Abstract

The dispersion of index-guiding microstructured polymer optical fibers is calculated for second-harmonic generation. The quadratic nonlinearity is assumed to come from poling of the polymer, which is chosen to be the cyclic olefin copolymer Topas. We found a very large phase mismatch between the pump and the second-harmonic waves. Therefore the potential for cascaded quadratic second-harmonic generation is investigated in particular or soliton compression of femtosecond pulses. We found that excitation of temporal solitons from cascaded quadratic nonlinearities requires an effective quadratic nonlinearity of 5pmV or more. This might be reduced if a polymer with a lower Kerr nonlinear refractive index is used. We also found that the group-velocity mismatch could be minimized if the design parameters of the microstructured fiber are chosen so the relative hole size is large and the hole pitch is of the order of the pump wavelength. Almost all design-parameter combinations resulted in cascaded effects in the stationary regime, where efficient and clean soliton compression can be found. We therefore did not see any benefit from choosing a fiber design where the group-velocity mismatch was minimized. Instead numerical simulations showed excellent compression of λ=800nm 120fs pulses with nanojoule pulse energy to few-cycle duration using a standard endlessly single-mode design with a relative hole size of 0.4.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2008 (2)

2007 (5)

2006 (3)

2005 (2)

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

G. Y. Guo and J. C. Lin, “Second-harmonic generation and linear electro-optical coefficients of BN nanotubes,” Phys. Rev. B 72, 075416 (2005).
[CrossRef]

2004 (2)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

F. Ö. Ilday, K. Beckwitt, Y.-F. Chen, H. Lim, and F. W. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376-383 (2004).
[CrossRef]

2003 (1)

2002 (2)

2001 (3)

G. Khanarian and H. Celanese, “Optical properties of cyclic olefin copolymers,” Opt. Eng. (Bellingham) 40, 1024-1029 (2001).
[CrossRef]

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

1999 (2)

X. Liu, L. Qian, and F. W. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascaded χ(2):χ(2) nonlinearity,” Opt. Lett. 24, 1777-1779 (1999).
[CrossRef]

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

1997 (3)

1996 (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2), cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

1994 (1)

1992 (1)

1989 (1)

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]

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).
[CrossRef]

Agrawal, G. P.

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

Alhammali, E.

Ashihara, S.

Bache, M.

Bang, O.

M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, “Limits to compression with cascaded quadratic soliton compressors,” Opt. Express 16, 3273-3287 (2008).
[CrossRef] [PubMed]

M. Bache, J. Lægsgaard, O. Bang, J. Moses, and F. W. Wise, “Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers,” Proc. SPIE 6588, 65880P (2007).
[CrossRef]

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490-2492 (2007).
[CrossRef] [PubMed]

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, “Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch,” Opt. Lett. 31, 1612-1614 (2006).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Baum, A.

Beckwitt, K.

Belardi, W.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Birks, T.

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

Birks, T. A.

Bjarklev, A.

Blow, K. J.

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]

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Busacca, A.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Celanese, H.

G. Khanarian and H. Celanese, “Optical properties of cyclic olefin copolymers,” Opt. Eng. (Bellingham) 40, 1024-1029 (2001).
[CrossRef]

Chang, C.

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

Chen, C.

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

Chen, Y.-F.

Chou, C. C.

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

Cooper, M.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

de Sterke, C. M.

DeSalvo, R.

Edmundson, D.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Eichenholz, J. M.

Faccio, D.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).
[CrossRef]

Grappe, B.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Guo, G. Y.

G. Y. Guo and J. C. Lin, “Second-harmonic generation and linear electro-optical coefficients of BN nanotubes,” Phys. Rev. B 72, 075416 (2005).
[CrossRef]

Hagan, D.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2), cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

Ilday, F. Ö.

Issac, R.

Jaroszynski, D. A.

Jeng, J. J.

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

Joannopoulos, J.

Johnson, S.

Jones, D.

Kazansky, P.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Kazansky, P. G.

P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-phase-matched optical fibers,” J. Opt. Soc. Am. B 14, 3170-3179 (1997).
[CrossRef]

P. G. Kazansky, Optoelectronics Research Centre, University of Southampton, Highfield, Southampton, S017 1BJ, UK (personal communication, 2007).

