Abstract

The significance of full vectorial pulse propagation through emerging waveguides has not been investigated. Here we report the development of a generalised vectorial model of nonlinear pulse propagation due to the effects of Stimulated Raman Scattering (SRS) in optical waveguides. Unlike standard models, this model does not use the weak guidance approximation, and thus accurately models the modal Raman gain of optical waveguides in the strong guidance regime. Here we develop a vectorial-based nonlinear Schrödinger Eq. (VNSE) to demonstrate how the standard model fails in certain regimes, with up to factors of 2.5 enhancement in Raman gain between the VNSE and the standard model. Using the VNSE we are able to explore opportunities for tailoring of the modal Raman gain spectrum to achieve effects such as gain flattening through design of the optical fiber.

© 2009 Optical Society of America

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    [Crossref]
  31. T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
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  37. A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
    [Crossref]
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    [Crossref]
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    [Crossref]
  41. V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20(2), 250–254 (2002).
    [Crossref]
  42. S. Cui, J. S. Liu, and X. M. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. 16(11), 2451–2453 (2004).
    [Crossref]
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2009 (2)

S. Afshar V and T. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17(4), 2298–2318 (2009).
[Crossref]

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[Crossref]

2008 (3)

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[Crossref]

M. Foster, A. Turner, M. Lipson, and A. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[Crossref]

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
[Crossref]

2007 (8)

A. Mussot, M. Beaugeois, M. Bouazaoui, and T. Sylvestre, “Tailoring CW supercontinuum generation in microstructured fibers with two-zero dispersion wavelengths,” Opt. Express 15(18), 11,553–11,563 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-18-11553.

M. Lamont, C. de Sterke, and B. Eggleton, “Dispersion engineering of highly nonlinear As_2S_3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15(15), 9458–9463 (2007).
[Crossref]

S. Afshar, V., S. Warren-Smith, and T. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15(26), 17,891–17,901 (2007).

M. Foster, A. Turner, R. Salem, M. Lipson, and A. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12,949–12,958 (2007).

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16,604–16,644 (2007).

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
[Crossref]

Q. Guanshi, R. Jose, and Y. Ohishi, “Design of ultimate gain-flattened O+ E and S+ C+ L ultrabroadband fiber amplifiers using a new fiber Raman gain medium,” J. Lightwave Technol. 25(9), 2727–2738 (2007). USA.

2006 (3)

X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(1–2), 160–170 (2006).
[Crossref]

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

2005 (4)

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
[Crossref]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref]

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
[Crossref]

C. Kakkar and K. Thyagarajan, “High gain Raman amplifier with inherent gain flattening and dispersion compensation,” Opt. Commun. 250(1–3), 77–83 (2005).
[Crossref]

2004 (11)

R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
[Crossref]

D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and Nonlinear Optical Processes in Silicon Waveguides,” Opt. Express 12(1), 149–160 (2004).
[Crossref]

K. Thyagarajan and C. Kakkar, “Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band,” J. Lightwave Technol. 22(10), 2279–2286 (2004).
[Crossref]

F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
[Crossref]

Q. Xu, V. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
[Crossref]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). URL http://ol.osa.org/abstract.cfm?URI=ol-29-11-1209.
[Crossref]

M. Foster and A. Gaeta, “Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,” Opt. Express 12(14), 3137–3143 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3137.
[Crossref]

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
[Crossref]

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
[Crossref]

S. Cui, J. S. Liu, and X. M. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. 16(11), 2451–2453 (2004).
[Crossref]

2003 (5)

A. Mori, H. Masuda, K. Shikano, and M. Shimizu, “Ultra-wide-band tellurite-based fiber Raman amplifier,” J. Lightwave Technol. 21(5), 1300–1306 (2003). USA.
[Crossref]

G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses,” Opt. Lett. 28(12), 989–991 (2003). URL http://ol.osa.org/abstract.cfm?URI=ol-28-12-989.
[Crossref]

A. Kireev and T. Graf, “Vector coupled-mode theory of dielectric waveguides,” IEEE J. Quantum Electron. 39(7), 866–873 (2003).
[Crossref]

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
[Crossref]

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
[Crossref]

2002 (4)

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20(2), 250–254 (2002).
[Crossref]

B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
[Crossref]

T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
[Crossref]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). USA.
[Crossref]

1996 (1)

C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13(10), 2170–2177 (1996).
[Crossref]

1977 (1)

R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5(1), 2–68 (1977).

