Abstract

Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented.

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2012 (2)

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibres for pulse generation and optical processing,” Int. J. Opt.2012, 159057 (2012), doi:.
[CrossRef]

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun.285(21-22), 4493–4499 (2012), doi:.
[CrossRef]

2011 (5)

2010 (2)

H. Byun, M. Y. Sander, A. Motamedi, H. Shen, G. S. Petrich, L. A. Kolodziejski, E. P. Ippen, and F. X. Kärtner, “Compact, stable 1 GHz femtosecond Er-doped fiber lasers,” Appl. Opt.49(29), 5577–5582 (2010), doi:.
[CrossRef] [PubMed]

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

2009 (2)

D. Krcmarík, R. Slavík, Y. Park, and J. Azaña, “Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter,” Opt. Express17(9), 7074–7087 (2009), doi:.
[CrossRef] [PubMed]

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
[CrossRef]

2008 (4)

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

T. Hirooka, M. Nakazawa, and K. Okamoto, “Bright and dark 40 GHz parabolic pulse generation using a picosecond optical pulse train and an arrayed waveguide grating,” Opt. Lett.33(10), 1102–1104 (2008), doi:.
[CrossRef] [PubMed]

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron.44(12), 1196–1203 (2008), doi:.
[CrossRef]

A. Bartels, D. Heinecke, and S. A. Diddams, “Passively mode-locked 10 GHz femtosecond Ti:sapphire laser,” Opt. Lett.33(16), 1905–1907 (2008), doi:.
[CrossRef] [PubMed]

2007 (3)

2006 (3)

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber Bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006), doi:.
[CrossRef]

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

C. Finot, F. Parmigiani, P. Petropoulos, and D. J. Richardson, “Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime,” Opt. Express14(8), 3161–3170 (2006), doi:.
[CrossRef] [PubMed]

2005 (4)

2004 (2)

2001 (1)

1992 (1)

1990 (1)

1989 (1)

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[CrossRef]

Agrawal, G. P.

Anderson, D.

Andrade Lucio, J. A.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Azaña, J.

Bale, B. G.

Bartels, A.

Bartelt, H.

Billet, C.

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Blow, K. J.

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “Time domain all-optical signal processing at a RZ optical receiver,” Opt. Express13(16), 6217–6227 (2005), doi:.
[CrossRef] [PubMed]

K. J. Blow and D. Wood, “Theoretical description of transient stimulated scattering in optical fibers,” IEEE J. Quantum Electron.25(12), 2665–2673 (1989), doi:.
[CrossRef]

Boscolo, S.

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibres for pulse generation and optical processing,” Int. J. Opt.2012, 159057 (2012), doi:.
[CrossRef]

B. G. Bale, S. Boscolo, K. Hammani, and C. Finot, “Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime,” J. Opt. Soc. Am. B28(9), 2059–2065 (2011), doi:.
[CrossRef]

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron.44(12), 1196–1203 (2008), doi:.
[CrossRef]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “Time domain all-optical signal processing at a RZ optical receiver,” Opt. Express13(16), 6217–6227 (2005), doi:.
[CrossRef] [PubMed]

Bosman, G. W.

Byun, H.

Chong, A.

Desaix, M.

Diddams, S. A.

Dudley, J. M.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
[CrossRef]

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys.3(9), 597–603 (2007), doi:.
[CrossRef]

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Ellis, A. D.

Ferriere, R.

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Finot, C.

Guryev, I. V.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Hammani, K.

Hartung, A.

Heidt, A. M.

Heinecke, D.

Hirooka, T.

Hult, J.

Iakushev, S. O.

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun.285(21-22), 4493–4499 (2012), doi:.
[CrossRef]

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Ibarra Manzano, O. G.

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Ibsen, M.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber Bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006), doi:.
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generations based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol.19(5), 746–752 (2001), doi:.
[CrossRef]

Ippen, E. P.

Jin, C.

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

Kärtner, F. X.

Kibler, B.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
[CrossRef]

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Kolodziejski, L. A.

Koshiba, M.

Krcmarík, D.

Krok, P.

Kuznetsova, L.

Lacourt, P.-A.

