Abstract

We solve a system of generalized nonlinear Schrödinger equations to study the nonlinear dynamics of ultrashort pulse propagation in multimode fibers. Due to pulse walk-off, permanent intermodal power transfer between modes is observed even in absence of phase matching. The strength of intermodal effects is found to depend strongly on modal symmetries, which results in preferential coupling between the LP0n modes. The scaling of nonlinear multimode effects in large-core fibers for the generation of ultra-high power spectral density supercontinua is finally discussed.

© 2009 Optical Society of America

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2008 (5)

2007 (7)

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

T. Chaipiboonwong, P. Horak, J. D. Mills, and W. S. Brocklesby, "Numerical study of nonlinear interactions in a multimode waveguide," Opt. Express 15, 9040-9047 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9040.
[CrossRef] [PubMed]

G. Genty, S. Coen, and J. M. Dudley, "Fiber supercontinuum sources (Invited)," J. Opt. Soc. Am. B 24, 1771-1785 (2007), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-8-1771.
[CrossRef]

C. Lesvigne, V. Couderc, A. Tonello, P. Leproux, A. Barthelemy, S. Lacroix, F. Druon, P. Blandin, M. Hanna, and P. Georges, "Visible supercontinuum generation controlled by intermodal four-wave mixing in microstructured fiber," Opt. Lett. 32, 2173-2175 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-15-2173.
[CrossRef] [PubMed]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Spatial-temporal structure of the femtosecond third harmonic generation in photonic-crystal fibers," Opt. Express 15, 11301-11312 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11301.
[CrossRef] [PubMed]

E. R. Martins, D. H. Spadoti, M. A. Romero, and B.-H. V. Borges, "Theoretical analysis of supercontinuum generation in a highly birefringent D-shaped microstructured optical fiber," Opt. Express 15, 14335-14347 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (2)

2004 (1)

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

2003 (3)

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[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]

A. Efimov, A. J. Taylor, F. G. Omenetto, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Nonlinear generation of very high-order UV modes in microstructured fibers," Opt. Express 11, 910-918 (2003).
[CrossRef] [PubMed]

2002 (2)

1997 (1)

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

1996 (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

1982 (1)

R. H. Stolen and J. B. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers" IEEE J. Sel. Top. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

1970 (1)

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]

Akozbek, N.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

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]

Andersen, T.

Baggett, J. C.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Barthelemy, A.

Baumberg, J. J.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Belardi, W.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Bertolotti, M.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Bjorkholm, J. B.

R. H. Stolen and J. B. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers" IEEE J. Sel. Top. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

Blandin, P.

Bloemer, M. J.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Borges, B.-H. V.

Brabec, T.

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

Brambilla, G.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Brocklesby, W. S.

Broderick, N. G. R.

Centini, M.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Chaipiboonwong, T.

Chau, A. H. L.

Cherif, R.

Coen, S.

Conforti, M.

Couderc, V.

Coyle, S.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Cumberland, B. A.

De Angelis, C.

de Ceglia, D.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Degiorgio, V.

Druon, F.

Dudley, J. M.

Ebendorff-Heidepriem, H.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Efimov, A.

Eggleton, B. J.

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Feng, X.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Finazzi, V.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3728.
[CrossRef] [PubMed]

Flanagan, J. C.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Furusawa, K.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Genty, G.

G. Genty, S. Coen, and J. M. Dudley, "Fiber supercontinuum sources (Invited)," J. Opt. Soc. Am. B 24, 1771-1785 (2007), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-24-8-1771.
[CrossRef]

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]

George, A. K.

Georges, P.

Gorbach, A. V.

Grossard, N.

Hanna, M.

Harvey, J. D.

Haus, J. W.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Horak, P.

F. Poletti and P. Horak, "Description of ultrashort pulse propagation in multimode optical fibers," J. Opt. Soc. Am. B 25, 1645-1654 (2008), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-10-1645.
[CrossRef]

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

T. Chaipiboonwong, P. Horak, J. D. Mills, and W. S. Brocklesby, "Numerical study of nonlinear interactions in a multimode waveguide," Opt. Express 15, 9040-9047 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9040.
[CrossRef] [PubMed]

Kaivola, 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]

Kalashnikov, V. L.

Kandidov, V. P.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Knight, J. C.

Kolesik, M.

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Kosareva, O. G.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Krausz, F.

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

Kudlinski, A.

Lacroix, S.

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]

Leong, J. Y. Y.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Leonhardt, R.

Leproux, P.

Lesvigne, C.

Limpert, J.

Locatelli, A.

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]

Maillotte, H.

Martins, E. R.

Martynkien, T.

Millot, G.

Mills, J. D.

Moloney, J. V.

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Monro, T. M.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3728.
[CrossRef] [PubMed]

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Mussot, A.

