Contents Introduction 介绍
Silicon photonics holds great promise in replacing conventional optical interconnects and electrical interconnects
in today's data centers as the bandwidth-length product demand keeps growing. Optical links based on silicon
photonics are one of the most promising candidates for meeting the demands of next-generation 400 G inter-rack
interconnects and 100 G intra-rack interconnects in data centers. To meet such demands, optical transceivers with
datarates at or higher than 50 Gb/s are of the most interest in both wavelength-division mutiplexed (WDM) and parallel
single-mode (PSM) systems. Recent years have seen great effort and rapid progress in the development and
commercialization of silicon photonic technologies ranging from platforms, devices, circuits to large-scale systems
[1]–
[9]. Moreover, silicon photonic modulators and optical transceivers beyond 50 Gb/s have recently been
demonstrated in various photonic platforms [10]–[15]. At these high data-rates it is critical to consider holistically
the design of the photonic and circuit components from the perspective of link energy-efficiency and bandwidth
density.
随着带宽长度产品需求的不断增长，硅光子学在取代当今数据中心的传统光学互连和电气互连方面具有很大的前景。基于硅光子学的光链路是满足数据中心下一代 400 G 机架间互连和 100 G 机架内互连需求的最有前途的候选者之一。为了满足这些需求，数据速率等于或高于 50 Gb/s 的光收发器在波分多工 （WDM） 和并行单模 （PSM） 系统中最受关注。近年来，从平台、设备、电路到大型系统，硅光子技术的开发和商业化都付出了巨大的努力和快速的进展 [1]– [9]。此外，最近在各种光子平台上展示了超过 50 Gb/s 的硅光子调制器和光收发器 [10]–[15]。在这些高数据速率下，从链路能效和带宽密度的角度全面考虑光子和电路组件的设计至关重要。
In state-of-the-art 50 Gb/s NRZ optical link based on Mach-Zehnder modulator (MZM), the driver and laser together
consume more than 10 pJ/b energy dominating the total link energy, compared to 1.4–3 pJ/b consumed by the
receiver [10], [11]. In contrast to
MZMs, microring modulators (MRM) can consume less than 100 fJ/b driver energy due to their compact sizes. The thermal
tuning overhead for microrings can be as low as a few milliwatts per channel [21]
, which has negligible impact on the overall energy efficiency of the transmitter. Microring modulators have
great potential for dense WDM systems due to their inherent wavelength selectivity. They have also shown promising
high-speed operations for single-wavelength 50 Gb/s links [12],
[18]. However, full optical links at such high datarate using microring
modulators are yet to be demonstrated, which is in part due to unoptimized device designs and the inherent trade-offs
between optical modulation amplitude (OMA) and optical bandwidth for microrings [19]
. For both types of modulators, there are different architecture choices and also trade-offs between laser power
and transmitter power. Additionally, they are both subject to the same technology constraints from the silicon
photonic platforms and link specifications. As a result, it is critical yet challenging to co-optimize photonics
alongside circuits. To date, there is still debate on which modulator architecture could be a better design choice for
50 Gb/s optical channels in WDM and PSM systems.
在基于马赫-曾德尔调制器 （MZM） 的最先进的 50 Gb/s NRZ 光链路中，驱动器和激光器总共消耗超过 10 pJ/b 的能量，在总链路能量中占主导地位，而接收器消耗的能量为 1.4-3 pJ/b[10]、[11]。与 MZM 相比，微环调制器 （MRM） 由于尺寸紧凑，其功耗可以低于 100 fJ/b 的驱动器能量。微环的热调谐开销可以低至每通道几毫瓦 [21] ，这对发射器的整体能效的影响可以忽略不计。由于其固有的波长选择性，微环调制器在密集 WDM 系统中具有很大的潜力。它们还显示出单波长 50 Gb/s 链路的高速操作前景广阔 [12]、[18]。然而，使用微环调制器以如此高的数据速率实现的全光链路还有待证明，这部分是由于未优化的器件设计以及微环的光调制幅度 （OMA） 和光带宽之间的固有权衡 [19] 。对于这两种类型的调制器，都有不同的架构选择，并且还需要在激光功率和发射器功率之间进行权衡。此外，它们都受到硅光子平台和链路规范的相同技术约束。因此，将光子学与电路协同优化至关重要，但又具有挑战性。迄今为止，对于WDM和PSM系统中50 Gb/s光通道来说，哪种调制器架构是更好的设计选择，仍然存在争议。
This paper is intended to answer the questions above and provide new insights and intuition into high-speed silicon
photonic transmitters. The paper focuses on a comparison between microring and Mach-Zehnder modulators given the same
technology constraints at 50 Gb/s. We begin with an overview of the optimization framework in
Section II and introduction of a compact model for phase shifters in
Section III. The phase shifter model is verified with experimental data and
later sets the foundation for microring and Mach-Zehnder modulator modeling. In
Section IV, the optimization of the microring-based transmitter is carried out for 50 Gb/s optical links to
obtain the best energy efficiency. A new Simulink toolbox is introduced to capture dynamic behaviors of MRMs. This
general-purpose toolbox can be used for simulating other optical systems as well. In addition, an MRM-based PAM4
transmitter is analyzed as a potential way to mitigate optical bandwidth constraints. In
Section V, a co-optimization of the Mach-Zehnder transmitter is carried out
for both multi-stage (MS) and traveling-wave (TW) drivers. Finally, a comparison between optimized MRM-based TX and
optimized MZM-based TX given the same technology constraints is discussed in
Section VI. Section VII concludes the paper.
本文旨在回答上述问题，并为高速硅光子发射器提供新的见解和直觉。本文重点介绍了在 50 Gb/s 的相同技术限制下，微环调制器和 Mach-Zehnder 调制器之间的比较。我们首先在第二节 中概述了优化框架，并在第三节 中介绍了移相器的紧凑模型。移相器模型用实验数据进行了验证，随后为微环和 Mach-Zehnder 调制器建模奠定了基础。在第四节 中，对基于微环的发射机进行了 50 Gb/s 光链路的优化，以获得最佳的能源效率。引入了一个新的 Simulink 工具箱来捕获 MRM 的动态行为。这个通用工具箱也可用于模拟其他光学系统。此外，还分析了基于 MRM 的 PAM4 发射机作为缓解光带宽限制的潜在方法。在第 V 部分中 ，对多级 （MS） 和行波 （TW） 驱动器进行了 Mach-Zehnder 发射器的协同优化。最后，在相同技术约束 下，讨论了基于 MRM 的优化 TX 和基于 MZM 的优化 TX 之间的比较。第七节 是本文的结论。
Overview of Co-Optimization Framework
协同优化框架概述
The objectives of the proposed framework are to lay the foundation for silicon photonic device and link co-design
and to be readily applicable to a multitude of silicon photonic platforms. This framework is called
“co-optimization” as it optimizes photonic device parameters such as doping levels and geometries
alongside CMOS circuits and architectural choices. The optimization goal is to minimize the overall energy-per-bit
(E/b) of the transmitter macro (laser plus driver) under both technology and link design constraints. The detailed
constraints, as well as the overview of optimization framework, are shown in
Fig. 1.
所提出的框架的目标是为硅光子器件和链路协同设计奠定基础，并易于适用于多种硅光子平台。该框架被称为“协同优化”，因为它优化了光子器件参数，例如掺杂水平和几何形状，以及 CMOS 电路和架构选择。优化目标是在技术和链路设计约束下，最大限度地降低发射器宏（激光加驱动器）的每比特总能量 （E/b）。详细的约束以及优化框架的概述如图 1 所示 。
The flowchart of the co-optimization framework for silicon photonic transmitters. The denotations here are
used in derivations in the paper.
硅光子发射器的协优化框架流程图。这里的指称用于论文的推导中。
Challenges for designing a comprehensive, yet general, co-optimization framework stem mainly from three important
criteria. First, the framework needs to be specific enough to capture the intricacies of technology-dependent photonic
device physics, without necessarily overburdening the optimizer. Second, the model needs to be generic enough to
characterize the common waveguide and junction designs across many silicon photonic platforms. Third, it needs to
consider key link constraints and provide a link-level picture that includes the transmitter, receiver and laser.
Previous literature on link-level analysis and modeling of silicon photonic transmitters
[21]–[23] often treats
the optical devices as black boxes and do not consider doping and device design parameters altogether. For example,
the critical trade-off between phase shift and optical loss under process constraints is often neglected. Other
literature focusing on photonic device modeling [23]–[27] often relies on analytical expressions of optical mode distribution in
the waveguide and can be too complex and cumbersome for link-level analysis. To overcome these issues, we model the
silicon photonic modulators based on a simple yet accurate compact model for phase shifters. The paper focuses on
depletion-mode pn-junction-based phase shifters, as they are widely used for high-speed modulators on different
silicon photonic platforms [1]–[8]. This compact model incorporates waveguide geometry, mode confinement
factor, and PN junction doping, all with some reasonable approximations. The compact model fits well with experimental
results in various silicon photonic platforms.
