Abstract

A system for supercontinuum generation by using a photonic crystal fiber within a synchronously pumped ring cavity is presented. The feedback led to an interaction of the generated supercontinuum with the following femtosecond laser pulses and thus to the formation of a nonlinear oscillator. The nonlinear dynamical behavior of this system was investigated experimentally and compared with numerical simulations. Steady state, period doubling and higher order multiplication of the repetition rate as well as limit cycle and chaotic behavior were observed in the supercontinuum generating system.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  26. M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, "Nonlinear dynamics of femtosecond supercontinuum generation with feedback," Opt. Express 17, 15827-15841 (2009).
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    [CrossRef]

2009

G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
[CrossRef]

M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, "Nonlinear dynamics of femtosecond supercontinuum generation with feedback," Opt. Express 17, 15827-15841 (2009).
[CrossRef] [PubMed]

2008

2007

2006

2005

2004

2003

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

2002

2001

2000

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]

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]

1995

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

1970

R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 °A via four-photon coupling in glass," Phys. Rev. Lett. 24, 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, 592-594 (1970).
[CrossRef]

1967

H. Degn, "Effect of Bromine Derivatives of Malonic Acid on the Oscillating Reaction of Malonic Acid, Cerium Ions and Bromate," Nature 213, 589-590 (1967).
[CrossRef]

Agrawal, G. P.

Aguirre, A. D.

Alfano, R. R.

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

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

Austin, D. R.

Bang, O.

Bolger, J. A.

Brauckmann, N.

Brown, T. G.

Buchholz, A.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Buchter, S. C.

Chudoba, C.

Coen, S.

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

J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
[CrossRef]

Cundiff, S. T.

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]

de Sterke, C. M.

Degn, H.

H. Degn, "Effect of Bromine Derivatives of Malonic Acid on the Oscillating Reaction of Malonic Acid, Cerium Ions and Bromate," Nature 213, 589-590 (1967).
[CrossRef]

Deng, Y.

Diddams, S. A.

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]

Dudley, J. M.

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

J. M. Dudley and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002).
[CrossRef]

Dudley, J.M.

G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
[CrossRef]

Eggleton, B. J.

G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
[CrossRef]

D.-I. Yeom, J. A. Bolger, G.D. Marshall, D. R. Austin, B. T. Kuhlmey, M. J. Withford, C. M. de Sterke, and B. J. Eggleton, "Tunable spectral enhancement of fiber supercontinuum," Opt. Lett. 32, 1644-1646 (2007).
[CrossRef] [PubMed]

Elder, A. D.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Fallnich, C.

Feder, K. S.

Frank, J. H.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Frosz, M. H.

Fujimoto, J.G.

Genty, G.

G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
[CrossRef]

E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, "Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers," Opt. Express 14, 7914-7923 (2006).
[CrossRef] [PubMed]

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

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Ghanta, R. K.

Groß, P.

Gu, W.

Hall, J. L.

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]

Hänsch, T.W.

T. Udem, R. Holzwarth, and T.W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Hänsel, M.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Hansen, K. P.

Hartl, I.

Heuer, M.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Holzwarth, R.

T. Udem, R. Holzwarth, and T.W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Jeyasekharan, A. D.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Jones, D. J.

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]

Kaivola, M.

E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, "Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers," Opt. Express 14, 7914-7923 (2006).
[CrossRef] [PubMed]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Kaminski, C. F.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Kimmelma, O.

Knight, J. C.

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Knox, W. H.

Ko, T. H.

Kopf, D.

Kues, M.

Kuhlmey, B. T.

Lederer, M.

Lehtonen, M.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Li, X. D.

Lin, Q.

Lu, F.

Ludvigsen, H.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

Marshall, G.D.

McConnell, G.

G. McConnell and E. Riis, "Ultra-short pulse compression using photonic crystal fibre," Appl. Phys. B 78, 557-563 (2004).
[CrossRef]

Mitschke, F.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Moselund, P. M.

Nicholson, J. W.

Nishizawa, N.

Popov, S.V.

Räikkönen, E.

Ranka, J. K.

Riis, E.

G. McConnell and E. Riis, "Ultra-short pulse compression using photonic crystal fibre," Appl. Phys. B 78, 557-563 (2004).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Schwache, A.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Seitz, W.

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, 592-594 (1970).
[CrossRef]

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

Steinmeyer, G.

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Stentz, A.

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]

Stentz, A. J.

Swartling, J.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Taylor, J. R.

Thomsen, C. L.

Travers, J. C.

Udem, T.

T. Udem, R. Holzwarth, and T.W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Venkitaraman, A. R.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Walbaum, T.

Westbrook, P. S.

Windeler, R. S.

Withford, M. J.

Yeom, D.-I.

Yu, S.

Zhang, H.

Zhang, J.

Zhu, Z.

