Abstract

We propose the use of silicon graphene waveguides to implement a tunable broadband microwave photonics phase shifter based on integrated ring cavities. Numerical computation results show the feasibility for broadband operation over 40 GHz bandwidth and full 360° radiofrequency phase-shift with a modest voltage excursion of 0.12 volt.

©2014 Optical Society of America

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References

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  1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  2. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  3. B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
    [Crossref]
  4. F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
  5. Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).
    [Crossref] [PubMed]
  6. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref] [PubMed]
  7. M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
    [Crossref] [PubMed]
  8. Z. Lu and L. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 6(6), 1490–1496 (2012).
    [Crossref]
  9. M. Midrio, S. Boscolo, M. Moresco, M. Romagnoli, C. De Angelis, A. Locatelli, and A. D. Capobianco, “Graphene-assisted critically-coupled optical ring modulator,” Opt. Express 20(21), 23144–23155 (2012).
    [Crossref] [PubMed]
  10. L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
    [Crossref]
  11. C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
    [Crossref] [PubMed]
  12. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
    [Crossref]
  13. J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
    [Crossref]
  14. D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
    [Crossref]
  15. G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
    [Crossref]
  16. D. B. Adams and C. Madsen, “A Novel Broadband Photonic RF Phase Shifter,” J. Lightwave Technol. 15(15), 2712–2717 (2008).
    [Crossref]
  17. M. Pu, L. Liu, W. Xue, Y. Ding, H. Ou, K. Yvind, J. M. Hvam, and J. M. Hvam, “Widely tunable microwave phase shifter based on silicon-on-insulator dual-microring resonator,” Opt. Express 18(6), 6172–6182 (2010).
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  18. M. Burla, D. Marpaung, L. Zhuang, C. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express 19(22), 21475–21484 (2011).
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2014 (1)

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

2013 (2)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
[Crossref]

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

2012 (5)

2011 (3)

M. Burla, D. Marpaung, L. Zhuang, C. Roeloffzen, M. R. Khan, A. Leinse, M. Hoekman, and R. Heideman, “On-chip CMOS compatible reconfigurable optical delay line with separate carrier tuning for microwave photonic signal processing,” Opt. Express 19(22), 21475–21484 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (1)

2008 (2)

G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

D. B. Adams and C. Madsen, “A Novel Broadband Photonic RF Phase Shifter,” J. Lightwave Technol. 15(15), 2712–2717 (2008).
[Crossref]

2007 (2)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Adams, D. B.

D. B. Adams and C. Madsen, “A Novel Broadband Photonic RF Phase Shifter,” J. Lightwave Technol. 15(15), 2712–2717 (2008).
[Crossref]

Bonnacorso, F.

F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Boscolo, S.

Burla, M.

Capmany, J.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Capobianco, A. D.

Chen, Y.

Dai, T.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

De Angelis, C.

Ding, Y.

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Ferrari, A. C.

F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Hanson, G. W.

G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

Hasan, T.

F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Heideman, R.

Hoekman, M.

Hu, T.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

Hvam, J. M.

Jena, D.

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

Jiang, X.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
[Crossref] [PubMed]

Jin, Y.

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Khan, M. R.

Leinse, A.

Li, Y.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).
[Crossref] [PubMed]

Liu, L.

Liu, M.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Locatelli, A.

Lu, S.

Lu, Z.

Z. Lu and L. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 6(6), 1490–1496 (2012).
[Crossref]

Madsen, C.

D. B. Adams and C. Madsen, “A Novel Broadband Photonic RF Phase Shifter,” J. Lightwave Technol. 15(15), 2712–2717 (2008).
[Crossref]

Marpaung, D.

Midrio, M.

Moresco, M.

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Ou, H.

Pei, C.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

Pu, M.

Roeloffzen, C.

Romagnoli, M.

Sales, S.

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
[Crossref]

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

Shen, A.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

Sun, Z.

F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wen, S.

Xing, H. G.

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

Xu, C.