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Larger, L.

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

Latkin, A. I.

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron.44(12), 1196–1203 (2008), doi:.
[CrossRef]

Li, H.

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

Limpert, J.

Lisak, M.

Meng, Y.

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

Millot, G.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
[CrossRef]

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys.3(9), 597–603 (2007), doi:.
[CrossRef]

C. Finot, S. Pitois, and G. Millot, “Regenerative 40 Gbit/s wavelength converter based on similariton generation,” Opt. Lett.30(14), 1776–1778 (2005), doi:.
[CrossRef] [PubMed]

Motamedi, A.

Nakazawa, M.

Ng, T. T.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

Okamoto, K.

Park, Y.

Parmigiani, F.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber Bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006), doi:.
[CrossRef]

C. Finot, F. Parmigiani, P. Petropoulos, and D. J. Richardson, “Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime,” Opt. Express14(8), 3161–3170 (2006), doi:.
[CrossRef] [PubMed]

Petrich, G. S.

Petropoulos, P.

Pitois, S.

Provost, L.

Quiroga-Teixeiro, M. L.

Richardson, D. J.

C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
[CrossRef]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys.3(9), 597–603 (2007), doi:.
[CrossRef]

C. Finot, L. Provost, P. Petropoulos, and D. J. Richardson, “Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device,” Opt. Express15(3), 852–864 (2007), doi:.
[CrossRef] [PubMed]

C. Finot, F. Parmigiani, P. Petropoulos, and D. J. Richardson, “Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime,” Opt. Express14(8), 3161–3170 (2006), doi:.
[CrossRef] [PubMed]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber Bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006), doi:.
[CrossRef]

P. Petropoulos, M. Ibsen, A. D. Ellis, and D. J. Richardson, “Rectangular pulse generations based on pulse reshaping using a superstructured fiber Bragg grating,” J. Lightwave Technol.19(5), 746–752 (2001), doi:.
[CrossRef]

Rohwer, E. G.

Rothhardt, J.

Saitoh, K.

Sander, M. Y.

Schwoerer, H.

Shen, H.

Shulika, O. V.

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun.285(21-22), 4493–4499 (2012), doi:.
[CrossRef]

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Slavík, R.

Sukhoivanov, I. A.

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun.285(21-22), 4493–4499 (2012), doi:.
[CrossRef]

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
[CrossRef]

Tünnermann, A.

Turitsyn, S. K.

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron.44(12), 1196–1203 (2008), doi:.
[CrossRef]

S. Boscolo, S. K. Turitsyn, and K. J. Blow, “Time domain all-optical signal processing at a RZ optical receiver,” Opt. Express13(16), 6217–6227 (2005), doi:.
[CrossRef] [PubMed]

Wang, X.

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

Wise, F.

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated scattering in optical fibers,” IEEE J. Quantum Electron.25(12), 2665–2673 (1989), doi:.
[CrossRef]

Zhang, S.

Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
[CrossRef]

Zhang, Z.

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

Zhou, S.

Appl. Opt. (1)

Electron. Lett. (1)

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fibre,” Electron. Lett.42(17), 965–966 (2006), doi:.
[CrossRef]

IEEE J. Quantum Electron. (3)

S. Boscolo, A. I. Latkin, and S. K. Turitsyn, “Passive nonlinear pulse shaping in normally dispersive fiber systems,” IEEE J. Quantum Electron.44(12), 1196–1203 (2008), doi:.
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C. Finot, J. M. Dudley, B. Kibler, D. J. Richardson, and G. Millot, “Optical parabolic pulse generation and applications,” IEEE J. Quantum Electron.45(11), 1482–1489 (2009), doi:.
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K. J. Blow and D. Wood, “Theoretical description of transient stimulated scattering in optical fibers,” IEEE J. Quantum Electron.25(12), 2665–2673 (1989), doi:.
[CrossRef]

IEEE Photon. Technol. Lett. (2)

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett.20(13), 1097–1099 (2008), doi:.
[CrossRef]

F. Parmigiani, P. Petropoulos, M. Ibsen, and D. J. Richardson, “Pulse retiming based on XPM using parabolic pulses formed in a fiber Bragg grating,” IEEE Photon. Technol. Lett.18(7), 829–831 (2006), doi:.
[CrossRef]

