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(a) TW-MZM top-view schematic, (b) SPP-MZM cross-section. BOX: buried oxide, M1/M2: metal layers and (c) SPP-MZM layout
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We present the design and characterization of O-band and C-band silicon photonic (SiP) traveling wave Mach-Zehnder modulators (TW-MZM) allowing 220 Gbps/ net rate operation. The designed modulators show over 45 GHz 3-dB E-O bandwidth with a single-segment design. In the O-band, with simple linear feed forward equalization, we transmit net 203 (200)...
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... this section, we describe the design and characterization of the TW-MZMs. The C-band and O-band modulator designs both adopt the series push-pull (SPP) configuration with a layout shown in Fig. 1, where the two PN junctions of each arm are connected back-to-back and a DC bias is applied to the common N++ region. This doubles the junction resistance and halves the junction capacitance [22]. The fabrication process admits a RF electrode design with two metal layers that reduces microwave attenuation. For each of the two optical ...
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... (LUT) [30], where a varied number of bits from 13 to 19 are mapped to a block of 10 symbols and provides a tunable information bit per symbol (IBPS) from 1.8 to 2.4 bits/symbol assuming 20% FEC overhead. Since the weight of the symbol sequences are set as the sequence power, the PS-PAM8 symbols approach the Maxwell-Boltzmann distribution. In Fig. 10, we show the NGMI of PS-PAM8 signals with varied IBPS at three different symbol rates at B2B. Note that only linear equalization is used at the receiver. We sweep the IBPS from 2 to 2.5 bits/symbol, which means for 90 Gbaud PS-PAM8 signals, we can tune the net throughput from 180 Gbps to 225 Gbps with a step of 9 Gbps. The histogram of ...
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... the 90 Gbaud signal for interface rates beyond 225 Gbps. Thus, at each desired throughput, the symbol rate and IBPS need to be appropriately determined. Next, we try to find the IBPS that achieves the highest NGMI at a target net data rate for our system after 2 km propagation with linear and non-linear equalization. The blue and red curves in Fig. 11 show the NGMI values at different symbol rates and corresponding SEs for net 210 Gbps and net 220 Gbps, respectively. We can see that PS-PAM8 with an IBPS of 2.4 bits/symbol delivers the highest NGMI for these net rates for both linear and non-linear equalization. Lower IBPS (2.3) at a high symbol rate is not a good choice because of ...
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... 10 km PAM transmission results 10 km transmission is important for LR (long reach) datacenter interconnects and Fig. 12 shows the BER performance over 10 km of SMF with different modulation formats and receiver VNLE. We can see that using PAM6 format, we can transmit net 200 Gbps (interface rate of 214 Gbps) below the HD-FEC threshold. In Fig. 13, we show the achievable NGMI for PAM8 format with linear and nonlinear equalization schemes. The 2 km curve ...
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... 10 km PAM transmission results 10 km transmission is important for LR (long reach) datacenter interconnects and Fig. 12 shows the BER performance over 10 km of SMF with different modulation formats and receiver VNLE. We can see that using PAM6 format, we can transmit net 200 Gbps (interface rate of 214 Gbps) below the HD-FEC threshold. In Fig. 13, we show the achievable NGMI for PAM8 format with linear and nonlinear equalization schemes. The 2 km curve with linear equalization is also added here for comparison. The maximum achievable throughput after 10 km of SMF is 216 Gbps, achieved with 86 Gbaud PAM8 format and VNLE. Like 2 km results, the NGMI gain with VNLE is not ...
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... schemes. The 2 km curve with linear equalization is also added here for comparison. The maximum achievable throughput after 10 km of SMF is 216 Gbps, achieved with 86 Gbaud PAM8 format and VNLE. Like 2 km results, the NGMI gain with VNLE is not significant, meaning the nonlinear degradation is not that severe for 10 km transmission as well. Fig. 13 also shows that compared to 2 km transmission, the results are slightly worse for the 10 km case. The effect of dispersion is negligible over 10 km of SMF at our wavelength of operation (1302.8 nm). Therefore, the degradation comes mostly from the reduced OSNR of the received signal. As mentioned earlier, the launch power into the ...
