Abstract

We resolve the ambiguity in existing definitions of the effective area of a waveguide mode that have been reported in the literature by examining which definition leads to an accurate evaluation of the effective Kerr nonlinearity. We show that the effective nonlinear coefficient of a waveguide mode can be written as the product of a suitable average of the nonlinear coefficients of the waveguide’s constituent materials, the mode’s group velocity and a new suitably defined effective mode area. None of these parameters on their own completely describe the strength of the nonlinear effects of a waveguide.

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2012 (2)

2011 (3)

2010 (9)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nature Photonics4, 535–544 (2010).
[CrossRef]

W. Astar, J. B. Driscoll, X. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “Tunable wavelength conversion by xpm in a silicon nanowire, and the potential for xpm-multicasting,” J. Lightwave Technol.28, 2499–2511 (2010).
[CrossRef]

X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

N.-C. Panoiu, J. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Selec. Quantum Electron.16, 257–266 (2010).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photonics4, 83–91 (2010).
[CrossRef]

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

M. Santagiustina, C. G. Someda, G. Vadalà, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express18, 21024–21029 (2010).
[CrossRef] [PubMed]

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

2009 (6)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

V. S. Afshar, W. Q. Zhang, H. Ebendorff-Heidepriem, and T. M. Monro, “Small core optical waveguides are more nonlinear than expected: experimental confirmation,” Opt. Lett.34, 3577–3579 (2009).
[CrossRef]

V. S. Afshar and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part i: Kerr nonlinearity,” Opt. Express17, 2298–2318 (2009).
[CrossRef]

W. Q. Zhang, V. S. Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express17, 19311–19327 (2009).
[CrossRef]

2008 (2)

T. Baba, “Slow light in photonic crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

2007 (2)

2006 (3)

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

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Selec. Quantum Electron.12, 1214–1220 (2006).
[CrossRef]

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. of Mater. Res.36, 467–495 (2006).
[CrossRef]

2004 (4)

2003 (3)

P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R.C. Moore, K. Frampton, D.J. Richardson, and T.M. Monro, “Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,” Opt. Express11, 3568–3573 (2003).
[CrossRef] [PubMed]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional kerr defects,” Phys. Rev. E67, 056604 (2003).
[CrossRef]

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

2002 (1)

2001 (2)

Agrawal, G. P.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett.37, 2295–2297 (2012).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

Agrawal, P.

P. Agrawal, Nonlinear Fiber Optics (Academic press, 2007).

Almeida, V. R.

Asimakis, S.

Astar, W.

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Bahl, M.

M. Bahl, N.-C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional kerr defects,” Phys. Rev. E67, 056604 (2003).
[CrossRef]

Barrios, C. A.

Belardi, W.

Bhat, N.

N. Bhat and J. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Blasco, J.

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Boyraz, O.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photonics4, 83–91 (2010).
[CrossRef]

Bräuer, A.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

Buck, J. A.

J. A. Buck, Fudamentals of Optical Fibers (John Wiley & Sons, 2004).

Bulla, D.

Bulla, D. A.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1990).
[CrossRef]

Carter, G. M.

Chen, X.

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

Choi, D.-Y.

X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
[CrossRef] [PubMed]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Combrié, S.

Corcoran, B.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1990).
[CrossRef]

Dadap, J. I.

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Driscoll, J. B.

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Ebendorff-Heidepriem, H.

Ebnali-Heidari, M.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nature Photonics5, 141–148 (2011).

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3chalcogenide fiber tapers,” Opt. Express15, 10324–10329 (2007).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Fan, S.

Feng, X.

Finazzi, V.

Foster, M.

Foster, M. A.

Frampton, K.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nature Photonics4, 535–544 (2010).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Fu, L. B.

Furusawa, K.

Gaeta, A.

Gaeta, A. L.

Gai, X.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photonics4, 83–91 (2010).
[CrossRef]

Green, W. M. J.

Grillet, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Han, T.

Ibanescu, M.

Ippen, E.

Jalali, B.

Joannopoulos, J. D.

Johnson, S. G.

Kito, C.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Koizumi, F.

