Abstract

We review recent research on nonlinear optical interactions in waveguides with sub-micron transverse dimensions, which are termed photonic nanowires. Such nanowaveguides, fabricated from glasses or semiconductors, provide the maximal confinement of light for index guiding structures enabling large enhancement of nonlinear interactions and group-velocity dispersion engineering. The combination of these two properties make photonic nanowires ideally suited for many nonlinear optical applications including the generation of single-cycle pulses and optical processing with sub-mW powers.

© 2008 Optical Society of America

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2008

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, A. L. Gaeta, "Signal regeneration using lowpower four-wave mixing on silicon chip," Nature Photonics 2, 35-38 (2008).
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2007

I.W. Hsieh, X. G. Chen, X. P. Liu, J. I. Dadap, N. C. Panoiu, C. Y. Chou, F. N. Xia,W. M. Green, Y. A. Vlasov, and R. M. Osgood, "Supercontinuum generation in silicon photonic wires," Opt. Express 15, 15242-15249 (2007).
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Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, G. P. Agrawal, "Dispersion of silicon nonlinearities in the near infrared region," Appl. Phys. Lett. 91, 021111 (2007).
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K. P. Nayak, P. N. Melentiev, M. Morinaga, F. L. Kien, V. I. Balykin, K. Hakuta, "Optical nanofiber as an efficient tool for manipulating and probing atomic fluorescence," Opt. Express 15, 5431-5438 (2007).
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E. C. Magi, L. B. Fu, H. C. Nguyen, M. R. Lamont, D. I. Yeom, B. J. Eggleton, "Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers," Opt. Express 15, 10324-10329 (2007).
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M. R. Lamont, C. M. de Sterke, and B. J. Eggleton, "Dispersion engineering of highly nonlinear As2S3 waveguides for parametric gain and wavelength conversion," Opt. Express 15, 9458-9463 (2007).
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L. Yin, Q. Lin, G. P. Agrawal, "Soliton fission and supercontinuum generation in silicon waveguides," Opt. Lett. 32, 391-393 (2007).
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I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, Jr., S. J. McNab, Y. A. Vlasov, "Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007).
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J. Zhang, Q. Lin, G. Piredda, R.W. Boyd, G. P. Agrawal, P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, A. L. Gaeta, "All-optical regeneration on a silicon chip," Opt. Express 15, 7802-7809 (2007).
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M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12949-12958 (2007).
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J. Meier, W. S. Mohammed, A. Jugessur, L. Qian, M. Mojahedi, J. S. Aitchison, "Group velocity inversion in AlGaAs nanowires," Opt. Express 15, 12755-12762 (2007).
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G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nature Photonics 1, 115-118 (2007).
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C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, "Nonlinear silicon-oninsulator waveguides for all-optical signal processing," Opt. Express 15, 5976-5990 (2007).
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N. A. Wolchover, F. Luan, A. K. George, J. C. Knight, and F. G. Omenetto, "High nonlinearity glass photonic crystal nanowires," Opt. Express 15, 829-833 (2007).
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M. V. Tognetti and H. M. Crespo, "Sub-two-cycle soliton-effect pulse compression at 800 nm in photonic crystal fibers," J. Opt. Soc. Am. B 24, 1410-1415 (2007).
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Q. Xu, M. Lipson, "All-optical logic based on silicon micro-ring resonators," Opt. Express 15924-929 (2007).
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S. F. Preble, Q. Xu, M. Lipson, "Changing the colour of light in a silicon resonator," Nature Photonics 1293-296 (2007).
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P. Dong, S. F. Preble, M. Lipson, "All-optical compact silicon comb switch," Opt. Express 159600-9605 (2007).
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2006

