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Journals >Photonics Research >Volume 4 >Issue 4 >Page 0153 > Article

Photonics Research
Vol. 4, Issue 4, 0153 (2016)

Modeling and optimization of a single-drive push–pull silicon Mach–Zehnder modulator

Yanyang Zhou¹, Linjie Zhou^1、*, Haike Zhu¹, Chiyan Wong², Yida Wen², Lei Liu², Xinwan Li¹, and Jianping Chen¹

Author Affiliations

¹State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

²Transmission Technology Research Department, Huawei Technology Co. Ltd., Shenzhen 518129, China

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DOI: 10.1364/prj.4.000153 Cite this Article Set citation alerts

Yanyang Zhou, Linjie Zhou, Haike Zhu, Chiyan Wong, Yida Wen, Lei Liu, Xinwan Li, Jianping Chen. Modeling and optimization of a single-drive push–pull silicon Mach–Zehnder modulator[J]. Photonics Research, 2016, 4(4): 0153 Copy Citation Text

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Abstract

We present an equivalent circuit model for a silicon carrier-depletion single-drive push–pull Mach–Zehnder modulator (MZM) with its traveling wave electrode made of coplanar strip lines. In particular, the partialcapacitance technique and conformal mapping are used to derive the capacitance associated with each layer. The PN junction is accurately modeled with the fringe capacitances taken into consideration. The circuit model is validated by comparing the calculations with the simulation results. Using this model, we analyze the effect of several key parameters on the modulator performance to optimize the design. Experimental results of MZMs confirm the theoretical analysis. A 56 Gb/s on–off keying modulation and a 40 Gb/s binary phase-shift keying modulation are achieved using the optimized modulator.

Keywords

Electro-optical devices Integrated optoelectronic circuits Modulators Optoelectronics

F (k_{i}) = \frac{K (k_{i})}{K (k_{i}^{'})},

(1)

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k_{0} = \sqrt{1 - {(\frac{x_{a}}{x_{b}})}^{2}},

(2)

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k_{i} = \sqrt{1 - \frac{\sinh^{2} (\frac{π x_{a}}{2 h_{i}})}{\sinh^{2} (\frac{π x_{b}}{2 h_{i}})}},

(3)

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G_{sub} = 2 σ_{sub} [\frac{F^{2} (k_{0})}{F (k_{1})} - \frac{F^{2} (k_{0})}{F (k_{2})}],

(4)

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C_{sub} = \frac{1}{2} ϵ_{0} ϵ_{si} [\frac{F^{2} (k_{0})}{F (k_{1})} - \frac{F^{2} (k_{0})}{F (k_{2})}],

(5)

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C_{sub_s} = ϵ_{0} ϵ_{o x} W_{m t} / h_{2},

(6)

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C_{sub} = \frac{C_{sub_s} C_{sub}}{C_{sub} + C_{sub_s}} + C_{sub 1} .

(7)

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C_{BOX} = \frac{1}{2} ϵ_{0} ϵ_{o x} [\frac{F^{2} (k_{0})}{F (k_{2})} - \frac{F^{2} (k_{0})}{F (k_{3})}] .

(8)

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C_{dep} = C_{∥} + C_{f} + C_{c p s t} + C_{c p s b},

(9)

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C_{∥} = ϵ_{0} ϵ_{si} \frac{H_{rib}}{W_{D}},

(10)

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C_{f} = ϵ_{0} \frac{ϵ_{o x}}{π} \ln (2 π \frac{H_{rib}}{W_{D}}),

(11)

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C_{c p s t, b} = ϵ_{0} ϵ_{o x} \frac{K (k^{'})}{K (k)},

(12)

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k = \sqrt{\frac{W_{D} (W_{D} + t_{n} + t_{p})}{(W_{D} + t_{n}) (W_{D} + t_{p})}},

(13)

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t_{p, n} = \frac{2 W_{D p, n} (ϵ_{o x})}{π},

(14)

