Abstract

A highly efficient phase shifter based on the silicon-organic hybrid (SOH) platform is theoretically investigated and experimentally tested. The device consists of a silicon slot waveguide covered with an organic liquid-crystal (LC) cladding. A record-low voltage-length product of UπL = 0.085 Vmm can be achieved for high-purity materials where an optimum operation point can be set by a DC bias. With standard materials and without a DC bias, we measure a phase shift of 35π with a drive voltage of only 5 V for a 1.7 mm long device corresponding to a voltage-length product of UπL = 0.24 Vmm. The power dissipation is about six orders of magnitude smaller than that of state-of-the-art thermo-optic devices, thereby enabling dense integration of LC phase shifters in advanced photonic integrated circuits.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Selvaraja, P. Jaenen, W. Bogaerts, D. Van Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27(18), 4076–4083 (2009).
    [CrossRef]
  2. M. Yang, W. M. J. Green, S. Assefa, J. Van Campenhout, B. G. Lee, C. V. Jahnes, F. E. Doany, C. L. Schow, J. A. Kash, and Y. A. Vlasov, “Non-blocking 4x4 electro-optic silicon switch for on-chip photonic networks,” Opt. Express 19(1), 47–54 (2011).
    [CrossRef] [PubMed]
  3. S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
    [CrossRef]
  4. M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
    [CrossRef]
  5. N. Walker and G. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8(3), 438–458 (1990).
    [CrossRef]
  6. C. Doerr, P. Winzer, Y.-K. Chen, S. Chandrasekhar, M. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
    [CrossRef]
  7. D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
    [CrossRef] [PubMed]
  8. L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
    [CrossRef] [PubMed]
  9. P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
    [CrossRef] [PubMed]
  10. A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
    [CrossRef]
  11. 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]
  12. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
    [CrossRef]
  13. J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
    [CrossRef]
  14. B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
    [CrossRef]
  15. W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011).
    [CrossRef] [PubMed]
  16. I.-C. Khoo, Liquid crystals, 2nd ed. (Wiley-Interscience, 2007).
  17. L. Alloatti, J. Pfeifle, J. Mendez, W. Freude, J. Leuthold, and C. Koos, “Liquid crystal phase shifter on the SOH platform with ultra-low power consumption,” in Optical Fiber Communication Conference (OTu1I.5.), (2012).
  18. 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).
    [CrossRef] [PubMed]
  19. R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in silicon-on-insulator,” Opt. Express 18(24), 25061–25067 (2010).
    [CrossRef] [PubMed]
  20. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
    [CrossRef] [PubMed]
  21. H. Desmet, K. Neyts, and R. Baets, “Liquid crystal orientation on patterns etched in Silicon on Insulator,” in Integrated Optics, Silicon Photonics, and Photonic Integrated Circuits, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (61831Z), (2006).
  22. CST - Computer Simulation Technology AG, CST Microwave Studio 2012, http://www.cst.com (2012).
  23. C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
    [CrossRef]
  24. W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011).
    [CrossRef]
  25. RSoft Design Group Inc, FemSIM 3.3 User Guide, http://www.rsoftdesign.com (2011).
  26. P. Mullner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
    [CrossRef]
  27. Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
    [CrossRef]
  28. T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
    [CrossRef]
  29. P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
    [CrossRef]
  30. M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
    [CrossRef]
  31. T. Alasaarela, D. Korn, L. Alloatti, A. Säynätjoki, A. Tervonen, R. Palmer, J. Leuthold, W. Freude, and S. Honkanen, “Reduced propagation loss in silicon strip and slot waveguides coated by atomic layer deposition,” Opt. Express 19(12), 11529–11538 (2011).
    [CrossRef] [PubMed]
  32. D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
    [CrossRef]
  33. G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley-Interscience, 2010).
  34. C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
    [CrossRef]
  35. H. Desmet, K. Neyts, and R. Baets, “Modeling nematic liquid crystals in the neighborhood of edges,” J. Appl. Phys. 98(12), 123517 (2005).
    [CrossRef]