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... 13 also shows that compared to 2 km transmission, the results are slightly worse for the 10 km case. The effect of dispersion is negligible over 10 km of SMF at our wavelength of operation (1302.8 nm). Therefore, the degradation comes mostly from the reduced OSNR of the received signal. ...
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... we focus on the shorter MZM with a phase shifter length of 1.5 mm. This modulator has a 3 dB E-O bandwidth of over 50 GHz and a lower optical propagation loss, but this comes at the expense of a higher V. The optimized reverse bias voltage for this modulator is found to be 0.5 V. From Table II and Fig. 14, we find that despite the higher E-O bandwidth, the shorter MZM shows worse transmission performance compared to the longer one for all formats. Fig. 14 plots the NGMI versus interface rate with this MZM at B2B and after 2 km propagation with a VNLE. The shorter MZM achieves 270 Gbps PAM8 (net 225 Gbps) at the B2B scenario and after 2 ...
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... of over 50 GHz and a lower optical propagation loss, but this comes at the expense of a higher V. The optimized reverse bias voltage for this modulator is found to be 0.5 V. From Table II and Fig. 14, we find that despite the higher E-O bandwidth, the shorter MZM shows worse transmission performance compared to the longer one for all formats. Fig. 14 plots the NGMI versus interface rate with this MZM at B2B and after 2 km propagation with a VNLE. The shorter MZM achieves 270 Gbps PAM8 (net 225 Gbps) at the B2B scenario and after 2 km, the highest interface rate that is above the NGMI threshold is 264 Gbps, corresponding to a throughput of 220 Gbps. As the roll-off factor chosen for ...
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... an important factor. In this section, we present the transmission results using the C-band modulator. As shown is Table I, the C-band modulator has a much higher V as compared to the O-band design. Based on the previous explanations, we choose the modulator with the longer phase shifter length (2.5 mm) for a better phase shifter efficiency. In Fig. 15, we show the BER of PAM4 and PAM6 format and NGMI of PAM8 signaling at different interface rates. The B2B BER for 100 Gbaud signaling is found to be 8.5e-3, which is worse than the O-band designs because of its higher V. Net 200 Gbps below the HD-FEC threshold is still achievable using 86 Gbaud PAM6 at B2B. After 500 m the maximum ...
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... format. For PAM8 signaling, at B2B maximum 264 Gbps (net 220 Gbps) is achievable above the NGMI threshold and for a 500 m transmission, it is reduced to 258 Gbps (net 216 Gbps). For 2 km reach, the signal is heavily affected due to dispersion induced power fading which is clear from the received electrical spectrum of the 85 Gbaud signal shown in Fig. 16. 72 Gbaud PAM8, which is equivalent to a net 180 Gbps signal can be transmitted over 2 km of SMF using receiver VNLE at the SD-FEC threshold. In this manuscript, we report the small-signal, and largesignal characterization of high bandwidth SiP MZM modulators. It is found that besides the importance of a high E-O bandwidth, the ...
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... Optical routers and multiplexers show high potential for transferring data between optical nodes with speeds matching the high-speed data transmission through optical fibers. Optical routers and splitters [3] based on integrated optical devices are usually based on photonic components such as multimode interferometers (MMIs) [4][5][6], Mach Zender interferometers [7,8], directional couplers [9,10], and ring resonators [11,12]. ...
The demand on fast and high-bandwidth data transmission is in continuous increase. These demands are highly dependent on optical signal manipulation, including switching, modulation, and routing. We demonstrate a two-port silicon optical router based on the multimode interferometer (MMI) configuration. The same MMI structure was used for both inward and backward waveguiding to reduce the total length of the device. A phase shifter consisting of two ring-like waveguides made of silicon p-n junctions was used to introduce the phase shift needed for optical routing upon voltage application. Two designs for the MMI optical router were studied: Firstly, a conventional MMI with a crosstalk ratio of 15.1 dB was investigated. Finally, an angled MMI reaching a crosstalk ratio of 18.2 dB at a wavelength of 1.55 μm was investigated.
... , there is a heightened emphasis on elevating single-wavelength data rates. However, achieving a single-lane data rate of 200 Gbit/s and beyond presents challenges for IM-DD optical interconnects [14][15][16], particularly when utilizing commercial components with limited bandwidth. Furthermore, a critical concern for IM-DD systems is the phenomenon of chromatic dispersion-induced power fading [17]. ...
