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Abstract
Electrical crosstalk severely degrades the performance of Mach-Zehnder modulator (MZM) array. However, conventional crosstalk suppression techniques incur losses of large amounts of chip area for signal isolation, which becomes a bottleneck of high-density electronic-photonic integrated circuit. In this paper, the electrical crosstalk of Traveling-Wave MZM array is originally analyzed with static and dynamic combined crosstalk coefficients. Circuit-level suppression techniques of differential dual-drive electrode schemes with tightly coupled electrode pairs and a virtual ground structure with full-matching termination circuit are investigated for noise-removing effects. Simulation results show that the dynamic electrical crosstalk coefficient between two adjacent modulators is reduced to below 1.5%, which is five times lower than the baseline. The electro-optical link measurements show that the BER is significantly reduced from 1E-3 to 1E-12 for multi-channel operation, which confirms the effectiveness of the crosstalk suppression techniques.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon photonics, which is an emerging technique for electronic-photonic integrated circuits, is compatible with the conventional CMOS process and enables the miniaturization and large integration of optical devices [1–3]. The Mach-Zehnder modulator (MZM), which is one of the important electro-optic modulator structures, has been widely utilized in many optical transceivers due to its wide spectrum ranges and thermal-insensitive property [4]. However, with the increasingly higher bandwidth-density and lower cost requirements of optical transceivers, crosstalk issues between MZMs, such as optical crosstalk [5,6], thermal crosstalk [7,8], and electrical crosstalk [9,10], have become a significant challenge.
The electrical crosstalk among traveling-wave MZM (TWMZM) channels can be attributed to radiated coupling and conducted coupling [11,12]. The radiated coupling (also called contactless coupling) is mainly caused by the coupling of capacitance and inductance, of which the coupling strength is closely related to the separation of MZM channels [13]. On the other hand, conducted coupling crosstalk occurs when the aggressor shares a common return current path, such as the shared ground path, with the victim [14]. In the case of large noise on the shared ground path, conducted coupling crosstalk would aggravate the electrical crosstalk even more serious than radiated coupling [9,15].
A straightforward and effective method to mitigate the crosstalk is to increase the physical isolation, such as by broadening the channel separation [13,15] or adding deep isolating trenches between MZMs [16]. However, it inevitably consumes greater chip area and reduces the channel integration scale. Another way to mitigate the crosstalk is by using the system-level digital pre-compensation technique [17]. Nevertheless, it requires the phase and amplitude information of the crosstalk, which is only available in an In-phase/Quadrature modulation system.
In this paper, we investigate circuit-level crosstalk suppression techniques, which are free from the large overhead area and limited application scenario of previous works. After studying the radiated and conducted coupling crosstalk in the TWMZM array with a new concept of static and dynamic crosstalk coefficients, we validate three crosstalk suppression techniques, including a differential dual-drive electrode scheme with tightly coupled electrode pairs, a virtual ground structure and a full-matching termination circuit. A high-density TWMZM array in IMEC’s silicon photonics technology is developed and demonstrated for crosstalk evaluation. The results show that the above techniques significantly suppress the radiated and conducted coupling crosstalk in the MZM array, thus improving the signal quality in high-speed and high-density optical interconnects.
This paper is organized as follows: Section 2 investigates the fundamental and evaluation methods of the electrical crosstalk between TWMZMs; Section 3 analyzes crosstalk suppression techniques for radiated coupling crosstalk and conducted coupling crosstalk; Section 4 presents a TWMZM array design based on the above crosstalk suppression techniques and provides the crosstalk evaluation results; Section 5 presents the measurement results of the prototype; finally, Section 6 concludes this paper.
2. Static and dynamic analysis of electrical crosstalk between TWMZMs
In this section, we take the case of two adjacent silicon TWMZMs as an example to investigate crosstalk coupling issues. Here, we introduce static and dynamic crosstalk coefficients, instead of traditional near-end and far-end port crosstalk analysis carried by the S parameters [13], to evaluate coupling crosstalk from the internal perspective of MZM. Therefore, the inside crosstalk impact along the traveling-wave electrode can be analyzed section-by-section.