2011 (6)

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011).
[CrossRef]

M. Yang, W. M. J. Green, S. Assefa, J. Van Campenhout, B. G. Lee, C. V. Jahnes, F. E. Doany, C. L. Schow, J. A. Kash, and Y. A. Vlasov, “Non-blocking 4x4 electro-optic silicon switch for on-chip photonic networks,” Opt. Express 19(1), 47–54 (2011).
[CrossRef] [PubMed]

T. Alasaarela, D. Korn, L. Alloatti, A. Säynätjoki, A. Tervonen, R. Palmer, J. Leuthold, W. Freude, and S. Honkanen, “Reduced propagation loss in silicon strip and slot waveguides coated by atomic layer deposition,” Opt. Express 19(12), 11529–11538 (2011).
[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).
[CrossRef] [PubMed]

W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011).
[CrossRef] [PubMed]

2010 (6)

2009 (3)

2008 (2)

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

2007 (2)

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]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

2006 (2)

P. Mullner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

2005 (2)

H. Desmet, K. Neyts, and R. Baets, “Modeling nematic liquid crystals in the neighborhood of edges,” J. Appl. Phys. 98(12), 123517 (2005).
[CrossRef]

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

2004 (3)

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[CrossRef] [PubMed]

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

2003 (1)

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

1990 (1)

N. Walker and G. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8(3), 438–458 (1990).
[CrossRef]

1982 (1)

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

Alasaarela, T.

Alloatti, L.

Almeida, V. R.

Ang, K.-W.

Asghari, M.

Asquini, R.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Assefa, S.

Baehr-Jones, T.

R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in silicon-on-insulator,” Opt. Express 18(24), 25061–25067 (2010).
[CrossRef] [PubMed]

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Baets, R.

Barbero, G.

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

Barklund, A.

Barrios, C. A.

Basak, J.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Beccherelli, R.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Beeckman, J.

Bellini, B.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Ben Ezra, S.

Ben Yoo, S. J.

Biaggio, I.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Bogaerts, W.

Bojko, R.

Bolle, C.

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Brosi, J.-M.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Chandrasekhar, S.

Chen, L.

Chen, Y.-K.

C. Doerr, P. Winzer, Y.-K. Chen, S. Chandrasekhar, M. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
[CrossRef]

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Chetrit, Y.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Cipparrone, G.

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

Claes, T.

Cohen, R.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

d’Alessandro, A.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Dalton, L.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Davies, J.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

De Cort, W.

Desimpel, C.

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

Desmet, H.

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

H. Desmet, K. Neyts, and R. Baets, “Modeling nematic liquid crystals in the neighborhood of edges,” J. Appl. Phys. 98(12), 123517 (2005).
[CrossRef]

Diederich, F.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Ding, R.

Ding, Z.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
[CrossRef] [PubMed]

Dinu, R.

Djordjevic, S. S.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Doany, F. E.

Doerr, C.

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

C. Doerr, P. Winzer, Y.-K. Chen, S. Chandrasekhar, M. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
[CrossRef]

Dong, P.

Donisi, D.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Dumon, P.

Earnshaw, M.

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Fan, Y.-H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

Fedeli, J.

Fedeli, J. M.

Feng, D.

Fernandez, F. A.

Fernández, F. A.

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

Fontaine, N. K.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Fournier, M.

Frank, B.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Freude, W.

Fujii, M.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

Gauza, S.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

Gilardi, G.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Gill, D.

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Green, W. M.

Green, W. M. J.

Guan, B.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Gunn, C.

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Hainberger, R.

P. Mullner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

Hillerkuss, D.

Hochberg, M.

R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in silicon-on-insulator,” Opt. Express 18(24), 25061–25067 (2010).
[CrossRef] [PubMed]

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Honkanen, S.

