Abstract

The influence of BaTiO3 ferroelectric domain orientations for high efficiency electro-optic modulation has been thoroughly analyzed. The Mach-Zehnder modulator structure is based on a CMOS compatible silicon/BaTiO3/silicon slot waveguide that supports both TE and TM polarizations whereas the Pockels effect is exploited by the application of a horizontal electric field with lateral electrodes placed on top of the BaTiO3 layer. The influence of the waveguide parameters has been optimized for each configuration and the lowest Vπ voltage combined with low losses has been determined. A VπL as low as 0.27 V·cm has been obtained for a-axis oriented BaTiO3 and TE polarization by rotating the waveguide structure to an optimum angle.

© 2015 Optical Society of America

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2015 (2)

2014 (4)

Y. Gao, X. Huang, and X. Xu, “Electro-optic modulator based on a photonic crystal slab with electro-optic polymer cladding,” Opt. Express 22(7), 8765–8778 (2014).
[Crossref] [PubMed]

P. Damas, X. Le Roux, D. Le Bourdais, E. Cassan, D. Marris-Morini, N. Izard, T. Maroutian, P. Lecoeur, and L. Vivien, “Wavelength dependence of Pockels effect in strained silicon waveguides,” Opt. Express 22(18), 22095–22100 (2014).
[Crossref] [PubMed]

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

2013 (5)

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21(21), 25573–25581 (2013).
[Crossref] [PubMed]

L. Chen, M. G. Wood, and R. M. Reano, “12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes,” Opt. Express 21(22), 27003–27010 (2013).
[Crossref] [PubMed]

2012 (1)

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

2011 (1)

2010 (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

2008 (1)

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

D. Y. Chen and J. D. Phillips, “Analysis and design optimization of electrooptic interferometric modulators for microphotonics applications,” J. Lightwave Technol. 24(6), 2340–2345 (2006).
[Crossref]

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

2005 (2)

D. Y. Chen and J. D. Phillips, “Extraction of electro-optic coefficient in thin-film linear electro-optic Mach-Zehnder interferometers with nonperiodic intensity-voltage output characteristics,” Opt. Eng. 44(3), 034601 (2005).
[Crossref]

P. Tang, A. L. Meier, D. J. Towner, and B. W. Wessels, “BaTiO3 thin-film waveguide modulator with a low voltage-length product at near-infrared wavelengths of 0.98 and 1.55 μm,” Opt. Lett. 30(3), 254–256 (2005).
[Crossref] [PubMed]

2004 (1)

2002 (1)

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

1994 (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Abel, S.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Ahn, C. H.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Alloatti, L.

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Atwater, H. A.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Baehr-Jones, T.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Baets, R.

Barklund, A.

Bernasconi, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Bhattacharya, K.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Blasco, J.

Bogaerts, W.

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Buchal, C.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

Caimi, D.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Cassan, E.

Chelnokov, A.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Chen, C.

Chen, D. Y.

D. Y. Chen and J. D. Phillips, “Analysis and design optimization of electrooptic interferometric modulators for microphotonics applications,” J. Lightwave Technol. 24(6), 2340–2345 (2006).
[Crossref]

D. Y. Chen and J. D. Phillips, “Extraction of electro-optic coefficient in thin-film linear electro-optic Mach-Zehnder interferometers with nonperiodic intensity-voltage output characteristics,” Opt. Eng. 44(3), 034601 (2005).
[Crossref]

Chen, L.

Chiles, J.

Cueff, S.

Damas, P.

Dicken, M. J.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Ding, R.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Dinu, R.

Duelli, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Dumon, P.

Erni, R.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

Fage-Pedersen, J.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Fathpour, S.

Fedeli, J.

Fomperyine, J.

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Fompeyrine, J.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

Fournier, M.

Frandsen, L. H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Freude, W.

Gao, Y.

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Garrett, M. H.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Günter, P.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Hamano, T.