设计一个全面而通用的协同优化框架的挑战主要来自三个重要标准。首先，框架需要足够具体，以捕捉与技术相关的光子器件物理学的复杂性，而不必使优化器负担过重。其次，该模型需要足够通用，以表征许多硅光子平台上的常见波导和结设计。第三，它需要考虑关键链路约束，并提供包括发射器、接收器和激光器在内的链路级图片。以前关于硅光子发射器链路级分析和建模的文献 [21]–[23] 经常将光学器件视为黑匣子，完全不考虑掺杂和器件设计参数。例如，在工艺约束下，相移和光损耗之间的关键权衡经常被忽视。其他专注于光子器件建模的文献 [23]–[27] 通常依赖于波导中光模式分布的解析表达式，对于链路级分析来说可能过于复杂和繁琐。为了克服这些问题，我们基于一个简单而准确的紧凑型移相器模型对硅光子调制器进行建模。本文重点介绍基于耗尽型 pn 结的移相器，因为它们广泛用于不同硅光子平台上的高速调制器 [1]–[8]。这个紧凑的模型结合了波导几何结构、模式约束因子和 PN 结掺杂，所有这些都具有一些合理的近似值。紧凑的模型非常适合各种硅光子平台中的实验结果。
As shown in Fig. 1, the co-optimization engine uses both technology and
link constraints. The technology constraints are related to the photonic processes and includes parameters for
waveguides, junctions, couplers and lasers. The link constraints are determined by the overall link budget and
specific transceiver circuits. The engine optimizes microring and Mach-Zehnder transmitters separately based on the
same phase shifter model with the goal of minimizing total E/b for laser and electronic driver combined. An optical
simulation toolbox is developed in Simulink to verify the large-signal time-domain performance of the co-optimized
transmitters. The optimizer is implemented in Matlab and can be integrated seamlessly with Simulink. Although this
paper focuses on the transmitter side, the simulation toolbox can be applied to full optical links as well along with
other communication toolboxes. This Simulink optical simulation toolbox is available online
[35].
如图 1 所示 ，协同优化引擎同时使用技术和链接约束。技术约束与光子过程有关，包括波导、结、耦合器和激光器的参数。链路约束由总链路预算和特定的收发器电路决定。该引擎基于相同的移相器模型分别优化了 Microring 和 Mach-Zehnder 发射器，目的是最大限度地减少激光器和电子驱动器的总 E/b。在 Simulink 中开发了一个光学仿真工具箱，用于验证协同优化发射机的大信号时域性能。优化器在 Matlab 中实现，可以与 Simulink 无缝集成。虽然本文侧重于发射机侧，但仿真工具箱也可以与其他通信工具箱一起应用于全光链路。此 Simulink 光学仿真工具箱可在线获取 [35]。
PN-Junction-Based Optical Phase Shifter
基于 PN 结的光学移相器
A. Compact Model of Optical Phase Shifter
A. 光学移相器的紧凑模型
The common building block for both MRM's and MZM's is the high-speed optical phase shifter. More
specifically, this phase shift allows the constructive or destructive interference of light exiting the transmit
waveguide, thereby creating a modulated output optical signal.
MRM 和 MZM 的通用构建模块是高速光学移相器。更具体地说，这种相移允许从发射波导射出的光产生相长或相消干涉，从而产生调制输出光信号。
Due to the lack of Pockels effect, silicon photonic phase shifters rely on the carrier plasma dispersion effect.
High-speed phase modulation is achieved with depletion-mode PN junctions. Within PN junctions, the number of excess
electrons and holes strongly dictate the refractive index and absorption coefficient. Combined with the applied
voltage across the junction, these factors affect the maximum phase shift as well as the loss. Device parameters for
phase shifters include intrinsic index and absorption, junction geometries and doping concentrations. The foundries
often provide a wide range of doping concentrations by default and can potentially tune the doping levels for
customers. Therefore, doping level is considered a key parameter in our optimization framework. There are three main
types of junction designs as shown in Fig. 2 In this section, we propose a
simplified phase shifter model that is applicable to most junction shapes.
由于缺乏普克尔斯效应，硅光子移相器依赖于载流子等离子体色散效应。高速相位调制是通过耗尽型 PN 结实现的。在 PN 结中，过剩电子和空穴的数量在很大程度上决定了折射率和吸收系数。结合结两端施加的电压，这些因素会影响最大相移和损耗。移相器的器件参数包括本征指数和吸收、结几何形状和掺杂浓度。默认情况下，代工厂通常提供广泛的掺杂浓度范围，并且可以为客户调整掺杂水平。因此，掺杂水平被认为是我们优化框架中的一个关键参数。结设计主要有三种类型，如图 2 所示。 在本节中，我们提出了一种适用于大多数结形状的简化移相器模型。
Mach-Zehnder and microring modulators based on different PN junction phase shifters. Three common types of
phase shifters are listed with top view or cross-section view. The corresponding feature lengths (
基于不同 PN 结移相器的 Mach-Zehnder 和微环调制器。三种常见的类型
移相器以 Top View 或 Cross section View 列出。还列出了这些 PN 结点的相应特征长度 （
The carrier plasma dispersion effect in crystalline silicon was first shown in
[30]. The wavelength-dependent expressions for the material properties were commonly used with fitting
parameters. According to the models in [28], both index and absorption vary
as wavelength
晶体硅中的载流子等离子体色散效应首次显示在 [30] 中。材料属性的波长相关表达式通常用于拟合
参数。根据 [28] 中的模型，指数和吸收率都不同
作为波长
查看源
\begin{align}
\Delta n(\lambda) &= -A \lambda ^2 \Delta N - B \lambda ^2 \Delta P^{0.8}\\
\Delta \alpha (\lambda) &= C \lambda ^2 \Delta N + D \lambda ^2 \Delta P\ (\text{cm}^{-1}),
\end{align}
where 其中
查看源
\begin{align}
n_{\mathrm{eff},d} &\approx n_{\mathrm{eff},i} -\gamma (A\lambda ^2 N_D + B\lambda ^2 N_A^{0.8})/2\\
\alpha _d &\approx \alpha _i + \gamma (C \lambda ^2 N_D + D \lambda ^2 N_A)/2.
\end{align}
其中
In reality, depletion region always exists in the PN junction of a depletion-mode phase shifter. As the second step,
we assume that bias voltage
实际上，耗尽区始终存在于耗尽型移相器的 PN 结中。作为第二步，
我们假设偏置电压
查看源
\begin{align}
n_{\mathrm{eff}}(V) &\approx n_{\mathrm{eff},d} + \frac{\gamma }{L_j}\left(A\lambda ^2 N_D x_n(V) + B\lambda ^2
N_A^{0.8}x_p(V)\right)\\
\alpha (V) &\approx \alpha _d - \frac{\gamma }{L_j}\left(C\lambda ^2 N_D x_n(V) + D\lambda ^2 N_A x_p(V)\right)
\end{align}
where 其中
查看源
\begin{align}
x_n(V) &= \sqrt{\frac{2\epsilon N_A (V_{bi} - V)}{qN_D(N_A+N_D)}}\\
x_p(V) &= \sqrt{\frac{2\epsilon N_D (V_{bi} - V)}{qN_A(N_A+N_D)}}\\
V_{bi} &= \frac{k_BT}{q}ln\frac{N_AN_D}{n_i^2}.
\end{align}
This model assumes that the perturbations in effective refractive index and absorption coefficient vary linearly as
depletion width. This is an accurate assumption for interleaved junctions, and is a simplified first-order
approximation for other junction designs with typical waveguide geometries. For lateral and vertical junctions, the
model assumes uniform distribution of optical power in the waveguide.
该模型假设有效折射率和吸收系数的扰动随耗尽宽度线性变化。这是交错结的准确假设，对于具有典型波导几何形状的其他结设计，这是一个简化的一阶近似。对于横向和垂直结点，该模型假设光功率在波导中的分布均匀。
B. Model Verification on Different Platforms
B. 在不同平台上进行模型验证
Next the phase shifter model is applied to various silicon photonic platforms developed by multiple foundries. The
model is verified against measurement data. Modulation efficiency
接下来，移相器模型应用于多家代工厂开发的各种硅光子平台。这
根据测量数据验证模型。调制效率
查看源
\begin{equation}
V_\pi L_\pi = \frac{\lambda V}{2(n_{\mathrm{eff}}(V) - n_{\mathrm{eff}}(0))}
\end{equation}
The relationship between 图 3 中绘制了不同
![Fig. 3. - Modulation efficiency $V\pi L\pi$
vs. junction doping level. Dashed lines are predicted $V\pi L\pi$
at −1 V reverse bias when $L_j/\gamma$
equals 200 nm, 400 nm, 600 nm and 800 nm. Reported data on various silicon photonic platforms
[1]–[7]
are marked here. Average concentration of n-type and p-type doping is used.](/mediastore/IEEE/content/media/50/8067628/8053768/lin3-2757945-large.gif)
Modulation efficiency
调制效率
More details about these waveguides and phase shifters are summarized in
Table I. Only phase shifters based on lateral and interleaved junctions are included here due to
insufficient measurement data for vertical junctions. Based on our proposed compact models, the mode confinement
表 I 总结了有关这些波导和移相器的更多详细信息。此处仅包含基于横向和交错结的移相器，因为
垂直交界处的测量数据不足。基于我们提出的紧凑模型，模态限制
![Fig. 4. - Modulation efficiency $V\pi L\pi$
vs. reversed bias voltage for phase shifters on three different platforms [4],
[5], [7]. Detailed information are
included in Table I. Note that [5]
refers to the interleaved phase shifter on that platform.](/mediastore/IEEE/content/media/50/8067628/8053768/lin4-2757945-large.gif)
Modulation efficiency
调制效率
表 I 在各种 Si 光子平台上建模移相器
For higher doping levels, modulation efficiency of the phase shifter improves at the cost of larger optical losses.
