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# Eye diagram after 2 km. (a) PAM-2 at 30 Gb/s, (b) PAM-2 at 50 Gb/s, (c) PAM-4 at 60 Gb/s, (d) PAM-4 at 80 Gb/s, (e) PAM-4 at 100 Gb/s, and (f) PAM-4 at 112 Gb/s.

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We present a silicon photonic traveling-wave Mach–Zehnder modulator operating near 1550 nm with a 3-dB bandwidth of 35 GHz. A detailed analysis of traveling-wave electrode impedance, microwave loss, and phase velocity is presented. Small- and large-signal characterization of the device validates the design methodology. We further investigate the pe...

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**Context 1**

... length by 5 GHz [12]. Fig. 8(d) demonstrates the extracted characteristic impedance of the TW-MZM from S-parameters under different bias voltages. The measured characteristic impedance has excel- lent agreement with the calculated results presented in Fig. 3(b), with less than 4% variations from the calculated values. The predicted impedance dispersion at higher frequencies is clearly observed in the measured results; however, over the 50 GHz frequency range, the impedance only varies by 2 . Moreover the EE 6.4 dB and the EO 3 dB bandwidths shown are very close, indicating that the performance of the modulator is not limited by velocity mismatch [12]; this validates the design methodology outlined in Section 2. The observed EE S 21 value of 21 GHz is lower than the calculated value of 25 GHz. This can be due to the neglected radiation losses and higher actual surface resistances. Next, we examine the large signal performance of the modulator using an Agilent wide band oscilloscope. At the input of the modulator a tunable laser with maximum output power of 14 dBm is used. The modulator is operated at the quadrature point using the tunable laser. At this wavelength, the modulated signal power is À 3.8 dBm and a 3 V DC bias voltage is applied using a RF probe to reverse bias the PN junctions. A 10 31 À 1 pseudorandom bit sequence (PRBS) signal generated by a SHF pulse pattern generator is amplified using a wide band microwave amplifier and attenuated by passive RF attenuators to obtain a 4.6 V pp driving signal This signal is then applied to the modulator using a high-frequency RF probe. Fig. 9 shows eye diagrams for 30, 40, 50, and 55 Gb/s with extinction ratios of 11.58, 7.59, 5.35, and 4.30 and SNR of 10.31, 6.55, 4.32, and 3.18, respectively. Eye diagrams, shown in Fig. 9, provide a visual qualitative presentation of the performance of the device. In order to quantitatively evaluate the performance of the modulator, bit error rate (BER) test of the system is performed. To do this, the input laser power to the modulator is set to 14.5 dBm. The output of the modulator is fed to an AC coupled Picometrix PD þ TIA receiver which is then connected to a SHF bit error tester. An error-free ð BER G 10 À 12 Þ operation up to 45 Gb/s is obtained with received power of À 3.5 dBm, limited by the bandwidth of the PD þ TIA receiver. The small optical insertion loss, together with the high optical extinction ratio of the transmission spectra and the high E-O bandwidth make this modulator an ideal transmitter for multilevel modulation formats. In this section we compare the performance of the modulator with PAM-2 and PAM-4 modulation formats over different lengths of fiber to reach a 100G Ethernet transport rate. At the input of the modulator, the same tunable laser with 14 dBm output power is used. The RF driving signal is generated using an AC coupled 8-bit Digital to Analog Converter (DAC) operating at 70 GSa/s. Use of a DAC allows us to apply digital signal processing (DSP) at the transmitter side. Four processes are applied to the waveform. First the symbol stream is up- sampled from one sample per symbol to 70 = R B , where ð R B Þ is the desired symbol rate. Next a root raised cosine pulse shaping filter is applied. Thirdly, to equalize the spacing between modulated optical power levels, the nonlinearity of the power transfer function of the TW-MZM is com- pensated by applying an arcsin function to the waveform. Finally the frequency response of DAC, RF amplifier and TW-MZM cascade is pre-compensated by applying an inverse response function. An amplifier is used to amplify the DAC output to 2.2 V pp which is then applied to the modulator using RF probes. The modulated signal is propagated through 1, 2, and 5 km of Corning SMF 28e þ fiber. The PD þ TIA is used for opto-electrical (O-E) conversion before an Agilent real time oscilloscope serving as an 8-bit Analog to Digital converter (ADC) sampling at 80 GSa/s. At the receiver side, the digital signal processing is performed offline. First