2.1 Radiated coupling induced crosstalk
The silicon TWMZM usually adopts long-length traveling-wave electrodes to reduce the driving voltage and improve the bandwidth [18–20]. In a multi-channel MZM array with millimeter-length level electrodes, signal transmission is always accompanied by the radiated coupling. Figure 1(a) shows the analysis method for radiated coupling induced crosstalk between two parallel traveling-wave electrodes when the aggressor electrode is activated for data transmission with the voltage V0. The equivalent circuit model is given in Fig. 1(b). In this case, the coupling currents, including inductive coupling current (IL) and capacitive coupling current (IC), can be divided into forward and backward parts, respectively, resulting in forward crosstalk voltage (Vf) and backward crosstalk voltage (Vb). As the aggressor signal propagates forward, the magnitude of Vf and Vb will increase with the coupling length. Especially, Vb will reach its saturation value if the total coupling length (Len) is larger than the saturation length, which is equal to half of the product of signal rise time (Tr) and propagation speed (v). Here, Vf and Vb,max are expressed in Eq. (1) and Eq. (2), respectively [12]:
Fig. 1. (a) The proposed analysis method for radiated coupling between two parallel traveling-wave electrodes. (b) The equivalent circuit model of aggressor and victim electrodes. (c) Radiated coupling crosstalk between two TWMZMs. Each electrode of MZM2 (victim) is subject to crosstalk interference from S1 of MZM1 (aggressor).
The total static crosstalk coefficients between MZMs can be calculated with the crosstalk coefficients of each electrode. For example, Fig. 1(c) shows two adjacent MZMs with traveling-wave electrodes connected to the phase shifter to deliver the driving signal. In this case, when the data is transmitted by S1 of MZM1, the radiated coupling occurs between MZM1 and MZM2, thus simultaneously introducing the crosstalk noise to G2 and S2 of MZM2. In this paper, the MZM1 serves as an aggressor and the MZM2 serves as a victim, unless specifically stated. Since the effective modulation voltage of MZM is the voltage difference between the signal and ground electrodes, the backward static crosstalk coefficient between MZMs (kb,MZM) can be expressed as Eq. (3):
where kb,S2-S1 and kb,G2-S1 are the backward crosstalk coefficients of S2 and G2 with the S1 of MZM1, respectively. The forward static crosstalk coefficient (kf,MZM) can be calculated in the same way, which is expressed as Eq. (4): where kf,S2-S1 and kf,G2-S1 are the forward crosstalk coefficients of S2 and G2 with the S1 of MZM1, respectively.2.2 Conducted coupling induced crosstalk
To improve the integration density, a shared ground electrode structure between two adjacent MZMs has been adopted in prior work [21], as shown in Fig. 2(a). However, this induces the conducted coupling crosstalk since the noise on the ground path is transmitted to adjacent channels through the shared common ground path.
Fig. 2. (a) MZM1 and MZM2 share the same ground electrode to reduce channel pitch. (b) The simulation setup for evaluating the near-end crosstalk noise of MZM2. (c) The near-end crosstalk noise of MZM2 with different inductance of input bonding wires.
For a TWMZM, there are two kinds of ground noise: ground bounce noise and reflection noise. Ground bounce noise is voltage noise created by the return current when it flows through non-zero or abrupt impedance of the ground path. Since the distance between the signal electrode and coplanar ground electrode is much smaller than that of the signal electrode and substrate ground plane, the adjacent coplanar ground electrode becomes the main path for the return current. In this case, a large ground bounce noise will be introduced if there is an impedance discontinuity on the ground path, such as the inductance mutation caused by bonding wires at input ground pads. As shown in Fig. 2(b), the coupling relationship between MZM2 and MZM1 is based on a distributed circuit model of a two-channel MZM array. The input and output pads used in the setup are modeled by S parameters extracted with an electromagnetic simulator. The inductance effect of bonding wire is simulated with a lump inductor. Different inductance values represent the bonding wire with different lengths. Both the near-end and far-end are terminated by the resistance Z0 of 50 Ω for signal matching. Besides, the S1 electrode of MZM1 is stimulated by a PRBS source with a data rate of 25 Gbps and a swing of 2 V. Here, the choose of PRBS source is used to simulate the real signal transmission. According to our simulation results (Fig. 2(c)), the conducted coupling crosstalk at the near-end increases linearly as the inductance of input bonding wire increases.