This inherent trade-off is critical for doping optimization for MRM and MZM devices. The optical losses of the phase
shifters, as calculated from 6, match well with measured
waveguide losses from various platforms in Fig. 5. Overall, the proposed
model considers junction design and mode confinement, captures the fundamental device trade-off between loss and phase
shift, and fits accurately the voltage dependency on these optical properties. Although the model can be extended to
include more physics details for specific designs such as junction asymmetry or actual mode profiles, it is efficient
and accurate enough for this paper's system-level optimization.
对于更高的掺杂水平，移相器的调制效率会提高，但代价是光损耗更大。这种固有的权衡对于 MRM 和 MZM 器件的掺杂优化至关重要。移相器的光损耗（从 6 开始计算）与图 5 中各种平台测得的波导损耗非常匹配。总体而言，所提出的模型考虑了结设计和模式限制，捕捉了损耗和相移之间的基本器件权衡，并准确拟合了电压对这些光学特性的依赖性。尽管该模型可以扩展为包含特定设计的更多物理细节，例如结不对称或实际模式剖面，但它对于本文的系统级优化来说足够高效和准确。
![Fig. 5. - Reported waveguide loss vs. predicted waveguide loss. The references for each date points are labeled in
the figure [1]–
[7].](/mediastore/IEEE/content/media/50/8067628/8053768/lin5-2757945-large.gif)
Optimization of Microring-Based Transmitter
基于微环的发射机的优化
A. Static Model of Microring Modulator
A. 微环调制器的静态模型
A microring modulator (MRM) typically consists of a silicon microring and three waveguide ports – input,
output and drop ports, as shown in Fig. 6. The microring has a very small
footprint compared to other modulators, with diameters as small as 10
微环调制器 （MRM） 通常由一个硅微环和三个波导端口组成 – 输入、
output 和 drop 端口，如图 6 所示 。微环有一个非常小的
与其他调制器相比，占地面积小至 10
![Fig. 6. - Micrograph of microring modulator in zero-change 45 nm SOI process [8]
. Model diagram of a microring modulator with drop port, where coupler and propagation coefficients for electric
fields are labeled.](/mediastore/IEEE/content/media/50/8067628/8053768/lin6-2757945-large.gif)
Microring modulators can be sensitive to temperature variations. For any practical system, the microring resonance
needs to be adaptively locked to the laser wavelength through a thermal tuning feedback loop. Robust and efficient
thermal tuning for microring modulators has been demonstrated with a running processor on the same chip
[8]. As the sensing part of feedback loop, a drop port waveguide is coupled to
the microring to provide a port for monitoring the optical power level inside the cavity (see
Fig. 6). The feedback loop can be closed with an embedded heater inside the
microring for tuning the temperature. More details about thermal tuning feedback designs and algorithms are shown in
[21].
微环调制器对温度变化很敏感。对于任何实际系统，都需要通过热调谐反馈回路将微环谐振自适应地锁定到激光波长。微环调制器的稳健和高效的热调谐已经通过在同一芯片上运行的处理器上得到证明 [8]。作为反馈回路的传感部分，一个落口波导耦合到微环上，以提供一个端口来监测腔内的光功率水平（见图 6）。反馈回路可以用微环内的嵌入式加热器来关闭，以调节温度。有关热调谐反馈设计和算法的更多详细信息，请参见 [21]。
To optimize the modulator performance, we begin with the introduction of the static model of MRM's which relies
on the phase shifter model in Section III. The static model of the
microring is derived based on the transfer matrix method (TMM), where the coupling between input/drop waveguides and
the ring is represented by transfer matrices [31]. As shown in
Fig. 6, the key device parameters for a microring include effective index
为了优化调制器性能，我们首先引入 MRM 的静态模型，该模型依赖于
关于第三节 中的移相器模型。静态模型的
微环是基于传递矩阵法 （TMM） 推导的，其中输入/压降波导和
该环由传递矩阵 [31] 表示。如
图 6，微环的关键器件参数包括有效指数
查看源
\begin{align}
P_t &= \left|\frac{t_1 - t_2e^{-\alpha _f L_{rt}+i\theta }}{1-t_1t_2e^{-\alpha _f L_{rt}+i\theta }}\right|^2\\
P_d &= \left|\frac{k_1^*k_2e^{(-\alpha _f L_{rt}+i\theta)/2}}{1-t_1t_2e^{-\alpha _f L_{rt}+i\theta }}\right|^2
\end{align}
where 其中
Assuming the bias voltage for 0 and 1 levels are
假设 0 和 1 电平的偏置电压分别为
查看源
\begin{equation}
\mathrm{OMA} = P_1 - P_0 = P_t(V_1) - P_t(V_0).
\end{equation}
Throughout the paper, OMA will be used to refer to the normalized optical modulation
amplitude (or modulation depth). The power transmission spectra of a typical microring modulator is shown in
Fig. 7. At two different biases, the transfer functions of the microring
have the same Lorentzian shape but different resonance wavelengths. The corresponding OMA can be calculated. The
optimal laser wavelength that maximizes OMA is shown in the figure with optical powers for bit 1 and bit 0 labeled by
在整篇论文中，OMA 将用于指代归一化光调制 振幅（或调制深度）。典型微环调制器的功率传输频谱如下所示 图 7.在两种不同的偏置下，微环的传递函数 具有相同的洛伦兹形状，但共振波长不同。可以计算相应的 OMA。这 使 OMA 最大化的最佳激光波长如图所示，位 1 和位 0 的光功率由
Modeled power transmission spectra of microring modulator under two different bias voltages. Optimal laser
wavelength to maximize OMA is labeled. For phase shifter model, we assumed that
模拟了微环调制器在两种不同偏置电压下的电力传输频谱。最佳激光
波长以最大化 OMA 进行标记。对于移相器模型，我们假设
The round-trip length of the microring,
假设微环
B. Transient Simulation in Simulink
B. Simulink 中的瞬态仿真
The fundamental trade-off between OMA and optical bandwidth is the most critical challenge for high-speed modulation
of microring modulators. Modeling dynamic behaviors of microrings accurately is the key for designing optical
transmitters, especially at very high datarate such as 50 Gb/s. According to coupled mode theory (CMT), the
electrical-to-optical modulation bandwidth of microrings should be inversely proportional to the photon lifetime
OMA 和光带宽之间的基本权衡是高速调制面临的最关键挑战
微环调制器。准确模拟微环的动力学行为是设计光学的关键
发射器，尤其是在非常高的数据速率（如 50 Gb/s）下。根据耦合模态理论 （CMT），
微环的电-光调制带宽应与光子寿命成反比
The photon lifetime
光子寿命
查看源
\begin{align}
Q &= \omega _0 \frac{P_cL_{rt}/v_g}{P_c\left(|k_1|^2+|k_2|^2+1-e^{-\alpha L_{rt}}\right)}\\
&\approx \frac{\omega _0 n_g L_{rt}}{c \left(|k_1|^2+|k_2|^2+\alpha L_{rt}\right)}
\end{align}
with the speed of light with the speed of light
查看源
\begin{equation}
\tau _p = \frac{Q}{\omega _0} = \frac{n_g L_{rt}}{c\left(|k_1|^2+|k_2|^2+\alpha L_{rt}\right)}
\end{equation}
光带宽或相应的半峰全宽 （FWHM） 带宽可以是 计算公式为
查看源
\begin{equation}
f_{optical} = \frac{1}{2 \pi \tau _p}
\end{equation}
MRM 的实际调制带宽
An open-source Simulink toolbox is developed for simulating silicon photonic devices and systems
[35]. The toolbox contains a library of the basic optical elements such as
lasers, waveguides, phase shifters and couplers. Complex photonic devices are constructed with these basic building
blocks. The basic theory behind Simulink simulation is the same as the previous Verilog-A co-simulation framework
[29]. One of the major differences is that the new toolbox adopts the proposed
phase shifter model in Section III, which allows more physical details to
be included. The Simulink toolbox works seamlessly with the co-optimization framework developed in MATLAB.
