Abstract

In modulators that rely on changing refractive index, switching energy is primarily dependent upon the volume of the active optical mode. Photonic crystal microcavities can exhibit extremely small mode volumes on the order of a single cubic wavelength with Q values above 106. In order to be useful for integration, however, they must be embedded in oxide, which in practice reduces Q well below 103, significantly increasing switching energy. In this work we show that it is possible to create a fully oxide-clad microcavity with theoretical Q on the order of 105. We further show that by using MOS charge depletion this microcavity can be the basis for a modulator with a switching energy as low as 1 fJ/bit.

© 2010 OSA

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2010

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[CrossRef]

S. P. Anderson and P. M. Fauchet, “Ultra-low energy switches based on silicon photonic crystals for on-chip optical interconnects,” Proc. SPIE 7606, 76060R (2010).
[CrossRef]

X. Zheng, J. Lexau, Y. Luo, H. Thacker, T. Pinguet, A. Mekis, G. Li, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-low-energy all-CMOS modulator integrated with driver,” Opt. Express 18(3), 3059–3070 (2010).
[CrossRef] [PubMed]

2009

2008

2007

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[CrossRef] [PubMed]

W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007).
[CrossRef] [PubMed]

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1(5), 293–296 (2007).
[CrossRef]

2006

2005

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

2004

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

2003

2002

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10(15), 670–684 (2002).
[PubMed]

2001

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

1997

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[CrossRef]

1990

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
[CrossRef]

1989

1987

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

J. P. Lorenzo and R. A. Soref, “1.3 µm electro-optic silicon switch,” Appl. Phys. Lett. 51(1), 6–8 (1987).
[CrossRef]

1984

J. W. Goodman, F. J. Leonberger, K. Sun-Yuan, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Albonesi, D. H.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Amberg, P.

Anderson, S. P.

S. P. Anderson and P. M. Fauchet, “Ultra-low energy switches based on silicon photonic crystals for on-chip optical interconnects,” Proc. SPIE 7606, 76060R (2010).
[CrossRef]

Asano, T.

Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009).
[CrossRef] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Athale, R. A.

J. W. Goodman, F. J. Leonberger, K. Sun-Yuan, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Barrios, C. A.

C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
[CrossRef]

C. A. Barrios, V. Rosa de Almeida, and M. Lipson, “Low-power-consumption short-length and high-modulation-depth silicon electrooptic modulator,” J. Lightwave Technol. 21(4), 1089–1098 (2003).
[CrossRef]

Beausoleil, R. G.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96(2), 230–247 (2008).
[CrossRef]

Bennett, B.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Bermel, P.

Burr, G. W.

Chen, G.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Chen, H.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Chen, L.

Chen, R. T.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Chen, X.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Chetrit, Y.

Ciftcioglu, B.

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Cunningham, J. E.

Dapkus, P. D.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

de Sterke, C. M.

Deotare, P. B.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[CrossRef]

El Melhaoui, L.

Englund, D.

Farjadpour, A.

Fauchet, P. M.

S. P. Anderson and P. M. Fauchet, “Ultra-low energy switches based on silicon photonic crystals for on-chip optical interconnects,” Proc. SPIE 7606, 76060R (2010).
[CrossRef]

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Fedeli, J. M.

Friedman, E. G.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Friedman, L.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
[CrossRef]

Giguere, S. R.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
[CrossRef]

Gondarenko, A.

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, K. Sun-Yuan, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Green, W. M.

Gu, L.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Hagino, H.

Haurylau, M.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Herzig, H. P.

Ho, R.

Ibanescu, M.

Izhaky, N.

Jiang, W.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Jiang, Y.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Krishnamoorthy, A. V.

Kuekes, P. J.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96(2), 230–247 (2008).
[CrossRef]

Kuga, T.

Kuramochi, E.

T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Lentine, A. L.

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
[CrossRef]

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, K. Sun-Yuan, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Lexau, J.

Li, G.

Liao, L.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Lipson, M.

Liu, A.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Loncar, M.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

Lorenzo, J. P.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
[CrossRef]

J. P. Lorenzo and R. A. Soref, “1.3 µm electro-optic silicon switch,” Appl. Phys. Lett. 51(1), 6–8 (1987).
[CrossRef]

Luo, Y.