Khanarian, G.

G. Khanarian and H. Celanese, “Optical properties of cyclic olefin copolymers,” Opt. Eng. (Bellingham) 40, 1024-1029 (2001).
[CrossRef]

Knight, J.

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

Knight, J. C.

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

Krolikowski, W.

M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, “Limits to compression with cascaded quadratic soliton compressors,” Opt. Express 16, 3273-3287 (2008).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Kuhlmey, B. T.

Kuo, W. J.

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

Kuroda, K.

Lægsgaard, J.

J. Lægsgaard, P. J. Roberts, and M. Bache, “Tailoring the dispersion properties of photonic crystal fibers,” Opt. Quantum Electron. 39, 995-1008 (2007).
[CrossRef]

M. Bache, J. Lægsgaard, O. Bang, J. Moses, and F. W. Wise, “Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers,” Proc. SPIE 6588, 65880P (2007).
[CrossRef]

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, “Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch,” Opt. Lett. 31, 1612-1614 (2006).
[CrossRef] [PubMed]

J. Lægsgaard, A. Bjarklev, and S. Libori, “Chromatic dispersion in photonic crystal fibers: fast and accurate scheme for calculation,” J. Opt. Soc. Am. B 20, 443-448 (2003).
[CrossRef]

Libori, S.

Lim, H.

Lin, J. C.

G. Y. Guo and J. C. Lin, “Second-harmonic generation and linear electro-optical coefficients of BN nanotubes,” Phys. Rev. B 72, 075416 (2005).
[CrossRef]

Liu, X.

McPhedran, R. C.

Menyuk, C. R.

Mogilevtsev, D.

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).
[CrossRef]

Monro, T.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Moses, J.

M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, “Limits to compression with cascaded quadratic soliton compressors,” Opt. Express 16, 3273-3287 (2008).
[CrossRef] [PubMed]

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490-2492 (2007).
[CrossRef] [PubMed]

M. Bache, J. Lægsgaard, O. Bang, J. Moses, and F. W. Wise, “Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers,” Proc. SPIE 6588, 65880P (2007).
[CrossRef]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, “Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams,” Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

M. Bache, J. Moses, and F. W. Wise, “Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities,” J. Opt. Soc. Am. B 24, 2752-2762 (2007).
[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

J. Moses and F. W. Wise, “Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal,” Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

J. Moses and F. W. Wise, “Derivation of nonlinear evolution equations for coupled and single fields in a quadratic medium,” arXiv:physics/0604170.

Neshev, D.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Nielsen, H.

Nikolov, N.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Nishina, J.

Pannell, C.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Perrie, W.

Pruneri, V.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

P. G. Kazansky and V. Pruneri, “Electric-field poling of quasi-phase-matched optical fibers,” J. Opt. Soc. Am. B 14, 3170-3179 (1997).
[CrossRef]

Qian, L.

Rasmussen, J.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Richardson, D.

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

Roberts, P. J.

J. Lægsgaard, P. J. Roberts, and M. Bache, “Tailoring the dispersion properties of photonic crystal fibers,” Opt. Quantum Electron. 39, 995-1008 (2007).
[CrossRef]

Russell, P. S.

Russell, P. St. J.

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

Schiek, R.

Scully, P. J.

Sheik-Bahae, M.

Shimura, T.

Stegeman, G.

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2), cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2), cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

C. R. Menyuk, R. Schiek, and L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434-2443 (1994).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Wise, F. W.

M. Bache, O. Bang, W. Krolikowski, J. Moses, and F. W. Wise, “Limits to compression with cascaded quadratic soliton compressors,” Opt. Express 16, 3273-3287 (2008).
[CrossRef] [PubMed]

M. Bache, J. Lægsgaard, O. Bang, J. Moses, and F. W. Wise, “Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers,” Proc. SPIE 6588, 65880P (2007).
[CrossRef]

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490-2492 (2007).
[CrossRef] [PubMed]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, “Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams,” Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

M. Bache, J. Moses, and F. W. Wise, “Scaling laws for soliton pulse compression by cascaded quadratic nonlinearities,” J. Opt. Soc. Am. B 24, 2752-2762 (2007).
[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

J. Moses and F. W. Wise, “Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal,” Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

F. Ö. Ilday, K. Beckwitt, Y.-F. Chen, H. Lim, and F. W. Wise, “Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes,” J. Opt. Soc. Am. B 21, 376-383 (2004).
[CrossRef]

X. Liu, L. Qian, and F. W. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascaded χ(2):χ(2) nonlinearity,” Opt. Lett. 24, 1777-1779 (1999).
[CrossRef]

J. Moses and F. W. Wise, “Derivation of nonlinear evolution equations for coupled and single fields in a quadratic medium,” arXiv:physics/0604170.

