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. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa. “Nonlinear-optic silicon-nanowire waveguides,” Japan. Journ. of Appl. Phys. 44:6541–6545, 2005.
[Crossref]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahasi, and S. Itabashi. “Four-wave mixing in silicon wire waveguides,” Opt. Express 13:4629–4637, 2005.
[Crossref] [PubMed]

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. Lightw. 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. Topics Quantum Electron. 11(1):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, November 2005.
[Crossref] [PubMed]

M. Lipson. “Guiding, modulating, and emitting light on silicon — challenges and opportunities,” J. Lightw. Tech-nol. 23:4222–4238, 2005.
[Crossref]

2004 (3)

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 (4)

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 1.5μm wavelength,” Appl. Phys. Lett. 80:416–418, 2002.
[Crossref]

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]

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]

1999 (1)

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve. “Non-linear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids. 256-257:353–360, 1999.
[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. Tech-nol. 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 1.5μm 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 1.319μm,” 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, February 1969.
[Crossref]

Aggarwal, I. D.

Agrawal, G. P.

G. P. Agrawal. Nonlinear Fiber Optics. Academic Press, San Diego, third edition, 2001.

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,” Japan. Journ. of 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 1.5μm wavelength,” Appl. Phys. Lett. 80:416–418, 2002.
[Crossref]

Asimakis, S.

J. Y. Y. Leong, P. Petropoulos, S. Asimakis, H. Ebendorff-Heideprim, R. C. Moore, Ken. Frampton, V. Finazzi, X. Feng, J. H. V. Price, T. M. Monro, and D. J. Richardson. “A lead silicate holey fiber with ?= 1860(Wkm)-1 at 1550nm,” In Optical Fiber Communication (OFC) Conference Anaheim (CA), USA, March 2005. PDP22.

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 1.5μm 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,” Japan. Journ. of Appl. Phys. 43:L673–L675, 2004.
[Crossref]

Baets, R.

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

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.

Beatty, R.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve. “Non-linear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids. 256-257:353–360, 1999.
[Crossref]

Beckx, S.

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

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 1.319μm,” Appl. Phys. Lett. 58:13–15, 1991.
[Crossref]

Bhowmik, A. K.

Bienstmann, P.

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

Bogaerts, W.

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

Bosshard, C.

U. Gubler and C. Bosshard. Molecular design for third-order nonlinear optics. Advances in Polymer Science158:123–191, 2002.
[Crossref]

Campenhout, J. Van

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

Cardinal, T.

T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. Le Foulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve. “Non-linear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids. 256-257:353–360, 1999.
[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. Tech-nol. 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,” Japan. Journ. of 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 1.5μm 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 1.5μm wavelength,” Appl. Phys. Lett. 80:416–418, 2002.
[Crossref]

Dulkeith, E.

Dumon, P.

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. Lightw. Technol. 23:401–412, 2005.
[Crossref]

Ebendorff-Heideprim, H.

J. Y. Y. Leong, P. Petropoulos, S. Asimakis, H. Ebendorff-Heideprim, R. C. Moore, Ken. Frampton, V. Finazzi, X. Feng, J. H. V. Price, T. M. Monro, and D. J. Richardson. “A lead silicate holey fiber with ?= 1860(Wkm)-1 at 1550nm,” In Optical Fiber Communication (OFC) Conference Anaheim (CA), USA, March 2005. PDP22.

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]

Feng, X.

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J. Y. Y. Leong, P. Petropoulos, S. Asimakis, H. Ebendorff-Heideprim, R. C. Moore, Ken. Frampton, V. Finazzi, X. Feng, J. H. V. Price, T. M. Monro, and D. J. Richardson. “A lead silicate holey fiber with ?= 1860(Wkm)-1 at 1550nm,” In Optical Fiber Communication (OFC) Conference Anaheim (CA), USA, March 2005. PDP22.

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J. Y. Y. Leong, P. Petropoulos, S. Asimakis, H. Ebendorff-Heideprim, R. C. Moore, Ken. Frampton, V. Finazzi, X. Feng, J. H. V. Price, T. M. Monro, and D. J. Richardson. “A lead silicate holey fiber with ?= 1860(Wkm)-1 at 1550nm,” In Optical Fiber Communication (OFC) Conference Anaheim (CA), USA, March 2005. PDP22.

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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.
[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.
[Crossref]

Taillaert, D.

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. Lightw. Technol. 23:401–412, 2005.
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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.
[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. Topics Quantum Electron. 11(1):232, 2005.
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[Crossref]

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[Crossref]

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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. Lightw. Technol. 23:401–412, 2005.
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[Crossref]

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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. Lightw. Technol. 23:401–412, 2005.
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[Crossref]

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 1.319μm,” Appl. Phys. Lett. 58:13–15, 1991.
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[Crossref]

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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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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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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