Appl. Phys. B

G. McConnell and E. Riis, "Ultra-short pulse compression using photonic crystal fibre," Appl. Phys. B 78, 557-563 (2004).
[CrossRef]

G. Genty, J.M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009).
[CrossRef]

Appl. Phys. Lett.

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, "Supercontinuum generation in a highly birefringent microstructured fiber," Appl. Phys. Lett. 82, 2197-2199 (2003).
[CrossRef]

J. Microsc.

J. H. Frank, A. D. Elder, J. Swartling, A. R. Venkitaraman, A. D. Jeyasekharan, and C. F. Kaminski, "A white light confocal microscope for spectrally resolved multidimensional imaging," J. Microsc. 227, 203-215 (2007).
[CrossRef] [PubMed]

Nature

T. Udem, R. Holzwarth, and T.W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

H. Degn, "Effect of Bromine Derivatives of Malonic Acid on the Oscillating Reaction of Malonic Acid, Cerium Ions and Bromate," Nature 213, 589-590 (1967).
[CrossRef]

Opt. Express

F. Lu and W. H. Knox, "Generation of a broadband continuum with high spectral coherence in tapered single mode optical fibers," Opt. Express 12, 347-353 (2004).
[CrossRef] [PubMed]

Z. Zhu and T. G. Brown, "Effect of frequency chirping on supercontinuum generation in photonic crystal fibers," Opt. Express 12, 689-694 (2004).
[CrossRef] [PubMed]

A. D. Aguirre, N. Nishizawa, J.G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, "Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm," Opt. Express 14, 1145-1160 (2006).
[CrossRef] [PubMed]

E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, "Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers," Opt. Express 14, 7914-7923 (2006).
[CrossRef] [PubMed]

H. Zhang, S. Yu, J. Zhang, and W. Gu, "Effect of frequency chirp on supercontinuum generation in photonic crystal fibers with two zero-dispersion wavelengths," Opt. Express 15, 1147-1152 (2007).
[CrossRef] [PubMed]

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, 11954-11968 (2008).
[CrossRef] [PubMed]

M. Kues, N. Brauckmann, T. Walbaum, P. Groß, and C. Fallnich, "Nonlinear dynamics of femtosecond supercontinuum generation with feedback," Opt. Express 17, 15827-15841 (2009).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

G. Steinmeyer, A. Buchholz, M. Hänsel, M. Heuer, A. Schwache, and F. Mitschke, "Dynamical pulse shaping in a nonlinear resonator," Phys. Rev. A 52, 830-838 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. R. Alfano and S. L. Shapiro, "Emission in the region 4000 to 7000 °A via four-photon coupling in glass," Phys. Rev. Lett. 24, 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, 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, 1135-1184 (2006).
[CrossRef]

Science

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]

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[CrossRef] [PubMed]

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup: The laser system consisted of a Titanium:Sapphire laser, a Faraday isolator, and a prism pulse compressor; BS: pellicle beamsplitter, MSF: microstructured fiber, MO: 40x microscope objective, GS: uncoated glass substrate (For more details see text).

Fig. 2.
Fig. 2.

Steady state: (a) simulated phase space representation for a wavelength component at 800 nm at an input power of 5 mW, (b) corresponding radio frequency spectrum, and (c) measured radio frequency spectrum.

Fig. 3.
Fig. 3.

Simulation of the SC evolution for a period-2 cycle at an average input power of 5 mW: optical spectrum in dependence of the number of feedback round trips.

Fig. 4.
Fig. 4.

Period-2 cycle: (a) simulated phase space representation for a wavelength component at 800nm at an input power of 5 mW; (b) corresponding radio frequency spectrum and (c) measured radio frequency spectrum.

Fig. 5.
Fig. 5.

Measured radio frequency spectra of period multiplication of order three (P3) up to the order of eight (P8).

Fig. 6.
Fig. 6.

Limit cycle: a) simulated phase space representation for a wavelength component at 800 nm at an input power of 6mW; details are explained in the text. Radio frequency spectrum of b) simulated data for an input power of 6mW (the gray-shaded area is explained in the text) and c) measured data for an input power of 7.5 mW.

Fig. 7.
Fig. 7.

Chaos: (a) simulated phase space representation for a wavelength component at 800 nm at an input power of 25 mW; (b) corresponding radio frequency spectrum and (c) measured radio frequency spectrum.

Fig. 8.
Fig. 8.

Chaos: (a) examples of simulated optical spectra at an average input power of 25mW from round trip number 200 to 500 (gray lines) and of the average optical spectrum without (dotted red line) and with feedback (solid black line), (b) example of the measured average optical spectrum at an average input power of 25mW without (dotted red line) and with feedback (solid black line).

Equations (2)

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S rf ( ν rf ) = FT ( W ( n ) ) = FT ( S ( λ , n ) ) .
f k ( A ) = A ,

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