Wood, D.

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]

Wyller, J.

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

Electron. Lett. (1)

D. Faccio, A. Busacca, W. Belardi, V. Pruneri, P. Kazansky, T. Monro, D. Richardson, B. Grappe, M. Cooper, and C. Pannell, “Demonstration of thermal poling in holey fibres,” Electron. Lett. 37, 107-108 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

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]

IEEE Photon. Technol. Lett. (1)

T. Birks, D. Mogilevtsev, J. Knight, and P. St. J. Russell, “Dispersion compensation using single-material fibers,” IEEE Photon. Technol. Lett. 11, 674-676 (1999).
[CrossRef]

J. Macromol. Sci., Polym. Rev. (1)

C. Chang, C. Chen, C. C. Chou, W. J. Kuo, and J. J. Jeng, “Polymers for electro-optical modulation,” J. Macromol. Sci., Polym. Rev. 45, 125-170 (2005).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

W. Krolikowski, O. Bang, N. Nikolov, D. Neshev, J. Wyller, J. Rasmussen, and D. Edmundson, “Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media,” J. Opt. B: Quantum Semiclassical Opt. 6, s288-s294 (2004).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Eng. (Bellingham) (1)

G. Khanarian and H. Celanese, “Optical properties of cyclic olefin copolymers,” Opt. Eng. (Bellingham) 40, 1024-1029 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (9)

R. DeSalvo, D. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28-30 (1992).
[CrossRef] [PubMed]

M. Bache, O. Bang, J. Moses, and F. W. Wise, “Nonlocal explanation of stationary and nonstationary regimes in cascaded soliton pulse compression,” Opt. Lett. 32, 2490-2492 (2007).
[CrossRef] [PubMed]

J. Moses, E. Alhammali, J. M. Eichenholz, and F. W. Wise, “Efficient high-energy femtosecond pulse compression in quadratic media with flattop beams,” Opt. Lett. 32, 2469-2471 (2007).
[CrossRef] [PubMed]

J. Moses and F. W. Wise, “Soliton compression in quadratic media: high-energy few-cycle pulses with a frequency-doubling crystal,” Opt. Lett. 31, 1881-1883 (2006).
[CrossRef] [PubMed]

X. Liu, L. Qian, and F. W. Wise, “High-energy pulse compression by use of negative phase shifts produced by the cascaded χ(2):χ(2) nonlinearity,” Opt. Lett. 24, 1777-1779 (1999).
[CrossRef]

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, “Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch,” Opt. Lett. 31, 1612-1614 (2006).
[CrossRef] [PubMed]

B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684-1686 (2002).
[CrossRef]

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

A. Baum, P. J. Scully, W. Perrie, D. Jones, R. Issac, and D. A. Jaroszynski, “Pulse-duration dependency of femtosecond laser refractive index modification in poly(methyl methacrylate),” Opt. Lett. 33, 651-653 (2008).
[CrossRef] [PubMed]

Opt. Quantum Electron. (2)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2), cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691-1740 (1996).
[CrossRef]

J. Lægsgaard, P. J. Roberts, and M. Bache, “Tailoring the dispersion properties of photonic crystal fibers,” Opt. Quantum Electron. 39, 995-1008 (2007).
[CrossRef]

Phys. Rev. B (1)

G. Y. Guo and J. C. Lin, “Second-harmonic generation and linear electro-optical coefficients of BN nanotubes,” Phys. Rev. B 72, 075416 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095-1098 (1980).
[CrossRef]

T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282-3285 (1997).
[CrossRef]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Bache, J. Lægsgaard, O. Bang, J. Moses, and F. W. Wise, “Soliton compression to ultra-short pulses using cascaded quadratic nonlinearities in silica photonic crystal fibers,” Proc. SPIE 6588, 65880P (2007).
[CrossRef]

Other (3)

P. G. Kazansky, Optoelectronics Research Centre, University of Southampton, Highfield, Southampton, S017 1BJ, UK (personal communication, 2007).