Int. J. Opt. (1)

S. Boscolo and C. Finot, “Nonlinear pulse shaping in fibres for pulse generation and optical processing,” Int. J. Opt.2012, 159057 (2012), doi:.
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J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Nat. Phys. (1)

J. M. Dudley, C. Finot, D. J. Richardson, and G. Millot, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys.3(9), 597–603 (2007), doi:.
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Opt. Commun. (2)

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers,” Opt. Commun.285(21-22), 4493–4499 (2012), doi:.
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Y. Meng, S. Zhang, C. Jin, H. Li, and X. Wang, “Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers,” Opt. Commun.283(11), 2411–2415 (2010).
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Opt. Express (9)

S. Zhou, L. Kuznetsova, A. Chong, and F. Wise, “Compensation of nonlinear phase shifts with third-order dispersion in short-pulse fiber amplifiers,” Opt. Express13(13), 4869–4877 (2005).
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A. M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. G. Rohwer, J. Limpert, and A. Tünnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express19(15), 13873–13879 (2011), doi:.
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A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express19(4), 3775–3787 (2011), doi:.
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A. Hartung, A. M. Heidt, and H. Bartelt, “Design of all-normal dispersion microstructured optical fibers for pulse-preserving supercontinuum generation,” Opt. Express19(8), 7742–7749 (2011), doi:.
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C. Finot, F. Parmigiani, P. Petropoulos, and D. J. Richardson, “Parabolic pulse evolution in normally dispersive fiber amplifiers preceding the similariton formation regime,” Opt. Express14(8), 3161–3170 (2006), doi:.
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K. Saitoh and M. Koshiba, “Empirical relations for simple design of photonic crystal fibers,” Opt. Express13(1), 267–274 (2005), doi:.
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S. Boscolo, S. K. Turitsyn, and K. J. Blow, “Time domain all-optical signal processing at a RZ optical receiver,” Opt. Express13(16), 6217–6227 (2005), doi:.
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C. Finot, L. Provost, P. Petropoulos, and D. J. Richardson, “Parabolic pulse generation through passive nonlinear pulse reshaping in a normally dispersive two segment fiber device,” Opt. Express15(3), 852–864 (2007), doi:.
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D. Krcmarík, R. Slavík, Y. Park, and J. Azaña, “Nonlinear pulse compression of picosecond parabolic-like pulses synthesized with a long period fiber grating filter,” Opt. Express17(9), 7074–7087 (2009), doi:.
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Opt. Lett. (6)

Proc. SPIE (1)

I. A. Sukhoivanov, S. O. Iakushev, O. V. Shulika, I. V. Guryev, J. A. Andrade Lucio, and O. G. Ibarra Manzano, “Formation of parabolic optical pulses in passive optical fibers,” Proc. SPIE8011, 801131, 801131-8 (2011), doi:.
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Other (4)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

www.thorlabs.com

http://www.nktphotonics.com/lmafibers-specifications

S. O. Iakushev, O. V. Shulika, and I. A. Sukhoivanov, “Sub-10-fs Pulses Produced From Compression of Supercontinuum Generated in All-Normal Dispersion Photonic Crystal Fiber,” in Frontiers in Optics Conference/ Laser Science, Technical Digest (CD) (Optical Society of America, 2012), paper FW3A.41. http://dx.doi.org/
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Spectral dependence of dispersion parameter D for fibers used in simulations (Thorlabs 780HP, LMA15, and ANDi PCF). (b) Microphotography of the cross-section and the core of the designed ANDi-PCF, Λ = 1.0 μm and d = 0.53 μm

Fig. 2
Fig. 2

Misfit parameter maps M( E 0 ,τ ) and contour curves of pulse duration τ( E 0 ,z ) (dashed lines) for the case z L D . The left column ([g1], [g2], [g3]) shows results for initial Gaussian pulse varying initial pulse duration τ 0 (FWHM) and initial pulse chirp C; right column ([s1], [s2], [s3]) shows results for initial secant pulse. The insets located in the upper right corner show the amount of initial pulse width (FWHM) and chirp.