Koonath, P.

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nature Photonics4, 535–544 (2010).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Krauss, T. F.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Kwong, D.-L.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

Lægsgaard, J.

Lamont, M. R. E.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3chalcogenide fiber tapers,” Opt. Express15, 10324–10329 (2007).
[CrossRef]

Lau, R. K. W.

Lee, J. H.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nature Photonics4, 535–544 (2010).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Liao, M.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Lipson, M.

Liu, X.

Loh, W. H.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1995).

Luan, F.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Luther-Davies, B.

Luther-Davis, B.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Madden, S.

Madden, S. J.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Mägi, E. C.

Maier, S.

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Selec. Quantum Electron.12, 1214–1220 (2006).
[CrossRef]

Martí, J.

Martínez, A.

McMillan, J.

N.-C. Panoiu, J. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Selec. Quantum Electron.16, 257–266 (2010).
[CrossRef]

McMillan, J. F.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

Member, S.

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

P. Sanchis, J. Blasco, S. Member, A. Martínez, and J. Martí, “Design of silicon-based slot waveguide configurations for optimum nonlinear performance,” J. Lightwave Technol.25, 1298–1305 (2007).
[CrossRef]

Ménard, M.

Michaelis, D.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Moll, K.

Monat, C.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Monro, T. M.

Monro, T.M.

Moore, R. C.

Moore, R.C.

Mori, A.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Moss, D. J.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Nguyen, H. C.

O’Faolain, L.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Ohishi, Y.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Okawachi, Y.

Osgood, R. M.

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

M. Bahl, N.-C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional kerr defects,” Phys. Rev. E67, 056604 (2003).
[CrossRef]

Osgood., R. M.

Panoiu, N. C.

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

Panoiu, N.-C.

N.-C. Panoiu, J. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Selec. Quantum Electron.16, 257–266 (2010).
[CrossRef]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional kerr defects,” Phys. Rev. E67, 056604 (2003).
[CrossRef]

Pelusi, M.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Pelusi, M. D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

Peschel, U.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

Petropoulos, P.

Petrovich, M. N.

Poletti, F.

Ponzo, G. M.

Prasad, A.

Premaratne, M.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett.37, 2295–2297 (2012).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

Pudo, D.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

Qin, G.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Raghunathan, V.

Richardson, D. J.

Richardson, D.J.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nature Photonics5, 141–148 (2011).

Rossi, A. D.

Rukhlenko, I. D.

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett.37, 2295–2297 (2012).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

S. Afshar, V.

Salem, R.

Sanchis, P.

Santagiustina, M.

Sipe, J.

N. Bhat and J. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1995).

Soljacic, M.

Someda, C. G.

Suzuki, T.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Turner-Foster, A. C.

Vadalà, G.

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Vlasov, Y. A.

Vo, T. D.

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

Wächter, C.

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

Wang, R.

White, T. P.

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

Wong, C. W.

N.-C. Panoiu, J. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Selec. Quantum Electron.16, 257–266 (2010).
[CrossRef]

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

Xu, Q.

Yan, X.

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

Yeom, D. I.

Yu, M.

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

Zhang, W. Q.

Ann. Rev. of Mater. Res. (1)

T. M. Monro and H. Ebendorff-Heidepriem, “Progress in microstructured optical fibers,” Ann. Rev. of Mater. Res.36, 467–495 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

J. F. McMillan, M. Yu, D.-L. Kwong, and C. W. Wong, “Observation of spontaneous raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett.93, 251105 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE J. Selec. Quantum Electron. (4)

C. Monat, B. Corcoran, D. Pudo, M. Ebnali-Heidari, C. Grillet, M. D. Pelusi, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhanced nonlinear optics in silicon photonic crystal waveguides,” IEEE J. Selec. Quantum Electron.16, 344–356 (2010).
[CrossRef]

S. Maier, “Plasmonics: Metal nanostructures for subwavelength photonic devices,” IEEE J. Selec. Quantum Electron.12, 1214–1220 (2006).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, S. Member, and G. P. Agrawal, “Nonlinear silicon photonics : Analytical tools,” IEEE J. Selec. Quantum Electron.16, 200–215 (2010).
[CrossRef]