Netti, C.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Omenetto, F. G.

Paschotta, R.

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Petropoulos, P.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

Pitois, S.

Poletti, F.

Popov, S. V.

Price, J. H. V.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Provino, L.

Richardson, D. J.

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3728.
[CrossRef] [PubMed]

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Romero, M. A.

Roppo, V.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Rulkov, A. B.

Russell, P. St. J.

Scalora, M.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Schimpf, D.

Schreiber, T.

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]

Shore, B. W.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Sibilia, C.

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Skryabin, D. V.

Sorokin, E.

Sorokina, I. T.

Spadoti, D. H.

Stolen, R. H.

R. H. Stolen and J. B. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers" IEEE J. Sel. Top. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

Stuart, B. C.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

T¨unnermann, A.

Tartara, L.

Taylor, A. J.

Taylor, J. R.

Tonello, A.

Travers, J. C.

Tse, V.

Urbanczyk, W.

Wabnitz, S.

Wadsworth, W. J.

Windeler, R. S.

Wojcik, J.

Zghal, M.

Appl. Phys. B (1)

J. H. V. Price, T. M. Monro, K. Furusawa, W. Belardi, J. C. Baggett, S. Coyle, C. Netti, J. J. Baumberg, R. Paschotta, and D. J. Richardson, "UV generation in a pure-silica holey fiber," Appl. Phys. B 77, 291-298 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

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]

IEEE J. Sel. Top. Quantum Electron. (2)

J. H. V. Price, T. M. Monro, H. Ebendorff-Heidepriem, F. Poletti, P. Horak, V. Finazzi, J. Y. Y. Leong, P. Petropoulos, J. C. Flanagan, G. Brambilla, X. Feng and D. J. Richardson, "Mid-IR supercontinuum generation from nonsilica microstructured fibers," IEEE J. Sel. Top. Quantum Electron. 13, 738-749 (2007).
[CrossRef]

R. H. Stolen and J. B. Bjorkholm, "Parametric amplification and frequency conversion in optical fibers" IEEE J. Sel. Top. Quantum Electron. 18, 1062-1072 (1982).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Express (11)

A. Efimov, A. J. Taylor, F. G. Omenetto, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Nonlinear generation of very high-order UV modes in microstructured fibers," Opt. Express 11, 910-918 (2003).
[CrossRef] [PubMed]

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-10-3728.
[CrossRef] [PubMed]

T. Schreiber, T. Andersen, D. Schimpf, J. Limpert, and A. T¨unnermann, "Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths," Opt. Express 13, 9556-9569 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-23-9556.
[CrossRef] [PubMed]

A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, "Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber," Opt. Express 14, 397-404 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-1-397.
[CrossRef] [PubMed]

A. Kudlinski, A. K. George, J. C. Knight, J. C. Travers, A. B. Rulkov, S. V. Popov, and J. R. Taylor, "Zerodispersion wavelength decreasing photonic crystal fibers for ultraviolet-extended supercontinuum generation," Opt. Express 14, 5715-5722 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5715.
[CrossRef] [PubMed]

T. Chaipiboonwong, P. Horak, J. D. Mills, and W. S. Brocklesby, "Numerical study of nonlinear interactions in a multimode waveguide," Opt. Express 15, 9040-9047 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9040.
[CrossRef] [PubMed]

V. L. Kalashnikov, E. Sorokin, and I. T. Sorokina, "Spatial-temporal structure of the femtosecond third harmonic generation in photonic-crystal fibers," Opt. Express 15, 11301-11312 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11301.
[CrossRef] [PubMed]

E. R. Martins, D. H. Spadoti, M. A. Romero, and B.-H. V. Borges, "Theoretical analysis of supercontinuum generation in a highly birefringent D-shaped microstructured optical fiber," Opt. Express 15, 14335-14347 (2007).
[CrossRef] [PubMed]

R. Cherif, M. Zghal, L. Tartara, and V. Degiorgio, "Supercontinuum generation by higherorder mode excitation in a photonic crystal fiber," Opt. Express 16, 2147-2152 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-3-2147.
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, "Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers," Opt. Express 16, 4858-4865 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-7-4858.
[CrossRef] [PubMed]

B. A. Cumberland, J. C. Travers, S. V. Popov, and J. R. Taylor, "29 W High power CW supercontinuum source," Opt. Express 16, 5954-5962 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-8-5954.
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

V. Roppo, M. Centini, C. Sibilia, M. Bertolotti, D. de Ceglia, M. Scalora, N. Akozbek, M. J. Bloemer, J. W. Haus, O. G. Kosareva, and V. P. Kandidov, "Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media", Phys. Rev. A 76, 033829 (2007).
[CrossRef]

Phys. Rev. B (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, "Nanosecond-tofemtosecond laser-induced breakdown in dielectrics," Phys. Rev. B 53, 1749-1761 (1996).
[CrossRef]

Phys. Rev. E (1)

M. Kolesik and J. V. Moloney, "Nonlinear optical pulse propagation: From Maxwell’s to unidirectional equations," Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Rev. Mod. Phys. (1)

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

Other (3)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes: the art of scientific computing, 3rd ed. (Cambridge University Press, New York, USA, 2007).