Abbott, D.

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
[Crossref]

Afshar, S.

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
[Crossref]

S. Afshar, V., S. Warren-Smith, and T. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15(26), 17,891–17,901 (2007).

Afshar V, S.

S. Afshar V and T. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17(4), 2298–2318 (2009).
[Crossref]

Aggarwal, I.

R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
[Crossref]

Agrawal, G. P.

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16,604–16,644 (2007).

C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13(10), 2170–2177 (1996).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

Almeida, V.

Q. Xu, V. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
[Crossref]

Almeida, V. R.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). URL http://ol.osa.org/abstract.cfm?URI=ol-29-11-1209.
[Crossref]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). USA.
[Crossref]

Asimakis, S.

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
[Crossref]

Atakaramians, S.

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
[Crossref]

Auguste, J.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
[Crossref]

Baker, N.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
[Crossref]

Barrios, C. A.

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Beloglazov, V.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
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F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). USA.
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S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
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Bolger, J.

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
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B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
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T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
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Bouazaoui, M.

A. Mussot, M. Beaugeois, M. Bouazaoui, and T. Sylvestre, “Tailoring CW supercontinuum generation in microstructured fibers with two-zero dispersion wavelengths,” Opt. Express 15(18), 11,553–11,563 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-18-11553.

Bouwmans, G.

F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

Bugar, I.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
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Cardinal, T.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
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Chen, X. G.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(1–2), 160–170 (2006).
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S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
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Choi, D.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
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Chorvat, D.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
[Crossref]

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
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Chou, C. Y.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and Nonlinear Optical Processes in Silicon Waveguides,” Opt. Express 12(1), 149–160 (2004).
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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
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G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

Cotter, D.

P. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, 1990).

Couny, F.

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

Cruz, C.

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

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S. Cui, J. S. Liu, and X. M. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. 16(11), 2451–2453 (2004).
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Dadap, J.

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
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Dadap, J. I.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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de Sterke, C.

M. Lamont, C. de Sterke, and B. Eggleton, “Dispersion engineering of highly nonlinear As_2S_3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15(15), 9458–9463 (2007).
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T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
[Crossref]

B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
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Delaye, P.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
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Delfyett, P.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
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Dimitropoulos, D.

D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and Nonlinear Optical Processes in Silicon Waveguides,” Opt. Express 12(1), 149–160 (2004).
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Driscoll, J.

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
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Dudley, J.

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
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Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
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Dulkeith, E.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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Ebendorff-Heidepriem, H.

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
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Efimov, A.

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
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Eggleton, B.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
[Crossref]

M. Lamont, C. de Sterke, and B. Eggleton, “Dispersion engineering of highly nonlinear As_2S_3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15(15), 9458–9463 (2007).
[Crossref]

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
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Février, S.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
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Finazzi, V.

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
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Finsterbusch, K.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
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Fischer, V., B.

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
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Foster, M.

M. Foster, A. Turner, M. Lipson, and A. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
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M. Foster, A. Turner, R. Salem, M. Lipson, and A. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12,949–12,958 (2007).

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
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M. Foster and A. Gaeta, “Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,” Opt. Express 12(14), 3137–3143 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3137.
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Fragnito, H.

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

Frampton, K.

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
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Frey, R.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
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Fu, L.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
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Fukuda, H.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
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Gaeta, A.

M. Foster, A. Turner, M. Lipson, and A. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
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M. Foster, A. Turner, R. Salem, M. Lipson, and A. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12,949–12,958 (2007).