Bandwidth limitation in optoelectrical components and the chromatic dispersion-induced power fading phenomenon cause severe inter-symbol interference (ISI) in high-speed intensity modulation and direct detection (IM-DD) optical interconnects. While the equalizer implemented in the receiver's digital signal processing procedure can mitigate ISI, it also inevitably enhances the noise located in the decayed frequency region, known as equalization-enhanced colored noise (EECN). Additionally, the nonlinear impairments of the modulator and photodetector also deteriorate the performance of the IM-DD system, especially for high-order modulation formats. In this work, we propose a gradient-descent noise whitening (GD-NW) algorithm to address EECN and extend it by introducing nonlinear kernels to simultaneously mitigate EECN and nonlinear impairments. The proposed algorithms are compared with conventional counterparts in terms of the achievable baud rate and the receiver optical power sensitivity. As a proof-of-concept experiment, we validate the principles of the proposed algorithms by successfully transmitting 360-GBd on-off-keying (OOK) and 180-GBd 4-level pulse-amplitude-modulation (PAM-4) signals in the back-to-back case under a 62-GHz brick-wall bandwidth limitation. 280-GBd OOK and 150-GBd PAM-4 transmissions are also demonstrated over 1-km standard single-mode fiber with a bit error rate below 7% hard-decision forward error correction aided by the proposed approach.
... Among the three modulation orders studied, M = 4 provides the best RS for all values of f 3dB,mod and V pp studied. This finding is consistent with [55], [56], which found that 4-PAM outperforms 6-PAM at the KP4-FEC BER threshold. It is important to emphasize that this finding is specific to the use of an error correction code with pre-FEC BER of 1.8 × 10 −4 . ...
Intra-data center links are subject to transmission impairments that pose challenges for efficient scaling of per- wavelength data rates beyond 100 Gb/s. Limited electrical and optical component bandwidths, limited data converter resolution, and direct detection induce significant signal-dependent distortion, degrading receiver sensitivity (RS) and chromatic dispersion tolerance. In this paper, we present a geometric shaping (GS) scheme that optimizes transmitted intensity levels based on symbol-error statistics observed at the receiver. The proposed GS scheme adjusts these levels to achieve substantially equal symbol-error probabilities at all decision thresholds. The scheme enables the levels most affected by signal-dependent distortion to be detected with the same reliability as other levels, thereby increasing the effectiveness of linear or nonlinear equalization techniques. This can be exploited to improve RS and extend transmission distance for a fixed equalization scheme or, alternatively, to reduce the complexity of signal processing needed to achieve a target RS or transmission distance. For example, in 200 Gb/s PAM links, GS and 21-tap linear equalization achieves RS and reach similar to uniform level spacing and Volterra nonlinear equalization with 21 linear and 3 second-order taps.
... Increasing a modulator's bandwidth is most commonly achieved by changing its electrode structure. Two traditional traveling wave electrodes (TWE) are coplanar waveguides (CPW) and coplanar strip lines (CPS) [3][4][5][6]. [7,8]. Changing CPS and CPW electrode parameters allows silicon optical modulators to have variable performance. ...
... Despite substantial attempts to improve the performance of silicon modulators, such as shortening the device length to 1mm [6] and device optimization [5], the electro-optic (EO) bandwidth has been limited to a maximum value of 46 GHz. The use of T-rail slow wave electrodes (TSWE) has been empirically demonstrated to enhance the refractive index of microwaves, thereby leading to an expansion in the bandwidth of optical modulators [7,[15][16][17][18][19]. ...
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.
... We demonstrate the at EO S 21 curves in different wavelengths of 1544.9, 1545.8, and 1546.8 nm using a 110-GHzbandwidth lightwave component analyzer (LCA) (Fig. 3b). The measured at EO responses were considerably better than those reported for advanced chip-scale dielectric or semiconductor modulators with a 3-dB roll-off 14,41 . We compare the state-of-the-art performance of chip-scale dielectric and semiconductor MZMs (Fig. 3c). ...