The reflection noise on the ground electrode is caused by the impedance mismatch. For a pair of G and S electrodes with only the differential signal terminated by two series resistors Zodd shown in Fig. 3(a), the common signal (Vcom) will be reflected at the far-end since it is regarded as an open circuit. It is confirmed by the transient simulation results based on the simulation setup shown in Fig. 3(b). The MZM simulated here is a single-drive push-pull MZM shown in Fig. 1(c). The termination resistances Z0 at input and far-end of electrodes are all the 50 Ω. The stimuli signal at the input port is a step signal raising from 0 V to 2 V with the time of 10 ps. The result is shown in Fig. 3(c), where Vc at the far-end has a ring up to 22% because of the common impedance mismatch.
Fig. 3. (a) Conventional termination for G-S electrode pair only with differential matching. (b) The simulation setup for evaluating the impedance mismatch. (c) The step response of differential (Vd) and common (Vc) signals of the far-end.
2.3 Electrical crosstalk evaluation model
For an MZM array with complex structures, such as input and output pads with tapered connections, PN junction loading, and non-ideal terminations, it is difficult to directly calculate the static crosstalk coefficients by using Eqs. (1)-(4). Therefore, to precisely evaluate the crosstalk impacts, we developed a distributed circuit model for the MZM array, as shown in Fig. 4(a), which takes the two channel MZMs as an example. It consists of a pair of pads, an N-stage circuit model of coupled traveling-wave electrodes with PN junction loading, and two termination resistors at the far-end. The pads and electrode segments in each stage are expressed by S parameters, while the PN junction loading and termination are represented by the lumped resistance and capacitance. In this model, the discontinuity of pads, the load effect of PN junctions, the coupling between electrodes, and the mismatch of termination circuits are all taken into account.
Fig. 4. (a) Distributed circuit model of a two-channel MZM array. (b) Distributed electro-optical modulation circuit model of MZM2.
Considering that the TWMZM electro-optic modulation is accompanied by the electrical signal traveling along the electrode, the crosstalk suffered by each section of the electrode will affect the final output optical signal. Therefore, we propose that the dynamic crosstalk coefficient between MZM1 and MZM2 can be calculated by Eq. (5):
where Vxtk2,i is the peak crosstalk noise of the i-th stage of MZM2, and V0,MZM1 is the transmitted signal of MZM1.To further evaluate the performance degradation on the output optical signal incurred by electrical crosstalk, we further characterize MZM2 with a distributed electro-optic modulation circuit, as shown in Fig. 4(b). Here, each stage represents a segment of 100 µm length phase shifter of MZM2, which is driven by the corresponding voltage of the stage shown in Fig. 4(a). The output optical signal is obtained after the optical combiner. By comparing the eye opening and SNR of the eye diagram of the output optical signal with and without electrical crosstalk, we can precisely evaluate the impact of crosstalk on system performance.
3. Crosstalk suppression techniques
3.1 Rejection of radiated coupling crosstalk
To reject the radiated coupling between adjacent MZMs in a silicon TWMZM array, we adopt a differential dual-drive electrode scheme based on tightly coupled upper and lower arms, as shown in Fig. 5(a). Here, the differential signal is transmitted on the signal electrodes S+ and S-, and the ground electrodes provide the DC bias of the PN junction and the return current path of the differential signal. To constrain the radiated coupling, the gap of the G-S pair is designed to be much smaller than the electrode width, which realizes the tightly-coupled design of G-S pair.
Fig. 5. (a) The adopted differential dual-drive electrode scheme for suppressing radiated coupling crosstalk. (b) The mechanism of crosstalk rejection for the upper arm of MZM2.