开发了一个开源的 Simulink 工具箱，用于仿真硅光子器件和系统 [35]。该工具箱包含一个基本光学元件库，例如激光器、波导、移相器和耦合器。复杂的光子器件就是用这些基本构建块构建的。Simulink 仿真背后的基本理论与之前的 Verilog-A 协同仿真框架相同 [29]。主要区别之一是新工具箱采用了第三节 中提出的移相器模型，该模型允许包含更多的物理细节。Simulink 工具箱可与 MATLAB 中开发的协同优化框架无缝协作。
The Simulink schematic of a microring-based optical link is shown in Fig. 8
. It consists of two 2 × 2 couplers for input and drop ports and two phase shifters with half the
round-trip length. The phase shifter blocks compute the phase shift and optical loss using the proposed compact model.
Within the phase shifter block, a built-in delay function is used to generate the propagation delay of the optical
signal in the waveguide.
基于微环的光链路的 Simulink 原理图如图 8 所示 。它由两个用于输入和分支端口的 2 × 2 耦合器以及两个往返长度一半的移相器组成。移相器模块使用所提出的紧凑模型计算相移和光损耗。在移相器模块中，使用内置的延迟函数来生成光信号在波导中的传播延迟。
Schematic of MRM-based optical link in Simulink and the close-ups of microring modulator (MRM) block and
the phase shifter (PS) block.
Simulink 中基于 MRM 的光链路原理图以及微环调制器 （MRM） 模块和移相器 （PS） 模块的特写。
As an example, the microring modulator in Fig. 7 is simulated using this
work's Simulink toolbox. A 25 Gb/s eye diagram is shown in Fig. 9. In
this transient simulation, the driver signal swings between 0.5 V and −1.5 V with ideal, sharp transitions.
Therefore, the eye diagram is solely governed by the optical dynamic behavior of the microring modulator. It is
interesting that the rising transition of the eye is faster than the falling transition and even causes a slight
overshoot. This is consistent with the small-signal analysis [27] where
larger laser detuning corresponds to larger small-signal bandwidth. The asymmetry in the eye diagram should be
balanced by adjusting driver strength for pulling up and pulling down.
例如，图 7 中的微环调制器是使用这项工作的 Simulink 工具箱进行仿真的。25 Gb/s 眼图如图 9 所示。在此瞬态仿真中，驾驶员信号在 0.5 V 和 −1.5 V 之间摆动，具有理想的急剧转换。因此，眼图完全由微环调制器的光学动力学行为控制。有趣的是，眼睛的上升过渡比下降过渡更快，甚至会导致轻微的过冲。这与小信号分析[27]一致，在小信号分析中，较大的激光失谐对应于较大的小信号带宽。应通过调整发球杆的上拉和下拉力度来平衡眼图中的不对称性。
Simulated eye diagram at 25 Gb/s. Device parameters are the same as the microring in
Fig. 7 with optical bandwidth of around 25 GHz. Laser detuning is set to
optimize OMA. A first-order low-pass filter approximation with 3 dB bandwidth of 20 GHz is represented with red dashed
line.
25 Gb/s 时的模拟眼图。器件参数与图 7 中的微环相同，光带宽约为 25 GHz。设置激光失谐以优化 OMA。3 dB 带宽为 20 GHz 的一阶低通滤波器近似值用红色虚线表示。
In our optimization engine, the modulation bandwidth is assumed to be limited by the slower falling edge. A
first-order low-pass filter with a 3 dB bandwidth
在我们的 optimization engine 中，假设 modulation bandwidth 受到较慢的 Falling edge 的限制。一个
Simulink 中使用带宽为 3 dB
查看源
\begin{equation}
f_{optical} \geq \frac{1}{T_b}.
\end{equation}
For a 50 Gb/s MRM, the optical bandwidth constraint is thereby set to 50 GHz with the actual
electrical-to-optical modulation bandwidth being around 40 GHz. Transient simulations will be used to further verify
the dynamic performance for 50 Gb/s optimized microring transmitters.因此，对于 50 Gb/s MRM，光带宽约束设置为 50 GHz，实际 电光调制带宽约为 40 GHz。瞬态仿真将用于进一步验证 50 Gb/s 优化微环发射机的动态性能。
C. Optimization of Microring Modulator Design
C. 微环调制器设计的优化
For a typical MRM-based transmitter, laser power dominates the total power consumption of the transmitter macro as
the driver power is usually much lower. Therefore, minimizing the overall E/b for the transmitter (driver plus laser)
is equivalent to maximizing the normalized OMA of the microring modulator.
对于典型的基于 MRM 的发射器，激光功率在发射器宏的总功耗中占主导地位，因为驱动器功率通常要低得多。因此，最小化发射器（驱动器加激光器）的总 E/b 相当于最大化微环调制器的归一化 OMA。
For analysis purposes, we choose to use a typical feature length
出于分析目的，我们在本文中选择使用典型的特征长度
For each doping level for the PN junction (
对于 PN 结 （
Optical bandwidth requirement:
光带宽要求：View Sourcefoptical≥fmin.(19)
查看源
\begin{equation}
f_{optical} \geq f_{\min }.
\end{equation}
Extinction ratio (ER) requirement:
消光比 （ER） 要求：View SourceER=Pt(V1)Pt(V0)≥ERmin(20)
查看源
\begin{equation}
\mathrm{ER} = \frac{P_t(V_1)}{P_t(V_0)} \geq ER_{\min }
\end{equation}
Enough average drop port power for thermal tuning:
足够的平均 drop port 功率用于热调谐：View SourcePd(V1)+Pd(V0)2≥Pd,min.(21)
查看源
\begin{equation}
\frac{P_d(V_1)+P_d(V_0)}{2} \geq P_{d,\min }.
\end{equation}
The extinction ratio requirement
消光比要求
![Fig. 10. - Optimized OMA for $f_{optical}$ 25
GHz, 35 GHz and 50 GHz versus doping levels in the PN junction. Bias conditions are
$V_0 = \text{0.5}\ {\text{V}}$ and
$V_1 = -\text{1.5}\ \text{V}$. Technology constraints: PN
junction feature length $L_j=\text{500}$ nm and
optical mode confinement factor $\gamma = 0.75$
. $L_{rt}$= 30
$\mu \text{m}$, intrinsic loss 13 dB/cm
[28]. Symmetric pn-junctions are assumed for simplicity.](/mediastore/IEEE/content/media/50/8067628/8053768/lin10-2757945-large.gif)
Optimized OMA for
针对
According to Fig. 10, an optimal doping level exists for each bandwidth
requirement. Intuitively, increasing doping could improve the modulation efficiency of the phase shifter and could
improve OMA. However, as we increase doping levels, the excessive optical loss in the ring might eventually lower the
Q factor and degrade the OMA. Therefore, it is critical to find the optimal doping levels. It is important that the
optimal doping level increases as the required optical bandwidth increases. The optimal doping for achieving 50 GHz
optical bandwidth is around
根据图 10，每个带宽都存在最佳掺杂水平
要求。直观地说，增加掺杂可以提高移相器的调制效率，并且可以
改善 OMA。然而，随着掺杂水平的增加，戒指中过多的光损耗最终可能会降低
Q 因子并降低 OMA 的 OMA。因此，找到最佳掺杂水平至关重要。重要的是，
最佳掺杂水平随着所需光带宽的增加而增加。实现 50 GHz 的最佳掺杂
光带宽约为
The corresponding device parameters given by the optimization engine are shown in
Fig. 11, including Q factor, extinction ratio (ER), insertion loss (IL), coupler coefficients (
优化 引擎给出的相应器件参数如图 11 所示，包括 Q 因子、消光比 （ER）、插入损耗 （IL）、耦合器系数 （
Key characteristics of the optimal microring designs for different doping levels with the design points
corresponding to maximum OMAs labeled. The optimization constraints corresponds to the curves in the
Fig. 10. Three operation regions (A-C) are labeled for 25 GHz operation as
an example. A is coupling-limited region, C is loss-limited region and B is the optimal region. Note that
不同掺杂水平的最佳微环设计的关键特性以及设计要点
对应于标记的最大 OMA。优化约束对应于
图 10.对于 25 GHz 操作，三个操作区域 （A-C） 标记为
一个例子。A 是耦合受限区域，C 是损耗受限区域，B 是最优区域。请注意，
For Fig. 11(a)–(f), we
define three different doping regions to get more insights into the microring optimization. The 25 GHz microring is
used as an example. Region A is the coupling-limited region where doping levels are relatively low. Q factor is
effectively controlled by the coupler designs assuming fixed ring circumference and negligible round trip ring loss.
