SCIENCE CHINA Information Sciences, Volume 61, Issue 12: 122301(2018) https://doi.org/10.1007/s11432-017-9349-5

A new method for extending rate equation based VCSEL model with multimode spectral characteristic

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  • ReceivedOct 20, 2017
  • AcceptedJan 24, 2018
  • PublishedSep 13, 2018


An accurate VCSEL model is important to evaluate the performance of VCSEL-based high speed short range optical interconnect system. Current VCSEL models show no evidence of the multimode spectral characteristic, which leads to an inaccurate performance estimation of VCSEL-based high speed optical interconnect system especially with large chromatic dispersion. To overcome this problem, we propose a new method to introduce multimode spectral characteristic into current VCSEL models, which extends the spatiotemporal multimode rate equations by calculating the wavelength shift of the VCSEL transverse modes. A VCSEL-multimode fiber (MMF) based short range optical interconnect simulation system is then built using our modified VCSEL model by VPItransmissionMaker. The symbol broadening and the BER performance of 15 Gb/s NRZ signal are tested in both left-tilted differential mode delay (DMD) profile MMF (L-MMF) and right-tilted DMD profile MMF (R-MMF). Simulation results validate our proposed method and indicate that the spectral characteristic is a key component for VCSEL models.


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  • Figure 1

    (Color online) VCSEL structure and equivalent step-index optical waveguide.

  • Figure 2

    Calculation flowchart of the output optical signal $E(t)$ based on our proposed VCSEL model.

  • Figure 3

    (Color online) Optical spectrum of (a) VISTAS original, (b) VISTAS with our proposed method, and normalized optical spectrum of (c) VISTAS with our proposed method.

  • Figure 4

    (Color online) Simulation block diagram.

  • Figure 5

    (Color online) Eye diagram of (a) BTB and (b) 300 m propagation of VISTAS without our proposed method, (c) BTB and (d) 300 m propagation of VISTAS with our proposed method.

  • Figure 6

    (Color online) BER performance of VISTAS with and without our proposed multimode spectral characteristic model.

  • Table 1   Model typical parameters
    Symbol Description Value
    $\eta$ Injection efficiency 0.8
    $e$ Elementary charge 1.6E$-$19 C
    $V$ Active region volume 1.2E$-$12 m$^3$
    $\tau_{\rm~N}$ Carrier lifetime 5E$-$10 s
    ${D_{\rm~N}}$ Diffusion coefficient 0.012 m$^2$/s
    $\beta$ Spontaneous recombination coefficient 3E$-$5
    $\tau_{\rm~S}$ Photon lifetime 2E$-$10 s
    $\alpha$ Linewidth enhancement factor 10
    $\Gamma$ Optical confinement factor 0.04
    $\upsilon_{\rm~g}$ Group velocity 7.14E+7 m/s
    ${N_{\rm~th}}$ Threshold carrier density 2.9E+18 m$^{-3}$
    $n_{\rm~c}$ Equivalent core index 3.6
    $n_{\rm~cl}$ Equivalent cladding index 3.56
    $a$ Diameter of oxide 3 ${\mu}$m

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