Huang, J.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Ibrahim, S.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
[CrossRef] [PubMed]

Izhaky, N.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Jaenen, P.

Jahnes, C. V.

James, R.

W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011).
[CrossRef]

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

Jen, A.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Kash, J. A.

Kawachi, M.

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

Kim, T.-D.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Kim, W. J.

Kobayashi, M.

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

Koos, C.

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).
[CrossRef] [PubMed]

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

Korn, D.

Krishnamoorthy, A. V.

Kung, C.-C.

Lawson, R.

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Lee, B. G.

Leuthold, J.

Li, G.

Li, J.

Liang, H.

Liao, L.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Liao, S.

Lin, Y.-H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

Liow, T.-Y.

Lipson, M.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
[CrossRef] [PubMed]

V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29(11), 1209–1211 (2004).
[CrossRef] [PubMed]

Liu, A.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Lo, G.-Q.

Luo, J.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Luo, L. W.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Luo, L.-W.

Marculescu, A.

Maune, B.

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Mullner, P.

P. Mullner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

Narkiss, N.

Neyts, K.

W. De Cort, J. Beeckman, R. James, F. A. Fernandez, R. Baets, and K. Neyts, “Tuning silicon-on-insulator ring resonators with in-plane switching liquid crystals,” J. Opt. Soc. Am. B 28(1), 79–85 (2011).
[CrossRef]

W. De Cort, J. Beeckman, T. Claes, K. Neyts, and R. Baets, “Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding,” Opt. Lett. 36(19), 3876–3878 (2011).
[CrossRef] [PubMed]

H. Desmet, K. Neyts, and R. Baets, “Modeling nematic liquid crystals in the neighborhood of edges,” J. Appl. Phys. 98(12), 123517 (2005).
[CrossRef]

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

Nguyen, H.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Nitkowski, A.

Noda, J.

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

Okamoto, K.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Pagliusi, P.

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

Palmer, R.

Paniccia, M.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Penkov, B.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Pfrang, A.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

Poitras, C. B.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
[CrossRef] [PubMed]

Poulton, C. G.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

Qian, W.

Rasras, M.

C. Doerr, P. Winzer, Y.-K. Chen, S. Chandrasekhar, M. Rasras, L. Chen, T.-Y. Liow, K.-W. Ang, and G.-Q. Lo, “Monolithic polarization and phase diversity coherent receiver in silicon,” J. Lightwave Technol. 28(4), 520–525 (2010).
[CrossRef]

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Ren, H.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

Rooks, M. J.

Rubin, D.

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

Säynätjoki, A.

Scherer, A.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Schimmel, T.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

Schow, C. L.

Scimeca, M.

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Sekaric, L.

Selvaraja, S.

Shafiiha, R.

Sigurdsson, G.

Sullivan, P.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Takayesu, J.

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Terui, H.

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

Tervonen, A.

Teschke, M.

Trotta, M.

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

Van Campenhout, J.

Van Thourhout, D.

Vlasov, Y. A.

Walker, G.

N. Walker and G. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8(3), 438–458 (1990).
[CrossRef]

Walker, N.

N. Walker and G. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8(3), 438–458 (1990).
[CrossRef]

Weiner, J.

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

Wieland, J.

Winter, M.

Winzer, P.

Worms, K.

Wu, S.-T.

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

Xiong, X. G.

Xu, Q.

Yang, M.

Yoo, S. J. B.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Yu, H.

Zappone, B.

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

Zheng, D.

Zheng, X.

Zhou, L.

