Abstract

The four-wave mixing process in coupled-resonator optical waveguides is considered in detail and an approximate and simple approach allowing one to estimate the conversion efficiency is proposed. The analytical results are verified through a reliable and complete numerical technique taking into account nonlinear induced phase modulations, the large-signal regime, and the pulse shape evolution along the structure. The conversion efficiency is enhanced by the slow down factor to the fourth power and the impact of attenuation and phase mismatch are carefully investigated. The main aim of this study is to provide a technique to design efficient and compact wavelength converters. Two examples of devices operating on signals at 10 and 50 Gbits/s are presented and discussed. Pulse distortions induced by chromatic dispersion, frequency detuning, and slow down factor wavelength dependence are examined and the beneficial role of the nonlinear induced phase modulation on the phase mismatch is pointed out. Numerical examples show that with typical semiconductor characteristics, very high conversion efficiencies with pump powers of only a few tenths of milliwatts are achievable.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2008

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115-116 (2008).
[CrossRef]

2007

2006

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14, 3853-3863 (2006).
[CrossRef]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14, 4357-4362 (2006).
[CrossRef]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600-4615 (2006).
[CrossRef]

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

2005

2004

2003

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

A. Melloni, M. Floridi, F. Morichetti, and M. Martinelli, “Equivalent circuit of Bragg gratings and its application to Fabry-Perot cavities,” J. Opt. Soc. Am. A 20, 273-281 (2003).

2002

2000

1998

J. A. Hudgings and Y. Lau, “Step-tunable all-optical wavelength conversion using cavity enhanced four-wave mixing,” IEEE J. Quantum Electron. 34, 1349-1355 (1998).
[CrossRef]

1993

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity enhanced highly nondenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757-2759 (1993).
[CrossRef]

1991

S. Murata, A. Tomita, J. Shimizu, M. Kitamura, and A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1 THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458-1460 (1991).
[CrossRef]

1989

P. Bayvel and I. P. Giles, “Frequency generation by four-wave mixing in all-fibre single-mode ring resonator,” Electron. Lett. 25, 1178-1180 (1989).

J. G. Provost and R. Frey, “Cavity enhanced highly nondegenerate four-wave mixing in GaAlAs semiconductor lasers,” Appl. Phys. Lett. 55, 519-521 (1989).
[CrossRef]

1987

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205-1210 (1987).
[CrossRef]

1966

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109-124 (1966).
[CrossRef]

Absil, P. P.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1999).

Ashkin, A.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109-124 (1966).
[CrossRef]

Baets, R.

Bayvel, P.

P. Bayvel and I. P. Giles, “Frequency generation by four-wave mixing in all-fibre single-mode ring resonator,” Electron. Lett. 25, 1178-1180 (1989).

Beckx, S.

Bellanca, G.

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

Bertolotti, M.

M. Bertolotti, A. Driessen, and F. Michelotti, “Microresonators as building block for VLSI photonics,” in AIP Conference Proceedings (AIP, 2004).

Bienstman, P.

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401-412 (2005).
[CrossRef]

Blair, S.

Bogaerts, W.

Boyd, G.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109-124 (1966).
[CrossRef]

Boyd, R. W.

Braun, R.

N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205-1210 (1987).
[CrossRef]

Breda, A.

Campenhout, J. V.

Canciamilla, A.

Cáp, J.

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

Chen, Y.

Cho, P. S.

Claps, R.

Dagenais, M.

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity enhanced highly nondenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757-2759 (1993).
[CrossRef]

De La Rue, R. M.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Dimitropoulos, D.

Driessen, A.

M. Bertolotti, A. Driessen, and F. Michelotti, “Microresonators as building block for VLSI photonics,” in AIP Conference Proceedings (AIP, 2004).

Dulkeith, E.

Dumon, P.

Dziedzic, J.

A. Ashkin, G. Boyd, and J. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109-124 (1966).
[CrossRef]

Eggleton, B. J.