N.-C. Panoiu, J. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Selec. Quantum Electron.16, 257–266 (2010).
[CrossRef]

J. Appl. Phys. (1)

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Highly nonlinear tellurite microstructured fibers for broadband wavelength conversion and flattened supercontinuum generation,” J. Appl. Phys.107, 043108 (2010).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Nature Photonics (7)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature Photonics4, 83–91 (2010).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nature Photonics2, 465–473 (2008).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nature Photonics3, 206–210 (2009).
[CrossRef]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nature Photonics3, 216–219 (2009).
[CrossRef]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nature Photonics4, 535–544 (2010).
[CrossRef]

M. Pelusi, F. Luan, T. D. Vo, M. R. E. Lamont, S. J. Madden, D. A. Bulla, D.-Y. Choi, B. Luther-Davis, and B. J. Eggleton, “Photonic-chip-based radio-frequency spectrum analyser with terahertz bandwidth,” Nature Photonics3, 139–143 (2009).
[CrossRef]

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nature Photonics5, 141–148 (2011).

Opt. Express (10)

X. Gai, T. Han, A. Prasad, S. Madden, D.-Y. Choi, R. Wang, D. Bulla, and B. Luther-Davies, “Progress in optical waveguides fabricated from chalcogenide glasses,” Opt. Express18, 26635–26646 (2010).
[CrossRef] [PubMed]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express12, 4094–4102 (2004).
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M. Foster, K. Moll, and A. Gaeta, “Optimal waveguide dimensions for nonlinear interactions.” Opt. Express12, 2880–7 (2004).
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V. S. Afshar and T. M. Monro, “A full vectorial model for pulse propagation in emerging waveguides with subwavelength structures part i: Kerr nonlinearity,” Opt. Express17, 2298–2318 (2009).
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F. Poletti, X. Feng, G. M. Ponzo, M. N. Petrovich, W. H. Loh, and D. J. Richardson, “All-solid highly nonlinear singlemode fibers with a tailored dispersion profile,” Opt. Express19, 66–80 (2011).
[CrossRef] [PubMed]

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. C. Moore, K. Frampton, F. Koizumi, D. J. Richardson, and T. M. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express12, 5082 (2004).
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M. Santagiustina, C. G. Someda, G. Vadalà, S. Combrié, and A. D. Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express18, 21024–21029 (2010).
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W. Q. Zhang, V. S. Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express17, 19311–19327 (2009).
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P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R.C. Moore, K. Frampton, D.J. Richardson, and T.M. Monro, “Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,” Opt. Express11, 3568–3573 (2003).
[CrossRef] [PubMed]

E. C. Mägi, L. B. Fu, H. C. Nguyen, M. R. E. Lamont, D. I. Yeom, and B. J. Eggleton, “Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3chalcogenide fiber tapers,” Opt. Express15, 10324–10329 (2007).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. E (3)

N. Bhat and J. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E64, 056604 (2001).
[CrossRef]

M. Bahl, N.-C. Panoiu, and R. M. Osgood, “Nonlinear optical effects in a two-dimensional photonic crystal containing one-dimensional kerr defects,” Phys. Rev. E67, 056604 (2003).
[CrossRef]

D. Michaelis, U. Peschel, C. Wächter, and A. Bräuer, “Reciprocity theorem and perturbation theory for photonic crystal waveguides,” Phys. Rev. E68, 065601 (2003).
[CrossRef]

Other (4)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1995).

J. A. Buck, Fudamentals of Optical Fibers (John Wiley & Sons, 2004).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1990).
[CrossRef]

P. Agrawal, Nonlinear Fiber Optics (Academic press, 2007).

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Figures (3)

Fig. 1
Fig. 1

(a), (c) and (e): Effective area A eff ( i ), i = 1, 2,..., 6; and (b), (d), (f): γ(i) as well as γV, versus core radius for a bismuth-air step index fiber and for (a) and (b): the HE11 mode; (c) and (d) TE01; and (e) and (f) TM01. The A eff ( i ) are calculated from Eqs. (1), (6), (11), (14)(16). Inset in (a) shows the color code for each of i = 1, 2,...,6. The dashed lines in (a), (c), and (e) show the geometrical area of the fiber core.