Lyan, P.

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

Mandelshtam, V. A.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[CrossRef]

Manipatruni, S.

Märki, I.

Mekis, A.

Miller, D. A. B.

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Nelson, N. A.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Nguyen, H.

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Noda, S.

Y. Takahashi, Y. Tanaka, H. Hagino, T. Sugiya, Y. Sato, T. Asano, and S. Noda, “Design and demonstration of high-Q photonic heterostructure nanocavities suitable for integration,” Opt. Express 17(20), 18093–18102 (2009).
[CrossRef] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Notomi, M.

T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, “Design of a high-Q air-slot cavity based on a width-modulated line-defect in a photonic crystal slab,” Opt. Express 16(18), 13809–13817 (2008).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

O'Brien, J. D.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

Painter, O.

Paniccia, M.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Pinckney, N.

Pinguet, T.

Poitras, C. B.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Preble, S. F.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1(5), 293–296 (2007).
[CrossRef]

Preston, K.

Quan, Q.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[CrossRef]

Raj, K.

Robinson, J. T.

Rodriguez, A.

Rooks, M. J.

Rosa de Almeida, V.

Roundy, D.

Rubin, D.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Salt, M.

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Sato, Y.

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Sekaric, L.

Shi, J.

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Snider, G. S.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96(2), 230–247 (2008).
[CrossRef]

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

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R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

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S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
[CrossRef]

J. P. Lorenzo and R. A. Soref, “1.3 µm electro-optic silicon switch,” Appl. Phys. Lett. 51(1), 6–8 (1987).
[CrossRef]

Srinivasan, K.

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11(6), 579–593 (2003).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10(15), 670–684 (2002).
[PubMed]

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

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Steel, M. J.

Sugiya, T.

Sun-Yuan, K.

J. W. Goodman, F. J. Leonberger, K. Sun-Yuan, and R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

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Tanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Tanaka, Y.

Taniyama, H.

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[CrossRef]

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Tomljenovic-Hanic, S.

Torii, Y.

Trotter, D. C.

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
[CrossRef]

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Vuckovic, J.

D. Englund and J. Vucković, “A direct analysis of photonic nanostructures,” Opt. Express 14(8), 3472–3483 (2006).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

Wang, S. Y.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96(2), 230–247 (2008).
[CrossRef]

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Watts, M. R.

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
[CrossRef]

Williams, R. S.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96(2), 230–247 (2008).
[CrossRef]

Xu, Q.

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1(5), 293–296 (2007).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Yamamoto, T.

Yoshikawa, Y.

Young, R. W.

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
[CrossRef]

Zhang, J.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
[CrossRef]

Zheng, X.

Zortman, W. A.

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
[CrossRef]

Appl. Phys. Lett.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88(4), 041112 (2006).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96(20), 203102 (2010).
[CrossRef]

J. P. Lorenzo and R. A. Soref, “1.3 µm electro-optic silicon switch,” Appl. Phys. Lett. 51(1), 6–8 (1987).
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Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87(22), 221105 (2005).
[CrossRef]

IEEE J. Quantum Electron.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38(7), 850–856 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. Haurylau, G. Chen, H. Chen, J. Zhang, N. A. Nelson, D. H. Albonesi, E. G. Friedman, and P. M. Fauchet, “On-chip optical interconnect roadmap: Challenges and critical directions,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1699–1705 (2006).
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Integr. VLSI J.

G. Chen, H. Chen, M. Haurylau, N. A. Nelson, D. H. Albonesi, P. M. Fauchet, and E. G. Friedman, “Predictions of CMOS compatible on-chip optical interconnect,” Integr. VLSI J. 40(4), 434–446 (2007).
[CrossRef]

J. Appl. Phys.

S. R. Giguere, L. Friedman, R. A. Soref, and J. P. Lorenzo, “Simulation studies of silicon electro-optic waveguide devices,” J. Appl. Phys. 68(10), 4964–4970 (1990).
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C. A. Barrios and M. Lipson, “Modeling and analysis of high-speed electro-optic modulation in high confinement silicon waveguides using metal-oxide-semiconductor configuration,” J. Appl. Phys. 96(11), 6008–6015 (2004).
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J. Chem. Phys.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals and its applications,” J. Chem. Phys. 107(17), 6756–6769 (1997).
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J. Lightwave Technol.