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
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M. Foster and A. Gaeta, “Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,” Opt. Express 12(14), 3137–3143 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3137.
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Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
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Graf, T.

A. Kireev and T. Graf, “Vector coupled-mode theory of dielectric waveguides,” IEEE J. Quantum Electron. 39(7), 866–873 (2003).
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J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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Guanshi, Q.

Q. Guanshi, R. Jose, and Y. Ohishi, “Design of ultimate gain-flattened O+ E and S+ C+ L ultrabroadband fiber amplifiers using a new fiber Raman gain medium,” J. Lightwave Technol. 25(9), 2727–2738 (2007). USA.

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R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
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Hongki, K.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
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Hsieh, I.

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
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Hsieh, I. W.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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Itabashi, S.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
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Jalali, B.

D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and Nonlinear Optical Processes in Silicon Waveguides,” Opt. Express 12(1), 149–160 (2004).
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Jankovic, L.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
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Jose, R.

Q. Guanshi, R. Jose, and Y. Ohishi, “Design of ultimate gain-flattened O+ E and S+ C+ L ultrabroadband fiber amplifiers using a new fiber Raman gain medium,” J. Lightwave Technol. 25(9), 2727–2738 (2007). USA.

R. Jose and Y. Ohishi, “Higher nonlinear indices, Raman gain coefficients, and bandwidths in the TeO/sub 2/-ZnO-Nb/sub 2/O/sub 5/-MoO/sub 3/quaternary glass system,” Appl. Phys. Lett.90(21), 211,104-1-211,104-211,104-3 (2007). USA.

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Kibler, B.

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
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Kireev, A.

A. Kireev and T. Graf, “Vector coupled-mode theory of dielectric waveguides,” IEEE J. Quantum Electron. 39(7), 866–873 (2003).
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Knight, J.

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
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Knight, J. C.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). USA.
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Koizumi, F.

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
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G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses,” Opt. Lett. 28(12), 989–991 (2003). URL http://ol.osa.org/abstract.cfm?URI=ol-28-12-989.
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Q. Xu, V. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
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J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses,” Opt. Lett. 28(12), 989–991 (2003). URL http://ol.osa.org/abstract.cfm?URI=ol-28-12-989.
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B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
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T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
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H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
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A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
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Sanghera, J.

R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
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S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
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Schulte, A.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
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J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
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Shaw, L.

R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
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A. Mori, H. Masuda, K. Shikano, and M. Shimizu, “Ultra-wide-band tellurite-based fiber Raman amplifier,” J. Lightwave Technol. 21(5), 1300–1306 (2003). USA.
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R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
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A. Snyder and J. Love, Optical waveguide theory (Kluwer Academic Pub, 1983).

Stegeman, G.

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Steinvurzel, P.

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
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Sylvestre, T.

A. Mussot, M. Beaugeois, M. Bouazaoui, and T. Sylvestre, “Tailoring CW supercontinuum generation in microstructured fibers with two-zero dispersion wavelengths,” Opt. Express 15(18), 11,553–11,563 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-18-11553.

Ta’eed, V.

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
[Crossref]

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
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Taylor, A.

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
[Crossref]

Thyagarajan, K.

C. Kakkar and K. Thyagarajan, “High gain Raman amplifier with inherent gain flattening and dispersion compensation,” Opt. Commun. 250(1–3), 77–83 (2005).
[Crossref]

K. Thyagarajan and C. Kakkar, “Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band,” J. Lightwave Technol. 22(10), 2279–2286 (2004).
[Crossref]

Trebino, R.

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
[Crossref]

Tsuchizawa, T.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref]

Turner, A.

M. Foster, A. Turner, M. Lipson, and A. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[Crossref]

M. Foster, A. Turner, R. Salem, M. Lipson, and A. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12,949–12,958 (2007).

Viale, P.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
[Crossref]

Vlasov, Y. A.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[Crossref]

Wadsworth, W.

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
[Crossref]

Warren-Smith, V., S.

