Abstract

The guided, single-mode propagation of ultrashort optical pulses is commonly described by a well studied and understood generalized nonlinear Schrödinger equation. Here we present and discuss an extended version for multimode optical fibers and waveguides including polarization effects, high-order dispersion, Kerr and Raman nonlinearities, self-steepening effects, as well as wavelength-dependent mode coupling and nonlinear coefficients. We then investigate the symmetry properties of the nonlinear coupling coefficients for the cases of step-index and circularly symmetric conventional fibers and for microstructured fibers with hexagonal symmetry. Finally, we study the computational complexity of the proposed algorithm.

© 2008 Optical Society of America

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2008 (3)

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]

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).
[CrossRef]

P. Dupriez, F. Poletti, P. Horak, M. N. Petrovich, Y. Jeong, J. Nilsson, D. J. Richardson, and D. N. Payne, “Efficient white light generation in secondary cores of holey fibers,” Opt. Express 15, 3729-3736 (2007).
[CrossRef]

J. Lægsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110-16123 (2007).
[CrossRef]

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

H.-G. Choi, C.-S. Kee, K.-H. Hong, J. Sung, S. Kim, D.-K. Ko, J. Lee, J.-E. Kim, and H. Y. Park, “Dispersion and birefringence of irregularly microstructured fiber with an elliptic core,” Appl. Opt. 46, 8493-8498 (2007).
[CrossRef]

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382-5387 (2007).
[CrossRef]

2006 (4)

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 (2006), paper CTuA4.

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297-1309 (2006).
[CrossRef]

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

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2006).

2005 (3)

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 (5)

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]

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[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]

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]

D. A. Akimov, E. E. Serebryannikov, A. M. Zheltikov, M. Schmitt, R. Maksimenka, W. Kiefer, K. V. Dukelskii, V. S. Shevandin, and Y. N. Kondratev, “Efficient anti-Stokes generation through phase-matched four-wave mixing in higher-order modes of a microstructure fiber,” Opt. Lett. 28, 1948-1950 (2003).
[CrossRef]

2002 (2)

2001 (1)

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

2000 (3)

1997 (1)

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

1995 (1)

1992 (1)

1990 (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]

1987 (1)

1981 (1)

1980 (1)

1975 (1)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides--I: Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421-429 (1975).
[CrossRef]

1973 (1)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276-278 (1973).
[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]

1969 (1)

A. W. Snyder, “Asymptotic expressions for the eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. 17, 1130-1138 (1969).
[CrossRef]

Agrawal, G. P.

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

Akimov, D. A.

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]

Baggett, J. C.

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 (2006), paper CTuA4.

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]

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]

Bhagwat, A. R.

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]

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.

Chaipiboonwong, T.

Chau, A. H. L.

Cherif, R.

Chernikov, S. V.

Choi, H.-G.

Coen, S.

Conforti, M.

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]

Crosignani, B.

De Angelis, C.

Degiorgio, V.

Delmonte, T.

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 (2006), paper CTuA4.

Di Porto, P.

Dudley, J. M.

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382-5387 (2007).
[CrossRef]

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

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, “Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765-771 (2002).
[CrossRef]

Dukelskii, K. V.

Dupriez, P.

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.

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]

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 (2006), paper CTuA4.

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]

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 (2006), paper CTuA4.

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]

Foster, M. A.

Freude, W.

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]

Gaeta, A. L.

Genty, G.

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382-5387 (2007).
[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]

Grossard, N.

Hand, D. P.

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 (2006), paper CTuA4.

Hänsch, T. W.

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297-1309 (2006).
[CrossRef]

Harvey, J. D.

Hasegawa, A.

Hong, K.-H.

Horak, P.

P. Dupriez, F. Poletti, P. Horak, M. N. Petrovich, Y. Jeong, J. Nilsson, D. J. Richardson, and D. N. Payne, “Efficient white light generation in secondary cores of holey fibers,” Opt. Express 15, 3729-3736 (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).
[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]

Ippen, E. P.