High-speed electro-optic modulators are key components in modern communication networks and various applications that require chip-scale modulation with large bandwidth, high modulation efficiency, and compact footprint. However, fundamental trade-offs make it challenging to achieve these metrics simultaneously, and thus new methodologies must be explored. To this end, we present the first demonstration of a Mach-Zehnder modulator harnessing topological slow-light waveguides and capacitively loaded slow-wave electrodes on silicon-nitride-loaded lithium niobate on an insulator platform. Owing to the slow-light effect in the one-dimensional topological waveguide, the increased light-matter interaction time and group index significantly improve the modulation efficiency. With the 1-mm-length modulation section, a record low half-wave voltage length product V π ∙L of 0.21 V∙cm is obtained, which is one order of magnitude smaller than that of conventional thin film lithium niobate Mach-Zehnder modulators. Slow-wave electrodes are employed for electro-optic velocity and impedance matching, enabling an unprecedented bandwidth of 110 GHz without roll-off. The achieved bandwidth-efficiency ratio of 524 GHz/V/cm is among the highest reported for all-dielectric and semiconductor modulators. Four- and eight-level pulse amplitude modulation signals of up to 240 and 300 Gbps, respectively, have been generated using the topological modulator. Our topological modulator provides ultra-large bandwidth, ultra-high efficiency, and a compact solution for next-generation electro-optic systems.
... We assume that the offset-bias driving voltage swings between V 0 + V pp and V 0 − V pp in the lower arm. Although producing chirp [41], the single-arm-drive operation would not suffer from the dispersion penalty for short-reach applications and can avoid halving the voltage dropped on the arm when compared to the single-drive push-pull configuration [28,[59][60][61]. In addition, although moving from the dual-drive push-pull [19][20][21] to the single-arm drive configuration cuts the phase difference in halves for a constant driving voltage, it also halves the power consumption [60]. ...
The realization of a high dynamic extinction ratio (ER) and optical modulation amplitude (OMA) while keeping the optical and radio-frequency (RF) signal losses low is a major issue for carrier-depletion Mach–Zehnder (MZ) silicon optical modulators. However, there is still room to improve modulator performance by applying the information gained from recent advanced testing technology to the modulator design. In this study, the extrinsic OMA (E-OMA) enhancement effect, which was discovered through the evaluation process and by revisiting the physics of the MZ interferometer (MZI), is investigated. First, we raise the issue of a periodic ripple observed on an MZI spectrum that has previously been overlooked but can affect modulator performance and attribute it to optical resonance between the multi-mode interferometers that compose an MZI. We show that, although having the effect of reducing the dynamic ER in the push-pull regime, as demonstrated experimentally, this resonance can take them beyond the realm of modulation efficiency and generate an E-OMA enhancement effect in the single-arm-drive regime without involving any optical and RF signal losses. By comparing two modulator structures that generate resonance internally, we successfully identify the factors that are responsible for increasing the E-OMA enhancement effect. We reveal that theoretically the OMA can easily be increased by 0.45 dB or more.
... Moreover, series push-pull (SPP) driving configuration can minimize RF losses by reducing the junction capacitance by half and doubling the junction resistance. In addition, a slight impedance mismatch can be implemented between the electrode and the termination to further extend the MZM bandwidth 19 . ...
... Alternatively, by optimizing the doping profile and the optical and the RF waveguides design, in 20 a 6-dB modulation bandwidth of 50 GHz at a 2 V reverse bias and a V π of 6.3 V was demonstrated. Further improvements were presented in 19 , where an impedance mismatch between the traveling wave electrode and the on-chip termination was deliberately introduced, achieving a 3-dB modulation of 46 GHz with a V π of 7.6 V and an insertion losses (IL) of 8.4 dB . As can be perceived from the aforementioned works, larger modulation bandwidth is achieved at the expense of higher power consumption and IL. ...
As an essential block in optical communication systems, silicon (Si) Mach-Zehnder modulators (MZMs) are approaching the limits of possible performance for high-speed applications. However, due to a large number of design parameters and the complex simulation of these devices, achieving high-performance configuration employing conventional optimization methods result in prohibitively long times and use of resources. Here, we propose a design methodology based on artificial neural networks and heuristic optimization that significantly reduces the complexity of the optimization process. First, we implemented a deep neural network model to substitute the 3D electromagnetic simulation of a Si-based MZM, whereas subsequently, this model is used to estimate the figure of merit within the heuristic optimizer, which, in our case, is the differential evolution algorithm. By applying this method to CMOS-compatible MZMs, we find new optimized configurations in terms of electro-optical bandwidth, insertion loss, and half-wave voltage. In particular, we achieve configurations of MZMs with a [Formula: see text] bandwidth and a driving voltage of [Formula: see text], or, alternatively, [Formula: see text] with a driving voltage of [Formula: see text]. Furthermore, the faster simulation allowed optimizing MZM subject to different constraints, which permits us to explore the possible performance boundary of this type of MZMs.
