Abstract

Values up to γ= 7 × 106/(Wkm) for the nonlinear parameter are feasible if silicon-on-insulator based strip and slot waveguides are properly designed. This is more than three orders of magnitude larger than for state-of-the-art highly nonlinear fibers, and it enables ultrafast all-optical signal processing with nonresonant compact devices. At λ = 1.55μm we provide universal design curves for strip and slot waveguides which are covered with different linear and nonlinear materials, and we calculate the resulting maximum γ.

© 2007 Optical Society of America

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2006 (5)

T. Fujisawa and M. Koshiba, "All-optical logic gates based on nonlinear slot-waveguide couplers," J. Opt. Soc. Am. B 23, 684-691 (2006).
[CrossRef]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

P. Müllner and R. Hainberger, "Structural optimization of silicon-on-insulator slot waveguides," IEEE Photon. Technol. Lett. 18, 2557-2559 (2006).
[CrossRef]

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]

T. Fujisawa and M. Koshiba, "Guided modes of nonlinear slot waveguides," IEEE Photon. Technol. Lett. 18, 1530-1532 (2006).
[CrossRef]

2005 (6)

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
[CrossRef] [PubMed]

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005).
[CrossRef]

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

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
[CrossRef]

Y. A. Vlasov, M. O’Bolye, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

M. Lipson, "Guiding, modulating, and emitting light on silicon—challenges and opportunities," J. Lightwave Technol. 23, 4222-4238 (2005).
[CrossRef]

2004 (4)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

2002 (5)

K. Kikuchi, K. Taira, and N. Sugimoto, "Highly nonlinear bismuth oxide-based glass fibers for all-optical signal processing," Electron. Lett. 38, 166 (2002).
[CrossRef]

J. M. Harbold, F. Ö. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, "Higly nonlinear As-S-Se glasses for all-optical switching," Opt. Lett. 27, 119-121 (2002).
[CrossRef]

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

U. Gubler and C. Bosshard, "Molecular design for third-order nonlinear optics,"Adv. Polym. Sci. 158, 123-191 (2002).
[CrossRef]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

2000 (2)

A. K. Bhowmik and M. Thakur, "Self-phase modulation in polydiacetylene single crystal measured at 720-1064nm," Opt. Lett. 26, 902-904 (2000).
[CrossRef]

T. Kaino, "Waveguide fabrication using organic nonlinear optical materials," J. Opt. A: Pure Appl. Opt. 2, R1-R7 (2000).
[CrossRef]

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

1995 (1)

M. Asobe, I. Yokohama, T. Kaino, S. Tomaru, and T. Kurihara, Nonlinear absorption and refraction in an organic dye functionalized main chain polymer waveguide in the 1.5 μm wavelength region, Appl. Phys. Lett. 67, 891-893 (1995).
[CrossRef]

1994 (1)

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

1993 (1)

D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
[CrossRef]

1991 (1)

K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
[CrossRef]

1990 (1)

H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
[CrossRef]

1989 (1)

1988 (1)

P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
[CrossRef]

1987 (1)

R. S. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089 (1987).
[CrossRef]

1969 (1)

J. J. Wynne. "Optical third-order mixing in GaAs, Ge, Si and InAs," Phys. Rev. 178, 1295-1301 (1969).
[CrossRef]

Aggarwal, I. D.

Almeida, V. R.

Andrejco, M. J.

Arakawa, Y.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005).
[CrossRef]

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Asobe, M.

M. Asobe, I. Yokohama, T. Kaino, S. Tomaru, and T. Kurihara, Nonlinear absorption and refraction in an organic dye functionalized main chain polymer waveguide in the 1.5 μm wavelength region, Appl. Phys. Lett. 67, 891-893 (1995).
[CrossRef]

Baba, T.

T. Fukazawa, F. Ohno, and T. Baba, "Very compact arrayed waveguide grating using Si photonic wire waveguides," Jpn. J. Appl. Phys. 43, L673-L675 (2004).
[CrossRef]

Baets, R.

Baker, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

Baker, G. L.

P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
[CrossRef]

Barrios, C. A.

Beckx, S.

Beranek, M. W.

K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
[CrossRef]

Bhowmik, A. K.

Bienstmann, P.

Bogaerts, W.

Bosshard, C.

U. Gubler and C. Bosshard, "Molecular design for third-order nonlinear optics,"Adv. Polym. Sci. 158, 123-191 (2002).
[CrossRef]

Cazzanelli, M.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Cha, M.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

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]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

Chu, S. T.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Chu, T.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005).
[CrossRef]

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

DeLong, K. W.