Xue, W.

Yan, R.

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

Yang, J.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
[Crossref] [PubMed]

Yang, L.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

C. Xu, Y. Jin, L. Yang, J. Yang, and X. Jiang, “Characteristics of electro-refractive modulating based on Graphene-Oxide-Silicon waveguide,” Opt. Express 20(20), 22398–22405 (2012).
[Crossref] [PubMed]

Yao, J.

Yin, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Yu, H.

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

Yvind, K.

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, H.

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhao, C.

Zhao, L.

Z. Lu and L. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 6(6), 1490–1496 (2012).
[Crossref]

Zheng, Z.

Zhuang, L.

IEEE Photon. Technol. Lett. (1)

L. Yang, T. Hu, A. Shen, C. Pei, Y. Li, T. Dai, H. Yu, Y. Li, X. Jiang, and J. Yang, “Proposal for a 2×2 Optical Switch Based on Graphene-Silicon-Waveguide Microring,” IEEE Photon. Technol. Lett. 26(3), 235–238 (2014).
[Crossref]

J. Appl. Phys. (1)

G. W. Hanson, “Dyadic Green’s function and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

J. Lightwave Technol. (2)

D. B. Adams and C. Madsen, “A Novel Broadband Photonic RF Phase Shifter,” J. Lightwave Technol. 15(15), 2712–2717 (2008).
[Crossref]

J. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).
[Crossref]

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

Z. Lu and L. Zhao, “Nanoscale electro-optic modulators based on graphene-slot waveguides,” J. Opt. Soc. Am. B 6(6), 1490–1496 (2012).
[Crossref]

Laser Photonics Rev. (1)

D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, and J. Capmany, “Integrated microwave photonics,” Laser Photonics Rev. 7(4), 506–538 (2013).
[Crossref]

Nano Lett. (1)

M. Liu, X. Yin, and X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nat. Photonics (2)

F. Bonnacorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene Photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Opt. Express (5)

Proc. IEEE (1)

B. Sensale-Rodriguez, R. Yan, L. Liu, D. Jena, and H. G. Xing, “Graphene for Reconfigurable THz Optoelectronics,” Proc. IEEE 107(7), 1705–1716 (2013).
[Crossref]

Science (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (Left) Real and imaginary parts of the intra-and inter-band conductivities of graphene for λ = 1550 n m , T = 300 º K , 1 / 2 Γ = 5.10 13 sec . (Right) Overall complex refractive index.
Fig. 2
Fig. 2 Deep silicon waveguide with a layer of graphene placed on top of it.
Fig. 3
Fig. 3 (Left) Effective indices and losses for the TE (a) and TM (b) modes of a deep GSW. (Right) 2D Effective indices and losses for the TE (c) and TM (d) modes of a deep GSW versus the wavelength and the chemical potential.
Fig. 4
Fig. 4 (Upper) principle of operation of a single-sideband microwave photonics RF phase shifter using an all pass optical filter resonance. (Lower) two stage RR GSW design of a tunable phase shifter (parameter details are given in the text).
Fig. 5
Fig. 5 (Left) impressed phased shift over the detected RF subcarrier (modulo 2π) as a function of the chemical potential of graphene where the RF frequency is taken as a parameter. (Right) impressed phase shift versus the subcarrier frequency, taking the chemical potential as a parameter.

Equations (6)

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

σ ( ω ) = σ intra ( ω ) + σ inter ( ω )
σ intra ( ω ) = i e 2 π 2 ( ω + i 2 Γ ) [ μ c k B T + 2 ln ( e ( μ c / k B T ) + 1 ) ]
Γ = e v F 2 μ μ c
σ inter ( ω ) i e 2 4 π ln ( 2 | μ c | ( ω 2 i Γ ) 2 | μ c | + ( ω 2 i Γ ) )
ε g ( ω ) = 1 + i σ ( ω ) ω ε o Δ
| μ c ( V g ) |= v F π| η( V g V o ) |

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