Drop port coupling should be used to match the input port coupling. By doing so, the microring can be brought closer
to critical coupling (
对于图 11（a）–（f），我们
定义三个不同的掺杂区域，以更深入地了解微环优化。25 GHz 微环是
用作示例。区域 A 是掺杂水平相对较低的耦合限制区域。Q 因子为
由耦合器设计有效控制，假设环圆周固定且往返环损耗可忽略不计。
应使用 Drop port 耦合来匹配 input port 耦合。通过这样做，可以使微环更近
到临界耦合 （）
The optimal design with the maximum OMA is achieved in region B, where doping levels are between the regions A and
C. For the optimal designs, input coupling is well balanced with the optical loss inside the cavity resulting in
minimum drop port coupling. The microrings are slightly under-coupled. In this region, input coupling decreases as
doping increase in order to maintain constant Q factor. If the available doping levels are not in region B, different
optimization strategies are needed according to the analysis above.
在区域 B 中实现了具有最大 OMA 的最优设计，其中掺杂水平介于区域 A 和 C 之间。对于最佳设计，输入耦合与腔内的光损耗保持良好平衡，从而实现最小的丢端口耦合。微环略微欠耦合。在这个区域，输入耦合随着掺杂的增加而降低，以保持恒定的 Q 因子。如果可用的掺杂水平不在 B 区，则根据上述分析需要不同的优化策略。
D. Microring-Based NRZ Transmitter Design
D. 基于微环的 NRZ 发射器设计
The driver circuit is modeled as shown in Fig. 12. It consists of a
high-speed serializer, pre-drivers and a final driver stage. The final stage driver can be a simple inverter driving
one electrode of the modulator in single-end fashion with voltage swing of
驱动器电路的建模如图 12 所示 。它由一个
高速串行器、预驱动器和最终驱动器级。最后阶段驱动器可以是简单的逆变器驱动
单端调制器的一个电极，电压摆幅
Transmitter circuits for ring modulator.
环形调制器的发射器电路。
In our optimization, we assume the voltage swing
在我们的优化中，我们假设电压摆幅
查看源
\begin{equation}
E_{dr} = \frac{1}{4\eta _d}V_{A}\int _{-V_{b}}^{V_A-V_b} \left(C_m(V) + C_{w}\right)dV.
\end{equation}
where driver efficiency 其中，考虑到 50 Gb/s 的预驱动器级的合理扇出，假设驱动器效率
The capacitance density of the PN junction is given by
PN 结的电容密度由下式给出
查看源
\begin{equation}
C_j(V) = \sqrt{\frac{q\epsilon N_A N_D}{2(V_{bi} - V)(N_A+N_D)}}.
\end{equation}
The modulator capacitance depends on the type of the PN junctions. For lateral junctions,
调制器电容取决于 PN 结的类型。对于横向连接处，
The total wiring capacitance
总接线电容
Even so, laser power dominates the total power for MRM transmitters. For a typical silicon photonic link in
Fig. 13, the optical power gets attenuated by three fiber-to-chip optical
couplers and the transmitter before it reaches the receiver-side photodetector. The minimal OMA required at the
receiver input to reach a certain BER target is defined as the receiver sensitivity, denoted by
即便如此，激光功率仍占 MRM 变送器总功率的主导地位。对于典型的硅光子链路
图 13，光功率被三个光纤到芯片的光学器件衰减
耦合器和发射器到达接收器侧光电探测器之前。所需的最低 OMA
接收器到达某个 BER 目标的输入定义为接收器灵敏度，在本文中用 表示
查看源
\begin{equation}
E_{laser} = \frac{P_{RX}}{\eta _m \cdot \eta _w \cdot \alpha _{c}^3 \cdot \mathrm{OMA_{mod}} \cdot f_b}
\end{equation}
where 其中
Diagram of a full optical link with external laser source.
带有外部激光源的完整光链路图。
The total E/b for MRM-based transmitter is the sum of the driver circuit and laser power:
基于 MRM 的发射器的总 E/b 是驱动电路和激光功率之和：
查看源
\begin{equation}
E_{tot} = E_{dr} + E_{laser}.
\end{equation}
Typical numbers for parameters used in 23
are listed in Table II. Based on the results in
Fig. 10, the energy-per-bit 23 中使用的参数的典型数字 列于表 II 中。根据 图 10， 每比特能量
Model-estimated total E/b for microring driver + laser for microring-based NRZ transmitter at 50 Gb/s.
Two different driver swings are considered (1 V and 2 V). The microring is optimized for each doping levels, which
corresponds to the designs in Figs. 10 and
11.
微环驱动器 + 基于微环的 NRZ 发射器的激光器在 50 Gb/s 时的模型估计总 E/b。考虑了两种不同的驱动器摆幅（1 V 和 2 V）。微环针对每个掺杂水平进行了优化，这与图 10 和图 11 中的设计相对应。
表 II 50 Gb/s 硅光子链路预算的参数
The results show that higher driver swing improves the overall energy efficiency for MRM transmitters as laser power
dominates and higher swing improves OMA. The total transmitter power is not sensitive to the increased driver power
due to higher swing. Therefore it makes sense to always choose high swing drivers if driver bandwidth allows. In
addition, it is also critical to co-optimize the modulator design to maximize OMA as discussed before. The 50 Gb/s
MRM-based NRZ transmitter with the optimized microring device and 2 V driver voltage swing consumes 1.7 pJ/b in total
– 1.5 pJ/b by laser and only 0.2 pJ/b by driver circuits. More results and the optimal dopings can be found in
Table III. Note that the above analysis is done assuming 3D hybrid
integration between circuits and photonics. Switching to monolithic integration would yield even lower driver power
and thus further improve the energy efficiency of the transmitter and be even further dominated by laser power.
结果表明，由于激光功率占主导地位，较高的驱动器摆幅可以提高 MRM 发射器的整体能效，而较高的摆幅会改善 OMA。由于较大的摆幅，发射器总功率对增加的驱动器功率不敏感。因此，如果驱动器带宽允许，始终选择高摆幅驱动器是有意义的。此外，如前所述，协同优化调制器设计以最大化 OMA 也很重要。基于 MRM 的 50 Gb/s NRZ 发射器具有优化的微环器件和 2 V 驱动器电压摆幅，总共消耗 1.7 pJ/b，激光消耗 1.5 pJ/b，驱动电路仅消耗 0.2 pJ/b。更多结果和最佳掺杂可在表 III 中找到。请注意，上述分析是假设电路和光子学之间的 3D 混合集成完成的。切换到单片集成将产生更低的驱动器功率，从而进一步提高发射器的能效，并进一步以激光功率为主。
表 III 50 Gb/s 微环 TX 最佳掺杂和功率 （pJ/b）
E. Microring-Based PAM4 Transmitter Design
E. 基于微环的 PAM4 发射机设计
As shown in Fig. 10, the microring modulator can achieve higher OMA at
the cost of optical bandwidth. In other words, reducing bandwidth requirement means improving OMA and lowering laser
power for MRM-based optical links. One potential way to relax the bandwidth constraint while maintaining the same
datarate is to use PAM4 instead of conventional NRZ modulation, where the front-end bandwidth is halved in a PAM4
modulation scheme to attain the same bit rate. There has been analysis comparing the energy efficiency of
microring-based PAM4 transmitters with NRZ transmitters [32]. In this paper,
we use the proposed optimization framework to optimize microring designs for NRZ and PAM4 separately. The optimized
microring-based PAM4 transmitter is then compared to the optimized NRZ transmitter at 50 Gb/s under the same process
constraints. Transient simulations are also used to verify the transmitter performances. Note that practical design
constraints outside the scope of this work would need to be taken into consideration as well to validate the benefits
of PAM4 versus NRZ. This paper is intended to give a first-pass, fundamental comparison between the two schemes.
如图 10 所示 ，微环调制器可以以光带宽为代价实现更高的 OMA。换句话说，降低带宽要求意味着提高基于 MRM 的光链路的 OMA 和降低激光功率。在保持相同数据速率的同时放宽带宽限制的一种潜在方法是使用 PAM4 而不是传统的 NRZ 调制，其中前端带宽在 PAM4 调制方案中减半以获得相同的比特率。已经有分析比较了基于微环的 PAM4 发射器和 NRZ 发射器的能效 [32]。在本文中，我们使用提出的优化框架分别优化 NRZ 和 PAM4 的微环设计。然后在相同的过程约束下，将优化的基于微环的 PAM4 变送器与优化的 NRZ 变送器以 50 Gb/s 的速度进行比较。瞬态仿真还用于验证发射机的性能。请注意，还需要考虑这项工作范围之外的实际设计约束，以验证 PAM4 与 NRZ 的优势。本文旨在对这两种方案进行初步的基本比较。
There are multiple ways to generate the PAM4 optical signal with silicon microring modulators. For the first
approach, an electrical DAC is used to drive the microring modulator [33],
[34]. This architecture is shown in
Fig. 15(a). Due to nonlinearity of the electrical-to-optical response of microrings, a lookup table is
required in order to pre-distort the drive signal and achieve symmetric PAM4 eyes. The second approach uses an optical
DAC to generate the PAM4 signals instead of using an electrical DAC [18]. As
shown in Fig. 15(b), the microring is segmented into
使用硅微环调制器有多种方法可以生成 PAM4 光信号。对于第一个
方法中，使用电 DAC 驱动微环调制器 [33]，
[34]. 这种架构如图 15（a） 所示 。由于微环的电-光响应的非线性，查找表为
需要，以便对驱动信号进行预失真并实现对称的 PAM4 眼图。第二种方法使用光学
DAC 生成 PAM4 信号，而不是使用电 DAC [18]。如
如图 15（b） 所示 ，微环被分割成
Microring-based PAM4 Transmitters: (a) electrical DAC driver (b) optical DAC based on segmented microring
(c) microring with two segments.
