Abstract

The delay and phase dependent behavior of a system for supercontinuum generation by using a microstructured fiber within a synchronously pumped ring resonator is presented numerically. The feedback introduced by the resonator led to an interaction of the supercontinuum with the following femtosecond laser pulses and thus to the formation of a nonlinear oscillator. Via the feedback phase different regimes of nonlinear dynamics, such as steady state, period multiplication, limit cycle and chaos can be adjusted systematically. The spectrum within one regime of nonlinear dynamics can additionally be modified independently from the regime of nonlinear dynamics.

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References

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  1. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
    [CrossRef]
  2. R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
    [CrossRef]
  3. 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]
  4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [CrossRef]
  5. P. M. Moselund, M. H. Frosz, C. L. Thomsen, and O. Bang, “Back-seeding of higher order gain processes in picosecond supercontinuum generation,” Opt. Express 16(16), 11954–11968 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
    [CrossRef]
  8. G. Sucha, D. S. Chemla, and S. R. Bolton, “Effects of cavity topology on the nonlinear dynamics of additive-pulse mode-locked lasers,” J. Opt. Soc. Am. B 15(12), 2847–2853 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. N. Brauckmann, M. Kues, T. Walbaum, P. Gross, and C. Fallnich, “Experimental investigations on nonlinear dynamics in supercontinuum generation with feedback,” Opt. Express 18(7), 7190–7202 (2010).
    [CrossRef] [PubMed]
  11. N. K. T. Photonics, “NL-PM-750 data sheet,” http://www.nktphotonics.com/files/files/NL-PM-750-090612.pdf .
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2010

2009

2008

2006

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

2005

2000

1998

1994

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
[CrossRef]

1970

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[CrossRef]

Agrawal, G. P.

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[CrossRef]

Bang, O.

Bolton, S. R.

Brauckmann, N.

Chemla, D. S.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Deng, Y.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Fallnich, C.

Frosz, M. H.

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Gross, P.

Jaspert, D.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
[CrossRef]

Knox, W. H.

Kues, M.

Lin, Q.

Lu, F.

Mitschke, F.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
[CrossRef]

Moselund, P. M.

Ranka, J. K.

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Steinmeyer, G.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
[CrossRef]

Stentz, A. J.

Sucha, G.

Thomsen, C. L.

Walbaum, T.

Windeler, R. S.

J. Opt. Soc. Am. B

Opt. Commun.

G. Steinmeyer, D. Jaspert, and F. Mitschke, “Observation of a period-doubling sequence in a nonlinear optical fiber ring cavity near zero dispersion,” Opt. Commun. 104(4-6), 379–384 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[CrossRef]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Other

N. K. T. Photonics, “NL-PM-750 data sheet,” http://www.nktphotonics.com/files/files/NL-PM-750-090612.pdf .

M. J. Litzkow, M. Livny, and M. W. Mutka, “Condor - a hunter of idle workstations,” in Proc. 8th Int. Conf. On Distributed Computing Systems (IEEE Computer Society Press, 1988), pp. 104–111.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the numerical SC feedback system: pulse propagating through the MSF (by solving the generalized nonlinear Schrödinger equation GNLSE), introduction of a variable delay and dispersion, superposition of a fraction (ε) of the SC and the next pump pulse. The magnitudes marked with tildes are the spectral electric fields, i.e., the Fourier transformed temporal electric fields. For details, see text.

Fig. 2
Fig. 2

Numerical simulation a) of a delay scan from −170 fs to 165 fs; blue: regimes of nonlinear dynamics, red: convolution function of the intensity profiles of the SC pulse after the first resonator roundtrip and the next laser pulse (pulse overlap), black: linear cross-correlation function of the two fields (energy of overlapped pulses), green: central wavelength of the overlapping SC interval; b) and c) zoom into the delay range from −5 fs to 45 fs; b) blue: regimes of nonlinear dynamics, black: linear cross-correlation function; c) corresponding optical spectra.

Fig. 3
Fig. 3

Three examples of phase dependent spectral evolutions, each spanning a delay interval of 2.6 fs (~2π) and recorded at different delay positions. The occurring nonlinear dynamics are noted on the right axis; a) delay interval from −1.8 fs to 0.4 fs; b) delay interval from 15.6 fs to 18.2 fs; c) delay interval from 38.8 fs to 41.4 fs. For details, see text.

Equations (1)

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C ( τ ) = | E p u m p ( t ) | 2 · | E r e s o n a t o r ( t τ ) | 2 d t .

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