... In recent years, many 200 Gb/s/lane IM/DD transmissions have been demonstrated using different types of enabling broadband optoelectronic components [4]. On the one hand, external modulator-based transmitters such as silicon-photonic [5,6], plasmonic [7][8][9], and thin-film Lithium Niobate-(TFLN) [10][11][12][13] Mach-Zehnder modulators (MZM) or micro-ring modulators (MRM) [14][15][16] have shown excellent performance in terms of bandwidth and modulation linearity for high baud rate operation, however, requiring high-power external light sources to operate. On the other hand, monolithically integrated transmitters such as electro-absorption modulated lasers (EML) [17][18][19][20][21][22][23][24][25] and directly modulated lasers (DML) [26][27][28][29][30][31] with a potentially smaller footprint and lower power consumption, also show promising characteristics in supporting over 200 Gb/s/lane transmissions. ...
We experimentally demonstrate an O-band single-lane 200 Gb/s intensity modulation direct detection (IM/DD) transmission system using a low-chirp, broadband, and high-power directly modulated laser (DML). The employed laser is an isolator-free packaged module with over 65-GHz modulation bandwidth enabled by a distributed feedback plus passive waveguide reflection (DFB+R) design. We transmit high baud rate signals over 20-km standard single-mode fiber (SSMF) without using any optical amplifiers and demodulate them with reasonably low-complexity digital equalizers. We generate and detect up to 170 Gbaud non-return-to-zero on-off-keying (NRZ-OOK), 112 Gbaud 4-level pulse amplitude modulation (PAM4), and 100 Gbaud PAM6 in the optical back-to-back configuration. After transmission over the 20-km optical-amplifier-free SSMF link, up to 150 Gbaud NRZ-OOK, 106 Gbaud PAM4, and 80 Gbaud PAM6 signals are successfully received and demodulated, achieving bit error rate (BER) performance below the 6.25%-overhead hard-decision (HD) forward-error-correction code (FEC) limit. The demonstrated results show the possibility of meeting the strict requirements towards the development of 200Gb/s/lane IM/DD technologies, targeting 800Gb/s and 1.6Tb/s LR applications.
... With the continuously growing popularity of various bandwidthhungry services like video streaming, artificial intelligence, cloud computing, and the Internet of things, the bandwidth demand for current datacenter interconnect systems has been constantly increasing. Since datacenter interconnect systems are particularly sensitive to cost, power consumption, and the footprint, an intensity modulation and direct detection (IM/DD) solution is still prioritized for datacenter interconnects within a 40-km transmission distance using standard single-mode fiber (SSMF) [1,2]. To meet the demand for highspeed optical interconnects, next-generation ethernet links aim at 800-gigabit ethernet (GE) or 1.6-terabit ethernet (TE), in which a 200-Gbit/s/λ IM/DD link is a promising solution [1][2][3]. ...
... Since datacenter interconnect systems are particularly sensitive to cost, power consumption, and the footprint, an intensity modulation and direct detection (IM/DD) solution is still prioritized for datacenter interconnects within a 40-km transmission distance using standard single-mode fiber (SSMF) [1,2]. To meet the demand for highspeed optical interconnects, next-generation ethernet links aim at 800-gigabit ethernet (GE) or 1.6-terabit ethernet (TE), in which a 200-Gbit/s/λ IM/DD link is a promising solution [1][2][3]. Beyond-200-Gbit/s/λ double-sideband (DSB) IM/DD transmissions with simple structures have been studied using pulse amplitude modulation (PAM) and orthogonal frequency division multiplexing (OFDM)/discrete multi-tone (DMT) signals [1][2][3]. Compared with PAM, OFDM features simple frequency-domain equalization (FDE), flexible modulation, and high tolerance to chromatic dispersion (CD) [4][5][6], which has also been widely studied in a passive optical network (PON) [5], radio-over-fiber (RoF) [6], and beyond-5G and 6G fronthaul (B5G/6G FH) [7]. ...