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Dulkeith, E.

Dumon, P.

Etemad, S.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

Eternad, S.

P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
[CrossRef]

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Franzo, G.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Friberg, R. S.

R. S. Friberg and P. W. Smith, "Nonlinear optical glasses for ultrafast optical switches," IEEE J. Quantum Electron. 23, 2089 (1987).
[CrossRef]

Fujisawa, T.

T. Fujisawa and M. Koshiba, "All-optical logic gates based on nonlinear slot-waveguide couplers," J. Opt. Soc. Am. B 23, 684-691 (2006).
[CrossRef]

T. Fujisawa and M. Koshiba, "Guided modes of nonlinear slot waveguides," IEEE Photon. Technol. Lett. 18, 1530-1532 (2006).
[CrossRef]

Fukazawa, T.

T. Fukazawa, F. Ohno, and T. Baba, "Very compact arrayed waveguide grating using Si photonic wire waveguides," Jpn. J. Appl. Phys. 43, L673-L675 (2004).
[CrossRef]

Fukuda, H.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
[CrossRef] [PubMed]

Gaburro, Z.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
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M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
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B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
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P. Müllner and R. Hainberger, "Structural optimization of silicon-on-insulator slot waveguides," IEEE Photon. Technol. Lett. 18, 2557-2559 (2006).
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Hamann, H. F.

Y. A. Vlasov, M. O’Bolye, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
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Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
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Haus, H. A.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

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D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
[CrossRef]

Iacona, F.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
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Ippen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
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H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
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B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
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K. Kikuchi, K. Taira, and N. Sugimoto, "Highly nonlinear bismuth oxide-based glass fibers for all-optical signal processing," Electron. Lett. 38, 166 (2002).
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D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
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Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
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P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
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H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
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T. Fujisawa and M. Koshiba, "All-optical logic gates based on nonlinear slot-waveguide couplers," J. Opt. Soc. Am. B 23, 684-691 (2006).
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K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
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H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
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M. Asobe, I. Yokohama, T. Kaino, S. Tomaru, and T. Kurihara, Nonlinear absorption and refraction in an organic dye functionalized main chain polymer waveguide in the 1.5 μm wavelength region, Appl. Phys. Lett. 67, 891-893 (1995).
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B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
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H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
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Little, B. E.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
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Matsushita, O.

H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
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Y. A. Vlasov, M. O’Bolye, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
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Meth, J.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
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Miao, E.

K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
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Möhlmann, G. R.

D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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P. Müllner and R. Hainberger, "Structural optimization of silicon-on-insulator slot waveguides," IEEE Photon. Technol. Lett. 18, 2557-2559 (2006).
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Nasu, H.

H. Nasu, O. Matsushita, K. Kamiya, H. Kobayashi, and K. Kubodera, "Third harmonic generation from Li2O-TiO2-TeO2 glasses," J. Non-Cryst. Solids. 124, 275-277 (1990).
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O’Bolye, M.

Y. A. Vlasov, M. O’Bolye, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
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T. Fukazawa, F. Ohno, and T. Baba, "Very compact arrayed waveguide grating using Si photonic wire waveguides," Jpn. J. Appl. Phys. 43, L673-L675 (2004).
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E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
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D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
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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).
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E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
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G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
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Priolo, F.

G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
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M. Dinu, F. Quochi, and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett. 82, 2954-2956 (2003).
[CrossRef]

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

Rochford, K.

K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
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Sanghera, J. S.

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P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
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Shirane, M.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, "Nonlinear-optic silicon-nanowire waveguides," Jpn. J. Appl. Phys. 44, 6541-6545 (2005).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
[CrossRef]

Stegeman, G. I.

K. Rochford, R. Zanoni, G. I. Stegeman, W. Krug, E. Miao, and M. W. Beranek, "Measurement of nonlinear refractive index and transmission in polydiacetlyene waveguides at 1.319 μm," Appl. Phys. Lett. 58, 13-15 (1991).
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V. Mizrahi, K. W. DeLong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, "Two-photon absorption as a limitation to all-optical switching," Opt. Lett. 14, 1140-1142 (1989).
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B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

Sugimoto, N.

K. Kikuchi, K. Taira, and N. Sugimoto, "Highly nonlinear bismuth oxide-based glass fibers for all-optical signal processing," Electron. Lett. 38, 166 (2002).
[CrossRef]

Sundheimer, M.