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

Appl. Phys. Lett. (3)

B. Maune, R. Lawson, C. Gunn, A. Scherer, and L. Dalton, “Electrically tunable ring resonators incorporating nematic liquid crystals as cladding layers,” Appl. Phys. Lett. 83(23), 4689–4691 (2003).
[CrossRef]

Y.-H. Fan, Y.-H. Lin, H. Ren, S. Gauza, and S.-T. Wu, “Fast-response and scattering-free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233–1235 (2004).
[CrossRef]

T. Baehr-Jones, B. Penkov, J. Huang, P. Sullivan, J. Davies, J. Takayesu, J. Luo, T.-D. Kim, L. Dalton, A. Jen, M. Hochberg, and A. Scherer, “Nonlinear polymer-clad silicon slot waveguide modulator with a half wave voltage of 0.25 V,” Appl. Phys. Lett. 92(16), 163303 (2008).
[CrossRef]

Electron. Lett. (1)

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43(22), 1196–1197 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Donisi, B. Bellini, R. Beccherelli, R. Asquini, G. Gilardi, M. Trotta, and A. d’Alessandro, “A switchable liquid-crystal optical channel waveguide on silicon,” IEEE J. Quantum Electron. 46(5), 762–768 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, “Radiation modes and roughness loss in high index-contrast waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1306–1321 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

P. Mullner and R. Hainberger, “Structural optimization of silicon-on-insulator slot waveguides,” IEEE Photon. Technol. Lett. 18(24), 2557–2559 (2006).
[CrossRef]

S. S. Djordjevic, L. W. Luo, S. Ibrahim, N. K. Fontaine, C. B. Poitras, B. Guan, L. Zhou, K. Okamoto, Z. Ding, M. Lipson, and S. J. B. Yoo, “Fully reconfigurable silicon photonic lattice filters with four cascaded unit cells,” IEEE Photon. Technol. Lett. 23(1), 42–44 (2011).
[CrossRef]

M. Rasras, D. Gill, M. Earnshaw, C. Doerr, J. Weiner, C. Bolle, and Y.-K. Chen, “CMOS silicon receiver integrated with Ge detector and reconfigurable optical filter,” IEEE Photon. Technol. Lett. 22(2), 112–114 (2010).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

M. Kobayashi, H. Terui, M. Kawachi, and J. Noda, “2×2 optical waveguide matrix switch using nematic liquid crystal,” IEEE Trans. Microw. Theory Tech. 30(10), 1591–1598 (1982).
[CrossRef]

J. Appl. Phys. (2)

P. Pagliusi, B. Zappone, G. Cipparrone, and G. Barbero, “Molecular reorientation dynamics due to direct current voltage-induced ion redistribution in undoped nematic planar cell,” J. Appl. Phys. 96(1), 218–223 (2004).
[CrossRef]

H. Desmet, K. Neyts, and R. Baets, “Modeling nematic liquid crystals in the neighborhood of edges,” J. Appl. Phys. 98(12), 123517 (2005).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

J. Phys. D Appl. Phys. (1)

C. Desimpel, J. Beeckman, H. Desmet, K. Neyts, R. James, and F. A. Fernández, “A four-electrode liquid crystal device for 2π in-plane director rotation,” J. Phys. D Appl. Phys. 38(21), 3976–3984 (2005).
[CrossRef]

Opt. Express (8)

M. Yang, W. M. J. Green, S. Assefa, J. Van Campenhout, B. G. Lee, C. V. Jahnes, F. E. Doany, C. L. Schow, J. A. Kash, and Y. A. Vlasov, “Non-blocking 4x4 electro-optic silicon switch for on-chip photonic networks,” Opt. Express 19(1), 47–54 (2011).
[CrossRef] [PubMed]

T. Alasaarela, D. Korn, L. Alloatti, A. Säynätjoki, A. Tervonen, R. Palmer, J. Leuthold, W. Freude, and S. Honkanen, “Reduced propagation loss in silicon strip and slot waveguides coated by atomic layer deposition,” Opt. Express 19(12), 11529–11538 (2011).
[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).
[CrossRef] [PubMed]

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009).
[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]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[CrossRef] [PubMed]

L.-W. Luo, S. Ibrahim, A. Nitkowski, Z. Ding, C. B. Poitras, S. J. Ben Yoo, and M. Lipson, “High bandwidth on-chip silicon photonic interleaver,” Opt. Express 18(22), 23079–23087 (2010).
[CrossRef] [PubMed]