J. Moses and F. W. Wise, “Derivation of nonlinear evolution equations for coupled and single fields in a quadratic medium,” arXiv:physics/0604170.

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

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Figures (8)

Fig. 1
Fig. 1

Microstructured fiber design considered here.

Fig. 2
Fig. 2

GVM parameter d 12 and phase mismatch Δ β for an mPOF with Λ = 7.0 μ m . In (a) the lines for single-mode operation are indicated for the FW and the SH modes. The FW zero dispersion point is also indicated; below this line the FW GVD is normal. Finally the X indicates the chosen fiber design for single-mode operation at λ 1 = 800 nm .

Fig. 3
Fig. 3

Dispersion for Λ = 7.0 μ m and D = d Λ = 0.4 . (a) The phase mismatch Δ β = β 2 2 β 1 and (b) GVM d 12 = β 1 ( 1 ) β 2 ( 2 ) versus λ 1 . (c) The GVD parameter D = 2 π c β ( 2 ) λ 2 versus λ. The material dispersion is also shown. (d) shows the effective nonlinearity required to achieve γ SHG > γ Kerr for n Kerr I = 15 × 10 20 m 2 W .

Fig. 4
Fig. 4

Numerical simulation of soliton compression in an mPOF with the design parameters of Fig. 3 and d eff = 10 pm V . Top left plot shows the FW compressing to 15 fs FWHM after 30 mm of propagation (at the dashed line) starting from 120 fs . Top right shows the spectral broadening and development of SPM-induced sidebands of the FW. The pulse parameters were N eff = 3 , P in = 4.6 kW , and the pulse energy was 0.6 nJ . The middle row shows a simulation for a higher soliton order ( N eff = 9 , P in = 41.8 kW , and a pulse energy of 5.7 nJ ), which compresses to 4.4 fs after 6 mm of propagation. A cut at z = 6 mm is shown in the bottom plot. Up to 10th order dispersion was included ( m d = 10 ) . 2 13 temporal points and > 15 z steps per coherence length were used.

Fig. 5
Fig. 5

As Fig. 2 but with Λ = 0.65 μ m . A zero GVM curve is indicated with black as well as the FW zero dispersion point (ZDP). The two crosses indicate the chosen fiber designs at λ 1 = 1040 nm .

Fig. 6
Fig. 6

(a) Dispersion as function of the relative hole size D as calculated for λ 1 = 1040 nm and Λ = 0.65 μ m . (b) The the effective nonlinearity required to achieve γ SHG > γ Kerr assuming n Kerr I = 15 × 10 20 m 2 W .

Fig. 7
Fig. 7

Dispersion calculated for D = 0.4 nm and Λ = 1.0 μ m . The lower plot shows the results of a numerical simulation, where a λ 1 = 800 nm T in = 120 fs FWHM input pulse is compressed to 5.5 fs . The pulse cut is shown after z = 7.0 mm of propagation. The fiber had d eff = 10 pm V as in Fig. 4. The input pulse had N eff = 9 , P in = 3.1 kW , and pulse energy 0.42 nJ .

Fig. 8
Fig. 8

Loss-parameter α used in the numerics: both linear losses (estimated to 0.5 dB cm [20]) and the absorption peaks of Topas, see [20], are modeled.

Tables (1)

Tables Icon

Table 1 Sellmeier Equation (C1) Fitting Parameters for Refractive Index Data Points in Topas Grade 5013 Measured in [20] at Various Temperatures and With Wavelengths Between 435.8 and 1014 nm

Equations (35)