Fig. 3
Fig. 3

Misfit parameter maps M( E 0 ,τ ) and contour curves of pulse duration τ( E 0 ,z ) (dashed lines) for the case L D <z<4 L D . The left column ([g1], [g2]) shows results for initial Gaussian pulse varying initial pulse duration τ 0 (FWHM) and initial pulse chirp C, right column ([s1], [s2]) shows results for initial secant pulse. The insets located in the upper right corner show the amount of initial pulse width (FWHM) and chirp.

Fig. 4
Fig. 4

Misfit parameter maps M( E 0 ,τ ) and contour curves of pulse duration τ( E 0 ,z ) (dashed lines). Top row ([g1], [s1]) shows results for the case z L D , bottom row ([g2], [s2]) - for L D <z<4 L D . The left column ([g1], [g2]) shows results for initial Gaussian pulse, right column ([s1], [s2]) - for initial secant pulse. The insets located in the upper right corner show the amount of initial pulse width (FWHM) and chirp.

Fig. 5
Fig. 5

Misfit parameter maps M( E 0 ,τ ) and contour curves of pulse duration τ( E 0 ,z ) (dashed lines). Top row ([g1], [s1]) shows results for the case z L D , bottom row ([g2], [s2]) - for L D <z<4 L D . The left column ([g1], [g2]) shows results for initial Gaussian pulse, right column ([s1], [s2]) - for initial secant pulse. The insets located in the upper right corner show the amount of initial pulse width (FWHM) and chirp.

Fig. 6
Fig. 6

Parabolic pulses generated in the ANDi PCF. The left column ([g1], [g2], [g3]) shows results (temporal intensity, chirp, spectrum) for parabolic pulse generated at the fiber length 10 cm from initial unchirped Gaussian pulse ( τ 0 =80 fs, E 0 =20 pJ). Right column ([s1], [s2], [s3]) parabolic pulse generated in the steady-state regime at the fiber length 30 cm from initial chirped Gaussian pulse ( τ 0 =80 fs, E 0 =15 pJ, C=1.24 ). The insets located in the upper right corner show the amount of misfit parameter M.

Fig. 7
Fig. 7

Calculated contours of misfit parameter maps: (g1) - the transient regime (Approach (A) under incidence of unchirped 100 fs Gaussian pulse; (g2) - the steady-state regime (Approach (B) under incidence of chirped (C = 1.73) 100 fs Gaussian pulse. Contours of maps for the four cases are shown: NLSE – without any higher order effects, HD – only higher order dispersion effects are included, HN - only higher order nonlinear effects are included, HN + HD – all effects are included. Black dot denotes parameter set used in calculation of Fig. 8

Fig. 8
Fig. 8

Parabolic pulse shapes and spectra formed in the Thorlabs 780 HP at particular points of misfit parameter maps shown in Fig. 7 (g1), 7(s1). The left column shows results for parabolic pulse generated from initial unchirped Gaussian pulse ( τ 0 =100 fs , E 0 =3 nJ , z=1.3 cm ). Right column shows parabolic pulse generated in the steady-state regime from initial chirped Gaussian pulse ( τ 0 =100 fs , C=1.73 , E 0 =0.75 nJ , z=15 cm ). In both cases pulse characteristics are shown for all maps: NLSE, HD, HN and HN + HD.

Tables (1)

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Table 1 Fibers’ parameters at the wavelength 800 nm used in simulations

Equations (5)

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A z = α 2 A( n2 β n i n1 n! n T n )A+iγ( 1+ 1 ω 0 T ) ×( ( 1 f R )A | A | 2 + f R A 0 h R (τ) | A(z,Tτ) | 2 dτ ),
h R (t)= τ 1 2 + τ 2 2 τ 1 τ 2 exp( t τ 2 )sin( t τ 1 ),
A chirp = A unchirp exp( iC T 2 2 T 0 2 ),
M= ( | A | 2 | A p | 2 ) 2 dτ | A | 4 d τ .
{ A p (T)= P p 12 T 2 / T p 2 , | T | T p / 2 A p (T)=0, | T |> T p / 2 ,

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