Hansen, O.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Harris, N. C.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Hillerkuss, D.

Hochberg, M.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Hu, X.

Huang, X.

Izard, N.

Jacobsen, R. S.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Jiang, H.

Khan, S.

Kong, M.

Koos, C.

Korn, D.

Kristensen, M.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Kumah, D.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Le Bourdais, D.

Le Roux, X.

Lecoeur, P.

Leuthold, J.

Lezec, H. J.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Li, J.

Ma, J.

Marchiori, C.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Maroutian, T.

Marris-Morini, D.

Marti, J.

Martínez, A.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Meier, A.

Meier, A. L.

Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Ngai, J. H.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Novack, A.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Offrein, B. J.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

Orobtchouk, R.

Ou, H.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Pacifici, D.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Palmer, R.

Pernice, W. H. P.

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Petraru, A.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

Peucheret, C.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Phillips, J. D.

D. Y. Chen and J. D. Phillips, “Analysis and design optimization of electrooptic interferometric modulators for microphotonics applications,” J. Lightwave Technol. 24(6), 2340–2345 (2006).
[Crossref]

D. Y. Chen and J. D. Phillips, “Extraction of electro-optic coefficient in thin-film linear electro-optic Mach-Zehnder interferometers with nonperiodic intensity-voltage output characteristics,” Opt. Eng. 44(3), 034601 (2005).
[Crossref]

Rabiei, P.

Reano, R. M.

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Reiner, J. W.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Romeo, P. R.

Rossel, C.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Rossell, M. D.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

Rytz, D.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Sanchis, P.

Schlesser, R.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Schmid, M.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

Schubert, J.

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

Sousa, M.

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Stöferle, T.

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Sun, D.

Sweatlock, L. A.

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Tang, H. X.

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Tang, P.

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Towner, D.

Towner, D. J.

Vivien, L.

Walker, F. J.

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

Wang, J.

Wessels, B.

Wessels, B. W.

Wieland, J.

Wood, M. G.

Wu, X.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Xiong, C.

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

Xu, X.

Xuan, Z.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Yu, H.

Zgonik, M.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Zhang, J.

Zhang, Y.

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

Zhu, Y.

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

A. Petraru, J. Schubert, M. Schmid, and C. Buchal, “Ferroelectric BaTiO3 thin-film optical waveguide modulators,” Appl. Phys. Lett. 81(8), 1375–1377 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (1)

W. H. P. Pernice, C. Xiong, F. J. Walker, and H. X. Tang, “Design of a silicon integrated electro-optic modulator using ferroelectric BaTiO3 films,” IEEE Photon. Technol. Lett. 26(13), 1344–1347 (2014).
[Crossref]

IEEE Solid-State Circuits Magazine (1)

M. Hochberg, N. C. Harris, R. Ding, Y. Zhang, A. Novack, Z. Xuan, and T. Baehr-Jones, “Silicon photonics: the next fabless semiconductor industry,” IEEE Solid-State Circuits Magazine 5(1), 48–58 (2013).
[Crossref]

J. Lightwave Technol. (3)

Nano Lett. (2)

C. Xiong, W. H. P. Pernice, J. H. Ngai, J. W. Reiner, D. Kumah, F. J. Walker, C. H. Ahn, and H. X. Tang, “Active silicon integrated nanophotonics: ferroelectric BaTiO₃ devices,” Nano Lett. 14(3), 1419–1425 (2014).
[Crossref] [PubMed]

M. J. Dicken, L. A. Sweatlock, D. Pacifici, H. J. Lezec, K. Bhattacharya, and H. A. Atwater, “Electrooptic modulation in thin film barium titanate plasmonic interferometers,” Nano Lett. 8(11), 4048–4052 (2008).
[Crossref] [PubMed]

Nanotechnology (1)