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

Fan, S.

Fathpour, S.

Ferrari, C.

Floridi, M.

Foster, M. A.

Freude, W.

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976-5990 (2007).
[CrossRef]

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

Frey, R.

J. G. Provost and R. Frey, “Cavity enhanced highly nondegenerate four-wave mixing in GaAlAs semiconductor lasers,” Appl. Phys. Lett. 55, 519-521 (1989).
[CrossRef]

Fu, L.

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

Fujii, M.

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

Fukuda, H.

Gaeta, A. L.

Giles, I. P.

P. Bayvel and I. P. Giles, “Frequency generation by four-wave mixing in all-fibre single-mode ring resonator,” Electron. Lett. 25, 1178-1180 (1989).

Gnan, M.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Green, W. M. J.

Heebner, J. E.

Ho, P.-T.

Hryniewicz, J. H.

Hudgings, J. A.

J. A. Hudgings and Y. Lau, “Step-tunable all-optical wavelength conversion using cavity enhanced four-wave mixing,” IEEE J. Quantum Electron. 34, 1349-1355 (1998).
[CrossRef]

Ibanescu, M.

Ippen, E.

Itabashi, S.

Jacome, L.

Jalali, B.

Jiang, S.

S. Jiang and M. Dagenais, “Observation of nearly degenerate and cavity enhanced highly nondenerate four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 62, 2757-2759 (1993).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Joneckis, L. G.

Kitamura, M.

S. Murata, A. Tomita, J. Shimizu, M. Kitamura, and A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1 THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458-1460 (1991).
[CrossRef]

Koos, C.

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976-5990 (2007).
[CrossRef]

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

Lau, Y.

J. A. Hudgings and Y. Lau, “Step-tunable all-optical wavelength conversion using cavity enhanced four-wave mixing,” IEEE J. Quantum Electron. 34, 1349-1355 (1998).
[CrossRef]

Lauritano, M.

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

Lee, R. K.

Leuthold, J.

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976-5990 (2007).
[CrossRef]

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

Lipson, M.

Little, B. E.

Littler, I. C. M.

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

Luther-Davies, B.

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

Luyssaert, B.

Macintyre, D. S.

M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115-116 (2008).
[CrossRef]

Maes, B.

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

Manolatou, C.

Martinelli, M.

F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15, 17273-17282 (2007).

A. Melloni, M. Floridi, F. Morichetti, and M. Martinelli, “Equivalent circuit of Bragg gratings and its application to Fabry-Perot cavities,” J. Opt. Soc. Am. A 20, 273-281 (2003).

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296-303 (2002).
[CrossRef]

A. Melloni, F. Morichetti, S. Pietralunga, and M. Martinelli, “Slow-wave wavelength converter,” in Proceedings of the 11th European Conference on Integrated Optics (2003), Vol. 1, pp. 97-100.

Melloni, A.

F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15, 17273-17282 (2007).

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

A. Melloni, M. Floridi, F. Morichetti, and M. Martinelli, “Equivalent circuit of Bragg gratings and its application to Fabry-Perot cavities,” J. Opt. Soc. Am. A 20, 273-281 (2003).

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

A. Melloni and M. Martinelli, “Synthesis of direct-coupled resonators bandpass filters for WDM systems,” J. Lightwave Technol. 20, 296-303 (2002).
[CrossRef]

A. Melloni, F. Morichetti, S. Pietralunga, and M. Martinelli, “Slow-wave wavelength converter,” in Proceedings of the 11th European Conference on Integrated Optics (2003), Vol. 1, pp. 97-100.

Michelotti, F.

M. Bertolotti, A. Driessen, and F. Michelotti, “Microresonators as building block for VLSI photonics,” in AIP Conference Proceedings (AIP, 2004).

Mookherjea, S.

S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
[CrossRef]

Morichetti, F.