J. Opt. A, Pure Appl. Opt.

O. Painter, K. Srinivasan, J. D. O'Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A, Pure Appl. Opt. 3(6), 161–170 (2001).
[CrossRef]

Nat. Mater.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005).
[CrossRef]

Nat. Photonics

S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1(5), 293–296 (2007).
[CrossRef]

Nature

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427(6975), 615–618 (2004).
[CrossRef] [PubMed]

Opt. Express

D. Englund and J. Vucković, “A direct analysis of photonic nanostructures,” Opt. Express 14(8), 3472–3483 (2006).
[CrossRef] [PubMed]

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10(15), 670–684 (2002).
[PubMed]

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11(6), 579–593 (2003).
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S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14(25), 12451–12456 (2006).
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A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
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J. T. Robinson, K. Preston, O. Painter, and M. Lipson, “First-principle derivation of gain in high-index-contrast waveguides,” Opt. Express 16(21), 16659–16669 (2008).
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[CrossRef]

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Proc. SPIE

M. R. Watts, D. C. Trotter, R. W. Young, A. L. Lentine, and W. A. Zortman, “Limits to silicon modulator bandwidth and power consumption,” Proc. SPIE 7221, 72210M (2009).
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Figures (11)

Fig. 1
Fig. 1

Empirical relationship between the optical mode volumes and resulting switching energies of several modulation techniques. MZI-based [16,17]; ring and disk [810]; and the present work.

Fig. 2
Fig. 2

Available bandgaps TE-like modes for air- and SiO2-clad silicon photonic crystals. Calculated for triangular lattice of low-index holes in a silicon slab of thickness h = 0.5a.

Fig. 3
Fig. 3

Dispersion diagram showing upper and lower bandedges and the relevant light lines for air- and SiO2-clad silicon photonic crystals. Shading corresponds to regions with low vertical leakage and thus high potential Q.

Fig. 4
Fig. 4

Microcavity geometry used in this work. The microcavity is symmetric in x and y, with lateral spacing between columns of holes greatest at the center, decreasing linearly from 1.025a down to a at the edge of the graded region. The linear grade is actually made up of a series of finite steps due to the discrete nature of photonic crystals.

Fig. 5
Fig. 5

Resonant mode of the graded microcavity, showing side-coupling to bus and drop waveguides, plotting Ey .

Fig. 6
Fig. 6

Cross-sectional schematic of device configuration on SOI. The size of the n+ polysilicon gate electrode is tailored to overlap only the area of the optical mode in the microcavity.

Fig. 7
Fig. 7

Change in the modal index as a function of substrate doping, assuming full depletion. The kink near NA = 1016 cm−3 occurs when the depletion depth is equal to the 250 nm thickness of the silicon slab. Depletion depth decreases with doping.

Fig. 8
Fig. 8

Reduction in both Q factor (left) and mode confinement (right) in the waveguide-coupled microcavity as the gate oxide thickness is reduced. Q is limited to approximately 20,000 due to coupling to the bus and drop waveguides.

Fig. 9
Fig. 9

Normalized transmission spectra present on drop waveguide for fully depleted (biased) and undepleted (unbiased) cases, for the device displayed in Fig. 5.

Fig. 10
Fig. 10

Cross-sectional view of the simulated optical mode (red) present in the cavity when the gate oxide thickness is t = 250 nm. The blue regions indicate the p-type silicon slab and the n+-type gate electrode, and white indicates SiO2. Brown indicates the depletion region, in which the index shift is induced.

Fig. 11
Fig. 11

Minimum switching energy required to achieve 6 dB extinction for a range of values of gate oxide thickness, determined by optimizing over gate voltage and substrate doping. For thin gate oxide, switching energy increases due to the degraded Q and lower confinement, while thicker gate oxides require a higher gate voltage.

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