Q. Xu, M. Lipson, "Carrier-induced optical bistability in silicon ring resonators," Opt. Lett. 31341-343 (2006).
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C. Manolatou, M. Lipson, "All-optical silicon modulators based on carrier injection by two-photon absorption," J. Lightwave Technol. 241433-1439 (2006).
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T. K. Liang, L. R. Nunes, M. Tsuchiya, K. S. Abedin, T. Miyazaki, D. Van Thourhout,W. Bogaerts, P. Dumon, R. Baets, H. K. Tsang, "High speed logic gate using two-photon absoprtion in silicon waveguides," Opt. Commun. 265171-174 (2006).
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D. Akimov, T. Siebert, W. Kiefer, and A. Zheltikov, "Optical parametric amplification of a blueshifted output of a photonic-crystal fiber," J. Opt. Soc. Am. B 23, 1988-1993 (2006).
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J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
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B. T. Kuhlmey, H. C. Nguyen, M. J. Steel, and B. J. Eggleton, "Confinement loss in adiabatic photonic crystal fiber tapers," J. Opt. Soc. Am. B 23, 1965-1974 (2006).
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C. Xiong, A. Witkowska, S. G. Leon-Saval, T. A. Birks, and W. J. Wadsworth, "Enhanced visible continuum generation from a microchip 1064nm laser," Opt. Express 14, 6188-6193 (2006).
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C. Grillet, C. Smith, D. Freeman, S. Madden, B. Luther-Davies, E. Magi, D. Moss, and B. Eggleton, "Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires," Opt. Express 14, 1070-1078 (2006).
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L. Yin, Q. Lin, G. P. Agrawal, "Dispersion tailoring and soliton propagation in silicon waveguides," Opt. Lett. 31, 1295-1297 (2006).
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E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, Y. A. Vlasov, "Group index and group velocity dispersion in silicon-on-insulator photonic wires," Opt. Express. 14, 3853-3863 (2006).
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A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
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G. A. Siviloglou, S. Suntsov, R. El-Ganainy, R. Iwanow, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, D. Modotto, A. Locatelli, C. De Angelis, F. Pozzi, C. R. Stanley, and M. Sorel, "Enhanced third-order nonlinear effects in optical AlGaAs nanowires," Opt. Express 14, 9377-9384 (2006).
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L. Shi, X. Chen, H. Liu, Y. Chen, Z. Ye, W. Liao, and Y. Xia, "Fabrication of submicrondiameter silica fibers using electric strip heater," Opt. Express 14, 5055-5060 (2006).
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R. R. Gattass, G. T. Svacha, L. Tong, and E. Mazur, "Supercontinuum generation in submicrometer diameter silica fibers," Opt. Express 14, 9408-9414 (2006).
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L. Tong, L. Hu, J. Zhang, J. Qiu, Q. Yang, J. Lou, Y. Shen, J. He, and Z. Ye, "Pho-tonic nanowires directly drawn from bulk glasses," Opt. Express 14, 82-87 (2006).
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S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J. Kirby, "Low-light-level optical interactions with rubidium vapor in a photonic band-gap fiber," Phys. Rev. Lett. 97, 023603 (2006).
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R. El-Ganainy, S. Mokhov, K. G. Makris, D. N. Christodoulides, R. Morandotti, "Solitons in dispersion-inverted AlGaAs nanowires," Opt. Express 14, 2277-2282 (2006).
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S. Blair, K. Zheng, "Intensity-tunable group delay using stimulated Raman scattering in silicon slow-light waveguides," Opt. Express 14, 1064-1069 (2006).
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Y. Okawachi, M. A. Foster, J. E. Sharping, A. L. Gaeta, Q. Xu, M. Lipson, "All-optical slow-light on a photonic chip," Opt. Express 14, 2317-2322 (2006).
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H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
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M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, A. L. Gaeta, "Broad-band optical parametric gain on a silicon photonic chip," Nature 441, 960-963 (2006).
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K. Yamada, H. Fukuda, T. Tsuchizawa, T. Watanabe, T. Shoji, S. Itabashi, "All-optical efficient wavelength conversion using silicon photonic wire waveguide," IEEE Photon. Technol. Lett. 18, 1046-1048 (2006).
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Q. Lin, J. Zhang, P. M. Fauchet, G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006).
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E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
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R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, M. Forst, "Ultrafast Kerr-induced alloptical wavelength conversion in silicon waveguides using 1.55 mfemtosecond pulses," Opt. Express 14, 8336-8346 (2006).
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Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, O. Cohen, "Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides," Opt. Express 14, 11721-11726 (2006).
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I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, Y. A. Vlasov, "Ultrafast-pulse selfphase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
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J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, P. Kumar, "Generation of correlated photons in nanoscale silicon waveguides," Opt. Express 14, 12388-12393 (2006).
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2005

