Closed-form expressions for the optimization of high speed electro-optical modulators

Fuste, Jose A. Ibarra; Santos, Maria C.

doi:10.1016/j.optlastec.2013.01.013

Cited by 5 publications

(5 citation statements)

References 13 publications

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“…where term T can be calculated by the formulas given in [24]. All circuit components except for the PN junction have been determined in Fig.…”

Section: Telegraphist Transmission Line Modelmentioning

confidence: 99%

“…Furthermore, it provides a valuable insight into the physical characteristics of the transmission line. Although the viability and efficiency of this method of similar circuit analysis have been demonstrated on CPS and CPW [21,22,24,25], there is a lack of corresponding research on T-rail electrode structures. Thus, the equivalent circuit model for the T-rail electrode is essential for designing silicon modulators.…”

Section: Introductionmentioning

confidence: 99%

“…Fig.2(b)shows the relationship between the circuit and the physical device. The above constituent circuit components can be transformed into a two-port transmission line model with effective components RLGC model[8,21,22,24] as shown in Fig.2(c). The resistance, conductance, inductance, and capacitance per unit length are represented by the symbols R [Ω/m], L [H/m], G [S/m], and C [F/m], respectively.…”

mentioning

confidence: 99%

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Equivalent circuit model of the carrier-depletion-based push-pull silicon optical modulators with T-rail slow wave electrodes

Na,

Zhuang,

Xie

et al. 2023

Preprint

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The T-rail electrode has emerged as an effective solution to improve the bandwidth of the silicon optoelectronic modulator. T-rail electrodes have shown to be a successful method of increasing the silicon optoelectronic modulator's bandwidth. Engineers frequently use finite-element numerical simulations, which necessitate intricate device modeling and massive computational resources, to design and optimize T-rail electrodes. To design and optimize T-rail electrodes, engineers often rely on finite-element numerical simulations that require complex device modeling and enormous computing resources. In this paper, we present an equivalent circuit model for carrier-depletion-based push-pull silicon modulators with T-rail electrodes. The analytical solution for the bandwidth of the modulator can be derived from the equivalent circuit. The utilization of the analytical solution offers advantages in terms of memory conservation and flexibility. The values calculated by the equivalent circuit model are in excellent agreement with the numerical full-wave HFSS simulations. Hence, the proposed model can accurately and efficiently develop silicon optical modulators.

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“…where term T can be calculated by the formulas given in [24]. All circuit components except for the PN junction have been determined in Fig.…”

Section: Telegraphist Transmission Line Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Equivalent circuit model of the carrier-depletion-based push-pull silicon optical modulators with T-rail slow wave electrodes

Na,

Zhuang,

Xie

et al. 2023

Preprint

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“…For this purpose, the closed‐form expressions for the CPW RF propagation parameters obtained in [16] will be used. The equations are simplified for a symmetric MZM LiNbO 3 thin‐film cross‐section as

n_{m} = \sqrt{[1 + \frac{(ε_{r} - 1) A_{1} s}{2 A_{0} s + t} B T] [1 + \frac{δ}{2 A_{0} s + t} ϝ]}

Z_{0} = \frac{s \sqrt{[1 + false(δ / false(2 A_{0} s + t false) false) ϝ]}}{2 ε_{0} c \sqrt{(2 A_{0} s + t) (2 A_{o} s + (ε_{r} - 1) A_{1} B T s + t)}}

α = \frac{π f δ s}{2 ε_{0} c^{2} Z_{0} false(2 A_{0} s + t false)^{2}} ϝ + ω ε_{0} (ε_{r} - 1) A_{1} Z_{0} \tan δ

with

ϝ = T (][, \frac{2 s false(s + w false)}{w false(w + 2 s false)} - \frac{s / 2}{w + 2 s + w_{g}} + \frac{s / 2}{s + w_{normalg}})

…”

Section: Theorymentioning

confidence: 99%

Analytical tool for the design and optimisation of high‐speed lithium niobate thin‐film Mach–Zehnder modulator

Fuste

2015

IET Optoelectronics

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“…According to L ext = 1 c 2 C 0 , the change in free-space capacitance will lead to a change in external inductance. On the other side, the skin effect field inside the conductors, gives rise to an additional line resistance R, and an internal inductance L int which can be calculated from L ext by using the Wheeler rule [85] [86]. Based on these ideas, in the next subsections C 0 , C s , L ext and L int will be obtained.…”

Section: Parallel Plate (Pp) Formulationmentioning

confidence: 99%

Design rules and optimization of electro-optic modulators based on coplanar waveguides