R. Ding, T. Baehr-Jones, W. J. Kim, X. G. Xiong, R. Bojko, J. M. Fedeli, M. Fournier, and M. Hochberg, “Low-loss strip-loaded slot waveguides in silicon-on-insulator,” Opt. Express 18(24), 25061–25067 (2010).
[CrossRef] [PubMed]

Opt. Lett. (2)

Proc. IEEE (1)

J. Leuthold, W. Freude, J.-M. Brosi, R. Baets, P. Dumon, I. Biaggio, M. Scimeca, F. Diederich, B. Frank, and C. Koos, “Silicon organic hybrid technology: A platform for practical nonlinear optics,” Proc. IEEE 97(7), 1304–1316 (2009).
[CrossRef]

Semicond. Sci. Technol. (1)

A. Liu, L. Liao, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “Recent development in a high-speed silicon optical modulator based on reverse-biased pn diode in a silicon waveguide,” Semicond. Sci. Technol. 23(6), 064001 (2008).
[CrossRef]

Other (6)

I.-C. Khoo, Liquid crystals, 2nd ed. (Wiley-Interscience, 2007).

L. Alloatti, J. Pfeifle, J. Mendez, W. Freude, J. Leuthold, and C. Koos, “Liquid crystal phase shifter on the SOH platform with ultra-low power consumption,” in Optical Fiber Communication Conference (OTu1I.5.), (2012).

H. Desmet, K. Neyts, and R. Baets, “Liquid crystal orientation on patterns etched in Silicon on Insulator,” in Integrated Optics, Silicon Photonics, and Photonic Integrated Circuits, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (61831Z), (2006).

CST - Computer Simulation Technology AG, CST Microwave Studio 2012, http://www.cst.com (2012).

RSoft Design Group Inc, FemSIM 3.3 User Guide, http://www.rsoftdesign.com (2011).

G. P. Agrawal, Fiber-Optic Communication Systems, 4th ed. (Wiley-Interscience, 2010).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Concept of the slot-waveguide liquid crystal phase shifter. (a) Cross-section of the strip-loaded slot waveguide. The silicon rails (refractive index n = 3.48) are connected to metal transmission lines by thin conductive silicon slabs. The waveguide is immersed in a low-index liquid crystal (LC) cladding. The orientation of the LC molecules in the slot region can be switched by the external voltage U, which drops entirely across the narrow slot and hence induces a large field strength. The color code represents the electric field magnitude of the fundamental quasi-TE mode. The high index contrast between the slot region and the silicon rails leads to strong interaction of the guided mode with the LC cladding. Insets (1) and (2): If no external voltage is applied to the slot waveguide (U = 0), the LC molecules align parallel to the waveguide axis (1); for nonzero voltages U ≠ 0, the LC will partly realign along the x-direction. (b) Illustration of a rod-like LC molecule. The director p represents the local direction of preferred LC orientation. Light polarized parallel (perpendicular) to the director experiences the extraordinary (ordinary) refractive index ne (no). (c) Artist impression of slot waveguide. The liquid crystal covers the entire waveguide structure and completely fills the slot.