S. Afshar, V., S. Warren-Smith, and T. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15(26), 17,891–17,901 (2007).

Watanabe, T.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref]

White, T.

B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
[Crossref]

T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
[Crossref]

Wiederhecker, G.

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

Winful, H. G.

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20(2), 250–254 (2002).
[Crossref]

Xia, F. N.

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[Crossref]

Xu, Q.

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). URL http://ol.osa.org/abstract.cfm?URI=ol-29-11-1209.
[Crossref]

Q. Xu, V. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
[Crossref]

Yamada, K.

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref]

Yasseri, S.

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[Crossref]

Yiou, S.

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
[Crossref]

Yu, G.

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
[Crossref]

Zheltikov, A.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
[Crossref]

Appl. Phys. B: Lasers and Optics (1)

M. Foster, J. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. Gaeta, “Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation,” Appl. Phys. B: Lasers and Optics 81(2), 363–367 (2005).
[Crossref]

Appl. Phys. Lett. (1)

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. Chorvat, D. Chorvat, V. Beloglazov, N. Skibina, M. Bloemer, and M. Scalora, “Self-phase modulation of submicrojoule femtosecond pulses in a hollow-core photonic-crystal fiber,” Appl. Phys. Lett. 85, 3690 (2004).
[Crossref]

IEEE J. Quantum Electron. (2)

X. G. Chen, N. C. Panoiu, and R. M. Osgood, “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(1–2), 160–170 (2006).
[Crossref]

A. Kireev and T. Graf, “Vector coupled-mode theory of dielectric waveguides,” IEEE J. Quantum Electron. 39(7), 866–873 (2003).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. Cui, J. S. Liu, and X. M. Ma, “A novel efficient optimal design method for gain-flattened multiwavelength pumped fiber Raman amplifier,” IEEE Photon. Technol. Lett. 16(11), 2451–2453 (2004).
[Crossref]

J. Lightwave Technol. (4)

Q. Guanshi, R. Jose, and Y. Ohishi, “Design of ultimate gain-flattened O+ E and S+ C+ L ultrabroadband fiber amplifiers using a new fiber Raman gain medium,” J. Lightwave Technol. 25(9), 2727–2738 (2007). USA.

A. Mori, H. Masuda, K. Shikano, and M. Shimizu, “Ultra-wide-band tellurite-based fiber Raman amplifier,” J. Lightwave Technol. 21(5), 1300–1306 (2003). USA.
[Crossref]

V. E. Perlin and H. G. Winful, “Optimal design of flat-gain wide-band fiber Raman amplifiers,” J. Lightwave Technol. 20(2), 250–254 (2002).
[Crossref]

K. Thyagarajan and C. Kakkar, “Novel fiber design for flat gain Raman amplification using single pump and dispersion compensation in S band,” J. Lightwave Technol. 22(10), 2279–2286 (2004).
[Crossref]

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

C. Headley and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13(10), 2170–2177 (1996).
[Crossref]

B. Kuhlmey, T. White, G. Renversez, D. Maystre, L. Botten, C. de Sterke, and R. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
[Crossref]

T. White, B. Kuhlmey, R. McPhedran, D. Maystre, G. Renversez, C. de Sterke, and L. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
[Crossref]

R. Slusher, G. Lenz, J. Hodelin, J. Sanghera, L. Shaw, and I. Aggarwal, “Large Raman gain and nonlinear phase shifts in high-purity As 2 Se 3 chalcogenide fibers,” J. Opt. Soc. Am. B 21(6), 1146–1155 (2004).
[Crossref]

Nature (1)

G. Wiederhecker, C. Cordeiro, F. Couny, F. Benabid, S. Maier, J. Knight, C. Cruz, and H. Fragnito, “Field enhancement within an optical fibre with a subwavelength air core,” Nature 1(2), 115–118 (2007).