F. Morichetti, A. Melloni, A. Breda, A. Canciamilla, C. Ferrari, and M. Martinelli, “A reconfigurable architecture for continuously variable optical slow-wave delay lines,” Opt. Express 15, 17273-17282 (2007).

F. Morichetti, A. Melloni, J. Čáp, J. Petráček, P. Bienstman, G. Priem, B. Maes, M. Lauritano, and G. Bellanca, “Self-phase modulation in slow-wave structures: a comparative numerical analysis,” Opt. Quantum Electron. 38, 761-780 (2006).

A. Melloni, M. Floridi, F. Morichetti, and M. Martinelli, “Equivalent circuit of Bragg gratings and its application to Fabry-Perot cavities,” J. Opt. Soc. Am. A 20, 273-281 (2003).

A. Melloni, F. Morichetti, and M. Martinelli, “Linear and nonlinear pulse propagation in coupled resonator slow-wave optical structures,” Opt. Quantum Electron. 35, 365-379 (2003).
[CrossRef]

A. Melloni, F. Morichetti, S. Pietralunga, and M. Martinelli, “Slow-wave wavelength converter,” in Proceedings of the 11th European Conference on Integrated Optics (2003), Vol. 1, pp. 97-100.

Moss, D. J.

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

Murata, S.

S. Murata, A. Tomita, J. Shimizu, M. Kitamura, and A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1 THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458-1460 (1991).
[CrossRef]

Park, Q.

Petrácek, J.

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V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
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V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
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M. Gnan, S. Thoms, D. S. Macintyre, R. M. De La Rue, and M. Sorel, “Fabrication of low-loss photonic wires in silicon-on-insulator using hydrogen silsesquioxane electron-beam resist,” Electron. Lett. 44, 115-116 (2008).
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S. Murata, A. Tomita, J. Shimizu, M. Kitamura, and A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1 THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458-1460 (1991).
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V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
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N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205-1210 (1987).
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S. Mookherjea and A. Yariv, “Second-harmonic generation with pulses in a coupled-resonator optical waveguide,” Phys. Rev. E 65, 026607 (2002).
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Y. Xu, R. K. Lee, and A. Yariv, “Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide,” J. Opt. Soc. Am. B 17, 387-400 (2000).
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J. G. Provost and R. Frey, “Cavity enhanced highly nondegenerate four-wave mixing in GaAlAs semiconductor lasers,” Appl. Phys. Lett. 55, 519-521 (1989).
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S. Murata, A. Tomita, J. Shimizu, M. Kitamura, and A. Suzuki, “Observation of highly nondegenerate four-wave mixing (>1 THz) in an InGaAsP multiple quantum well laser,” Appl. Phys. Lett. 58, 1458-1460 (1991).
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N. Shibata, R. Braun, and R. Waarts, “Phase-mismatch dependence of efficiency of wave generation through four-wave mixing in a single-mode optical fiber,” IEEE J. Quantum Electron. 23, 1205-1210 (1987).
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S. Mookherjea and A. Yariv, “Coupled resonator optical waveguides,” IEEE J. Sel. Top. Quantum Electron. 8, 448-456 (2002).
[CrossRef]

V. G. Taeed, M. Shokooh-Saremi, L. Fu, I. C. M. Littler, D. J. Moss, M. Rochette, B. J. Eggleton, Y. Ruan, and B. Luther-Davies, “Self-phase modulation-based integrated optical regeneration in chalcogenide waveguides,” IEEE J. Sel. Top. Quantum Electron. 12, 360-370 (2006).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Fujii, C. Koos, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear FDTD analysis and experimental verification of four-wave mixing in InGaAsP-InP racetrack microresonators,” IEEE Photon. Technol. Lett. 18, 361-363 (2006).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Express

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Phys. Rev. E

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A. Melloni, F. Morichetti, S. Pietralunga, and M. Martinelli, “Slow-wave wavelength converter,” in Proceedings of the 11th European Conference on Integrated Optics (2003), Vol. 1, pp. 97-100.

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