• Photonics Research
  • Vol. 12, Issue 1, 51 (2024)
Jonathan Peltier1、2、4、*, Weiwei Zhang3、5、*, Leopold Virot2, Christian Lafforgue1, Lucas Deniel1, Delphine Marris-Morini1, Guy Aubin1, Farah Amar1, Denh Tran3, Xingzhao Yan3, Callum G. Littlejohns3, Carlos Alonso-Ramos1, Ke Li3, David J. Thomson3, Graham Reed3, and Laurent Vivien1
Author Affiliations
  • 1University Paris-Saclay, CNRS, Centre for Nanoscience and Nanotechnology (C2N), Palaiseau 91120, France
  • 2University Grenoble Alpes, CEA, LETI, Grenoble 38000, France
  • 3Optoelectronics Research Centre, Zepler Institute for Photonics and Nanoelectronics, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton SO17 1BJ, UK
  • 4e-mail: jonathan.peltier@c2n.upsaclay.fr
  • 5e-mail: Weiwei.Zhang@soton.ac.uk
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    DOI: 10.1364/PRJ.488867 Cite this Article Set citation alerts
    Jonathan Peltier, Weiwei Zhang, Leopold Virot, Christian Lafforgue, Lucas Deniel, Delphine Marris-Morini, Guy Aubin, Farah Amar, Denh Tran, Xingzhao Yan, Callum G. Littlejohns, Carlos Alonso-Ramos, Ke Li, David J. Thomson, Graham Reed, Laurent Vivien. High-speed silicon photonic electro-optic Kerr modulation[J]. Photonics Research, 2024, 12(1): 51 Copy Citation Text show less

    Abstract

    Silicon-based electro-optic modulators contribute to easing the integration of high-speed and low-power consumption circuits for classical optical communications and data computations. Beyond the plasma dispersion modulation, an alternative solution in silicon is to exploit the DC Kerr effect, which generates an equivalent linear electro-optical effect enabled by applying a large DC electric field. Although some theoretical and experimental studies have shown its existence in silicon, limited contributions relative to plasma dispersion have been achieved in high-speed modulation so far. This paper presents high-speed optical modulation based on the DC Kerr effect in silicon PIN waveguides. The contributions of both plasma dispersion and Kerr effects have been analyzed in different waveguide configurations, and we demonstrated that the Kerr induced modulation is dominant when a high external DC electric field is applied in PIN waveguides. High-speed optical modulation response is analyzed, and eye diagrams up to 80 Gbit/s in NRZ format are obtained under a d.c. voltage of 30 V. This work paves the way to exploit the Kerr effect to generate high-speed Pockels-like optical modulation.
    Δn(t)=3χ(3)2nsi(FDC2+12FRF2+2FDCFRFcosΩt+12FRF2cos2Ωt),

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    ΔnDC(VDC)=λrΔλr(VDC)FSR(λr)L,

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    P(t)P0=12{1+cos[Δϕ(t)+Δθ]},

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    mΩ=mΩ,k+mΩ,c,

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    mΩ,k=Γ2πλLeff13χ(3)nsiFDCFRF,

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    Δϕ(t)=mΩcosΩt+m2Ωcos2Ωt,

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    m2Ω=Γ2πλLeff23χ(3)4nsiFRF2,

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    PΩ(t)P0=sin(Δθ)J1(mΩ)cosΩt,

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    P2Ω(t)P0=[cos(Δθ)J2(mΩ)+sin(Δθ)J0(mΩ)J1(m2Ω)]cos2Ωt,

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    mΩ,k=4FDCLeff1FRFLeff2m2Ω.

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    Δneff=2nsiNwg|E|2Δndxdy,(B1)

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    N=1cϵ0(E×H*+E*×H)·z^dxdy.(B2)

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    Γ=2nsiNwg|E|2dxdy,(B3)

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    Δneff=Γwg|E|2Δndxdywg|E|2dxdy.(B4)

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    Δneff=Γ3χ(3)2nsiwg|E|2F2(t)dxdywg|E|2dxdy.(B5)

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    Δneff=Γ3χ(3)2nsiF2(t).(B6)

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    ΔnΩ=Γ3χ(3)nsiFDCFRFcosΩt+Δncarrier,(B7)

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    Δn2Ω=Γ3χ(3)4nsiFRF2cos2Ωt.(B8)

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    FRF(z)=FRF(0)exp(αRFz).(C1)

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    Δϕ=2πλ0LΔndz.(C2)

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    mΩ,k=Γ2πλ0L3χ(3)nsiFDCFRFexp(αz)dz,(C3)

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    mΩ,k=Γ2πλLeff13χ(3)nsiFDCFRF.(C4)

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    Leff1=1exp(αRFL)αRF.(C5)

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    m2Ω=Γ2πλ0L3χ(3)4nsiFRF2exp(2αz)dz,(C6)

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    m2Ω=Γ2πλLeff23χ(3)4nsiFRF2.(C7)

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    Leff2=1exp(2αRFL)2αRF.(C8)

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    FDC=VDC+Vbiw,(D1)

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    Vbi=kTqln(NANDni2)(D2)

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    w=wi+2ϵ0ϵSiqNA+NDNANDVbi+VDC.(D3)

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    FRFdFDCdVDCVRF.(D4)

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    dΔnΩdFDC=Γ3χ(3)nsiFRF+Γ3χ(3)nsiFDCdFRFdFDC+dΔncarrierdFDC.(E1)

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    χ(3)dΔnΩdFDCnsi3ΓFRF.(E2)

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    PDCP0=12[1+cos(Δθ)J0(mΩ)J0(m2Ω)],(F1)

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    PΩ(t)P0=[cos(Δθ)J1(mΩ)J1(m2Ω)+sin(Δθ)J0(m2Ω)J1(mΩ)]cosΩt,(F2)

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    P2Ω(t)P0={cos(Δθ)[J0(m2Ω)J2(mΩ)J2(mΩ)J2(m2Ω)]+sin(Δθ)J0(mΩ)J1(m2Ω)}cos2Ωt.(F3)

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    Jonathan Peltier, Weiwei Zhang, Leopold Virot, Christian Lafforgue, Lucas Deniel, Delphine Marris-Morini, Guy Aubin, Farah Amar, Denh Tran, Xingzhao Yan, Callum G. Littlejohns, Carlos Alonso-Ramos, Ke Li, David J. Thomson, Graham Reed, Laurent Vivien. High-speed silicon photonic electro-optic Kerr modulation[J]. Photonics Research, 2024, 12(1): 51
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