Abstract

Geometry, nonlinearity, dispersion and two-photon absorption figure of merit of three basic silicon-organic hybrid waveguide designs are compared. Four-wave mixing and heterodyne pump-probe measurements show that all designs achieve high nonlinearities. The fundamental limitation of two-photon absorption in silicon is overcome using silicon-organic hybrid integration, with a five-fold improvement for the figure of merit (FOM). The value of FOM = 2.19 measured for silicon-compatible nonlinear slot waveguides is the highest value published.

© 2009 OSA

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2009

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

2008

H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. 23(6), 064007 (2008).
[CrossRef]

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

T. Vallaitis, C. Koos, R. Bonk, W. Freude, M. Laemmlin, C. Meuer, D. Bimberg, and J. Leuthold, “Slow and fast dynamics of gain and phase in a quantum dot semiconductor optical amplifier,” Opt. Express 16(1), 170–178 (2008).
[CrossRef] [PubMed]

2007

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15(10), 5976–5990 (2007).
[CrossRef] [PubMed]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

2006

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

2005

2004

M. Wu and W. I. Way, “Fiber Nonlinearity Limitations in Ultra-Dense WDM Systems,” J. Lightwave Technol. 22(6), 1483–1498 (2004).
[CrossRef]

G. W. Rieger, K. S. Virk, and J. F. Young, “Nonlinear propagation of ultrafast 1.5 µm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

2003

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

T.-T. Kung, C.-T. Chang, J.-C. Dung, and S. Chi, “Four-Wave Mixing Between Pump and Signal in a Distributed Raman Amplifier,” J. Lightwave Technol. 21(5), 1164–1170 (2003).
[CrossRef]

1996

1994

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

1989

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(20), 1140–1142 (1989).
[CrossRef] [PubMed]

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[CrossRef]

Agrawal, G. P.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

Andrejco, M. J.

Baehr-Jones, T.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005).
[CrossRef]

Baker, G.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Beckx, S.

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

Bienstman, P.

Bimberg, D.

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005).
[CrossRef]

Bonk, R.

Boyd, R. W.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

Cha, M.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Chang, C.-T.

Chen, B.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Chi, S.

Dalton, L.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

DeLong, K. W.

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[CrossRef]

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(20), 1140–1142 (1989).
[CrossRef] [PubMed]

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005).
[CrossRef]

Dung, J.-C.

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

Etemad, S.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Fauchet, P. M.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

Foster, M. A.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

Freude, W.

Gaeta, A. L.

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

Harvard, K.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Hochberg, M.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Jacome, L.

Jen, A. K. Y.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Kang, J. U.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Koos, C.

Kung, T.-T.

Laemmlin, M.

Lawrence, B. L.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Lawson, R.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Leuthold, J.

Lin, Q.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

Lipson, M.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

Liu, Y.

H. K. Tsang and Y. Liu, “Nonlinear optical properties of silicon waveguides,” Semicond. Sci. Technol. 23(6), 064007 (2008).
[CrossRef]

Luo, J.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Luyssaert, B.

Mecozzi, A.

Meth, J.

B. L. Lawrence, M. Cha, J. U. Kang, W. Toruellas, G. Stegeman, G. Baker, J. Meth, and S. Etemad, “Large purely refractive nonlinear index of single crystal P-toluene sulphonate (PTS) at 1600 nm,” Electron. Lett. 30(5), 447–448 (1994).
[CrossRef]

Meuer, C.

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, “All-optical high-speed signal processing with silicon-organic hybrid slot waveguides,” Nat. Photonics 3(4), 216–219 (2009).
[CrossRef]

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

Mizrahi, V.

Mørk, J.

Piredda, G.

Q. Lin, J. Zhang, G. Piredda, R. W. Boyd, P. M. Fauchet, and G. P. Agrawal, “Dispersion of silicon nonlinearities in the near infrared region,” Appl. Phys. Lett. 91(2), 021111 (2007).
[CrossRef]

Poulton, C.

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[CrossRef]

Rieger, G. W.

G. W. Rieger, K. S. Virk, and J. F. Young, “Nonlinear propagation of ultrafast 1.5 µm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Rochford, K. B.

K. W. DeLong, K. B. Rochford, and G. I. Stegeman, “Effect of two-photon absorption on all-optical guided-wave devices,” Appl. Phys. Lett. 55(18), 1823–1825 (1989).
[CrossRef]

Saifi, M. A.

Salem, R.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2007).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

Scherer, A.

M. Hochberg, T. Baehr-Jones, G. Wang, M. Shearn, K. Harvard, J. Luo, B. Chen, Z. Shi, R. Lawson, P. Sullivan, A. K. Y. Jen, L. Dalton, and A. Scherer, “Terahertz all-optical modulation in a silicon-polymer hybrid system,” Nat. Mater. 5(9), 703–709 (2006).
[CrossRef] [PubMed]

Scimeca, M. L.

B. Esembeson, M. L. Scimeca, T. Michinobu, F. Diederich, and I. Biaggio, “A high optical quality supramolecular assembly for third- order integrated nonlinear optics,” Adv. Mater. 20(23), 4584–4587 (2008).
[CrossRef]

Shearn, M.

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Figures (7)

Fig. 1
Fig. 1

Geometry and electric field distribution of three highly nonlinear CMOS-compatible waveguides. All silicon-on insulator waveguide structures are covered with an organic nonlinear cladding material (NL). (a) “Core nonlinearity”: A strip waveguide operated in TE mode (dominant electric field component along the x-direction), where the light is concentrated in the waveguide core. The third-order nonlinearity is dominated by the complex-valued χ(3) of silicon, while the effect of the cladding material is negligible. (b) “Cladding nonlinearity”: A strip waveguide operated in TM mode (dominant electric field component along the y-direction). The optical signal is squeezed into the cladding allowing to exploit the real valued nonlinearity of the cladding. (c) “Slot nonlinearity”: In the slot geometry, the light is almost completely confined to the slot filled with nonlinear material. For a cladding material with a real susceptibility, the TPA figure of merit is high for (b) and (c). All waveguides have been fabricated on the same chip with the same cladding material to allow for a fair comparison.