... To meet the demand for highspeed optical interconnects, next-generation ethernet links aim at 800-gigabit ethernet (GE) or 1.6-terabit ethernet (TE), in which a 200-Gbit/s/λ IM/DD link is a promising solution [1][2][3]. Beyond-200-Gbit/s/λ double-sideband (DSB) IM/DD transmissions with simple structures have been studied using pulse amplitude modulation (PAM) and orthogonal frequency division multiplexing (OFDM)/discrete multi-tone (DMT) signals [1][2][3]. Compared with PAM, OFDM features simple frequency-domain equalization (FDE), flexible modulation, and high tolerance to chromatic dispersion (CD) [4][5][6], which has also been widely studied in a passive optical network (PON) [5], radio-over-fiber (RoF) [6], and beyond-5G and 6G fronthaul (B5G/6G FH) [7]. ...
A receive-diversity-aided power-fading compensation (RDA-PFC) scheme is proposed and demonstrated to eliminate the chromatic dispersion (CD)-induced power fading for C-band double-sideband (DSB) intensity modulation and direct detection (IM/DD) orthogonal frequency division multiplexing (OFDM) systems. By combining the responses before and after a dispersive element using a maximal-ratio combining (MRC) algorithm, the CD-induced power fading dips within the signal bandwidth of around 50 GHz can be effectively compensated for, which results in an up to 17.6-dB signal-to-noise ratio (SNR) improvement for the fading subcarriers after transmission over 10 km of standard single-mode fiber (SSMF). Using the 16 quadrature amplitude modulation (QAM) format, a diversity receiver with the proposed RDA-PFC scheme can support 170.6-Gbit/s OFDM signal transmission over a 10-km SSMF and reduces the bit error rate (BER) by more than an order of magnitude compared with a conventional receiver. Moreover, 208.1-Gbit/s adaptive bit and power loading OFDM signal transmission over a 10-km SSMF is realized by the proposed RDA-PFC scheme, which improves the capacity by 15.3% compared with the case without RDA-PFC at a BER of 3.8 × 10⁻³. The proposed RDA-PFC scheme shows great potential in CD-induced power-fading compensation for high-speed IM/DD OFDM systems.
... Moreover, series push-pull (SPP) driving configuration can minimize RF losses by reducing the junction capacitance by half and doubling the junction resistance. In addition, a slight impedance mismatch can be implemented between the electrode and the termination to further extend the MZM bandwidth 19 . ...
... Alternatively, by optimizing the doping profile and the optical and the RF waveguides design, in 20 a 6-dB modulation bandwidth of 50 GHz at a 2 V reverse bias and a V π of 6.3 V was demonstrated. Further improvements were presented in 19 , where an impedance mismatch between the traveling wave electrode and the on-chip termination was deliberately introduced, achieving a 3-dB modulation of 46 GHz with a V π of 7.6 V and an insertion losses (IL) of 8.4 dB. As can be perceived from the aforementioned works, larger modulation bandwidth is achieved at the expense of higher power consumption and IL. ...
As an essential block in optical communication systems, silicon (Si) Mach-Zehnder modulators (MZMs) are approaching the limits of possible performance for high-speed applications. However, due to a large number of design parameters and the complex simulation of these devices, achieving high-performance configuration employing conventional optimization methods result in prohibitively long times and use of resources. Here, we propose a design methodology based on artificial neural networks and heuristic optimization that significantly reduces the complexity of the optimization process. First, we implemented a deep neural network model to substitute the 3D electromagnetic simulation of a Si-based MZM, whereas subsequently, this model is used to estimate the figure of merit within the heuristic optimizer, which, in our case, is the differential evolution algorithm. By applying this method to CMOS-compatible MZMs, we find new optimized configurations in terms of electro-optical bandwidth, insertion loss, and half-wave voltage. In particular, we achieve configurations of MZMs with a 40 GHz bandwidth and a driving voltage of 6.25 V, or, alternatively, 47.5 GHz with a driving voltage of 8 V. Furthermore, the faster simulation allowed optimizing MZM subject to different constraints, which permits us to explore the possible performance boundary of this type of MZMs.
