Abstract

This paper presents a theoretical analysis of a silicon all-optical modulator based on free-carrier injection by two-photon absorption (TPA) in a highly light-confining structure. In spite of the weak optoelectronic properties of silicon, strong light confinement allows high modulation depths in very compact devices requiring low-energy pump pulses. This analysis is applied to 1-5 µm radius silicon ring resonators with the pump pulse coupled on-chip and including in the model the scattering loss due to sidewall roughness originating from the fabrication process. The calculations show that using this scheme, modulation depths greater than 80% can be achieved, with no more than 3 pJ of pump pulse energy, at speeds on the order of 10 GHz.

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Other (28)

R. A. Soref, "Silicon-based optoelectronics," Proc. IEEE, vol. 81, no. 12, pp. 1687-1706, Dec. 1993.

K. Wada, H. C. Luan, C. Lim and D. R. L. C. Kimerling, "On-chip interconnection beyond semiconductor roadmap: Silicon microphotonics," in Proc. SPIE-Int. Soc. Opt. Eng., vol. 4870, Boston, MA, 2002, pp. 437-443.

M. Dinu, F. Quochi and H. Garcia, "Third-order nonlinearities in silicon at telecom wavelengths," Appl. Phys. Lett., vol. 82, no. 18, pp. 2954-2956, May 2003.

R. A. Soref, "Electrooptical effects in silicon," IEEE J. Quantum Electron., vol. QE-23, no. 1, pp. 123-129, Jan. 1987.

R. A. Soref and B. R. Bennett, "Kramers-Kronig analysis of electro-optical switching in silicon," in Proc. SPIE, vol. 704, Cambridge, MA, 1987, pp. 32-37.

N. D. Sankey, D. F. Prelewitz and T. G. Brown, "All-optical switching in a nonlinear periodic-waveguide structure," Appl. Phys. Lett., vol. 12, no. 23, pp. 1427-1429, Mar. 1992.

A. Hache and M. Bourgeois, "Ultrafast all-optical switching in a silicon-based photonic crystal," Appl. Phys. Lett., vol. 77, no. 25, pp. 4089-4091, Dec. 2000.

F. Z. Henari, K. Morgenstern, W. J. Blau, V. A. Karavanskii and V. S. Dneprovskii, "Third-order optical nonlinearity and all-optical switching in porous silicon," Appl. Phys. Lett., vol. 67, no. 3, pp. 323-325, Jul. 1995.

C. Z. Zhao, G. Z. Li, E. K. Liu, Y. Gao and X. D. Liu, "Silicon on insulator Mach-Zehnder waveguide interferometers operating at 1.3 µm," Appl. Phys. Lett., vol. 67, no. 17, pp. 2448-2449, Oct. 1995.

S. Stepanov and S. Ruschin, "Modulation of light by light in silicon-on insulator waveguides," Appl. Phys. Lett., vol. 83, no. 25, pp. 5151-5153, Dec. 2003.

V. Van, T. A. Ibrahim, K. Ritter, P. P. Absil, F. G. Johnson, R. Grover, J. Goldhar and P.-T. Ho, "All-optical nonlinear switching in GaAs-AlGaAs microring resonators," IEEE Photon. Technol. Lett., vol. 14, no. 1, pp. 74-76, Jan. 2002.

V. Van, T. A. Ibrahim, P. P. Absil, F. G. Johnson, R. Grover and P.-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Sel. Topics Quantum Electron., vol. 8, no. 3, pp. 705-713, May/Jun. 2002.

T. A. Ibrahim, W. Cao, Y. Kim, J. Li, J. Goldhar, P.-T. Ho and C. H. Lee, "All-optical switching in a laterally coupled microring resonator by carrier injection," IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 36-38, Jan. 2003.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, M. A. Foster, D. G. Ouzounov and A. L. Gaeta, "All-optical switching on a silicon chip," Opt. Lett., vol. 29, no. 24, pp. 2867-2869, Dec. 2004.

V. R. Almeida, C. A. Barrios, R. R. Panepucci and M. Lipson, "All-optical control of light on a silicon chip," Nature, vol. 431, no. 7012, pp. 1081-1084, Oct. 2004.

Q. Xu, V. R. Almeida and M. Lipson, "Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides," Opt. Express, vol. 12, no. 19, pp. 4437-4442, Sep. 2004.

R. L. Espinola, J. I. Dadap, R. M. Osgood Jr., S. J. McNab and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express, vol. 12, no. 16, pp. 3713-3718, Aug. 2004.

T. K. Liang and H. K. Tsang, "On Raman gain in silicon waveguides: Limitations from two-photon-absorption generated carriers," in Proc. Conf. Lasers and Electro-Optics (CLEO), vol. 2, San Francisco, CA, May 2004,Paper CThT48,. p. 2.

O. Boyraz and B. Jalali, "Demonstration of a silicon Raman laser," Opt. Express, vol. 12, no. 21, pp. 5269-5273, Oct. 2004.

R. Jones, H. Rong, A. Liu, A. W. Fang, M. J. Paniccia, D. Hak and O. Cohen, "Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering," Opt. Express, vol. 13, no. 2, pp. 519-525, Jan. 2005.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang and M. Paniccia, "An all-silicon Raman laser," Nature, vol. 433, no. 7023, pp. 292-294, Jan. 2005.

H. M. van Driel, S. W. Leonard, H.-W. Tan, A. Birner, J. Schilling, S. L. Schweizer, R. B. Wehrspohn and U. Gosele, "Tuning 2D photonic crystals," in Proc. SPIE, vol. 5511, Denver, CO, Aug. 2004, pp. 1-9.

Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express, vol. 12, no. 8, pp. 1622-1631, Apr. 2004.

H. A. Haus, Waves and Fields in Optoelectronics, Chapter, Englewood Cliffs, NJ: Prentice-Hall, 1984.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi and J.-P. Laine, "Microring resonator channel-dropping filters," J. Lightw. Technol., vol. 15, no. 6, pp. 998-1005, Jun. 1997.

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett., vol. 36, no. 4, pp. 321-322, Feb. 2000.

A. Chin, K. Y. Lee, B. C. Lin and S. Horng, "Picosecond photoresponse of carriers in Si ion-implanted Si," Appl. Phys. Lett., vol. 69, no. 5, pp. 653-655, Jul. 1996.

M. Popovic, "Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures," Integr. Photon. Res., Trends Opt. Photon. Series, vol. 91, pp. 143-145, Jun. 2003.

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