Q. Xu, V. R. Almeida, M. Lipson, "Demonstration of high Raman gain in a submicrometer-size silicon-oninsulator waveguide," Opt. Lett. 30, 35-37 (2005).
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V. Raghunathan, R. Claps, D. Dimitropoulos, B. Jalali, "Parametric Raman Wavelength Conversion in Scaled Silicon Waveguides," J. Lightwave Technol. 23, 2094-2102 (2005).
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R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, O. Cohen, "Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 13, 519-525 (2005).
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H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Panniccia, "An all-silicon Raman laser," Nature 433, 292-294 (2005).
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H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, M. Paniccia, "A continuous-wave Raman silicon laser," Nature 433, 725-728 (2005).
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R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Resonant optical interactions with molecules confined in photonic band-gap fibers," Phys. Rev. Lett. 94, 093902 (2005).
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J. T. Robinson, C. Manolatou, L. Chen, M. Lipson, "Ultrasmall mode volumes in dielectric optical microcavities," Phys. Rev. Lett. 95, 143901 (2005).
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E. Magi, H. Nguyen, and B. Eggleton, "Air-hole collapse and mode transitions in microstructured fiber photonic wires," Opt. Express 13, 453-459 (2005).
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D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, "Lifetime of photogenerated carriers in silicon-on-insulator rib wavegudies," Appl. Phys. Lett. 86071115 (2005).
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A. Zheltikov, "Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibers and photonic wires," J. Opt. Soc. Am. B 221100-1104 (2005).
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M. A. Foster, A. L. Gaeta, Q. Cao, and R. Trebino, "Soliton-effect compression of supercontinuum to few-cycle durations in photonic nanowires," Opt. Express 13, 6848-6855 (2005).
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C. M. B. Cordeiro, W. J. Wadsworth, T. A. Birks, and P. S. J. Russell, "Engineering the dispersion of tapered fibers for supercontinuum generation with a 1064 nm pump laser," Opt. Lett. 30, 1980-1982 (2005).
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J. C. Travers, S. V. Popov, and J. R. Taylor, "Extended blue supercontinuum generation in cascaded holey fibers," Opt. Lett. 30, 3132-3134 (2005).
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B. Kibler, J. M. Dudley, and S. Coen, "Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective area," Appl. Phys. B 81, 337-342 (2005).
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M. A. Foster, J.M. Dudley, B. Kibler, Q. Cao, D. Lee, R. Trebino, and A. L. Gaeta, "Nonlinear pulse propagation and supercontinuum generation in photonic nanowires: experiment and simulation," Appl. Phys. B 81, 363-367 (2005).
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R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, "C-band wavelength conversion in silicon photonic wire waveguides," Opt. Express 13, 4341-4349 (2005).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, S. Itabashi, "Four-wave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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H. Rong, Y. -H. Kuo, A. Liu, M. Paniccia, O. Cohen, "High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides," Opt. Express 14, 1182-1188 (2006).
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R. Jones, H. Rong, A. Liu, A. Fang, M. Paniccia, D. Hak, O. Cohen, "Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express 13, 519-525 (2005).
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R. Claps, V. Raghunathan, D. Dimitropoulos, B. Jalali, "Influence of nonlinear absorption on Raman amplification in Silicon waveguides," Opt. Express 12, 2774-2780 (2004).
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Q. Xu, V. Almeida, M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express 12, 4437-4442 (2004).
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O. Boyraz, B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express 12, 5269-5273 (2004).
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Q. Lin, J. Zhang, P. M. Fauchet, G. P. Agrawal, "Ultrabroadband parametric generation and wavelength conversion in silicon waveguides," Opt. Express 14, 4786-4799 (2006).
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E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, R. M. Osgood, Jr., "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
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R. Dekker, A. Driessen, T. Wahlbrink, C. Moormann, J. Niehusmann, M. Forst, "Ultrafast Kerr-induced alloptical wavelength conversion in silicon waveguides using 1.55 mfemtosecond pulses," Opt. Express 14, 8336-8346 (2006).
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Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, O. Cohen, "Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides," Opt. Express 14, 11721-11726 (2006).
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I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, Y. A. Vlasov, "Ultrafast-pulse selfphase modulation and third-order dispersion in Si photonic wire-waveguides," Opt. Express 14, 12380-12387 (2006).
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J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, P. Kumar, "Generation of correlated photons in nanoscale silicon waveguides," Opt. Express 14, 12388-12393 (2006).
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I. W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, Jr., S. J. McNab, Y. A. Vlasov, "Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires," Opt. Express 15, 1135-1146 (2007).
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J. Zhang, Q. Lin, G. Piredda, R.W. Boyd, G. P. Agrawal, P. M. Fauchet, "Optical solitons in a silicon waveguide," Opt. Express 15, 7682-7688 (2007).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, A. L. Gaeta, "All-optical regeneration on a silicon chip," Opt. Express 15, 7802-7809 (2007).
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M. A. Foster, A. C. Turner, R. Salem, M. Lipson, A. L. Gaeta, "Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides," Opt. Express 15, 12949-12958 (2007).
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Opt. Express.