Fig. 2
Fig. 2

Comparison of electrode configurations and electric control fields. To prevent optical loss a certain minimum distance of approximately 4 µm has to be maintained between the metal transmission lines. (a) Strip-loaded slot waveguide: The metal transmission lines are connected to the silicon rails by thin conductive slabs of doped silicon, and the applied control voltage drops entirely across the narrow slot. For a slot of 120 nm width and an external control voltage of only U = 1 V, a control field strength of 8 V/µm can be achieved within the slot. (b) Corresponding electric field in the vicinity of the waveguide core, exhibiting a homogeneous distribution in the slot region. (c) Conventional slot waveguide: Due to the large electrode spacing of 4 µm, a control voltage of U = 36 V is required to obtain an electric control field of approximately 8 V/µm in the slot region. (d) Numerically calculated control field, exhibiting a homogeneous distribution in the vicinity of the waveguide core. For the numerical calculations of the control fields, the rail and slot widths are 240 nm and 120 nm, respectively, and the thickness of the metal is 600 nm. For the strip-loaded slab waveguide, the height of the Si slab is 60 nm, and a conductivity of 182 (Ω cm)−1 is assumed for the Si slabs and rails. Note that in (a) and (c) the numerically calculated field lines just illustrate the direction of the local control field; the density of the field lines does not correspond to the field strength. In (b) and (d) the field is represented by line elements, the length of which is proportional to the local field strength.

Fig. 3
Fig. 3

Comparison of different slot- and strip-waveguide LC phase shifter designs. (a) Cross-sectional geometry and mode fields of the investigated waveguide structure: (1) Strip-loaded slot waveguide and (2) conventional slot waveguide with remotely located metal electrodes; (3) – (6) strip waveguides operated in different polarizations with remotely located metal electrodes that induce a homogeneous electric control field in the horizontal or vertical direction. (b) Computed data for the achievable phase shift ΔϕCB5 per length L (negative values plotted above ΔϕCB5 = 0) for a strip-loaded (1) and a conventional (2) slot waveguide with various slot and rail widths wsl and wr. The thickness of the slab region is kept constant at d = 60 nm. (c) Corresponding data (negative values plotted above ΔϕCB5 = 0) for strip waveguides of different widths wst. For all simulations, the waveguide height amounts to h = 220 nm and the refractive index of the silicon waveguide core and the oxide buffer layer is assumed to be 3.48 and 1.44, respectively.

Fig. 4
Fig. 4

Fabricated prototype phase shifter. (a) SEM picture of strip-loaded slot waveguide and metal transmission line prior to application of the LC overcladding. The SiO2 mask was used as an etch stop layer for the metallization process. The slot was accidently etched 1 µm deep into the buried oxide, which increases optical loss but does not affect the phase-shifting performance significantly. (b) Chemical formula and molecular structure of liquid crystal used as a cladding (Sigma-Aldrich, product #366854). The material is in its nematic phase at room temperature and covers the entire chip.

Fig. 5
Fig. 5

Measurement setup: The phase shift of the strip-loaded slot waveguide is measured by a fiber-based Mach-Zehnder interferometer (MZI). Light from a 1550 nm laser source is split by a 3 dB directional coupler. One part is launched in the device under test (DUT) by grating couplers. At the output of the chip, the optical power is monitored by a 3 dB coupler and a photodetector (PD2). The remaining light coming from the device interferes with light from the fiber arm of the MZI. The interference pattern is recorded with a balanced photodetector (PD1). The phase shift is deduced from the number of fringes that occur during one cycle of the control voltage U.

Fig. 6
Fig. 6

Phase shift of an LC-clad slot waveguide when applying a 100 Hz sawtooth signal with 5V amplitude and without bias. (a) Time resolved measurement of the phase shift Δϕ (black curve) induced by the control signal (red curve). Negative values of Δϕ are again plotted above Δϕ = 0. The blue curve shows the excess insertion loss due to the variation of the liquid crystal orientation. (b) Phase shift as a function of control voltage. The phase shift magnitude saturates at approximately 35π. The highest slope | d( Δϕ ) / dU |=20π/V is found at a control voltage of approximately 1.3 V; the ideal operation point is indicated by a circle. This measured slope corresponds to a voltage-length product UπL = 0.085 Vmm for the L = 1.7 mm long device.