S. Abel, M. Sousa, C. Rossel, D. Caimi, M. D. Rossell, R. Erni, J. Fompeyrine, and C. Marchiori, “Controlling tetragonality and crystalline orientation in BaTiO₃ nano-layers grown on Si,” Nanotechnology 24(28), 285701 (2013).
[Crossref] [PubMed]

Nat. Commun. (1)

S. Abel, T. Stöferle, C. Marchiori, C. Rossel, M. D. Rossell, R. Erni, D. Caimi, M. Sousa, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “A strong electro-optically active lead-free ferroelectric integrated on silicon,” Nat. Commun. 4, 1671 (2013).
[Crossref] [PubMed]

Nat. Photonics (1)

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010).
[Crossref]

Nature (1)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Opt. Eng. (1)

D. Y. Chen and J. D. Phillips, “Extraction of electro-optic coefficient in thin-film linear electro-optic Mach-Zehnder interferometers with nonperiodic intensity-voltage output characteristics,” Opt. Eng. 44(3), 034601 (2005).
[Crossref]

Opt. Express (7)

P. Tang, D. Towner, T. Hamano, A. Meier, and B. Wessels, “Electrooptic modulation up to 40 GHz in a barium titanate thin film waveguide modulator,” Opt. Express 12(24), 5962–5967 (2004).
[Crossref] [PubMed]

L. Alloatti, D. Korn, R. Palmer, D. Hillerkuss, J. Li, A. Barklund, R. Dinu, J. Wieland, M. Fournier, J. Fedeli, H. Yu, W. Bogaerts, P. Dumon, R. Baets, C. Koos, W. Freude, and J. Leuthold, “42.7 Gbit/s electro-optic modulator in silicon technology,” Opt. Express 19(12), 11841–11851 (2011).
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P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21(21), 25573–25581 (2013).
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L. Chen, M. G. Wood, and R. M. Reano, “12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes,” Opt. Express 21(22), 27003–27010 (2013).
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Y. Gao, X. Huang, and X. Xu, “Electro-optic modulator based on a photonic crystal slab with electro-optic polymer cladding,” Opt. Express 22(7), 8765–8778 (2014).
[Crossref] [PubMed]

P. Damas, X. Le Roux, D. Le Bourdais, E. Cassan, D. Marris-Morini, N. Izard, T. Maroutian, P. Lecoeur, and L. Vivien, “Wavelength dependence of Pockels effect in strained silicon waveguides,” Opt. Express 22(18), 22095–22100 (2014).
[Crossref] [PubMed]

X. Hu, S. Cueff, P. R. Romeo, and R. Orobtchouk, “Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator,” Opt. Express 23(2), 1699–1714 (2015).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. B Condens. Matter (1)

M. Zgonik, P. Bernasconi, M. Duelli, R. Schlesser, P. Günter, M. H. Garrett, D. Rytz, Y. Zhu, and X. Wu, “Dielectric, elastic, piezoelectric, electro-optic, and elasto-optic tensors of BaTiO3 crystals,” Phys. Rev. B Condens. Matter 50(9), 5941–5949 (1994).
[Crossref] [PubMed]

Proc. SPIE (1)

S. Abel, D. Caimi, M. Sousa, T. Stöferle, C. Rossel, C. Marchiori, A. Chelnokov, and J. Fomperyine, “Electro-optical properties of barium titanate films epitaxially grown on silicon,” Proc. SPIE 8263, 82630Y (2012).
[Crossref]

Other (2)

C. O. M. S. O. L. Multiphysics, http://www.comsol.com/

S. Abel, T. Stöferle, C. Marchiori, D. Caimi, L. Czornomaz, C. Rossel, M. Rossell, R. Erni, M. Sousa, H. Siegwart, J. Hofrichter, M. Stuckelberger, A. Chelnokov, B. J. Offrein, and J. Fompeyrine, “Electro-Optical Active Barium Titanate Thin Films in Silicon Photonics Devices,” in Advanced Photonics 2013, H. Chang, V. Tolstikhin, T. Krauss, and M. Watts, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper IW4A.5.

