G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (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, 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), arXiv:0706.1933.

[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), arXiv:0706.1507.

[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), arXiv:physics/0511244.

[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. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).

[Crossref]
[PubMed]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006), see also arXiv:physics/0604170.

[Crossref]
[PubMed]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

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 Semiclass. Opt. 6, s288 (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]

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[Crossref]
[PubMed]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

W. Krolikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).

[Crossref]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[Crossref]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and Induced Kerr effects in quasi-phase-matched Quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[Crossref]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).

[Crossref]
[PubMed]

K. C. Chan and M. S. F. Liu, “Short-pulse generation by higher-order soliton-effect compression: Effects of fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

[Crossref]

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]

G. P. Agrawal, Applications of nonlinear fiber optics (Academic Press, London, 2001).

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).

[Crossref]
[PubMed]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).

[Crossref]
[PubMed]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[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), arXiv:0706.1933.

[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), arXiv:0706.1507.

[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), arXiv:physics/0511244.

[Crossref]
[PubMed]

M. Bache, O. Bang, and W. Krolikowski, (2008), in preparation.

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), arXiv:0706.1933.

[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), arXiv:physics/0511244.

[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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

W. Krolikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).

[Crossref]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and Induced Kerr effects in quasi-phase-matched Quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[Crossref]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

M. Bache, O. Bang, and W. Krolikowski, (2008), in preparation.

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

K. C. Chan and M. S. F. Liu, “Short-pulse generation by higher-order soliton-effect compression: Effects of fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and Induced Kerr effects in quasi-phase-matched Quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

V. Dmitriev, G. Gurzadyan, and D. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer, Berlin, 1999).

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

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]

V. Dmitriev, G. Gurzadyan, and D. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer, Berlin, 1999).

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).

[Crossref]
[PubMed]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and Induced Kerr effects in quasi-phase-matched Quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

W. Krolikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).

[Crossref]

M. Bache, O. Bang, and W. Krolikowski, (2008), in preparation.

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).

[Crossref]
[PubMed]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[Crossref]

K. C. Chan and M. S. F. Liu, “Short-pulse generation by higher-order soliton-effect compression: Effects of fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[Crossref]
[PubMed]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[Crossref]

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]

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), arXiv:0706.1507.

[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, 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), arXiv:0706.1933.

[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, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006), see also arXiv:physics/0604170.

[Crossref]
[PubMed]

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

V. Dmitriev, G. Gurzadyan, and D. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer, Berlin, 1999).

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[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]

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[Crossref]
[PubMed]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).

[Crossref]
[PubMed]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[Crossref]
[PubMed]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[Crossref]

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]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[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), arXiv:0706.1507.

[Crossref]

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, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006), see also arXiv:physics/0604170.

[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. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[Crossref]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[Crossref]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[Crossref]

S. Ashihara, T. Shimura, K. Kuroda, N. E. Yu, S. Kurimura, K. Kitamura, M. Cha, and T. Taira, “Optical pulse compression using cascaded quadratic nonlinearities in periodically poled lithium niobate,” Appl. Phys. Lett. 84, 1055–1057 (2004).

[Crossref]

K. C. Chan and M. S. F. Liu, “Short-pulse generation by higher-order soliton-effect compression: Effects of fiber characteristics,” IEEE J. Quantum Electron. 31, 2226–2235 (1995).

[Crossref]

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 Semiclass. Opt. 6, s288 (2004).

[Crossref]

K.-T. Chan and W.-H. Cao, “Improved soliton-effect pulse compression by combined action of negative thirdorder dispersion and Raman self-scattering in optical fibers,” J. Opt. Soc. Am. B 15, 2371–2376.

I. V. Shadrivov and A. A. Zharov, “Dynamics of optical spatial solitons near the interface between two quadratically nonlinear media,” J. Opt. Soc. Am. B 19, 596–602 (2002).

[Crossref]

S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).

[Crossref]

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), arXiv:0706.1507.

[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]

G. Xie, D. Zhang, L. Qian, H. Zhu, and D. Tang, “Multi-stage pulse compression by use of cascaded quadratic nonlinearity,” Opt. Commun. 273, 207–213 (2007).

[Crossref]

X. Zeng, S. Ashihara, N. Fujioka, T. Shimura, and K. Kuroda, “Adiabatic compression of quadratic temporal solitons in aperiodic quasi-phase-matching gratings,” Opt. Express 14, 9358–9370 (2006).

[Crossref]
[PubMed]

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003).

[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), arXiv:physics/0511244.

[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, 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, 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), arXiv:0706.1933.

[Crossref]
[PubMed]

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]

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]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).

[Crossref]
[PubMed]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, “Self-focusing and solitonlike structures in materials with competing quadratic and cubic nonlinearities,” Phys. Rev. E 55, 3555–3570 (1997).

[Crossref]

W. Krolikowski, O. Bang, J. J. Rasmussen, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).

[Crossref]

W. Krolikowski and O. Bang, “Solitons in nonlocal nonlinear media: Exact solutions,” Phys. Rev. E 63, 016610 (2000).

[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).

[Crossref]

P. Di Trapani, A. Bramati, S. Minardi, W. Chinaglia, C. Conti, S. Trillo, J. Kilius, and G. Valiulis, “Focusing versus defocusing nonlinearities due to parametric wave mixing,” Phys. Rev. Lett. 87, 183902 (2001).

[Crossref]

C. B. Clausen, O. Bang, and Y. S. Kivshar, “Spatial solitons and Induced Kerr effects in quasi-phase-matched Quadratic media,” Phys. Rev. Lett. 78, 4749–4752 (1997).

[Crossref]

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]

J. Moses and F. W. Wise, “Controllable self-steepening of ultrashort pulses in quadratic nonlinear media,” Phys. Rev. Lett. 97, 073903 (2006), see also arXiv:physics/0604170.

[Crossref]
[PubMed]

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).

[Crossref]

D. V. Skryabin, F. Luan, J. C. Knight, and P. S. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science 301, 1705–1708 (2003).

[Crossref]
[PubMed]

V. Dmitriev, G. Gurzadyan, and D. Nikogosyan, Handbook of Nonlinear Optical Crystals, Vol. 64 of Springer Series in Optical Sciences (Springer, Berlin, 1999).

On dimensional form R(t)=R(t/Tin)/Tin, which is independent on Tin since τa,b in Eqs. (10,12) must be replaced by the dimensional form ta,b=τa,bTin. In the frequency domain both R̃ and R̃ are dimensionless.

M. Bache, O. Bang, and W. Krolikowski, (2008), in preparation.

The factor sa on the RHS of Eq. (17) was unfortunately lost during the proofs in Eq. (12) of Ref. [10].

These experiments were actually done in the nonstationary regime according to the nonlocal theory.

This is a typical experimental situation: the optimal compression point zopt scales with Neff [11], and since the nonlinear crystal length is a constant parameter one adjusts the intensity so zopt coincides with the crystal length.

G. P. Agrawal, Applications of nonlinear fiber optics (Academic Press, London, 2001).

J. A. Moses, J. Nees, B. Hou, K.-H. Hong, G. Mourou, and F. W. Wise, “Chirped-pulse cascaded quadratic compression of 1-mJ, 35-fs pulses with low wavefront distortions,” In Conference on Lasers and Electro-Optics, p. CTuS5 (Optical Society of America, 2005).