Fig. 2
Fig. 2

(a)–(d): 2 and n 2 avg (normalized to n2 of bismuth), vg (normalized to the speed of light in the glass, c/n), A eff ( 3 ), and γV, respectively, for HE11 (black), TE01 (blue), and TM01 (red) modes. Dashed curves in (a) show the behavior of 2, as defined in Eq. (7). Vertical dashed lines in figures (b)–(d) show the positions of minima, for vg and Aeff, or maxima for γV. The solid horizontal green line in (b) represents the speed of light in air.

Fig. 3
Fig. 3

Nonlinear properties of circular step-index fibers versus core refractive index, optimized with respect to core radius. Vertical dashed lines correspond to silica, SF57, bismuth, and chalcogenide. (a) Minimum of A eff ( 3 ); (b) minimum vg; (c) n 2 avg / n 2 versus core radius. Solid and dashed curves were evaluated based on Eqs. (11) and (12), respectively; (d) maximum of γV/n2; (e) maximum of γV. The solid curve follows from Miller’s rule, whereas the four red data points are for the specific n2 values for the four materials. (f) Core radii corresponding to the minimum of A eff ( 3 ) (blue), vg (red), and maximum of γV (black), as a function of the refractive index.

Equations (17)

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

γ = 2 π λ n 2 A eff , where A eff ( 1 ) = ( | e t | 2 d A ) 2 | e t | 4 d A .
z a ( z , t ) i n ( i / t ) n n ! β ( n ) a ( z , t ) = i γ V | a ( z , t ) | 2 a ( z , t ) ,
γ V = 2 π λ ε 0 μ 0 n 2 ( x , y ) n 2 ( x , y ) [ 2 | e | 4 + | e 2 | 2 ] d A 3 | ( e × h * ) z ^ d A | 2 .
γ V = 2 π λ n 2 , core A eff , where A eff = μ 0 ε 0 3 n 2 , core | ( e × h * ) z ^ d A | 2 n 2 ( x , y ) n 2 ( x , y ) [ 2 | e | 4 + | e 2 | 2 ] d A .
A eff = μ 0 ε 0 3 | ( e × h * ) z ^ d A | 2 n core 2 NL [ 2 | e | 4 + | e 2 | 2 ] d A .
A eff 2 = | ( e ν × h ν * ) z ^ d A | 2 / | ( e ν × h ν * ) z ^ | 2 d A ,
γ V = 2 π λ n 2 ¯ A eff ( 2 ) , where , n 2 ¯ = ε 0 μ 0 n 2 ( x , y ) n 2 ( x , y ) [ 2 | e ν | 4 + | e ν 2 | 2 ] d A 3 | ( e ν × h ν * ) . z ^ | 2 d A ,
v g = 1 2 ( e × h * ) z d A λ 2 4 { ε 0 | e | 2 d d λ n 2 λ μ 0 λ 2 | h | 2 } d A ,
v g = 2 e × h * z d A ε 0 [ 2 n 2 ( λ d n 2 / d λ ) ] | e | 2 d A ,
v g = e × h * z d A ε 0 n 2 | e | 2 d A .
γ V = 2 π λ ( c n core v g ) 2 n 2 avg A eff ( 3 )
n 2 avg = n core 2 n 2 n 2 [ 2 | e | 4 + | e 2 | 2 ] d A 3 n 4 | e | 4 d A , and A eff ( 3 ) = ( n 2 | e | 2 d A ) 2 n 4 | e | 4 d A .
n 2 avg n core 2 n 2 n 2 | e | 4 d A n 4 | e | 4 d A .
n 2 avg n 2 n core 4 N L | e | 4 d A n 4 | e | 4 d A ,
A eff 4 = a NL S z d A / NL S z d A ,
A eff ( 5 ) = 2 π r 2 S z d A / S z d A ,
A eff ( 6 ) = ( | e t | 2 d A ) 2 / NL | e t | 4 d A ,

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