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W_{D} = W_{D p} + W_{D n} = \sqrt{\frac{2 ϵ_{0} ϵ_{si}}{q} (\frac{N_{A} + N_{D}}{N_{A} N_{D}}) (V_{j} - V_{b} - \frac{2 k_{B} T}{q})},

(15)

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R_{p, n} = \frac{ρ_{p, n}}{1 + j ω_{m} ρ_{p, n} ϵ_{0} ϵ_{si}} (\frac{S_{dop}}{H_{slab}} + \frac{S_{p, n}}{H_{rib}}),

(16)

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S_{p} = \frac{W_{rib}}{2} + Δ_{jun} - W_{D p},

(17)

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S_{n} = \frac{W_{rib}}{2} - Δ_{jun} - W_{D n},

(18)

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ρ_{p, n} = \frac{1}{q μ_{p, n} N_{A, D}},

(19)

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C_{via} = ϵ_{0} ϵ_{o x} h_{4} / G_{via} .

(20)

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C_{m t} = ϵ_{0} T_{m t} / G_{m t} .

(21)

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C_{air} = ϵ_{0} F^{2} (k_{0}) - \frac{1}{2} ϵ_{0} \frac{F^{2} (k_{0})}{F (k_{1})} .

(22)

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R_{slab} = \frac{ρ_{p^{+ +}}}{1 + j ω_{m} ρ_{p^{++}} ϵ_{0} ϵ_{s i}} \frac{2}{H_{slab} W_{p}},

(23)

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C_{slab} = ϵ_{0} ϵ_{si} \frac{W_{p} H_{slab}}{d} \frac{1}{Λ},

(24)

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L = 2 L_{CPW},

(25)

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R = R_{G} + R_{S} = 2 R_{CPW},

(26)

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Z = \sqrt{\frac{R_{eff} + j w L_{eff}}{G_{eff} + j w C_{eff}}},

(27)

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γ = α + j β = \sqrt{(R_{eff} + j w L_{eff}) (G_{eff} + j w C_{eff})} .

(28)

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V_{avg} (ω_{m}) = V_{g} \frac{(1 + ρ_{1}) \exp (i β_{0} L) (V_{+} + ρ_{2} V_{-})}{2 [\exp (γ L) + ρ_{1} ρ_{2} \exp (- γ L)]},

(29)

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V_{\pm} = \exp [\pm i \frac{(- i γ \mp β_{0}) L}{2}] \frac{\sin [(- i γ \mp β_{0}) L / 2]}{(- i γ \mp β_{0}) L / 2},

(30)

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ρ_{1} = \frac{Z - Z_{s}}{Z + Z_{s}},

(31)

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ρ_{2} = \frac{Z_{t} - Z}{Z_{t} + Z},

(32)

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β_{0} = \frac{ω_{m}}{c} n_{g o},

(33)

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S_{21} (ω_{m}) = (1 + Γ_{s}) (1 + Γ_{t}) e^{- γ L},

(34)

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S_{11} (ω_{m}) = Γ_{s},

(35)

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Γ_{s} = \frac{Z_{i n} - Z_{s}}{Z_{i n} + Z_{s}},

(36)

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Γ_{t} = \frac{Z_{i n} - Z_{t}}{Z_{i n} + Z_{t}},

(37)

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Z_{i n} = Z \frac{Z_{t} - Z \tanh (γ L)}{Z - Z_{t} \tanh (γ L)} .

(38)

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V_{dep} (ω_{m}) = \frac{V_{avg} (ω_{m})}{1 + j ω (R_{p} + R_{n}) C_{dep}} .

(39)

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m (ω_{m}) = | \frac{V_{dep} (ω_{m})}{V_{dep} (ω_{0})} | .

(40)

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V_{π} \frac{2 π}{λ} {\frac{d n_{eff o}}{d V} |}_{V = V_{b}} = π,

(41)

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References (29)

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Yanyang Zhou, Linjie Zhou, Haike Zhu, Chiyan Wong, Yida Wen, Lei Liu, Xinwan Li, Jianping Chen. Modeling and optimization of a single-drive push–pull silicon Mach–Zehnder modulator[J]. Photonics Research, 2016, 4(4): 0153

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