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276-278 (1973).
[CrossRef]

Jeong, Y.

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]

Kee, C.-S.

Kibler, B.

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382-5387 (2007).
[CrossRef]

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

Kiefer, W.

Kim, J.-E.

Kim, S.

Kinsler, P.

Knight, J. C.

Ko, D.-K.

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]

Kondratev, Y. N.

Krausz, F.

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

Kremp, T.

Lægsgaard, J.

Lee, J.

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]

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Lipson, M.

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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 (2006), paper CTuA4.

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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]

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P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides--I: Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421-429 (1975).
[CrossRef]

Menyuk, C. R.

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]

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 (2006), paper CTuA4.

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]

Murdoch, S. G.

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]

Nilsson, J.

O'Driscoll, E. J.

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 (2006), paper CTuA4.

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2006).

Omenetto, F. G.

Park, H. Y.

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]

Payne, D. N.

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]

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 (2006), paper CTuA4.

Petrovich, M. N.

Pitois, S.

Poletti, F.

P. Dupriez, F. Poletti, P. Horak, M. N. Petrovich, Y. Jeong, J. Nilsson, D. J. Richardson, and D. N. Payne, “Efficient white light generation in secondary cores of holey fibers,” Opt. Express 15, 3729-3736 (2007).
[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]

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]

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 (2006), paper CTuA4.

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.

Ranka, J. K.

Richardson, D. J.

P. Dupriez, F. Poletti, P. Horak, M. N. Petrovich, Y. Jeong, J. Nilsson, D. J. Richardson, and D. N. Payne, “Efficient white light generation in secondary cores of holey fibers,” Opt. Express 15, 3729-3736 (2007).
[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. 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 (2006), paper CTuA4.

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]

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Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef]

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Schmitt, M.

Serebryannikov, E. E.

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).
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Shevandin, V. S.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

A. W. Snyder, “Asymptotic expressions for the eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. 17, 1130-1138 (1969).
[CrossRef]

Spadoti, D. H.

Stentz, A. J.

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R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276-278 (1973).
[CrossRef]

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Tartara, L.

Taylor, A. J.

Tonello, A.

Trillo, S.

Turner, A. C.

Urbanczyk, W.

Wabnitz, S.

Wadsworth, W. J.

Watson, M. A.

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 (2006), paper CTuA4.

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[CrossRef]

Zghal, M.

Zheltikov, A. M.

Appl. Opt. (1)

Appl. Phys. B (2)

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]

B. Kibler, J. M. Dudley, and S. Coen, “Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area,” Appl. Phys. B 81, 337-342 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

R. H. Stolen and E. P. Ippen, “Raman gain in glass optical waveguides,” Appl. Phys. Lett. 22, 276-278 (1973).
[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]

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 J. Sel. Top. Quantum Electron. (1)

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]

IEEE Trans. Microwave Theory Tech. (2)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides--I: Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421-429 (1975).
[CrossRef]

A. W. Snyder, “Asymptotic expressions for the eigenfunctions and eigenvalues of a dielectric or optical waveguide,” IEEE Trans. Microwave Theory Tech. 17, 1130-1138 (1969).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Express (10)

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

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 (2005).
[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).
[CrossRef]

P. Dupriez, F. Poletti, P. Horak, M. N. Petrovich, Y. Jeong, J. Nilsson, D. J. Richardson, and D. N. Payne, “Efficient white light generation in secondary cores of holey fibers,” Opt. Express 15, 3729-3736 (2007).
[CrossRef]

R. Cherif, M. Zghal, L. Tartara, and V. Degiorgio, “Supercontinuum generation by higher-order mode excitation in a photonic crystal fiber,” Opt. Express 16, 2147-2152 (2008).
[CrossRef]