the signal is resampled from ADC rate of 80 GSa/s to twice the symbol rate R B . Next a matched filter defined at 2 samples per symbol is applied to the signal. The stream of samples is then fil- tered by a linear FIR filter. To recover the transmitter's clock and to apply symbol decision at the correct sampling instant, a digital clock recovery algorithm is implemented [7]. The output symbols are then used for error counting and to calculate the signal to noise ratio (SNR) and quality factor of the system. The DSP applied at the transmitter and receiver sides is discussed in detail in [7]. Fig. 10 illustrates the block diagram of the transmission system explained above. We present the system performance qualitatively using eye diagrams and quantitatively by measuring BER and SNR. BER measurement is done by error counting. For PAM-N formats, SNR is defined as the ratio of the average signal power over average noise power. Fig. 11 shows eye diagrams for PAM-2 and PAM-4 formats at different baud rate after propagating through 2 km of fiber. In currently deployed metro and long haul fiber optic transmission systems, Forward Error Correction (FEC) is used to significantly lower the BER. Based on OT4U standard [2], a client payload of 100 Gb/s is transmitted at line rate of 112 Gb/s, which includes 6.7% (FEC) over head. A BER measurement below the pre-BER threshold of 4 : 4 Â 10 À 3 results in an output BER G 10 À 15 , viewed as error free transmission in the context of optical transmission. In this paper we assume FEC encoding and decoding at the transmitter and receiver side. All eye diagrams are obtained after receiver DSP. A successful 100 Gb/s PAM-4 post-FEC error-free transmission through 2 km of fiber is achieved in all cases. After 5 km, for the same bit rate of fiber the pre-FEC BER is measured at 4 Â 10 À 3 which is slightly lower than FEC threshold of 4 : 4 Â 10 À 3 . For PAM-2, a maximum of 64 Gb/s transmission was achieved at pre- FEC BER of 1 : 31 Â 10 À 4 which was limited by DAC's bandwidth. Fig. 12 illustrates SNR and BER at various bit rates. We observe that, as the bit rate increases, the SNR and BER performance of the system degrades. The DAC has a 3 dB bandwidth of 15 GHz; however, using Nyquist sampling theory, the DAC can generate frequencies up to 35 GHz when sampling at 70 GSa/s. At higher bit rates the signal has higher frequency content. After digital compensation of the frequency response of the DAC, a signal of larger spectral content will have reduced V pp swing out of the DAC, worsening the RF signal quality. At the receiver side, the same large bandwidth signal will integrate more inband noise power, further deteriorating the SNR. The cumulative effect of transmitter and receiver signal worsening as the symbol rate increases is observed in Fig. 12. The low insertion loss of the device allowed the full operation of the modulator without the need for optical amplifiers, which further differentiates this work from other modulators presented in the literature [5], [7], [12]. In this paper, we present the design and characterization of a low voltage silicon photonic traveling wave modulator. A thorough analysis of the implemented traveling wave electrode is presented. It is shown that using a CPS geometry, it is possible to minimize the mismatch between the microwave phase velocity and optical group velocity by careful design. As a result, the main bandwidth limiting factor is determined to be the microwave loss. A 3 dB electro-optic bandwidth of 35 GHz under 3 V DC bias is demonstrated. We further investigate the performance of the device in a short reach transmission system. By applying digital signal processing on transmitter and the receiver side we obtain a successful 112 Gb/s transmission of 4 level pulse amplitude modulation over 5 km of SMF below pre-FEC hard decision threshold of 4 : 4 Â 10 À 3 . We present an alternative solution to 4 Â 25 Gb/s WDM transmission systems. We demonstrate that higher modulation formats such as PAM-4, together with digital signal processing can be used to achieve 100 Gb/s transmission on a single wavelength. The authors gratefully acknowledge CMC Microsystems for enabling fabrication and providing access to simulation and CAD ...

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## Citations

... Hence, the performances of the silicon photonic modulators based on CPS and CPW are limited. The reported bandwidths of silicon optoelectronic modulators based on these two electrode configurations are both generally less than 40 GHz [10][11][12][13][14][15]. For example, At a bias voltage of 0.5V, for a 2mm modulator based on CPS has a relatively low bandwidth of only 10G and a relative low Vπ of 2V [16]. ...

