Abstract

A type of modulator based on a shallow-etched photonic crystal (PC) slab of silicon-on-insulator material with electro-optic (EO) polymer cladding is designed and investigated. The transmission spectra of the PC slab with the EO polymer are calculated using a finite-difference time-domain method. The band structure and the field distribution of the guided mode resonance are calculated and analyzed. The modulation voltage and bandwidth of the hybrid modulator are simulated. It is shown that flexible designs of low-voltage modulation (0.2 V) or high-bandwidth modulation (62 GHz) can be obtained with the hybrid modulator.

© 2014 Optical Society of America

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  1. H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011).
    [CrossRef] [PubMed]
  2. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012).
    [CrossRef] [PubMed]
  3. X. Xiao, H. Xu, X. Li, Z. Li, T. Chu, Y. Yu, J. Yu, “High-speed, low-loss silicon Mach-Zehnder modulators with doping optimization,” Opt. Express 21(4), 4116–4125 (2013).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. J. M. Brosi, C. Koos, L. C. Andreani, M. Waldow, J. Leuthold, W. Freude, “High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide,” Opt. Express 16(6), 4177–4191 (2008).
    [CrossRef] [PubMed]
  6. J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
    [CrossRef]
  7. C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
    [CrossRef]
  8. M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
    [CrossRef] [PubMed]
  9. X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
    [CrossRef]
  10. S. H. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
    [CrossRef]
  11. C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).
  12. W. X. Liu, Z. Q. Lai, H. Guo, Y. Liu, “Guided-mode resonance filters with shallow grating,” Opt. Lett. 35(6), 865–867 (2010).
    [CrossRef] [PubMed]

2013 (1)

2012 (2)

Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012).
[CrossRef] [PubMed]

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

2011 (2)

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

H. C. Nguyen, Y. Sakai, M. Shinkawa, N. Ishikura, T. Baba, “10 Gb/s operation of photonic crystal silicon optical modulators,” Opt. Express 19(14), 13000–13007 (2011).
[CrossRef] [PubMed]

2010 (2)

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

W. X. Liu, Z. Q. Lai, H. Guo, Y. Liu, “Guided-mode resonance filters with shallow grating,” Opt. Lett. 35(6), 865–867 (2010).
[CrossRef] [PubMed]

2009 (1)

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

2008 (1)

2004 (1)

M. Soljacić, J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

2002 (2)

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

S. H. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Andreani, L. C.

Aoki, I.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Baba, T.

Brosi, J. M.

Bruns, J.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Chakravarty, S.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Chen, J. B.

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

Chen, R. T.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Chu, T.

Di Falco, A.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Eich, M.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Erben, C.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Fan, S. H.

S. H. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Freude, W.

Gill, D. M.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Gopalan, P.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Guo, H.

Hampe, J.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Heber, J. D.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Hu, Y.

Inoue, S.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Ishikura, N.

Jen, A. K. Y.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Joannopoulos, J. D.

M. Soljacić, J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

S. H. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Katz, H. E.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Koishi, M.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Koos, C.

Krauss, T. F.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Lai, W. C.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Lai, Z. Q.

Lee, B. S.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Lee, M.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Leuthold, J.

Li, X.

Li, Z.

Lin, C. Y.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Liu, W. X.

Liu, Y.

Luo, J. D.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

McGee, D. J.

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

Mori, Y.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Nakaya, A.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Nguyen, H. C.

Otomo, A.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Petrov, A.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Piao, X. Q.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Qiu, C. Y.

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

Sakai, Y.

Shinkawa, M.

Soljacic, M.

M. Soljacić, J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

Waldow, M.

Wang, X. L.

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

Wülbern, J. H.

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

Xia, Y.

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

Xiao, X.

Xiong, K.

Xu, H.

Xu, Q. F.

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

Yokoyama, S.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Yu, J.

Yu, Y.

Zhang, X. M.

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Appl. Phys. Lett. (2)

J. H. Wülbern, J. Hampe, A. Petrov, M. Eich, J. D. Luo, A. K. Y. Jen, A. Di Falco, T. F. Krauss, J. Bruns, “Electro-optic modulation in slotted resonant photonic crystal heterostructures,” Appl. Phys. Lett. 94(24), 241107 (2009).
[CrossRef]

C. Y. Lin, X. L. Wang, S. Chakravarty, B. S. Lee, W. C. Lai, J. D. Luo, A. K. Y. Jen, R. T. Chen, “Electro-optic polymer infiltrated silicon photonic crystal slot waveguide modulator with 23 dB slow light enhancement,” Appl. Phys. Lett. 97(9), 093304 (2010).
[CrossRef]

J. Polym. Sci. Pol. Chem. (1)

X. Q. Piao, X. M. Zhang, Y. Mori, M. Koishi, A. Nakaya, S. Inoue, I. Aoki, A. Otomo, S. Yokoyama, “Nonlinear Optical Side-Chain Polymers Post-Functionalized with High-beta Chromophores Exhibiting Large Electro-Optic Property,” J. Polym. Sci. Pol. Chem. 49(1), 47–54 (2011).
[CrossRef]

Nat. Mater. (1)

M. Soljacić, J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. B (1)

S. H. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002).
[CrossRef]

Sci. Rep-Uk (1)

C. Y. Qiu, J. B. Chen, Y. Xia, Q. F. Xu, “Active dielectric antenna on chip for spatial light modulation,” Sci. Rep-Uk 2, 855 (2012).