The mechanism of radiated coupling crosstalk rejection is that when applying the differential signal to the S1 + and S1- electrodes in MZM1, all electrodes of the MZM2 will suffer from two opposite kinds of phase crosstalk noise known as Pos-Xtalk and Neg-Xtalk. In this case, the crosstalk interference effect on each electrode of the MZM2 is weakened because of the opposite noise superposition. For example, as shown in Fig. 5(b), the crosstalk noise on S2 + and G2 + electrodes of the upper arm of the MZM2 are far less than that of the structure without the differential scheme because of the superposition of Pos-Xtalk and Neg-Xtalk. Moreover, S2 + and G2 + are exposed to approximately equal coupling noise because of the tightly coupled G-S pair. As a result, for the PN junction of the upper arm, the crosstalk noise can be cancelled out to a significant degree through the subtraction of S2 + and G2 + . Therefore, the backward crosstalk coefficient between MZM1 and MZM2 (kb,MZM2/MZM1) is calculated by the Eq. (6), while the forward crosstalk coefficient can be calculated through the same way.
To prove the effectiveness of the adopted electrode structure, we perform quasi-static electromagnetic field simulations and calculate the forward (kf) and backward (kb) static crosstalk coefficients between MZMs. We compare the adopted differential dual-drive structure with the conventional single-drive structure illustrated in Fig. 1(c). Here, the gap of G-S pair is set to 30 µm for the single-drive TWMZM [13] and 3.5 µm [21] for our adopted structure, and the electrode width of both structures is set to 30 µm.
As shown in Fig. 6(a) and 6(b), kf,MZM and kb,MZM decrease with the increase of channel pitch for both structures. Compared to the single-drive structure, the adopted structure shows lower kf,MZM (kb,MZM), where the kf,MZM (kb,MZM) drops 8.5% (2.6%) and 1.85% (0.9%) when the channel pitch rises from 200 µm to 500 µm. Especially, kf,MZM and kb,MZM achieve reductions of 6% and 1.7%, respectively, at a channel pitch of 300 µm, which will be adopted as the channel pitch of MZM array in subsequent sections. In conclusion, the differential dual-drive electrode structure exhibits remarkable capability for radiated coupling crosstalk rejection.
Fig. 6. (a) Forward and (b) Backward static crosstalk coefficient between MZM1 and MZM2 for different MZM electrode schemes.
3.2 Reduction of conducted coupling crosstalk
To eliminate the ground bounce noise caused by impedance mutation in the ground path, a virtual ground structure based on the bridged ground electrodes is adopted, i.e., a low-resistance path (M2) is constructed between the ground electrodes of upper and lower arms near the input PADs, as shown in Fig. 7(a). Taking MZM1 as an example, since the driving signals of S1 + and S1- are complementary, the return current and ground bounce noise of the G1 + and G1- are also complementary. As a result, the complementary ground bounce noises can be cancelled out with each other when the G1 + and G1- are connected by the short metal M2. Therefore, it can be regarded as virtual ground.
Fig. 7. (a) Ground electrodes are bridged by short metal M2 to eliminate the opposite phase of ground bounce noises, just like constructing a virtual ground. (b) Full-matching termination topology based on the tee termination circuits that achieves both the differential and common impedance matching simultaneously.
Moreover, to reduce the reflection noise caused by the common impedance mismatch mentioned above, a full-matching termination circuit is also adopted, as shown in Fig. 7(b). Two tee-termination structures, consisting of two Z1 resistors and a Z2 resistor, are connected at the far-end of G-S electrode pairs, where Z1 = Zodd and Z2 = (Zeven - Zodd)/2. Here, Zodd and Zeven are the odd mode and even mode impedance of the G-S pair, respectively. To absorb the opposite common signals of the two arms, the ends of upper arm (P) and lower arm (N) are connected. Since the series combination of two Z1 resistors matches the differential impedance at the end of G-S pair, the differential signal Vdiff is terminated. Meanwhile, the common signal Vcom is terminated simultaneously because the combination of two Z1 resistors in parallel with a Z2 resistor in series matches the common impedance.
Compared with the conventional differential matching structure shown in Fig. 3(a), our adopted full-matching circuit eliminates the ring effect of the common signal with 22% ripple voltage, as shown in Fig. 8(a). Moreover, the far-end voltage of the full-matching structure has a smoother rise edge for both differential and common signals (i.e., the red and blue solid lines are smoother than the dotted ones), which proves the efficient reduction of the reflection.
