossRef]

T. A. Birks, J. C. Knight, P. S. Russell, "Endlessly single-mode photonic crystal fiber,�?? Opt. Lett. 22, 961�??963 (1997).
[CrossRef] [PubMed]

J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, "Four-wave mixing in microstructure fiber,�?? Opt. Lett. 26, 1048�??1050 (2001).
[CrossRef]

M. Fiorentino, J. E. Sharping, P. Kumar, A. Porzio, and R. S. Windeler, "Soliton squeezing in microstructure fiber,�?? Opt. Lett. 27, 649�??651 (2002).
[CrossRef]

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

Phys. Rev. Lett. (4)

R. Holzwarth, T. Udem, T. W. Hansch, J. C. Knight, W. J. Wadsworth, P. S. J. Russell "Optical frequency synthesizer for precision spectroscopy,�?? Phys. Rev. Lett. 85, 2264�??2267 (2000).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. S. J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,�?? Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

A. V. Husakou, J. Herrmann, "Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,�?? Phys. Rev. Lett. 87, 2264�??2267 (2000).

R. S. Judson and H. Rabitz, "Teaching lasers to control molecules,�?? Phys. Rev. Lett. 68, 1500-1503 (1992).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

A. M. Weiner, "Femtosecond optical pulse shaping and processing,�?? Prog. Quantum Electron. 19, 161�??237 (1995).
[CrossRef]

Science (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S.Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,�?? Science 288, 635�??639 (2000).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

Supplementary Material (1)

» Media 1: AVI (324 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

(a) The bandwidth of experimentally measured output spectra from a 5 cm long MSF as a function of the input pulse cubic phase. Inset: output spectra from a 5 cm long MSF as a function of the input pulse cubic phase. (b) The experimentally observed output spectra from a 70 cm MSF as a function of the input pulse cubic phase.

Fig. 2.
Fig. 2.

(a) The experimentally observed output spectrum from a 70 cm MSF obtained with a transform-limited pulse (black curve), and forward (red curve) and backward (green curve) ‘ramp’ pulses . Inset: the temporal intensity and phase profile of the ‘ramp’ pulse. (b) NSLE simulation of the supercontinuum from a transform-limited pulse (black curve) and the shaped ‘ramp’ pulse (red curve).

Fig. 3.
Fig. 3.

Adaptive optimization of spectral bandwidth from using an 2 nJ, 30 fs pulse. (a) Evolution of the cost function during the optimization. (b) The experimentally observed evolution of the output spectrum, showing increased bandwidth as the optimization progresses.

Fig. 4.
Fig. 4.

Experimentally adaptive generations of SFS soliton corresponding to different target soliton wavelengths and widths. (a) Three soliton generations with different center wavelengths and a fixed width. (b) Three soliton generations with a fixed center wavelength and different widths.

Fig. 5.
Fig. 5.

An example of the experimentally determined optimizing driving pulse for soliton generation in frequency domain and time domain. (a) The spectral intensity and phase of the driving pulse. (b) The temporal intensity and phase of the driving pulse. Inset: temporal intensity on a larger time scale.

Fig. 6.
Fig. 6.

Spectra comparison of experimentally optimized soliton generation and simulated soliton using experimentally determined driving input pulse.

Fig. 7.
Fig. 7.

Simulation of control of soliton formation in a MSF (323 kb). The upper panel displays the evolution of the spectrum; the lower panel displays the temporal evolution in the co-moving frame of the pulse. Only 400 fs of the pulse is shown for clarity.

Equations (6)

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

A ( z , t ) z + α 2 A ( z , t ) + i = 1 β i ( i ) A ( z , t ) t ( i ) = ( 1 + i ω 0 t ) ( A ( z , t ) + R ( t ) A ( z , t t ) 2 dt )
A ( z , t ) = A ( z , t ) exp ( ( z , t ) )
R ( t ) = ( 1 f r ) δ ( t ) + f r h r ( t )
h r ( t ) = τ 1 2 + τ 2 2 τ 1 τ 2 exp ( t τ 2 ) sin ( t τ 1 )
J = 500 nm 570 nm I ( λ ) + 950 nm 1020 nm I ( λ )
J = W λ exp [ ( λ λ target σ λ ) 2 ] + W Δ λ 1 + ( Δ λ Δ λ target σ Δ λ ) 2

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