Science (1)

M. Lee, H. E. Katz, C. Erben, D. M. Gill, P. Gopalan, J. D. Heber, D. J. McGee, “Broadband modulation of light by using an electro-optic polymer,” Science 298(5597), 1401–1403 (2002).
[CrossRef] [PubMed]

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Figures (14)

Fig. 1
Fig. 1

Normal incidence transmission spectra for various slab thicknesses. The index of the slab is 3.4, and the index of the background is 1.5.

Fig. 2
Fig. 2

Normal incidence transmission spectra of an ordinary PC slab with and without a cladding layer. The PC period is a, the hole radius is 0.25a, the slab thickness is h = 0.34 a , the index of the slab is 3.4, the cladding layer and the material filling in the holes is a polymer of index 1.5, the substrate layer is S i O 2 , and the index is assumed to be 1.5.

Fig. 3
Fig. 3

Normal incidence transmission spectra of an ordinary PC slab, a shallow-etched PC slab and a changed-radius ordinary PC slab. The ordinary PC slab has a radius of 0.25a and is etched to 1.0h ( h = 0.34 a ), as in Fig. 2. The shallow-etched PC slab has a radius of 0.25a and is shallowly etched to 0.4h. The changed-radius PC slab has a radius of 0.16a and is etched to 1.0h. The etch ratios of the shallow-etched PC slab and the changed radius PC slab are the same. Other conditions are the same as those in Fig. 2.

Fig. 4
Fig. 4

Frequency and Q value for modes in PC slabs as a function of etch ratio. 'SE-low' corresponds to the mode at a frequency around 0.40 a / λ of the shallow-etched PC slab. 'SE-high' corresponds to the mode at a frequency around 0.47 a / λ of the shallow-etched PC slab. 'CR-low' corresponds to the mode at a frequency around 0.40 a / λ of the changed-radius PC slab. 'CR-high' corresponds to the mode at a frequency around 0.47 a / λ of the changed-radius slab.

Fig. 5
Fig. 5

Band structure of even symmetry with respect to the Y = 0 plane, which refers to TM-like modes. This band structure is for the PC slab with the same structure parameters used in the ordinary PC slab with polymer cladding in Fig. 2. Γ point ( k x = 0 ) are marked by red squares.

Fig. 6
Fig. 6

Band structure of odd symmetry with respect to the Y = 0 plane, which refers to TE-like modes. This band structure is for the PC slab with the same structure parameters used in the ordinary PC slab with polymer cladding in Fig. 2. Γ points ( k x = 0 ) are marked by red squares.

Fig. 7
Fig. 7

Structure of the EO polymer modulator with a shallow-etched PC Si slab. (A) Side view; (B) top view.

Fig. 8
Fig. 8

Transmission spectra with n z shifts of 0%, 2%, 4% and 6%. The PC period is a, the hole radius is 0.2a, the slab thickness is h = 0.34 a and the etching depth is 0.3 h = 0.1 a . The cladding layer and the material filling in the holes is EO polymer of index 1.5. The other refractive index parameters are the same as those used in Fig. 2.

Fig. 9
Fig. 9

Frequency and Q value as functions of n z shifts of the structures in Fig. 8.

Fig. 10
Fig. 10

Band structure of even symmetry with respect to the Y = 0 plane, which refers to TM-like modes. This band structure is for the PC slab with the same structure parameters used in the shallow-etched PC slab with the 0% n z shift polymer cladding in Fig. 8. Γ points ( k x = 0 ) are marked by red squares.

Fig. 11
Fig. 11

Band structure of odd symmetry with respect to the Y = 0 plane, which refers to TE-like modes. This band structure is for the PC slab with the same structure parameters used in the shallow-etched PC slab with the 0% n z shift polymer cladding in Fig. 8. Γ points ( k x = 0 ) are marked by red squares.

Fig. 12
Fig. 12

Energy and field distributions for the corresponding modes in Fig. 8. (A) Side view of the energy distribution of frequency 0.65 a / λ mode. (B) Side view of the electric field distribution of frequency 0.65 a / λ mode. (C) Side view of the energy distribution of frequency 0.66 a / λ mode. (D) Side view of the electric field distribution of frequency 0.66 a / λ mode.

Fig. 13
Fig. 13

Transmission spectra of the high-Q modulator. The lattice constant of the PC slab is 1 μ m , the hole radius is 200 n m , the slab thickness is 340 n m , the etching depth is 100 n m and the index of the slab is 3.4. The cladding layer and the material filling in the holes is the EO polymer whose index is 1.5. The substrate layer is S i O 2 , and the index is also assumed to be 1.5.

Fig. 14
Fig. 14

Transmission spectra of the low-Q modulator with n z changes. The PC period is 1 μ m , the hole radius is 250 n m , the slab thickness is 340 n m , the etching depth is 136 n m and the index of the slab is 3.4. The cladding layer and the material filling in the holes is EO polymer with index 1.5. The substrate layer is SiO2, and the index is also assumed to be 1.5.

Equations (9)

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

1 f M = 1 f RC + 1 f τ p
f RC = 1 2πRC
C= εS 4πkd
f RC =1.6× 10 12 Hz=1.6THz.
f τ p = 1 2π τ p
τ p = Q ω 0
ω 0 =2π c λ
f τ p = c λQ
f M = f τ p f RC f τ p + f RC = 3×1600 3+1600 3GHz

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