Opt. Commun. (1)

C. Kakkar and K. Thyagarajan, “High gain Raman amplifier with inherent gain flattening and dispersion compensation,” Opt. Commun. 250(1–3), 77–83 (2005).
[Crossref]

Opt. Express (19)

A. Efimov, A. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003).
[Crossref]

D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, “Phase-matching and Nonlinear Optical Processes in Silicon Waveguides,” Opt. Express 12(1), 149–160 (2004).
[Crossref]

V. Ta’eed, N. Baker, L. Fu, K. Finsterbusch, M. Lamont, D. Moss, H. Nguyen, B. Eggleton, D. Choi, S. Madden, and B. Luther-Davies, “Ultrafast all-optical chalcogenide glass photonic circuits,” Opt. Express 15(15), 9205–9221 (2007).
[Crossref]

J. Driscoll, X. Liu, S. Yasseri, I. Hsieh, J. Dadap, and R. Osgood, “Large longitudinal electric fields (E_z) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[Crossref]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16,604–16,644 (2007).

A. Mussot, M. Beaugeois, M. Bouazaoui, and T. Sylvestre, “Tailoring CW supercontinuum generation in microstructured fibers with two-zero dispersion wavelengths,” Opt. Express 15(18), 11,553–11,563 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-18-11553.

M. Foster, A. Turner, R. Salem, M. Lipson, and A. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12,949–12,958 (2007).

M. Nagel, A. Marchewka, and H. Kurz, “Low-index discontinuity terahertz waveguides,” Opt. Express 14(21), 9944–9954 (2006).
[Crossref]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref]

S. Afshar V and T. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part I: Kerr nonlinearity,” Opt. Express 17(4), 2298–2318 (2009).
[Crossref]

M. Foster, A. Turner, M. Lipson, and A. Gaeta, “Nonlinear optics in photonic nanowires,” Opt. Express 16(2), 1300–1320 (2008).
[Crossref]

M. Lamont, C. de Sterke, and B. Eggleton, “Dispersion engineering of highly nonlinear As_2S_3 waveguides for parametric gain and wavelength conversion,” Opt. Express 15(15), 9458–9463 (2007).
[Crossref]

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. Moore, K. Frampton, F. Koizumi, D. Richardson, and T. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12(21), 5082–5087 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-21-5082.
[Crossref]

S. Yiou, P. Delaye, A. Rouvie, J. Chinaud, R. Frey, G. Roosen, P. Viale, S. Février, P. Roy, J. Auguste, and J. Blondy, “Stimulated Raman scattering in an ethanol core microstructured optical fiber,” Opt. Express 13(12), 4786–4791 (2005).
[Crossref]

S. Atakaramians, S. Afshar, V., B. Fischer, D. Abbott, and T. Monro, “Porous fibers: a novel approach to low loss THz waveguides,” Opt. Express 16(12), 8845–8854 (2008).
[Crossref]

M. Foster and A. Gaeta, “Ultra-low threshold supercontinuum generation in sub-wavelength waveguides,” Opt. Express 12(14), 3137–3143 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3137.
[Crossref]

Y. Lizé, E. Mägi, V. Ta’eed, J. Bolger, P. Steinvurzel, and B. Eggleton, “Microstructured optical fiber photonic wires with subwavelength core diameter,” Opt. Express 12(14), 3209–3217 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-14-3209.
[Crossref]

S. Afshar, V., S. Warren-Smith, and T. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15(26), 17,891–17,901 (2007).

Opt. Lett. (4)

G. Renversez, B. Kuhlmey, and R. McPhedran, “Dispersion management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses,” Opt. Lett. 28(12), 989–991 (2003). URL http://ol.osa.org/abstract.cfm?URI=ol-28-12-989.
[Crossref]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004). URL http://ol.osa.org/abstract.cfm?URI=ol-29-11-1209.
[Crossref]

Q. Xu, V. Almeida, R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004).
[Crossref]

R. Stegeman, L. Jankovic, K. Hongki, C. Rivero, G. Stegeman, K. Richardson, P. Delfyett, G. Yu, A. Schulte, and T. Cardinal, “Tellurite glasses with peak absolute Raman gain coefficients up to 30 times that of fused silica,” Opt. Lett. 28(13), 1126–1128 (2003). USA.
[Crossref]

Phys. Rev. Lett. (1)

F. Benabid, G. Bouwmans, J. Knight, P. Russell, and F. Couny, “Ultrahigh Efficiency Laser Wavelength Conversion in a Gas-Filled Hollow Core Photonic Crystal Fiber by Pure Stimulated Rotational Raman Scattering in Molecular Hydrogen,” Phys. Rev. Lett. 93(12), 123,903 (2004).