G. Genty, P. Kinsler, B. Kibler, and J. M. Dudley, “Nonlinear envelope equation modeling of subcycle dynamics and harmonic generation in nonlinear waveguides,” Opt. Express 15, 5382-5387 (2007).
[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]

M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16, 1300-1320 (2008).
[CrossRef]

A. R. Bhagwat and A. L. Gaeta, “Nonlinear optics in hollow-core photonic bandgap fibers,” Opt. Express 16, 5035-5047 (2008).
[CrossRef]

J. Lægsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110-16123 (2007).
[CrossRef]

Opt. Lett. (8)

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)

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

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

Rev. Mod. Phys. (2)

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

T. W. Hänsch, “Nobel lecture: passion for precision,” Rev. Mod. Phys. 78, 1297-1309 (2006).
[CrossRef]

Science (1)

P. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003).
[CrossRef]

Other (4)

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 (2006), paper CTuA4.

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

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic, 2006).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer, 2000).

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Figures (3)

Fig. 1
Fig. 1

Distribution of the magnitude of coupling coefficients Q p l m n ( 1 ) and Q p l m n ( 2 ) for the first ten modes of a step-index fiber with a 6 μ m core radius, a core refractive index of 1.45, and a cladding refractive index of 1.44 at 1.5 μ m wavelength. Dashed curve: exact mode functions with rotational symmetry [Eq. (17)]; solid curve: exact real-valued mode functions; dashed-dotted curve: five approximate e + polarized mode functions only. See text for details.

Fig. 2
Fig. 2

(a) Distribution of the magnitude of coupling coefficients Q p l m n ( 1 ) and Q p l m n ( 2 ) of the first 7, 10, and 12 modes of the MOF shown in (b). The fiber presents Λ = 6 μ m , d Λ = 0.92 , D = 6 μ m and a glass refractive index of 1.444 at a wavelength of 1.5 μ m .

Fig. 3
Fig. 3

(a) Execution time of the main functional blocks of numerical simulations of the MM-GNLSE as a function of the number of modes M. The markers indicate the measured times while the lines are the best fit, corresponding to the equation in the legend. (b) Total execution time as a function of the grid size N for 1, 3, and 5 modes. The markers indicate the measured times and the lines the best logarithmic fit, as shown in the legend.

Tables (2)

Tables Icon

Table 1 Symmetry Properties of Step-Index Fiber Modes

Tables Icon

Table 2 Fourier Series Representation for the Radial and Azimuthal Components of the Electric Field for the Eight Symmetry Classes of a C 6 v Waveguide a

Equations (32)

Equations on this page are rendered with MathJax. Learn more.