... A 2mm long modulator using CPW electrodes can achieve a bandwidth of 20G and a Vπ of 6.4 V [17]. The 4.2mm-long modulator using CPS and segmented PN junction has a high bandwidth of 35G and a Vπ up to 7.5V [14]. Despite substantial attempts to improve the performance of silicon modulators, such as shortening the device length to 1mm [7] and implementing an impedance mismatch [6], the electro-optic (EO) bandwidth of modulators based on CPS and CPW has been limited to a maximum value of 46 GHz [6]. ...

... The modulator's small signal electro-optic response as a function of velocity mismatch and total microwave loss can be calculated by [14]: ...

The t-rail electrode is an effective method to enhance the silicon optoelectronic modulator's performance. 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.

... Microwave losses consist of conductive, dielectric and radiation losses, where radiation losses are negligible in our TL geometry. Conductive losses have a strong frequency dependency and become the dominant loss factor for broadband operation [26], hence conductive losses should be minimized as much as possible. Hence, the width of the signal line in a coplanar-TL needs to be increased. ...

A monolithically integrated electronic-photonic Mach-Zehnder modulator is presented, incorporating electronic linear drivers along with photonic components. Electro-optical 3 dB & 6 dB bandwidths of 24 GHz and 34 GHz, respectively, were measured. The measurements are in good agreement with electronic-photonic post-layout simulation results and verify the design methodology. A full π phase shift was achieved by applying a differential input voltage of
V
π = 420 mV to the driver input, effectively decreasing the required modulation voltage by a factor of approximately 10.

... Hence, the performances of the silicon photonic modulators based on CPS and CPW are limited. The reported bandwidths of silicon optoelectronic modulators based on these two electrode configurations are both generally less than 40 GHz [9][10][11][12][13][14]. ...

... The circuit model maintains an accuracy within 2% when compared to the HFSS simulation. The modulator's small signal electro-optic response as a function of velocity mismatch and total microwave loss can be calculated by [13]: The response of the EO modulator, as calculated by the use of HFSS and the equivalent circuit model, is depicted in Fig. 7. The increase in bias voltage given to the PN junction leads to an observed increase in the bandwidth of the electro-optic modulator, as demonstrated by both calculation approaches. ...

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.

... Because the calculations of OCU are all passive, its power consumption mainly comes from the data loading and photodetection process. Schemes of a photonics modulator with small driving voltage [61][62][63] have been proposed recently to provide low power consumption; further, integrated photodetectors [64,65] are also investigated with negligible energy consumed. Therefore, the total power of an OCU with equivalent kernel size of H can be calculated as Eq. ...

Ever-growing deep-learning technologies are making revolutionary changes for modern life. However, conventional computing architectures are designed to process sequential and digital programs but are burdened with performing massive parallel and adaptive deep-learning applications. Photonic integrated circuits provide an efficient approach to mitigate bandwidth limitations and the power-wall brought on by its electronic counterparts, showing great potential in ultrafast and energy-free high-performance computation. Here, we propose an optical computing architecture enabled by on-chip diffraction to implement convolutional acceleration, termed “optical convolution unit” (OCU). We demonstrate that any real-valued convolution kernels can be exploited by the OCU with a prominent computational throughput boosting via the concept of structral reparameterization. With the OCU as the fundamental unit, we build an optical convolutional neural network (oCNN) to implement two popular deep learning tasks: classification and regression. For classification, Fashion Modified National Institute of Standards and Technology (Fashion-MNIST) and Canadian Institute for Advanced Research (CIFAR-4) data sets are tested with accuracies of 91.63% and 86.25%, respectively. For regression, we build an optical denoising convolutional neural network to handle Gaussian noise in gray-scale images with noise level σ =10, 15, and 20, resulting in clean images with an average peak signal-to-noise ratio (PSNR) of 31.70, 29.39, and 27.72 dB, respectively. The proposed OCU presents remarkable performance of low energy consumption and high information density due to its fully passive nature and compact footprint, providing a parallel while lightweight solution for future compute-in-memory architecture to handle high dimensional tensors in deep learning.

... Because the calculations of OCU are all passive, its power consumption mainly comes from the data loading and photodetection process. Schemes of photonics modulator with small driving voltage [57,58,59] have been proposed recently to provide low power consumption, and integrated photodetectors [60,61] are also investigated with negligible energy consumed. Therefore, the total power of an OCU with equivalent kernel size of H can be calculated as Eq. ...