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the Mach-Zehnder modulator and (b) waveguide structure with electrodes. W is the waveguide width, G is the waveguide-to-electrode separation and taSi, tBTO and tSi are the amorphous, BaTiO3 and crystalline silicon thicknesses.

Fig. 2
Fig. 2

(a) Effective index and (b) upper bound of the EO overlap integral as a function of the waveguide width taking into account tBTO = 50nm and taSi = 220nm. Propagation losses due to electrodes are also shown for c) TE and (d) TM and different waveguide-to-electrode separations. The horizontal dashed line is for 1dB/cm propagation losses.

Fig. 3
Fig. 3

(a) BaTiO3 crystal structure and (b) index ellipsoid. The crystallographic axes, a1, a2 and c, are aligned along the coordinate system with axes x, y, and z, respectively.

Fig. 4
Fig. 4

Waveguide structure for a-axis oriented BaTiO3. The optical axis (z-axis) is in-plane in the BaTiO3 layer and can be (a) parallel or (b) perpendicular to the applied electric field. (c) The waveguide can also be rotated by an angle of ϕ in the yz plane to enhance the EO performance.

Fig. 5
Fig. 5

(a) EO coefficient for TE polarization. (b) EO overlap and (c) Vπ voltage as a function of the rotation angle for both polarizations.

Fig. 6
Fig. 6

Vπ voltage for TE polarization and ϕ = 55° as a function of (a) the amorphous silicon thickness and G = 1μm and (b) the waveguide-to-electrode separation and taSi = 220nm. Results are shown for different waveguide widths.

Fig. 7
Fig. 7

Waveguide structure for c-axis oriented BaTiO3. (a) The optical axis (z-axis) is out-of-plane in the BaTiO3 layer. (b) However, there is a rotation in the xz plane (θ-angle) when a voltage is applied in the electrodes.

Fig. 8
Fig. 8

(a) Induced rotation angle of the BaTiO3 principal axes as a function of the applied voltage and for different waveguide-to-electrode separations. (b) Simulated and analytic phase shift for both polarizations as a function of the applied voltage for G = 1μm.

Fig. 9
Fig. 9

Vπ voltage for (a) TE and (b) TM polarizations as a function of the amorphous silicon thickness taken into account different waveguide-to-electrode separations and a waveguide width of 600nm.

Equations (13)

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( 1 n o 2 + r 13 E z ) x 2 +( 1 n o 2 + r 13 E z ) y 2 +( 1 n e 2 + r 33 E z ) z 2 +( r 51 E y )2yz+( r 51 E x )2zx=1
y= y ' cos( ϕ )+ z ' sin( ϕ ) z= y ' sin( ϕ )+ z ' cos(ϕ)
n z' ( ϕ )= n o n e n e 2 sin 2 ( ϕ )+ n o 2 cos 2 (ϕ)
r z' ( ϕ )= r 33 cos 3 ( ϕ )+( r 13 +2 r 51 ) sin 2 ( ϕ )cos( ϕ )
n x = n o
r x ( ϕ )= r 13 cos( ϕ )
Γ( ϕ )= S V BTO E e ( ϕ ) | E o ( ϕ ) | 2 dxdz' | E o ( ϕ ) | 2 dxdz'
V π,TE ( ϕ ) λS Γ TE n z' 3 ( ϕ ) r z' ( ϕ )L
V π,TM ( ϕ ) λS Γ TM n o 3 r 13 cos( ϕ )L
θ= 1 2 atan( 2 r 51 V S[ 1 n e 2 1 n o 2 ] )
V π,TE = ( 1 n e 2 1 n o 2 )λ S 2 Γ TE n o 3 r 51 2 L
V π,TM = ( 1 n e 2 1 n o 2 )λ S 2 Γ TM n e 3 r 51 2 L
V π,TM V π,TE S TM S TE Γ TE Γ TM

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