基于微环的 PAM4 发射器：（a） 电 DAC 驱动器 （b） 基于分段微环的光 DAC （c） 具有两个段的微环。
Linearity is the key criterion for choosing microring-based PAM4 architectures, which can be evaluated with the
static model in Section IV. The optical responses of a 4-bit electrical
DAC and a 4-bit optical DAC are compared in Fig. 16(a). For the
comparison, the total voltage swing of the electrical DAC equals that of the driver for each small segment in the
optical DAC. The same optimized microring modulators are used with 25 GHz optical bandwidth and 50 Gb/s targeted
datarate. For such microrings, the optical response of the optical DAC is more linear compared to that of the
electrical DAC. It also shows that the third architecture using two segments should offer sufficient linearity for
generating the balanced PAM4 signals at 50 Gb/s.
线性度是选择基于微环的 PAM4 架构的关键标准，可以使用第 IV 节 中的静态模型进行评估。图 16（a） 比较了 4 位电 DAC 和 4 位光 DAC 的光响应。为了进行比较，电气 DAC 的总电压摆幅等于光 DAC 中每个小段的驱动器的总电压摆幅。相同的优化微环调制器用于 25 GHz 光带宽和 50 Gb/s 目标数据速率。对于此类微环，与电 DAC 相比，光 DAC 的光响应更加线性。它还表明，使用两个段的第三种架构应该提供足够的线性度来生成 50 Gb/s 的平衡 PAM4 信号。
(a) Linearity comparison between 5-bit electrical DAC and 5-bit optical DAC for MRM-based transmitter. (b)
Transmission spectra for a microring with two binary weighted segments. The microring here has an optical bandwidth of
25 GHz.
（a） 基于 MRM 的发射器的 5 位电 DAC 和 5 位光 DAC 之间的线性度比较。（b） 具有两个二进制加权段的微环的透射光谱。这里的微环具有 25 GHz 的光带宽。
The second and third architectures should be chosen depending on whether programmability is required to handle
process variations. Despite of the architecture difference, they are both based on the same operation principles. The
common transfer functions are shown in Fig. 16 as different portion of the
ring is reverse biased by the corresponding driver. The microring design and laser detuning are optimized for 50 Gb/s
PAM4, and the four optical levels show very good linearity.
应根据是否需要可编程性来处理流程变化来选择第二种和第三种体系结构。尽管架构不同，但它们都基于相同的操作原则。常见的传递函数如图 1 所示。16 时，环的不同部分由相应的驱动器反向偏置。微环设计和激光失谐针对 50 Gb/s PAM4 进行了优化，四个光学电平显示出非常好的线性度。
For 50 Gb/s PAM4, the optimization engine optimizes the OMA of a microring modulator with 25 GHz optical bandwidth,
as shown in Fig. 10. A 25 Gb/s NRZ receiver could achieve a sensitivity
of −14 dBm according to [10]. In our analysis, the required total eye
height for 50 Gb/s PAM4 receiver is approximated as 3x single eye height for 25 Gb/s NRZ receiver, neglecting any
other circuit overhead. Therefore the new receiver sensitivity
对于 50 Gb/s PAM4，优化引擎优化了具有 25 GHz 光带宽的微环调制器的 OMA，
如图 10 所示 。25 Gb/s NRZ 接收器可实现灵敏度
根据 [10] 为 −14 dBm。在我们的分析中，所需的全眼
50 Gb/s PAM4 接收器的高度近似为 25 Gb/s NRZ 接收器单眼高度的 3 倍，忽略任何
other circuit 开销。因此，新的接收器灵敏度
查看源
\begin{equation}
E_{dr} = \frac{1}{2}\cdot \frac{1}{4\eta _d}V_{A}\int _{-V_{b}}^{V_A-V_b} \left(C_m(V) + 2C_{w}\right)dV
\end{equation}
Now the total energy
现在是车手的总能量
Model estimated total E/b for microring driver+laser for microring-based PAM4 transmitter at 50 Gb/s. Two
different driver swings are considered (1 V and 2 V). The microring is optimized for each doping levels, which
corresponds to the designs in Figs. 10 and
11.
模型估计了基于微环的 PAM4 发射器在 50 Gb/s 下微环驱动器 + 激光器的总 E/b。考虑了两种不同的驱动器摆幅（1 V 和 2 V）。微环针对每个掺杂水平进行了优化，这与图 10 和图 11 中的设计相对应。
Transient simulations are carried out in order to verify the performance of 50 Gb/s microring NRZ and PAM4
transmitters. The device parameters for modulators in Simulink framework are set by the output of the optimization
engine. The driver swings are assumed to be the same. The simulated eye diagrams are shown in
Fig. 18. The modulators are optimized under the same technology and link
constraints by the engine. The eye heights for PAM4 and NRZ in these two eye diagrams can be compared directly as the
optical power is normalized. Total OMA height for PAM4 microring is increased by about 50% from NRZ microring.
Detailed full link optimization including receiver circuits will be required to compare the full link power. For
driver and laser portion, the potential power saving for PAM4 is around 20% at 50 Gb/s. Another observation is
that microring PAM4 eye diagram is not balanced due to the asymmetry of the rise and fall time. Therefore, it is even
more critical for PAM4 drivers to adjust pull-up and pull-down strengths compared with NRZ drivers. By doing so, the
four signal levels in the optical PAM4 eye diagram can be well balanced.
进行瞬态仿真是为了验证 50 Gb/s 微环 NRZ 和 PAM4 发射机的性能。Simulink 框架中调制器的器件参数由优化引擎的输出设置。假定驱动程序摆动相同。模拟的眼图如图 18 所示 。调制器在相同的技术和 link constraints 下由引擎进行优化。当光功率归一化时，可以直接比较这两个眼图中 PAM4 和 NRZ 的眼高。PAM4 微环的总 OMA 高度比 NRZ 微环增加约 50%。需要详细的全链路优化，包括接收器电路，以比较全链路功率。对于驱动器和激光器部分，PAM4 在 50 Gb/s 时的潜在功耗节省约为 20%。另一个观察结果是，由于上升和下降时间的不对称，微环 PAM4 眼图不平衡。因此，与 NRZ 驱动器相比，PAM4 驱动器调整上拉和下拉强度更为重要。通过这样做，光学 PAM4 眼图中的四个信号电平可以很好地平衡。
Transient simulation of the 50 Gb/s MRM-based NRZ transmitter and PAM4 transmitter. The microrings are
optimized in each case with the same process and link constraints. The optical power for y-axis is normalized to the
input power for microrings.
基于 50 Gb/s MRM 的 NRZ 发射机和 PAM4 发射机的瞬态模拟。在每种情况下，微环都使用相同的工艺和链接约束进行优化。y 轴的光功率归一化为微环的输入功率。
Optimization of Mach-Zehnder Transmitter
Mach-Zehnder 发射器的优化
A. Overview of Mach-Zehnder Modulator
A. Mach-Zehnder 调制器概述
Mach-Zehnder modulators (MZM) have traditionally been used for optical communication due to its simple
interferometric structure. A MZM consists of two balanced arms with embedded phase shifters. The output light
intensity is modulated as a result of optical interference when phase shifts are introduced in the arms. On silicon
photonic platforms, the phase shifters are normally made of PN junctions. The same set of technology constraints need
to be applied. There are two major challenges for designing an energy efficient MZM. First, there is a trade-off
between phase modulation efficiency and propagation loss for phase shifters. This would cause high insertion loss and
low OMA for the MZM. Second, the device capacitance is much larger than microrings and the driver power could dominate
the total power consumption. As a result, co-optimization of electrical driver and optical modulator is essential for
designing low power MZM transmitters.