The ever-growing deep learning technologies are making revolutionary changes for modern life. However, conventional computing architectures are designed to process sequential and digital programs, being extremely burdened with performing massive parallel and adaptive deep learning applications. Photonic integrated circuits provide an efficient approach to mitigate bandwidth limitations and power-wall brought by its electronic counterparts, showing great potential in ultrafast and energy-free high-performance computing. Here, we propose an optical computing architecture enabled by on-chip diffraction to implement convolutional acceleration, termed optical convolution unit (OCU). We demonstrate that any real-valued convolution kernels can be exploited by OCU with a prominent computational throughput boosting via the concept of structral re-parameterization. With OCU as the fundamental unit, we build an optical convolutional neural network (oCNN) to implement two popular deep learning tasks: classification and regression. For classification, Fashion-MNIST and CIFAR-4 datasets are tested with accuracy of 91.63% and 86.25%, respectively. For regression, we build an optical denoising convolutional neural network (oDnCNN) to handle Gaussian noise in gray scale images with noise level {\sigma} = 10, 15, 20, resulting clean images with average PSNR of 31.70dB, 29.39dB and 27.72dB, respectively. The proposed OCU presents remarkable performance of low energy consumption and high information density due to its fully passive nature and compact footprint, providing a highly parallel while lightweight solution for future computing architecture to handle high dimensional tensors in deep learning.

... Thus, PAM4 has been standardized for short reach interconnects up to 10 km because of its simplicity and lower power requirements compared to the other modulation formats [1]. PAM modulation can be achieved through using directly modulated lasers (DMLs) [2], externally modulated lasers (EMLs) [3], or external optical modulators [4][5][6][7][8][9]. The main material systems used in fabricating these modulators are lithium niobite (LiNbO3), indium phosphide (InP), gallium arsenide (GaAs), and silicon (Si), out of which silicon is the only material system that is fully compatible with the complementary metal oxide semiconductor (CMOS) processing. ...

... Thus, silicon photonics modulators are anticipated to dominate the market because of the low fabrication costs and scalable production [10,11]. Si-photonic modulators have a very slow roll-off frequency response, allowing the operation at high symbol rates [4,5,7,9,12]. Moreover, the advancement on the electronics side is pushing the limits of what can be achieved with Si-photonics. ...

... It has a 4 mm phase-shifter at a fill factor of 85%, and it is terminated on-chip with a 50 Ω highly doped Si resistor. The TW electrodes are designed such that a good velocity matching between the optical signal and the RF signal is established at a characteristic impedance of 50 Ω [7]. The measured DC Vπ is 5 V at 0 V reverse bias, corresponding to an inverse phase-shifting efficiency (VπL) of 2 V.cm. ...

In this work, IBM, CMC, AMF, and McGill University work together to verify a simplified packaging scheme for Si-photonic devices based on incorporating IBM’s polymer photonic interface into AMF’s Si-photonic fabrication process flow. The proposed procedure is used in packaging an O-band Si-photonic traveling wave Mach-Zehnder modulator (TW-MZM) yielding a fiber-to-fiber insertion loss of 16.5 dB and 16 GHz 3-dB bandwidth. Employing the packaged module without RF or optical amplification, we demonstrate the transmission of 28 Gbaud PAM4 (net 53 Gbps) over 2 km of SSMF using a linear feed-forward equalizer below the 2.4×10
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup>
KP4-FEC BER threshold with 750 mVpp, and under the 3.8×10
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup>
HD-FEC threshold at 500 mVpp. Besides, we transmit 36 Gbaud (net 67 Gbps) under HD-FEC at 830 mVpp. Operating with an RF driver; we transmit 70 Gbaud PAM4 below HD-FEC, which corresponds to a net rate of 131 Gbps. The achieved transmission performance highlights the potential of the proposed packaging scheme.

... Therefore, it affects the performance in terms of FOM 2 according to Eq. (7). Initially, the maximal doping concentration possible was considered [28], lowering the doping levels results in higher heat conductivity and lower electrical conductivity which both provide better results. In addition, when attenuation is taken into account as well, lower doping level produce less attenuation. ...