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R. Hellwarth, “Third-order optical susceptibilities of liquids and solids,” Prog. Quantum Electron. 5(1), 2–68 (1977).

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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
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Science (1)

F. Benabid, J. C. Knight, G. Antonopoulos, and P. S. J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298(5592), 399–402 (2002). USA.
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G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2007).

P. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, 1990).

K. Okamoto, Fundamentals of Optical Waveguides (Academic Press, 2006).

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R. Jose and Y. Ohishi, “Higher nonlinear indices, Raman gain coefficients, and bandwidths in the TeO/sub 2/-ZnO-Nb/sub 2/O/sub 5/-MoO/sub 3/quaternary glass system,” Appl. Phys. Lett.90(21), 211,104-1-211,104-211,104-3 (2007). USA.

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Figures (3)

Fig. 1.
Fig. 1.

Left: Effective area of a chalcogenide nanowire versus core diameter, using the VNLSE (Red) and SM (Blue). Right: Effective Raman gain coefficient of a chalcogenide nanowire versus core diameter using VNLSE (Red) and the bulk Raman gain coefficient is shown in blue.

Fig. 2.
Fig. 2.

Modal Raman gain of a Chalcogenide nanowire for varying core diameter. SM in blue, VNSE in red, ASM in green and VNSE ORTH in Pink. Pump wavelength 1550 nm, Stokes wavelength at 1608 nm.

Fig. 3.
Fig. 3.

a) Approximation of the bulk Raman gain coefficient spectrum of tellurite glass. b) Modal Raman gain spectrum of a tellurite nanowire for 1.5µm core diameter (cyan) and 0.5µm core diameter (red) calculated with the VNSE. c) Ratio (R) of the two peaks for varying core diameter. d) Plot of the amount of decrease in modal Raman gain due to finite overlap of the Stokes fields with the pump fields and the Raman active core.

Equations (52)