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D. G. Ouzounov, F. R. Ahmad, D. Muller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, "Generation of megawatt optical solitons in hollow-core photonic band-gap fibers," Science 301, 1702-1704 (2003).
[CrossRef] [PubMed]

Other

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, "Ultra-low power nonlinear frequency conversion in a silicon photonic structure," submitted for publication.

P. V. Mamyshev, "All-optical data regeneration based on self-phase modulation effect," in Proc. European Conference on Optical Communications (ECOC98), p. 475, (1998).

M. A. Foster, Q. Cao, R. Trebino, and A. L. Gaeta, "Pulse Self-Compression of Supercontinuum in Photonic Nanowires," in 15th International Conference on Ultrafast Phenomena, OSA Technical Digest Series (CD) (Optical Society of America, 2006), paper WC5.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, Boston, 1989).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 1983).

C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2003).

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Figures (14)

Fig. 1.
Fig. 1.

Examples of various types of glass and semiconductor photonic nanowires. (a) Silica-glass photonic nanowire [8]. (b) Cross-section of a random hole silica glass microstructured fiber in which the interstitial regions are used as sub-µm guiding cores [9]. (c) Cross-sections of a tapered silicaglass microstructured fiber [10] and a (d) tapered SF6-glass microstructured fiber [11]. (e) Chalcogenide glass planar nanowaveguide with a microstructured photonic crystal cladding [12]. (f) Silicon nanowaveguide with an integrated resonant structure [13]. (g) Cross-section of a unclad silicon nanowaveguide [14]. (h) InGaAs photonic nanowire ring laser (top view) [15]. (i) Cross-section of an AlGaAs photonic nanowire [16].

Fig. 2.
Fig. 2.

Field intensity distribution inside glass-rod-in-air and silicon-on-insulator photonic nanowires for various sub-micron core sizes and wavelengths of 800 nm (glass-rod-in-air) and 1550 nm (silicon-on-insulator). The field remains confined as the core is reduced until a point at which the evanescent field dominates. This point occurs at larger core areas in the glass-rod-in-air due to the smaller index contrast.

Fig. 3.
Fig. 3.

Nonlinearity as a function of core area of a silica glass rod in air and silicon waveguide with a 1-to-1.5 aspect ratio embedded in a SiO2 cladding.

Fig. 4.
Fig. 4.

Waveguide contribution to the group-velocity dispersion (GVD) in (a) silica-glass and (b) silicon photonic nanowires of various dimensions. As the core is reduced in size, the point at which the waveguide-GVD changes from anomalous to normal shifts to shorter wavelengths. The overall behavior of the waveguide dispersion among nanowires of different materials exhibits similar features that occur at smaller (larger) characteristic dimensions for larger (smaller) index contrasts.