马赫-曾德尔调制器 （MZM） 由于其简单的干涉结构，传统上用于光通信。MZM 由两个带有嵌入式移相器的平衡臂组成。当镜臂中引入相移时，由于光干扰，输出光强度会受到调制。在硅光子平台上，移相器通常由 PN 结制成。需要应用相同的技术约束。设计节能型 MZM 面临两大挑战。首先，移相器的相位调制效率和传播损耗之间需要权衡。这将导致 MZM 的高插入损耗和低 OMA。其次，器件电容远大于微环，驱动器功率可能主导总功耗。因此，电气驱动器和光调制器的协同优化对于设计低功耗 MZM 发射器至关重要。
There are two basic architectures for MZM transmitter, one based on multi-stage drivers and one based on
traveling-wave drivers, as shown in Fig. 19. For multi-stage MZM
(MS-MZM), the arms are segmented into multiple segments which are modulated individually by distributed voltage
drivers. Delay units are inserted between these electrical drivers to match with the propagation velocity of optical
signal inside the waveguide. For traveling-wave MZM (TW-MZM), the transmission lines are used as the electrodes. Delay
matching is also required between optical waveguide and electrical transmission line. Traveling-wave drivers are
typically more energy efficient than multi-stage drivers at high datarates [24]
. Because the power of TW driver is independent of the device capacitance of MZM and gets amortized at high
datarates. However TW-MZM may suffer from limited OMA due to lower voltage swing and high transmission line loss.
Therefore, electronic-photonic co-optimization is needed to compare the overall energy efficiency of these two
architectures,
MZM 发射器有两种基本架构，一种基于多级驱动器，一种基于行波驱动器，如图 19 所示 。对于多级 MZM （MS-MZM），臂被分割成多个段，这些段由分布式电压驱动器单独调制。在这些电气驱动器之间插入延迟单元，以匹配波导内光信号的传播速度。对于行波 MZM （TW-MZM），传输线用作电极。光波导和输电线路之间还需要延迟匹配。在高数据速率下，行波驱动器通常比多级驱动器更节能 [24] 。因为 TW 驱动器的功率与 MZM 的器件电容无关，并且在高数据速率下得到摊销。然而，由于较低的电压摆幅和高传输线损耗，TW-MZM 可能会受到有限的 OMA 影响。因此，需要电子光子协同优化来比较这两种架构的整体能效，
(a) Architecture of Multi-stage Mach-Zehnder Modulator (MS-MZM) (b) Architecture of Traveling wave
Mach-Zehnder Modulator (TW-MZM).
（a） 多级马赫-曾德尔调制器 （MS-MZM） 的结构;（b） 行波马赫-曾德尔调制器 （TW-MZM） 的结构。
The normalized transmitted power of both MZMs can be approximated as the following
[24]:
两种MZM的归一化发射功率可以近似地表示如下[24]：
查看源
\begin{equation}
P_{t} = e^{-\alpha L} \sin ^2\left(\frac{\Delta \phi }{2}\right)
\end{equation}
where 其中
B. Multi-Stage Mach-Zehnder Transmitter
B. 多级马赫-曾德尔发射机
Since the same voltage swing is applied to each segment of the arm, the total modulation phase shift for one arm now
becomes
由于对臂的每个部分施加相同的电压摆幅，因此现在一个臂的总调制相移
成为
查看源
\begin{equation}
\Delta \phi _{mod} = (2\pi L/\lambda) \cdot (n_{\mathrm{eff}}(V_1) - n_{\mathrm{eff}}(V_0))
\end{equation}
where 其中
查看源
\begin{align}
P_{t1} &= e^{-\alpha L} \sin ^2\left(\frac{ \phi _0 + \Delta \phi _{mod}}{2}\right)\\
P_{t0} &= e^{-\alpha L} \sin ^2\left(\frac{ \phi _0 - \Delta \phi _{mod}}{2}\right)
\end{align}
归一化的 OMA 和 ER 由下式给出
查看源
\begin{align}
\mathrm{OMA} &= P_{t1} - P_{t0}\\
\mathrm{ER} &= P_{t1}/P_{t0}
\end{align}
激光器
MS-MZM drivers are generally very power hungry. The total E/b for the modulator drivers is calculated as follows:
MS-MZM 驱动程序通常非常耗电。调制器驱动器的总 E/b 计算如下：
查看源
\begin{equation}
E_{dr,MS} = \frac{1}{4\eta _d}V_{dd}\int _{-V_{dd}}^0 \left(C_m(V) + C_{w}L\right)dV.
\end{equation}
where driver efficiency 其中，驾驶员效率
The objective of the MZM optimization engine is to minimize total transmitter energy-per-bit E/b, including both
laser wall-plug energy and TX driver energy. When the arms are driven differentially as in
Fig. 19(a), the total transmitter energy for MS-MZM is given by
MZM 优化引擎的目标是最小化每比特发射机总能量 E/b，包括两者
激光电光转换能量和 TX 驱动器能量。当机械臂以差速方式驱动时，如
图 19（a），MS-MZM 的总发射机能量由下式给出
查看源
\begin{equation}
E_{TX,MS} = E_{laser} + 2E_{dr,MS}
\end{equation}
For each doping level in the PN junction (
对于 PN 结 （
Co-optimization is carried out for MS-MZMs with two different driver voltages (1 V and 2 V) across the typical
doping range. The total transmitter E/b, the laser power and the optimal arm length
对具有两种不同驱动器电压（1 V 和 2 V）的 MS-MZM 进行协同优化，典型值
掺杂范围。优化引擎找到的总发射器 E/b、激光功率和最佳臂长
Optimization results for multi-stage MZM transmitters at 50 Gb/s with two peak-to-peak voltage swings (1 V
and 2 V). (a) the total transmitter E/b, (b) laser E/b, (c) the optimal arm length
多级 MZM 发射器的优化结果，速率为 50 Gb/s，具有两个峰峰值电压摆幅 （1 V）
和 2 V）。（a） 总发射机 E/b，（b） 激光器 E/b，（c） 最佳臂长
表 IV 50 Gb/s MZM 最优设计参数和功耗 （pJ/b）
C. Traveling-Wave Mach Zehnder Transmitter
C. 行波马赫曾德尔发射机
The driver for traveling-wave MZM could potentially be more energy efficient at high datarates. The output signal of
the driver propagates along the on-chip electrode as shown in Fig. 19(b).
In the optimized design, the RF and optical group velocities are matched. Any mismatch in them degrades the OMA and
thus increases the total optimal transmitter energy. In our optimization engine, such velocity matching condition is
assumed to be satisfied for first-order system analysis. The impact of mismatch can simulated in time domain through
the proposed Simulink toolbox for specific designs [35].
行波 MZM 的驱动器在高数据速率下可能更节能。驱动器的输出信号沿片上电极传播，如图 19（b） 所示 。在优化后的设计中，RF 和光群速度匹配。它们中的任何不匹配都会降低 OMA，从而增加总最佳发射机能量。在我们的优化引擎中，假设一阶系统分析满足这种速度匹配条件。失配的影响可以通过针对特定设计的 Simulink 工具箱在时域中进行仿真 [35]。
The final stage of the driver can be a CML driver with load resistance
驱动器的最后阶段可以是具有负载电阻的 CML 驱动器
查看源
\begin{align}
\Delta \phi _{mod} &= \frac{2\pi }{\lambda } \int _0^L \left[ n_{\mathrm{eff}} \left(-V(z)\right) -
n_{\mathrm{eff}} \left(V(z) \right) \right] dz\\
V(z) &= \frac{V_{TW}}{2} e^{-\alpha _t z}
\end{align}
where the effective index 其中，有效指数
When a CML driver is used for the final stage with supply voltage
当 CML 驱动器用于电源电压
查看源
\begin{equation}
E_{dr, TW} = \frac{1}{\eta _d \cdot f_b} \cdot \frac{V_{TW}}{2(Z_0/2)} \cdot V_{DD} = \frac{V_{TW} V_{DD}}{\eta _d Z_0
\cdot f_b}
\end{equation}
The effective load impedance of the parallel transmission lines is 并联传输线的有效负载阻抗为
Under the same technology and link constraints, the optimization engine minimizes the total E/b for TW-MZM
transmitter by finding the optimal arm length for different doping levels. For 50 Gb/s TW-MZM transmitter,
co-optimizations are carried out for three different
在相同的技术和链路约束下，优化引擎使 TW-MZM 的总 E/b 最小
通过找到不同掺杂水平的最佳臂长来发射机。对于 50 Gb/s TW-MZM 发射器，
对典型掺杂范围内的三种不同
Optimization results for traveling-wave MZM transmitters at 50 Gb/s with three differential peak-to-peak
voltage swings
具有三个差分峰峰值的 50 Gb/s 行波 MZM 发射机的优化结果
电压摆动
The optimal doping levels for MS-MZM and TW-MZM as well as their corresponding laser and driver power are listed in
Table IV. At 50 Gb/s, the optimized TW-MZM tends to consume more laser
power, whereas MS-MZM consumes more driver power. Overall, the optimized TW-MZM transmitter consumes around 5.1 pJ/b
energy, slightly higher than the 4.7 pJ/b consumed by the optimized MS-MZM transmitter. For both transmitter
architectures, optimizing doping levels is crucial for achieving the best energy efficiency.