T. Delmonte, M. A. Watson, E. J. O’Driscoll, X. Feng, T. M. Monro, V. Finazzi, P. Petropoulos, J. H. V. Price, J. C. Baggett, W. Loh, D. J. Richardson, and D. P. Hand, "Generation of mid-IR continuum using tellurite microstructured fiber," in Conference on Lasers and Electro-Optics, paper CTuA4, Long Beach, USA (2006).

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

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Figures (8)

Fig. 1.
Fig. 1.

(Top) Transverse mode functions, calculated at 850 nm, of the 7 circularly polarized modes guided by HF1, an HF with ∧ = 2.7 μm and d = 2.5 μm [21]. (Bottom left) Effective index and (bottom right) GVD curves.

Fig. 2.
Fig. 2.

Examples of multimode nonlinear propagation after 7.5 mm (central column) and 30 mm (right column), for a 100 fs, sech pump centered at 850 nm. (a) Only M1 is excited with a 50 kW peak power pulse; (b) both M1 and M2 are excited with a 50 kW peak power pulse; (c) typical unoptimized launch condition, where a 100 kW Gaussian beam excites M1-M7 with different efficiencies (see main text for details).

Fig. 3.
Fig. 3.

Normalized overlap integrals for HF1 sorted in descending order. The color codes illustrate the type of nonlinear interaction controlled by each coefficient. The inset shows the two main parametric processes occurring when only the mode p is pumped (see text).

Fig. 4.
Fig. 4.

(a) Multimode output spectrum after 0.4 mm propagation in HF1, where two signals where launched in M1 and M2 with a spectral offset and P 0 = 100 kW (solid lines). Dashed lines indicate signals amplified from noise through intermodal FWM. The color code is shown on the extreme right. (b) Dynamic gain evolution for each individual mode showing the oscillatory behavior typical of non phase-matched parametric processes.

Fig. 5.
Fig. 5.

Longitudinal evolution of the gain of M4 under the same conditions as in Fig. 4.

Fig. 6.
Fig. 6.

Propagation of a T 0 = 100 fs and P 0 = 500 kW sech pulse centered at 725 nm and launched in: (a) M1 only (blue, solid line); (b) M2 only (green, dashed line); (c) both M1 and M2, and (d) both M1 and M2 when all intermodal XPM coefficients are set to zero.

Fig. 7.
Fig. 7.

Optical properties of three HFs with the structure shown in the inset of Fig. 1 and different core diameters D. Only the first 16 modes are shown. The top row shows the effective index (neff) of the modes; the middle row shows the dispersion curves; the bottom row shows the group delay difference (gdd) between two pairs of modes. Red, green and pink lines indicate the HE11 (M1), TE01 (M2) and HE12 (M6) modes, respectively.

Fig. 8.
Fig. 8.

Output energy spectral density (ESD) after propagation in 30 mm of (a) HF1 and (b) HF4, when only the LP01 mode (blue) is launched. Only the LP0n higher order modes are considered: LP02 (yellow), LP03 (green), LP04 (red), LP05 (cyan), LP06 (magenta). The total output energy in each mode is indicated next to each curve. Input conditions for HF1 are the same as in Fig. 2(a); the same input fluence and soliton number N were used for the pump in HF4, by launching it with P 0 = 753 kW and at λp = 1185 nm.

Equations (6)

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E ( x , y , z , t ) = n d ω 1 2 { F n ( x , y , ω ) N n ( ω ) e i β ( n ) ( ω ) z A n ( z , ω ) e iωt + c . c } .
A p ( z , t ) z = i ( β 0 ( p ) β 0 ) A p ( z , t ) ( β 0 ( p ) β 1 ) A p ( z , t ) t + i n 2 β n ( p ) n ! ( i t ) n A p ( z , t )
+ i n 2 ω 0 c ( 1 + i τ 0 t ) l , m , n { Q plmn ( ω 0 ) [ 2 ( 1 f R ) A l ( z , t ) A m ( z , t ) A n * ( z , t )
+ 3 f R A l ( z , t ) h ( τ ) A m ( z , t τ ) A n * ( z , t τ ) ] } ,
Q plmn ( ω ) = ε 0 2 n 0 2 c 2 12 d x d y [ F p * ( ω ) · F l ( ω ) ] [ F m ( ω ) · F n * ( ω ) ] N p ( ω ) N l ( ω ) N m ( ω ) N n ( ω ) ,
L NL < L W ,

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