D. Y. Kim, M. Sundheimer, A. Otomo, G. Stegeman, W. H. G. Horsthuis, and G. R. Möhlmann, "Third order nonlinearity of 4-dialkyamino-4’nitro-stilbene waveguides at 1319nm," Appl. Phys. Lett. 63, 290-292 (1993).
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Taira, K.

K. Kikuchi, K. Taira, and N. Sugimoto, "Highly nonlinear bismuth oxide-based glass fibers for all-optical signal processing," Electron. Lett. 38, 166 (2002).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
[CrossRef] [PubMed]

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Tamechika, E.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Toen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
[CrossRef]

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M. Asobe, I. Yokohama, T. Kaino, S. Tomaru, and T. Kurihara, Nonlinear absorption and refraction in an organic dye functionalized main chain polymer waveguide in the 1.5 μm wavelength region, Appl. Phys. Lett. 67, 891-893 (1995).
[CrossRef]

Toruellas, W.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegemann, G. Baker, J. Meth, and S. Etemad, "Large purely refractive nonlinear index of single-crystal P-toluene sulphonate (PTS) at 1600nm," Electron. Lett,  30, 447-448 (1994).
[CrossRef]

Townsend, P. D.

P. D. Townsend, G. L. Baker, N. E. Schlotter, C. F. Klausner, and S. Eternad, "Waveguiding in spun films of soluble polydiacetylenes," Appl. Phys. Lett. 53, 1782-1784 (1988).
[CrossRef]

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H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
[CrossRef]

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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
[CrossRef]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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Van Thourhout, D.

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G. Vijaya Prakash, M. Cazzanelli, Z. Gaburro, L. Pavesi, F. Iacona, G. Franzo, and F. Priolo, "Linear and nonlinear optical properties of plasma-enhanced chemical-vapour deposition grown silicon nanocrystals," J. Mod. Opt. 49, 719-730 (2002).
[CrossRef]

Vlasov, Y. A.

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood, "Self-phase-modulation in submicron silicon-on-insulator photonic wires," Opt. Express 14, 5524-5534 (2006).
[CrossRef] [PubMed]

Y. A. Vlasov, M. O’Bolye, H. F. Hamann, and S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).
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T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, "Microphotonics devices based on silicon microfabrication technology," IEEE J. Sel. Tops. Quantum Electron. 11, 232 (2005).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi, "Fourwave mixing in silicon wire waveguides," Opt. Express 13, 4629-4637 (2005).
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H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength," Appl. Phys. Lett. 80, 416-418 (2002).
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Supplementary Material (1)

» Media 1: MOV (64 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Waveguide cross-sections (a) Strip waveguide. For core or cover nonlinearity, the nonlinear interaction domain D inter is limited to the core domain (D inter = D core) or to the cover domain (D inter = D cover), respectively. (b) Slot waveguide. The nonlinear interaction domain is limited to the cover domain (D inter = D cover).

Fig. 2.
Fig. 2.

TM-operated strip waveguide with core nonlinearity. Optimized geometrical parameters for a minimum effective area A eff (a) Optimal strip width w and height h as a function of the refractive index n cover of the linear cover material (b) Minimized effective area A eff of nonlinear interaction. (c) Dominant component (E μy ) of the electric modal field for n cover = 1.5

Fig. 3.
Fig. 3.

TE-operated strip waveguide with core nonlinearity. Optimized geometrical parameters for a minimum effective area A eff (a) Optimal strip width w and height h as a function of the refractive index n cover of the linear cover material (b) Optimized effective area A eff of nonlinear interaction (c) Dominant component (E μx ) of the electric modal field for n cover = 1.5

Fig. 4.
Fig. 4.

TM-operated strip waveguide with cover nonlinearity. Optimized geometrical parameters for a minimum effective area A eff (a) Optimal strip width w and height h as a function of the linear refractive index n cover of the nonlinear cover material (b) Minimized effective area A eff of nonlinear interaction (c) Dominant component (E μy ) of the electric modal field for n cover = 1.5

Fig. 5.
Fig. 5.

TE-operated strip waveguide with cover nonlinearity. Optimized geometrical parameters for a minimum effective area A eff (a) Optimal strip width w and height h as a function of the linear refractive index n cover of the nonlinear cover material (b) Minimized effective area A eff of nonlinear interaction (c) Dominant component (E μx ) of the electric modal field for n cover = 1.5

Fig. 6.
Fig. 6.