表 IV 列出了 MS-MZM 和 TW-MZM 的最佳掺杂水平及其相应的激光器和驱动器功率。在 50 Gb/s 时，优化的 TW-MZM 往往消耗更多的激光功率，而 MS-MZM 消耗更多的驱动器功率。总体而言，优化的 TW-MZM 发射机消耗的能量约为 5.1 pJ/b，略高于优化的 MS-MZM 发射机消耗的 4.7 pJ/b。对于这两种变送器架构，优化掺杂水平对于实现最佳能效至关重要。
Comparisons 比较
The optimization framework allows us to compare the energy efficiency of MRM and MZM optical transmitters including
laser and driver power. PAM4 modulation is discussed as a potential way to mitigate the inherent optical bandwidth
constraint for microrings. For Mach-Zehnder modulators, we have focused on NRZ modulation and analyzed both
multi-stage and traveling-wave MZ-modulators. All the transmitters are optimized under the same technology and link
constraints. The impact of doping levels for transmitter designs has been addressed in depth using the optimization
framework.
优化框架使我们能够比较 MRM 和 MZM 光发射机的能效，包括激光器和驱动器功率。PAM4 调制被讨论为减轻微环固有光带宽限制的一种潜在方法。对于 Mach-Zehnder 调制器，我们专注于 NRZ 调制，并分析了多级和行波 MZ 调制器。所有发射机都在相同的技术和链路约束下进行了优化。使用优化框架，已经深入解决了掺杂水平对发射机设计的影响。
For microring modulators, thermal tuning is essential for keeping the resonant frequency of microring locked to the
laser frequency. Microring's thermal tuning can be done via an embedded microheater and a feedback mechanism. The
heaters have been implemented in silicon or polysilicon to be more efficient and robust to electromigration. In a
recent work [21], the thermal tuner for microrings achieves a 524 GHz (
对于微环调制器，热调谐对于保持微环的谐振频率锁定在
激光频率。Microring 的热调谐可以通过嵌入式微加热器和反馈机制来完成。这
加热器已在硅或多晶硅中实现，以提高效率和抗电迁移能力。在
最近的工作 [21]，用于 MicroRings 的 Thermal Tuner 达到 524 GHz（
For the analysis above, we have set the link margin to 3 dB and assumed 3 dB coupler loss, 10% laser
wall-plug efficiency and −10 dBm receiver sensitivity for NRZ at 50 Gb/s. In practice, any deviation from these
link constraints can be considered by adjusting the link margin. Now we consider three different link margins (0 dB, 3
dB and 6 dB) and show how the energy efficiency comparison would change between the different transmitter
architectures at 50 Gb/s. The new energy breakdowns are shown in Fig. 22
with different link margins. For Mach-Zehnder modulators, the optimized multi-stage MZM transmitter can be more energy
efficient than traveling-wave MZM transmitter when higher link margin is used. Because the MS-MZM uses significantly
less laser power. If a smaller link margin or further relaxed link constraints are used, traveling-wave MZM may become
more energy efficient. In this case, the driver energy takes up larger portion of total energy budget and the
optimized traveling-wave MZM transmitter benefits from its relatively low driver E/b.
对于上述分析，我们将链路裕量设置为 3 dB，并假设 50 Gb/s 时 NRZ 的耦合器损耗为 3 dB，激光电光转换效率为 10%，接收器灵敏度为 −10 dBm。在实践中，可以通过调整链路边距来考虑与这些链路约束的任何偏差。现在我们考虑三种不同的链路余量（0 dB、3 dB 和 6 dB），并展示 50 Gb/s 时不同发射机架构之间的能效比较如何变化。新能源 细分如图 22 所示，具有不同的链路裕量。对于马赫-曾德尔调制器，当使用更高的链路裕量时，优化的多级 MZM 发射器可能比行波 MZM 发射器更节能。因为 MS-MZM 使用的激光功率要少得多。如果使用较小的链路余量或进一步放宽的链路约束，行波 MZM 可能会变得更加节能。在这种情况下，驱动器能量占据总能量预算的较大部分，而优化的行波 MZM 发射器受益于其相对较低的驱动器 E/b。
Detailed energy breakdown and energy efficiency comparison between optimized (A) NRZ-MRM, (B) PAM4-MRM, (C)
MS-MZM and (D) TW-MZM transmitters at 50 Gb/s. Three different link margins are considered: 0 dB, 3 dB and 6 dB.
优化的 （A） NRZ-MRM、（B） PAM4-MRM、（C） MS-MZM 和 （D） TW-MZM 发射机在 50 Gb/s 下的详细能量细分和能效比较。考虑了三种不同的链路余量：0 dB、3 dB 和 6 dB。
For 50 Gb/s NRZ optical links with a typical 3 dB link margin, MRM transmitters could save more than 60% of
the total power compared to MZM transmitters when both are optimized through co-optimization framework. For microring
modulators, switching to PAM4 modulation could further save around 20% total transmitter power from NRZ
modulation. For all the cases here, we assumed a fixed receiver sensitivity, a fixed datarate and the same technology
constraints from the same silicon photonic platform.
对于链路裕量通常为 3 dB 的 50 Gb/s NRZ 光链路，当两者通过协同优化框架进行优化时，与 MZM 发射机相比，MRM 发射机可以节省 60% 以上的总功率。对于微环调制器，切换到 PAM4 调制可以进一步从 NRZ 调制中节省约 20% 的总发射机功率。对于这里的所有情况，我们假设来自同一硅光子平台的固定接收器灵敏度、固定数据速率和相同的技术约束。
As the datarate increases, the sensitivity of the high-speed optical receivers would drop mainly due to the
bandwidth limitations of the circuit blocks as shown in Fig. 23. In our
optimization framework, we set the receiver sensitivity based on the measurement results of the 65 Gb/s receiver
design in 14 nm FinFet [10]. In addition to receiver sensitivity, the optical
bandwidth of microrings and the transmission line loss also vary as the targeted datarate varies. The minimum E/b for
transmitters using the optimized NRZ-MRM, MS-MZM and TW-MZM are obtained for 32–60 Gb/s, as shown in
Fig. 23. Only NRZ links are considered limited to the available receiver
sensitivity data. It is clear that the optimized microring modulator always consumes much less power than the
optimized Mach-Zehnder modulator for the datarates of interest. This is generally due to the compact size of
microrings. The optimizations at different datarate are also done under the same technology and link constraints.
随着数据速率的增加，高速光接收器的灵敏度会下降，主要是由于电路模块的带宽限制，如图 23 所示 。在我们的优化框架中，我们根据 14 nm FinFet 中 65 Gb/s 接收器设计的测量结果来设置接收器灵敏度 [10]。除了接收器灵敏度外，微环的光带宽和传输线损耗也会随着目标数据速率的变化而变化。使用优化的 NRZ-MRM、MS-MZM 和 TW-MZM 的发射机的最小 E/b 为 32–60 Gb/s，如图 23 所示 。只有 NRZ 链路被认为仅限于可用的接收机灵敏度数据。很明显，对于感兴趣的数据速率，优化的微环调制器消耗的功率总是比优化的 Mach-Zehnder 调制器少得多。这通常是由于微环的紧凑尺寸。不同数据速率的优化也是在相同的技术和链路约束下完成的。
![Fig. 23. - Energy efficiency comparison between optimized NRZ-MRM, MS-MZM and TW-MZM transmitters at different
datarates. The gray line shows the receiver sensitivity vs datarate according to measurement in
[10].](/mediastore/IEEE/content/media/50/8067628/8053768/lin23-2757945-large.gif)
Conclusion 结论
This paper proposes a co-optimization framework for designing high-speed silicon photonic transmitters. The new
framework integrates a simple but accurate compact model for optical phase shifters, analytical models for photonic
modulators and a new Simulink simulation toolbox. It allows us to explore the design trade-offs in depth for microring
and Mach-Zehnder optical transmitters and compare their performances given the same set of technology and link
constraints. Our results show that silicon photonic links, especially microring-based links, have great potential to
provide energy-efficient optical solutions for next-generation inter-rack and intra-rack links.
本文提出了一个用于设计高速硅光子发射器的协优化框架。新框架集成了简单而准确的光学移相器紧凑模型、光子调制器分析模型和新的 Simulink 仿真工具箱。它使我们能够深入探索微环和 Mach-Zehnder 光发射机的设计权衡，并比较它们在相同技术和链路约束下的性能。我们的结果表明，硅光子链路，尤其是基于微环的链路，具有为下一代机架间和机架内链路提供节能光学解决方案的巨大潜力。
Although the paper does not go into circuit implementation details, it provides a useful co-optimization and
verification framework for designing high-speed silicon photonic transmitters in the context of a practical optical
link. This framework can be applicable to most of today's silicon photonic platforms that rely on PN junction
based phase shifters. It can be extended to include receiver designs and thermal tuning designs, and assist the
co-optimization of the next-generation silicon photonic interconnects.
虽然本文没有深入探讨电路实现细节，但它为在实际光链路环境中设计高速硅光子发射器提供了一个有用的协同优化和验证框架。该框架适用于当今大多数依赖基于 PN 结的移相器的硅光子平台。它可以扩展为包括接收器设计和热调谐设计，并协助下一代硅光子互连的协同优化。