Fig. 5.
Fig. 5.

Net group-velocity dispersion of (a) silica glass photonic nanowires and (b) silicon photonic nanowires of various dimensions compared to the bulk dispersion of their respective core material. As the core is reduced in size the zero-GVD points shift to shorter wavelengths. The overall behavior of the net-GVD is characterized primarily by the waveguide-GVD (Fig. 4) and is consistent among nanowires of different materials although they occur at smaller (larger) characteristic dimensions for larger (smaller) index contrasts.

Fig. 6.
Fig. 6.

Supercontinuum generated in silica glass photonic nanowires. (a) Generated spectra from a 2-cm long 510-nm diameter tapered single-mode fiber using 600-ps 140-nJ pulses with a 532 center wavelength [10]. (b) Generated spectra from a 3.5-cm long 650-nm diameter tapered microstructured fiber using 25-fs 125-pJ pulses with an 820-nm center wavelength [39].

Fig. 7.
Fig. 7.

Retrieved few-optical-cycle pulse self-compressed from the 70-fs input pulse by propagation in the 980-nm core diameter and 2-mm-long photonic nanowire pictured above the plot [50].

Fig. 8.
Fig. 8.

Wavelength of phase-matched dispersive radiation as a function of core diameter of a silicaglass photonic nanowire.

Fig. 9.
Fig. 9.

Generation of 350-nm dispersive radiation using Cherenkov-type phase-matching in photonic nanowires [55].

Fig. 10.
Fig. 10.

An all-optical switch based on TPA-induced free-carrier dispersion in a silicon nanowaveguide ring resonator. (a) SEM image of the device. (b) Experimental switching realization [65].

Fig. 11.
Fig. 11.

All-optical pulse delay in a silicon nanowaveguide using stimulated Raman scattering. (a) Picture of the device. (b) Experimental measurement of a 1.3 pulse width delay [87].

Fig. 12.
Fig. 12.

All-optical SPM-based regenerator using a silicon nanowaveguide and integrated ring resonator band-pass filter (BPF). (a) Diagram of the device. (b) Experimental and simulated power transfer function. (c) Experimentally measured SPM broadening and filtered output for several pump powers [106].

Fig. 13.
Fig. 13.

Wavelength conversion across four telecommunications bands using four-wave mixing in silicon nanowaveguides (a) Conversion efficiency as a function of wavelength. The efficiency is shaped by the combined effects of the GVD and the fourth order dispersion of the nanowaveguide. (b) Experimentally observed FWM wavelength conversion from 1477 nm to 1672 nm [107].

Fig. 14.
Fig. 14.

Effective nonlinearity as a function of core diameter of a silica-glass photonic nanowire assuming a gaseous nonlinear cladding material with a nonlinear index coefficient n 2. As a comparison the effective nonlinearity of a commercially available 800-nm hollow-core photonic bandgap fiber (Crystal Fiber HC-800-02) with a 5-µm mode field diameter and γλ 3/n 2=0.205 is shown by the red dashed line.

Equations (7)

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𝒜 = 0.573 λ 2 ( n core + n clad ) 1.2 ( n core n clad ) 0.8 ,
n ( ω d ) ω d c ω d v g = n ( ω p ) ω p c ω p v g + n 2 I ω p 2 c .
Δ t eff = Δ z v g ω p Δ z ω d c [ n ( ω p ) + c v g n 2 I 2 ] .
1 v eff = Δ t eff Δ z = 1 v g ω p ω d c [ n ( ω p ) + c v g n 2 I 2 ] .
n ( ω d ) c = 1 v g ω p ω d c [ n ( ω p ) + c v g n 2 I 2 ]
Δ n = e 2 λ 2 8 π 2 c 2 ε 0 n [ Δ N e m ce * + Δ N h m ch * ] ,
Δ α = e 3 λ 2 4 π 2 c 3 ε 0 n [ Δ N e m ce * 2 μ e + Δ N h m ch * 2 μ h ] ,

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