Fig. 8. (a) Differential and common voltage at the far end of upper arm for both termination structures. (b) Dynamic crosstalk coefficients between MZM1 and MZM2 to validate the effects of full-matching termination (T-term), virtual ground structure (bridged G), and the combined methods (both). (c-d) The near-end and far-end crosstalk results obtained by S-parameter simulation.
To evaluate the effectiveness of the conducted coupling crosstalk reduction, we perform transient crosstalk simulations between MZM1 and MZM2 based on the distributed circuit model developed in Section 2.3. As shown in Fig. 8(b), when the bonding wire inductance is 500 pH, the original scheme without any suppression technique shows a high KMZM of 7.2%; the coefficients KMZM of MZM structures with full-matching termination (T-term) and virtual ground (bridged G) are 5.7% and 2.4%, respectively. It is worth mentioning that the KMZM drops to 1.4% when these two methods are both utilized, and it is always less than 1.5% with a bonding wire inductance ranging from 0 to 800 pH. Based on the simulation, it can be concluded that the suppression effect of virtual ground structure is in a dominant place, whereas the combined methods will provide a better result. Moreover, the S-parameter simulation also shows that full-matching termination and virtual ground structure have obvious crosstalk suppression effect, as shown in Fig. 8(c) and Fig. 8(d). For example, compared with the original design, the structure with full-matching leads to a differential-mode crosstalk (SDD) decrease about 5 dB both at near-end (NEXT) and far-end (FEXT), and the structure with virtual ground exhibits a crosstalk reduction of 20 dB.
4. TWMZM array design and crosstalk evaluation
Based on the mentioned crosstalk suppression techniques in Section 3, we develop a TWMZM array design and perform electro-optical co-simulations to evaluate the crosstalk suppression under different operating channels and data rates. Figure 9(a) shows the developed TWMZM array, in which the MZMs adopt the differential dual-drive electrode scheme, full-matching termination circuit, and virtual ground structure. The channel pitch between MZMs is 300 µm and the length of the phase shifter is 1.5 mm. Meanwhile, a baseline TWMZM array, in which MZMs adopt the same G-S-S-G electrode structure but only with shared G PADs, is utilized for comparison.
Fig. 9. (a) The structure design of TWMZM array with crosstalk suppression techniques. (b) Simulation platform for evaluating crosstalk in MZM array.
We then establish a simulation platform for the output optical eye diagram and BER evaluation, as shown in Fig. 9(b). The platform consists of a two-channel MZM array, two MZM drivers fed with the independent pseudo-random binary sequence (PRBS) sources, an optical attenuator, and an optical receiver. Here, the MZM array is characterized with the distributed modulation circuit demonstrated in Section 2.3. The parasitic resistance and capacitance of PN junction loading are 6.5 Ω·mm and 250 fF/mm, respectively, and the modulation efficiency VπLπ of the phase shifter is 2 V·cm. All these parameters are same as in [21]. We set MZM1 as the aggressor source and MZM2 as the signal channel. By adjusting the output amplitude of Driver-1 to be zero, one, and two times of Driver-2, we can simulate the corresponding 1-channel, 2-channel, and 3-channel operation, respectively.
With the established simulation platform, we performed transient electro-optical co-simulations for both TWMZM array designs. The eye diagram results with different operating channels at the received optical power of -4 dBm are shown in Fig. 10(a). For the baseline, when the operating channels increase from one to three, the eye-opening factor decreases from 0.45 to 0.12 with a reduction of 73.3%, and the SNR decreases from 15.6 dB to 10.4 dB with a reduction of 5.2 dB, as shown at the top of Fig. 10(a). In contrast, our design shows a significant tolerance to the crosstalk noise. As shown at the bottom of Fig. 10(a), when the number of operating channels increases to three, the eye-opening factor and the SNR of the design only decrease by 4.2% and 0.8 dB, respectively. We further calculate the BER from the eye diagrams with the Gaussian algorithm [22]. As shown in Fig. 10(b), the BER of the design in 3-channel operation at 25 Gbps can be reduced lower than 1E-12 when the received optical power is larger than -8.3 dBm. In addition, the power penalty of 3-channel operation is negligible, which is only 0.25 dB and 0.4 dB with BERs equal to 1E-9 and 1E-12, respectively.