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

g (m1W1)=gRAeff,
×E(r,ω)=i μ0 ω H (r,ω),
×H(r,ω)=i ω [ε0E(r,ω)+PκL(r,ω)] ,
F (r,t)=12πF(r,ω)eiωtdω.
P˜κL(r,ω)=ε0χ(1)(ω;ω)·E˜oκ,
n2(r,ω)=1 + χ(1) (ω;ω).
E˜oκ=12Eκμδ(ωωκ),
H˜oκ=12Hκμδ(ωωκ),
Eκμ=eκμ(x,y)eiβκμzNκμ + c . c . , Hκμ =hκμ(x,y)eiβκμzNκμ+c.c.,
12(eκμ*×hκη)×ẑdA=Nκμηδμη=Nκμ,Nκμ=12(eκμ*×hκμ)×ẑdA.
E˜κ=12Σηa˜κη(z,ωωκ)Eκη,
H˜κ=12ηα˜κη(z,ωωκ)Hκη.
× E˜κ=iμ0ω2ηα˜κηHκm,
× H˜κ=iωε0n2(r,ω)2 ηα˜κηEκηiωP˜κNL,
zFcs·ẑdA= · Fcs d A ,
Fcs=E˜os*×H˜s+E˜s+H˜os* .
a˜sμ(z,ωωs)z=i Δ ωs βsμ1 a˜sμ (z,ωωs)+iΔωsnμβsη1a˜sη(z,ωωs)+O(Δωs2)
+ i2 Esμ* · ω P˜sNL (r,ω)dA
βsμ1=14Nsμ[μ0hsμ2+ε0[ω(ωn2(r,ω))]ω=ωs|esμ2] dA
βsη1=ei(βsηβsμ)z4NsηNsμ[μ0hsη.hsμ*+ε0[ω(ωn2(r,ω))]|ω=ωsesη.esμ*]dA
αsμ(z,t)z=D̂asu(z,t)eiωstteβsμz2Nsμesμ*PsNL(r,t)dA
D̂=i βsμ1 t + i ημ βsη1 t + O (2t2) ,
Pωs(3) (t)=3ε02R(3)(r,tt1,tt2,tt3)Eωp(r,t1)Eωp*(r,t2)Eωs(r,t3)
exp (ir=13ωr(ttr)) d t1 d t2 d t3 ,
R(3)(tt1,tt2,tt3)=R (x,y,tt2)δ(tt2)δ(t2t3).
Pωs(3) (t)=3ε02η,σ,ξei(βpηβpσ+βsξ)NpηNpσNsξαpη(z,t)
× R (x,y,tt2)epηepσ*esξapσ*(z,t2)asξ(z,t2)
× exp (iΔω(tt2))dt2,
asμ(z,t)z=D̂asμ(z,t)+iωs(1+iωst)eiβsμz4Nsμesμ*·Pωs(3)(t)dA
=D̂asμ(z,t)+i3ε0ωs8(1+iωst)n,σ,ξei(βpηβpσ+βsξiβsμz)NpηNpσNsξNsμapη(z,t)
esμ* · R (x,y,tt2) epη epη* esξ apσ* (z,t2) asξ (z,t2)
exp (iΔω(tt2)) d t2 d A .
R(x,y,τ)=χxxxx(3)2(faha(τ)δijδkl+12fbhb(τ)(δikδjl+δilδjk)),
Xxxxx(3)(x,y)=4ε0cn2(x,y)n2(x,y)3
asμ(z,t)z=D̂asμ(z,t)+iε02cωs4(1+iωst)η,σ,ξei(βpηβpσ+βsξiβsμz)NpηNpσNsξNsμapη(z,t)
× fa n2 n2 (esμ*·epη)(epσ*·esξ)
× ha (tt2)apσ*(z,t2)asξ(z,t2)exp(iΔω(tt2))dt2
+ 12 f b n2 n2 {(epσ*·epη)(esμ*·esξ)+(esμ*·epσ*)(epη·esξ*)}
× hb (tt2)apσ*(z,t2)asξ(z,t2)exp(iΔω(tt2))dt2dA.
asμ(Z,t)t=D̂asμ+ε02c28(1+iωst)η,σ,ξei(βpηβpσ+βsξiβsμz)NpηNpσNsξNsμapηapσ*asξ
ga n2 (esμ*·epη)(epσ*·esξ)
+ 12 g bn2 [(epσ*·epη)(esμ*·esξ)+(esμ*·epσ*)(epη·esξ)] d A
asμ(z,t)z=D̂asμ+gμμ2[1+iωst]apμ2asμ
+ ημgμη2[1+iωst]apη2asμ
+ phaseterms .
g μ η=ε02c24NpηNsμgan2epη·esμ*2+gbn2(epη·esμ2+epη2esμ2)dA.
g=g̅RAeff,
A̅eff=(epη*×hpη.ẑdA)(esμ*×hsμ.ẑdA)(epη*×hpη.ẑ)(esμ*×hsμ.ẑ)dA,
g̅R=ε02cgan2epη·esμ*2+gbn2(epη·esμ2+epη2esη2)dA(epη*×hpη·ẑ)(esμ*×hsμ·ẑ)dA .
A̅eff=(eμ×hμ·ẑ)dA2(eμ×hμ·ẑ)2dA.
g=ε02c24NpηNsμgRn2epη·esμ*2dA,
g̅R=ε02c2gRn2epn·esμ*2dA(epη*×hpη·ẑ)(esμ*×hsμ·ẑ)dA.

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