Ibarra Fusté

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Electro-optical traveling wave modulators (EO-TWM) are basic building blocks of the optical communications industry which is leading a revolution in the way we communicate, work and live. As a result, the demand for high-speed data transmission with low driving voltage is continuously growing up with costs that should be kept below a minimum. Besides communications, a growing number of applications for EO-TWM is continuously emerging with equally stringent requirements. This Thesis is concerned with advances in the eld of systematic design and optimization of EO-TWM for coping inverse of the velocity matching constant has been shown to govern the low-loss limit (LL), while in the velocity matching limit (VM), a constant bandwidth times squared-length rule proportional to the inverse of the squared loss constant has been found more appropriate. In this work we provide insights into the trade-o issue in EO-TWM, and a complete picture of the applicable gures of merit for every operative range. Besides the known LL and VM gures of merit, two intermediate ranges, the quasi-low loss (QLL) and the quasi-velocity matching (QVM), have been identi ed. Also novel closed-forms expressions fully accounting for the e ffects of the skin-e ffect electrode loss and optical-electrical wave velocity mismatch, explicitly relating the operative bandwidth and the electrode length in EO-TWM, have been found. Novel bandwidth and electrode-length charts have been created, which constitute a useful tool for the optimization and design of this modulators. A graphical interface tool called MZM-GIT has been built integrating the analytical optimization and design strategies developed throughout the Thesis. With the aid of the MZM-GIT, several proposals of optimized MZM designs based on practical structures described in literature, and also based on the industry trends, are made and analyzed. with the industrial demands. In EO-TWM, the accumulated electro-optic e ect over the optical wave grows with the co-propagated traveling wave (TW) length, allowing to reduce the required RF driving power. However, in typical electro-optic materials for modulators, among which LiNbO3 stands up, due to the natural mismatch between the velocity of the RF and the optical waves, the modulation bandwidth decreases with the TW length, giving place to a well-known trade-o ff. In typical LiNbO3 substrates, in which this Thesis is focused, this trade-off is seen to mainly depend on the values of the electrical loss constant and the e ective wave velocity mismatch in the TW structure that forms the electrodes, usually a coplanar waveguide (CPW). Special emphasis has historically been placed on the optimized design of the CPW in EO-TWM. In this Thesis the study of closed-form expressions for the propagation parameters of CPW as a function of the geometry, has proven useful for the design and optimization procedures sought. Although some interesting approaches to closed-form formulations have been found in literature, none of them completely ful lls the desired requirements of providing a reliable yet simple description of propagation in CPW, appropriate to systematic and easy to follow design rules for EO-TWM, and therefore new simpli ed closed-form expressions for the CPW transmission parameters have been developed. In a second part of the Thesis, the bandwidth-length trade-off has been examined. To date, two bandwidth-length rules have been proposed: a constant bandwidth-length product proportional to the inverse of the velocity matching constant has been shown to govern the low-loss limit (LL), while in the velocity matching limit (VM), a constant bandwidth times squared-length rule proportional to the inverse of the squared loss constant has been found more appropriate. In this work we provide insights into the trade-off issue in EO-TWM, and a complete picture of the applicable fi gures of merit for every operative range. Besides the known LL and VM gures of merit, two intermediate ranges, the quasi-low loss (QLL) and the quasi-velocity matching (QVM), have been identi ed. Also novel closed-forms expressions fully accounting for the e ffects of the skin-eff ect electrode loss and optical-electrical wave velocity mismatch, explicitly relating the operative bandwidth and the electrode length in EO-TWM, have been found. Novel bandwidth and electrode-length charts have been created, which constitute a useful tool for the optimization and design of this modulators. A graphical interface tool called MZM-GIT has been built integrating the analytical optimization and design strategies developed throughout the Thesis. With the aid of the MZM-GIT, several proposals of optimized MZM designs based on practical structures described in literature, and also based on the industry trends, are made and analyzed.

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Closed-form expressions for the optimization of high speed electro-optical modulators

Cited by 5 publications

References 13 publications

Equivalent circuit model of the carrier-depletion-based push-pull silicon optical modulators with T-rail slow wave electrodes

Equivalent circuit model of the carrier-depletion-based push-pull silicon optical modulators with T-rail slow wave electrodes

Analytical tool for the design and optimisation of high‐speed lithium niobate thin‐film Mach–Zehnder modulator

Design rules and optimization of electro-optic modulators based on coplanar waveguides

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