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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2009 (2)

2008 (3)

2007 (7)

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.

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. 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]

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).

2006 (3)

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]

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]

2005 (4)

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]

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]

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]

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]

2004 (6)

2003 (4)

2002 (4)

1996 (1)

1977 (1)

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

Aggarwal, I.

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]

Almeida, V.

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]

Atakaramians, S.

Auguste, J.

Baker, N.

Beloglazov, V.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Benabid, 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, 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]

Bloemer, M.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Blondy, J.

Botten, L.

Bugar, I.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Cao, Q.

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]

Cardinal, T.

Chen, X. G.

Chinaud, J.

Choi, D.

Chorvat, D.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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. ChorvatJr, 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]

Chou, C. Y.

Claps, R.

Coen, S.

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

Cordeiro, 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).

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).

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).

Cui, S.

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]

Dadap, J.

Dadap, J. I.

de Sterke, C.

Delaye, P.

Delfyett, P.

Dimitropoulos, D.

Driscoll, J.

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).
[CrossRef]

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).
[CrossRef]

Dulkeith, E.

Efimov, A.

Eggleton, B.

Février, S.

Finsterbusch, K.

Foster, M.

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).

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]

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).

Frey, R.

Fu, L.

Fukuda, H.

Gaeta, 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).

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]

Genty, G.

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

Graf, T.

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

Green, W. M. J.

Guanshi, Q.

Headley, C.

Hellwarth, R.

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

Hodelin, J.

Hongki, K.

Hsieh, I.

Hsieh, I. W.

Itabashi, S.

Jalali, B.

Jankovic, L.

Jose, R.

Kakkar, C.

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]

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).
[CrossRef]

Kireev, A.

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

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).

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]

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.
[CrossRef]

Konorov, S.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Kuhlmey, B.

Kurz, H.

Lamont, M.

Lee, D.

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]

Lenz, G.

Lin, Q.

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).

Lipson, M.

Liu, J. S.

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]

Liu, X.

Liu, X. P.

Luther-Davies, B.

Ma, X. M.

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]

Madden, S.

Maier, S.

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).

Marchewka, A.

Masuda, H.

Maystre, D.

McNab, S. J.

McPhedran, R.

Mori, A.

Moss, D.

Nagel, M.

Nguyen, H.

Ohishi, Y.

Omenetto, F.

Osgood, R.

Osgood, R. M.

Painter, O. J.

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).

Panepucci, R.

Panoiu, N. C.

Perlin, V. E.

Raghunathan, V.

Renversez, G.

Richardson, K.

Rivero, C.

Roosen, G.

Rouvie, A.

Roy, P.

Russell, P.

Russell, P. S. J.

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]

Salem, R.

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).

Sanghera, J.

Scalora, M.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Schulte, A.

Sekaric, L.

Shaw, L.

Shikano, K.

Shimizu, M.

Shoji, T.

Sidorov-Biryukov, D.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Skibina, N.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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]

Slusher, R.

Stegeman, G.

Stegeman, R.

Ta’eed, V.

Takahashi, J.

Takahashi, M.

Taylor, A.

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.

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.

Vlasov, Y. A.

Wadsworth, W.

Watanabe, T.

White, T.

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.

Xia, F. N.

Xu, Q.

Yamada, K.

Yasseri, S.

Yiou, S.

Yu, G.

Zheltikov, A.

S. Konorov, D. Sidorov-Biryukov, A. Zheltikov, I. Bugar, D. ChorvatJr, 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. ChorvatJr, 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)

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

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 (15)

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. 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]

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).

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]

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]

Opt. Lett. (2)

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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).
[CrossRef]

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.
[CrossRef]

Other (12)

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).

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

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

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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]

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. 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.

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), 211,104-1-211,104-3 (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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