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[ i ξ sgn ( β 1 ( 2 ) ) 2 2 τ 2 ] U 1 + N Kerr 2 U 1 U 1 2 = N SHG 2 U 1 * d s R ± ( s ) U 1 2 ( ξ , τ s ) .
Δ β sr = d 12 2 2 β 2 ( 2 ) = π d 12 2 D 2 λ 2 2 .
[ i ξ sgn ( β 1 ( 2 ) ) 2 2 τ 2 ] U 1 [ sgn ( Δ β ) N SHG 2 N Kerr 2 ] U 1 U 1 2 = i N SHG 2 s a τ R , SHG U 1 2 U 1 τ .
N Kerr 2 = L D , 1 L Kerr ,
γ Kerr = n Kerr I ω 1 c A eff , 1 ,
A eff , 1 = ( d x F 1 ( x ) 2 ) 2 P d x F 1 ( x ) 4 .
N SHG 2 = L D , 1 L SHG ,
γ SHG = n SHG I ω 1 c A SHG ,
A SHG = a 1 2 a 2 P d x [ F 1 * ( x ) ] 2 F 2 ( x ) 2 ,
n SHG I = 4 π d eff 2 c ε 0 λ n eff , 1 2 n eff , 2 Δ β .
N eff 2 = N SHG 2 N Kerr 2 = P in L D , 1 ( γ SHG γ Kerr ) .
[ i ξ 1 2 2 τ 2 ] U 1 N eff 2 U 1 U 1 2 = i N SHG 2 s a τ R , SHG U 1 2 U 1 τ .
τ R , SHG 2 d 12 Δ β T in .
L ̂ 1 E 1 + κ SHG , 1 S ̂ 1 E 1 * E 2 e i Δ β z + κ Kerr , 1 S ̂ 1 [ E ̂ 1 ( F 11 E 1 2 + 2 F 12 E 2 2 ) ] = 0 ,
L ̂ 2 E 2 + κ SHG , 2 S ̂ 2 E 1 2 e i Δ β z + κ Kerr , 2 S ̂ 2 [ E 2 ( F 22 E 2 2 + 2 F 12 E 1 2 ) ] = 0 .
E j ( x , z , t ) = E j ( z , t ) F j ( x ) e i β j z ,
L ̂ 1 i z + i α 2 + D ̂ 1 ,
L ̂ 2 i z + i α 2 i d 12 τ + D ̂ 2 , eff ,
D ̂ j m = 2 m d i m β j ( m ) m ! m τ m ,
D ̂ 2 , eff D ̂ 2 + S ̂ 2 1 d 12 2 2 β 2 2 τ 2 ,
κ SHG , j ω 1 2 c n eff , j d x χ ( 2 ) ( x ) [ F 1 * ( x ) ] 2 F 2 ( x ) a j = ω 1 d eff c n eff , j P d x [ F 1 * ( x ) ] 2 F 2 ( x ) a j ,
a j d x F j ( x ) 2 ,
κ Kerr , j = 3 ω j Re ( χ ( 3 ) ) 8 c n eff , j a j = ω j c a j n Kerr , j ,
F j k P d x F j ( x ) 2 F k ( x ) 2 .
L ̂ 1 U 1 + Δ β N SHG S ̂ 1 U 1 * U 2 e i Δ β z + N Kerr 2 S ̂ 1 U 1 [ U 1 2 + 2 n ¯ f 12 f 11 U 2 2 ] = 0 ,
L ̂ 2 U 2 + Δ β N SHG S ̂ 2 U 1 2 e i Δ β z + 2 n ¯ 2 f 22 f 11 N Kerr 2 S ̂ 2 U 2 [ U 2 2 + 2 f 12 n ¯ f 22 U 1 2 ] = 0 ,
f j k F j k a j a k = P d x F j ( x ) 2 F k ( x ) 2 d x F j ( x ) 2 d x F k ( x ) 2 .
L ̂ 1 i z + i α 2 + D ̂ 1 ,
L ̂ 2 i z + i α 2 i d 12 τ + D ̂ 2 , eff ,
D ̂ j m = 2 m d i m δ j ( m ) m τ m ,
d 12 d 12 L D , 1 T in , δ j ( m ) L D , 1 1 T in m m ! β j ( m ) .
D ̂ 2 , eff D ̂ 2 + S ̂ 2 1 ν 2 2 τ 2 ,
S ̂ 2 1 = m = 0 ( i s 2 ) m m τ m ,
D ̂ 2 , eff = m = 2 m d i m [ δ 2 ( m ) + ν 2 ( s 2 ) m 2 ] m τ m .
n 2 ( λ ) = 1 + B ( 1 A λ 2 ) ,

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