× E ( x , t ) = μ 0 t H ( x , t ) ,
× H ( x , t ) = ϵ 0 n ( x , y ) 2 t E ( x , t ) + t P NL ( x , t ) .
P NL ( x , t ) = ϵ 0 χ ( 3 ) E ( x , t ) d τ R ( t τ ) E ( x , τ ) 2 .
1 4 d x d y [ F m * ( ω ) × H n ( ω ) + F n ( ω ) × H m * ( ω ) ] e z = δ m n N n ( ω ) 2 ,
E ( x , 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 i ω t + c.c. } .
A p ( z , ω ) z = i ω 4 N p ( ω ) d x d y F p * ( ω ) P NL ( ω ) e i β p ( ω ) z .
A p ( z , t ) z = i ( β 0 ( p ) β 0 ) A p ( z , t ) ( β 1 ( 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 l , m , n { ( 1 + i τ p l m n ( 1 ) t ) Q p l m n ( 1 ) ( ω 0 ) 2 A l ( z , t ) d τ R ( τ ) A m ( z , t τ ) A n * ( z , t τ ) + ( 1 + i τ p l m n ( 2 ) t ) Q p l m n ( 2 ) ( ω 0 ) A l * ( z , t ) d τ R ( τ ) A m ( z , t τ ) A n ( z , t τ ) e 2 i ω 0 τ } = D ( p ) ( z , t ) + N ( p ) ( z , t ) .
Q p l m n ( 1 ) ( 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 ) ,
Q p l m n ( 2 ) ( 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 ) ,
τ p l m n ( 1 , 2 ) = 1 ω 0 + { ω ln [ Q p l m n ( 1 , 2 ) ( ω ) ] } ω 0 .
R ( t ) = ( 1 f R ) δ ( t ) + 3 2 f R h ( t ) ,
N 1 2 ( ω ) n eff ( ω ) ϵ 0 c 2 d x d y F 2 ( ω ) ,
Q 1111 ( 1 ) ( ω ) = Q 1111 ( 2 ) ( ω ) = n 0 2 3 n eff 2 ( ω ) d x d y F 4 ( ω ) [ d x d y F 2 ( ω ) ] 2 = n 0 2 3 n eff 2 ( ω ) A eff ( ω ) ,
τ 1 = τ 1111 ( 1 ) = τ 1111 ( 2 ) = 1 ω 0 + { ω ln [ n eff 2 ( ω ) A eff ( ω ) ] } ω 0 ,
N ( 1 ) ( z , t ) = i n 2 ω 0 c A eff ( ω 0 ) ( 1 + i τ 1 t ) A 1 ( z , t ) d τ R ( τ ) A 1 ( z , t τ ) 2 ,
N ( 1 ) ( z , t ) = i n 2 ω 0 c A eff ( ω 0 ) ( 1 + i τ 1 t ) { ( 1 f R ) A 1 ( z , t ) [ 2 3 A 1 ( z , t ) 2 + 4 3 A 2 ( z , t ) 2 ] + f R A 1 ( z , t ) d τ h ( τ ) [ A 1 ( z , t τ ) 2 + A 2 ( z , t τ ) 2 ] } ,
n d t A n ( z , t ) 2 = const ,
Q p l m n ( 1 ) = Q n m l p ( 1 ) = Q l p n m ( 1 ) * = Q m n p l ( 1 ) * ,
Q p l m n ( 2 ) = Q l p m n ( 2 ) = Q p l n m ( 2 ) = Q l p n m ( 2 ) = Q m n p l ( 2 ) * = Q m n l p ( 2 ) * = Q n m p l ( 2 ) * = Q n m l p ( 2 ) * .
F p ( r , ϕ ) = F p ( r ) exp ( i m p ϕ ) ,
Q p l m n ( 1 ) = 0 for m p + m l + m m m n 0 ,
Q p l m n ( 2 ) = 0 for m p m l + m m + m n 0 .
Q p l m n ( 1 ) = 0 for σ p σ l or σ m σ n ,
Q p l m n ( 2 ) = 0 for σ p = σ l or σ m = σ n .
t 2 F r , p 2 r 2 F ϕ , p ϕ + r ( F r , p d ln n 2 d r ) F r , p r 2 + ( n 2 k 2 β 2 ) F r , p = 0 ,
t 2 F ϕ , p + 1 r ( d ln n 2 d r + 2 r ) F r , p ϕ F ϕ , p r 2 + ( n 2 k 2 β 2 ) F ϕ , p = 0 ,
F p ( r , ϕ ) = e σ p F p ( r ) exp ( i m p ϕ ) ,
d ϕ [ F p * F l ] = d ϕ [ F r , p * F r , l + F ϕ , p * F ϕ , l + F z , p * F z , l ] = 0 for P p P l ,
Q p l m n ( 1 , 2 ) = 0 for P p + P l + P m + P n = 2 M + 1 , M = 2 , 3 , 4 , .
Q p l m n ( 1 , 2 ) = 0 for ± K p ± K l ± K m ± K n 6 N , N = 0 , ± 1 , ± 2 ,
Q p l m n ( 1 ) = 0 for K p + K l + K m K n 6 N , N = 0 , ± 1 ,
Q p l m n ( 2 ) = 0 for all modes p , l , m , n .

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