Fig. 10. (a) Eye diagrams and (b) BER curves with the different operation channels running at 25 Gbps.
Moreover, our proposed design is also effective with a high data rate. As shown in Fig. 11(a), the eye-opening factor in 3-channel operation at 40 Gbps is still 0.41 and the SNR remains at 15 dB. In contrast, the SNR of the baseline reduces to 8.8 dB and the eye diagram is closed. Th proposed design still guarantees the error-free transmission (BER < 1E-9) at 40 Gbps. As shown in Fig. 11(b), for the received optical power of -3.8 dBm, the BER is 1.2E-11, which is 9 orders of magnitude lower than that of the baseline. In conclusion, the proposed design significantly improves the metrics of eye-opening and BERs for multi-channel and high data rate operation.
5. Prototype experiment results
Based on the crosstalk suppression techniques, we prototyped a silicon photonics transmitter chip (PIC) with a four-channel TWMZM array by using the silicon photonics technology of IMEC, as shown in Fig. 12(a). Then, a test board (Fig. 12(b)), including an MZM driver IC, on-board bias-tee circuits, and the PIC prototype with a vertically coupled optical fiber array, was developed to verify the effectiveness of crosstalk suppression.
Fig. 12. (a) Chip photograph of 4-channel silicon photonic TWMZM array. (b) Photograph of the four-channel optical transmitter test board. (c) Electro-optical link experiment setup.
The electro-optical link experimental setup (Fig. 12(c)) for the proposed transmitter prototype consists of a PRBS generator, an erbium-doped fiber amplifier (EDFA), an optical receiver including a germanium photodetector (PD) and a linear transimpedance amplifier (TIA), as well as the measurement instruments, including the Keysight DCA 86100D and an error detector. We measured the eye diagrams and BERs of the signal channel at the 1-channel, 2-channel, and 3-channel operations with this setup because most crosstalk noise occurs between the immediately adjacent channels [12]. Here, we set MZM2 as the signal channel, while MZM1 and MZM3 are aggressor channels.
Figure 13(a) shows the eye diagram results of the optical receiver, in which the received optical power is fixed at -5 dBm. Compared with the 1-channel operation, the eye diagram deterioration in 2-channel and 3-channel operation is negligible, and the SNR is only reduced by 0.3 dB and 0.4 dB, respectively. Moreover, despite the additional crosstalk introduced by the driver, PCB transmission lines, and bonding wires, the proposed prototype achieves error free transmissions with BERs lower than 1E-12 in a 3-channel operation at 25 Gbps, while the power penalty is only 0.9 dB, as shown in Fig. 13(b). As a result, the adopted techniques have a great capability to suppress electrical crosstalk in the prototype.
Fig. 13. (a) Receiver eye diagrams in 1-channel, 2-channel and 3-channel operations with the received optical power of -5 dBm. (b) BER curves in 1- channel, 2-channel and 3-channel operations with the different received optical powers.
6. Conclusion
In this paper, we investigate the electrical crosstalk issues in the TWMZM array from the internal perspective by using a static and dynamic crosstalk coefficient, which opens up a new way to separately analyze the crosstalk caused by radiated coupling and conducted coupling. Moreover, three circuit-level electrical crosstalk suppression techniques, including the differential dual-drive electrode scheme based on tightly-coupled electrode pairs to suppress the radiated coupling crosstalk, the full-matching termination circuit, and the virtual ground structure to reduce the conducted coupling crosstalk, have been confirmed. Based on the adopted techniques, we develop a high-density design of the TWMZM array. Crosstalk evaluation results show that the dynamic crosstalk coefficient between two adjacent MZMs is reduced to 1.5%, which is five times smaller than that of prior works. The TWMZM array achieves error-free transmissions with BERs of 1.2E-11 for multi-channel operation at 40 Gbps, which is 9 orders less than the baseline. The experimental results of transmitter prototype based on the MZM array show that the power penalty in 3-channel operation at 25 Gbps is only 0.9 dB, which also confirms the effectiveness of the adopted crosstalk suppression techniques. In conclusion, it provides a promising solution for high-density MZM array design with high throughput as well as low crosstalk noise.
Funding
National Key Research and Development Program of China (2018YFB2202303).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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