Thermo-optic phase shifter (TOPS) based on doped silicon (Si) heaters is commonly used to compensate for device structure imbalance of high-speed Mach-Zehnder modulator (MZM) due to fabrication errors. However, this functionality required more electrical power for setting the MZM to be active around the linear transfer function at π/2 phase shift. To solve this issue, we proposed an optimal design of doped Si heaters using the standard commercial 220 nm Si layer in rib waveguide structure which can improve the electrical energy efficiency and reduce optical losses. Numerical simulations and optimizations were carried out on the key parameters, heater locations, doping concentration, etching depth, and laser wavelength drift. Results show that the optimal design has a low power consumption of 19.1 mW for obtaining a phase shift of π with a good time constant of 2.47 µs and low optical losses of 2.37 dB/cm at the 1550 nm operated wavelength. Thus, an excellent figure of merit (FOM) of 47.2 mWµs is obtained for the optimal design. Also, the proposed device has good stability to the laser wavelength drift effect in the C-band range. This TOPS can be very useful for improving the transmitter system performances based on high-speed MZM technology.

... It consists of two child MZMs placed in each arm of a parent MZI. The design of the child MZMs is based on the single drive series push-pull traveling wave MZM described in [22]. The modulators are realized with lateral pn-junction phase shifters using the iSiPP50G silicon photonics platform of IMEC [23]. ...

An integrated photonics based scheme for radio-frequency self-interference cancellation is proposed and demonstrated. It is achieved using a dual-parallel Mach-Zehnder modulator that eliminates the interference signal in the optical domain. The output of the modulator is a carrier suppressed double-sideband waveform that contains only the signal of interest. Finally, the signal of interest is recovered by combining the modulator output with a local optical carrier and detecting it at a high-speed photodetector. We present a detailed theoretical analysis and derive the optimal condition for self-interference cancellation for small modulation indices. The modulators were designed and fabricated on IMEC’s Silicon-on-Insulator iSiPP50G platform. Using this technique, we experimentally obtain a cancellation depth of 30 dB and a signal to interference ratio of 25 dB for frequencies up to 20 GHz, limited only by the equipment used. This is the first demonstration of self-interference cancellation on a silicon photonics platform and a further expansion of the functionalities offered by integrated microwave photonics.

... The designed chip has been fabricated in a multi-project wafer run, on a silicon-on-insulator (SOI) wafer (see Supplement 1). Figure 3(a) shows the structure of the balanced Mach-Zehnder modulator (MZM). The modulator is a 3-mm long, single drive series push-pull SiP travellingwave MZM operating near 1550 nm with a DC reverse bias of 3 V [15]. The details of the MZM design are provided in Supplement 1. Figure 3(b) illustrates the measured electro-optic (EO) response of the modulator. ...

Precise and agile detection of radio frequency (RF) signals over an ultra-wide frequency range is a key functionality in modern communication, radar, and surveillance systems, as well as for radio astronomy and laboratory testing. However, current microwave solutions are inadequate for achieving the needed high performance in a chip-scale format, with the desired reduced cost, size, weight, and power. Photonics-based technologies have been identified as a potential solution but the need to compensate for the inherent noise of the involved laser sources have prevented on-chip realization of wideband RF signal detection systems. Here, we report an approach for ultra-wide range, highly-accurate detection of RF signals using a conceptually novel feed-forward laser’s noise cancelling architecture integrated on chip. The technique is applied to realization of an RF scanning receiver as well as a complete radar transceiver integrated on a CMOS-compatible silicon-photonics chip, offering an unprecedented selectivity > 80 dB, spectral resolution < 1 kHz, and tunability in the full 0.5–35 GHz range. The reported work represents a significant step towards the development of integrated system-on-chip platforms for signal detection, analysis and processing in cognitive communication and radar network applications.

... For the 1.5 mm lumped MZM studied in this work, the corresponding f τ of 22.9 GHz should be investigated for the 25 Gbaud PAM4 signals in question. As a judge of its potential impact, Fig. 5 plots the magnitude squared of the frequency response resulting from (9). Notably, the roll-off is virtually identical over this range of frequencies to that of a fourth-order Bessel filter with the same 3 dB bandwidth. ...

The use of electrical precompensation for high-speed operation of lumped MZMs is demonstrated for 50 Gb/s PAM4 modulation through experiment and simulation. An accurate equivalent circuit model is fitted to S11 measurements and then used to analyse design trade-offs in terms of system performance, energy consumption and drive voltage requirements. If precompensation is not used, careful selection of source resistance with respect to electrode and packaging inductance is shown to be crucial for high-speed modulation. Increasing the electrode inductance is shown to be beneficial as it introduces inductive peaking, which allows optimum performance with a higher source impedance. Furthermore, combining precompensation with a slight inductive peaking and optimised source resistance is demonstrated to reduce drive voltage requirements and further reduce the energy dissipated in the equivalent circuit.