Fig. 7
Fig. 7

Small-signal phase response Δ ϕ 1 of the device when applying a 100 Hz sawtooth signal u1 with 1V amplitude on top of a DC bias of U0 = 8 V. (a) Time-resolved measurement of the small-signal phase shift Δ ϕ 1 (black curve) induced by the time-dependent control signal u1 (red curve). (b) Small-signal phase shift Δ ϕ 1 as a function of voltage u 1 . We find an approximately linear behavior with a slope of | Δ ϕ 1 / u 1 |12.7π/V at u1 = 0 V. This corresponds to a voltage-length product of UπL ≈0.13 Vmm for the 1.7 mm long device.

Fig. 8
Fig. 8

Definition of coordinate systems and angles: (a) Definition of the local (u,v,w)-coordinate system that is given by the local orientation of the director p such that p e w . (b) The (x,y,z)-coordinate system is defined by the waveguide geometry as shown in Fig. 1(c). The angles φ and ψ define the orientation of the director p within the (x,y,z)-coordinate system.

Tables (1)

Tables Icon

Table 1 Slopes | Δ ϕ 1 / u 1 | at u1 = 0 V and Corresponding Voltage-length Products Obtained from Small-signal Measurements with Different Bias Voltages U0

Equations (21)

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

Δϕ= Δn Δ n CB5 Δ ϕ CB5 .
Δ ϕ CB5 L =β( U=0 )β( U ).
FOM ϕ = Δβ Δα /2 =2 Δϕ ΔαL >0.
ε ¯ a ( x,y )= ε ¯ i ( x,y )+Δ ε ¯ ( x,y ).
ε ¯ a, uvw = ε 0 ( n o 2 0 0 0 n o 2 0 0 0 n e 2 ),
ε ¯ i = ε 0 n e 2 + n o 2 2 I,
Δ ε ¯ uvw = ε 0 n e 2 n o 2 2 ( 1 0 0 0 1 0 0 0 1 ).
Δ ε ¯ = ε 0 Δn n o ( cos2ψ sinφsin2ψ cosφsin2ψ sinφsin2ψ cos 2 φ+ sin 2 φcos2ψ sin2φ cos 2 ψ cosφsin2ψ sin2φ cos 2 ψ cos 2 φcos2ψ sin 2 φ )
× E ¯ ( x,y,z )=jω μ 0 H ¯ ( x,y,z ),
× H ¯ ( x,y,z )=jω( ε ¯ i ( x,y )+Δ ε ¯ ( x,y ) ) E ¯ ( x,y,z ),
E ¯ ( x,y,z )= ν A ¯ ν ( z ) ¯ v ( x,y )exp( j β i, ν z ) ,
H ¯ ( x,y,z )= ν A ¯ ν ( z ) ¯ ν ( x,y )exp( j β i, ν z ) .
1 4 ( ε ¯ ν ( x,y )× H ¯ v ( x,y )+ ε ¯ μ * ( x,y )× H ¯ v ( x,y ) ) e z dxdy = P v δ νμ
P ν = 1 2 Re{ ¯ ν ( x,y )× H ¯ ν * ( x,y ) } e z dxdy
P ν ( z )= | A ¯ ν ( z ) | 2 P ν .
d A ¯ μ ( z ) dz =j ν κ μν A ¯ ν ( z )exp( j( β ν β μ )z ),
κ μν = ω 2 ( Δ ε ¯ ( x,y ) ¯ ν ( x,y ) ) ¯ μ * ( x,y ) dxdy Re{ ¯ μ ( x,y )× ¯ μ * ( x,y ) } e z dxdy .
d A ¯ ν ( z ) dz =jΔ β ν A ¯ ν ( z ),
Δ β ν =Re{ Δ β ¯ ν };Δ β ¯ ν = ω 2 ( Δ ε ¯ ( x,y ) ¯ ν ( x,y ) ) ¯ ν * ( x,y ) dxdy Re{ ¯ ν ( x,y )× ¯ ν * ( x,y ) } e z dxdy .
FOM ϕ = Re{ Δ β ¯ ν } Im{ Δ β ¯ ν } .
β ν = β i,ν +Δ β ν .

Metrics