Fig. 2
Fig. 2

Effective areas for third order interaction in silicon (-, Si) and in the nonlinear cladding material (-, Cladding). For a fixed waveguide height of 220 nm the width of the strip or slot is varied. Following (1) the nonlinearity parameter is large for small effective areas. Small arrows (↓) mark the optimum dimensions [5]. The data points (□,●) indicate the effective areas of the samples investigated in this paper. (a) In the waveguide with the core nonlinearity the dominant nonlinear contribution comes from the silicon, as the silicon effective area can be strongly minimized. (b) In waveguides with cladding nonlinearity both silicon and the nonlinear cladding material contribute alike. (c) The nonlinear effect of waveguides with slot nonlinearity mainly depends on the slot width. Decreasing the slot width decreases the effective area and thereby increases the nonlinearity parameter.

Fig. 3
Fig. 3

(a) Four-wave mixing setup and (b) example spectrum measured in a bandwidth of 0.1 nm. Co-polarized light from two amplified laser sources is launched into the device under test (DUT) and the four-wave mixing spectrum is recorded in an optical spectrum analyzer (OSA). From the ratio of the idler to the signal the nonlinearity parameter γ can be extracted. (TLS: tunable laser source, EDFA: erbium-doped fiber amplifier, BPF: optical band pass filter, P: polarizer)

Fig. 4
Fig. 4

Dependence of the nonlinearity parameter Re{γ} times η, the normalized four-wave mixing efficiency, as a function of the wavelength detuning Δλ ; measurement (°) and fit (-).η describes the normalized degradation of the four-wave mixing efficiency with increasing phase mismatch, for perfect phase-matching η=1 holds. The data are obtained by dividing the measured four-wave mixing conversion efficiency by the effective waveguide length, in order to emphasize the fundamental influence of dispersion, leaving out the technical issue of the propagation loss. The given parameters are averaged over multiple waveguides and measurements. All waveguides show high nonlinearities. (a) The strip waveguides with pure silicon core nonlinearity show the largest effect. (b) Waveguides with cladding nonlinearity have low linear losses but significant waveguide dispersion, which causes a large phase mismatch for detuning larger than 5 nm. (c) The slot waveguides show a strong nonlinear effect as well but provide larger phase-matching tolerance. All experimental results are summarized in Table 1.

Fig. 5
Fig. 5

Schematic illustration of (a) amplitude and (b) phase effects. At zero time delay, the Kerr effect causes an instantaneous phase change. If free carriers are created by two-photon absorption of the pulse, the plasma effect leads to an undesired phase change with the opposite sign and a long time constant. The amplitude transmission (a) shows the instantaneous loss caused by two-photon absorption and a permanently reduced transmission due to free carrier absorption. The dashed line shows the spectral artifact of the measurement principle, which is expected for strong Kerr media [17].

Fig. 6
Fig. 6

Amplitude transmission TA and phase ΔϕNL dynamics of the highly nonlinear waveguides for different pump power levels. All waveguides show strong Kerr nonlinearities. However, the (a) silicon core nonlinearity waveguide shows strong two-photon absorption accompanied with simultaneous strong free-carrier absorption. The experiment leads to a figure of merit FOMTPA=0.38±0.17 . (b) The waveguide with cladding nonlinearity shows a significantly lower detrimental TPA effect. It has a FOMTPA=1.21±0.19 . (c) Waveguide with slot nonlinearity showing a Kerr nonlinearity with nearly no two-photon absorption, negligible free carrier absorption, and a FOMTPA=2.19±0.25 .

Fig. 7
Fig. 7

Measured inverse power transmission 1/TP of a silicon strip waveguide with core nonlinearity as a function of the on-chip peak power. For an effective waveguide length of Leff=2.5  mm , the two-photon absorption coefficient is calculated from the slope of a linear fit to a value of α2=(0.8±0.2)  cm/GW .

Tables (1)

Tables Icon

Table 1 Dimensions and optical properties of basic silicon-organic hybrid waveguide designs determined from four-wave mixing and heterodyne pump-probe experiments at a center wavelength of λ = 1.55 µm. (*) Effective areas of silicon and nonlinear cladding material are obtained from a finite-element simulation.

Equations (15)

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

Re{γ}=n2ωcAeff(3),
FOMTPA=14πRe{γ}Im{γ}.
Pi(L)=eα0L(ηRe{γ}Pp(0)Leff)2Ps(0),
Leff=1eα0Lα0.
η2=α02α02+Δβ2[1+4eα0Lsin2(LΔβ/2)(1eα0L)2].
dPP(z)dz=α0PP(z)+2Im{γ}PP2(z),
dϕP,NL(z)dz=Re{γ}PP(z),
PP(z)=eα0z12LeffIm{γ}PP,0PP,0.
dPS(z)dz=α0PS(z)+4Im{γ}PP(z)PS(z),
dϕNL(z)dz=2Re{γ}PP(z).
PS(z)=eα0z(12LeffIm{γ}PP,0)2PS,0.
TP=PS(PP>0)PS(PP=0)=1(12LeffIm{γ}PP,0)2,
ΔϕNL=Re{γ}Im{γ}ln(12LeffIm{γ}PP,0).
FOMTPA=14πRe{γ}Im{γ}=ΔϕNL4πlnTA.
1TP=1TA2=12Im{γ}PP,0Leff.

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