TE-operated slot waveguide with cover nonlinearity. Optimized geometrical parameters for a minimum effective area A eff (a) Optimal strip width w as a function of the linear refractive index n cover of the nonlinear cover material for various slot widths w slot μx {60nm, 80nm,…,200nm} (b) Optimal strip height h (c) Minimized effective area A eff for nonlinear interaction (d) Dominant component (E μx ) of the electric modal field for n cover = 1.5 and w slot = 100nm. Click for an animation of E μx for w slot = 100nm and increasing n cover (file size 700kB). [Media 1]

Tables (2)

Tables Icon

Table 1. Core nonlinearity. Calculated maximum nonlinearity parameters Re{γ} ∝ 1/A eff for optimized strip waveguides with a nonlinear silicon core and a linear air cladding n cover = 1, operated in TM or TE polarization. The calculation is based on data for silicon at the specified wavelengths: Linear refractive index n 0, nonlinearity coefficient n 2 and TPA figure of merit FOMTPA were taken from the references listed in the last column. — The resulting nonlinear parameters Re{γ} ≈ 400/(Wm) are remarkably large. However, the material suffers from non-negligible two-photon absorption leading to a figure of merit FOMTPA ≈ 0.3…0.9.

Tables Icon

Table 2. Cover nonlinearity. Calculated maximum nonlinearity parameters Re{γ} ∝ 1/A eff for optimized strip and slot waveguides with a linear silicon core and various nonlinear cover materials, operated in TM or TE polarization. The calculation is based on cover material data at the specified wavelengths: Linear refractive index n 0, nonlinearity coefficient n 2 and TPA figure of merit FOMTPA were taken from the references listed in the last column. Three material groups are considered: Inorganic materials like glasses, organic substances, and nanocomposites. — Most remarkable are the large nonlinear parameters Re{γ} ≈ (70… 150)/(Wm) and Re{γ} ≈ 300/(Wm) for chalcogenide glasses and for the side-chain polymer DANS, respectively, and the record value of Re{γ} ≈ 7000/(Wm) for the single-crystalline organic material PTS, a number which is 1000 times larger than for a higly nonlinear bismite glass. These material groups have also very good TPA figures of merit in the order of FOMTPA ≈ 4… 27.

Equations (17)

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A eff = Z 0 2 n inter 2 D tot Re { μ ( x , y ) × μ * ( x , y ) } e z d x d y 2 D inter μ ( x , y ) 4 d x d y .
n 2 = 3 Z 0 Re { χ ˜ ( 3 ) } 4 n 0 2 ,
α 2 = 3 k 0 Z 0 Im { x ˜ ( 3 ) } 2 n 0 2 .
FOM TPA = 1 2 π Re { γ } 2 Im { γ } = n 2 α 2 λ .
× H ( r , t ) = D ( r , t ) t
× E ( r , t ) = B ( r , t ) t ,
P ( nl ) ( t ) = ε 0 χ ̲ ( 3 ) ( τ 1 , τ 2 , τ 3 ) E ( t τ 1 ) E ( t τ 2 ) E ( t τ 3 ) 1 2 3 ,
E μ ( r , t ) = Re { A μ ( z , t ) μ ( x , y , ω c ) 𝒫 μ e j ( ω c t β μ ( ω c ) z ) } ,
H μ ( r , t ) = Re { A μ ( z , t ) μ ( x , y , ω c ) 𝒫 μ e j ( ω c t β μ ( ω c ) z ) } .
𝒫 μ = 1 2 Re { μ ( x , y , ω c ) × μ * ( x , y , ω c ) } e z d x d y .
1 4 [ ( μ × μ * ) + ( μ * × μ ) ] e z d x d y = 𝒫 μ δ μ , μ ,
β ( ω ) = β μ + ( ω ω c ) β μ ( 1 ) + 1 2 ( ω ω c ) 2 β μ ( 2 ) ,
A μ ( z , t ) z + β μ ( 1 ) A μ ( z , t ) t j 1 2 β μ ( 2 ) 2 A μ ( z , t ) t 2 = j γ A μ ( z , t ) 2 A μ ( z , t ) ,
γ = 3 ω c ε 0 16 𝒫 μ 2 [ χ ˉ ˜ ( 3 ) ( ω c : ω c , ω c , ω c ) μ ( ω c ) μ ( ω c ) μ * ( ω c ) ] μ * ( ω c ) d x d y .
A eff = z 0 2 n inter 2 D tot Re { μ ( x , y ) × μ * ( x , y ) } e z d x d y 2 D inter μ ( x , y ) 4 d x d y .
γ = 3 ω c ε 0 z 0 2 4 A eff n inter 2 χ ˜ ( 3 ) .
A eff ( D tot F ( x , y ) 2 d x d y ) 2 D tot F ( x , y ) 4 d x d y .

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