## Abstract

In this paper, transmission performances of directly modulated laser (DML), electro-absorption modulated laser (EML) and Mach-Zehnder modulator (MZM) are experimentally compared in dispersion-unmanaged high-speed transmission systems with digital signal processing (DSP). We show that, although the DML based transmitter is often believed to be less favorable in C-band high-speed transmissions, it exhibits superior performance over the other two transmitters when either linear or nonlinear digital signal processing is adopted. By theoretical and experimental analysis, we reveal that the superiority of DML can be attributed to the compensation of fiber power fading by its inherent adiabatic chirp as well as the mitigation of chirp induced distortions by the linear or nonlinear equalization. Experimental results of 56Gb/s 4-level pulse amplitude modulation (PAM4) signals under various equalization schemes including linear feedforward equalization, simplified nonlinear Volterra equalization and partial response signaling are presented. Particularly, we show that for DML a 40km transmission distance can be achieved to satisfy the extended range-4 (ER4) Ethernet interconnect using a simplified Volterra equalizer, and a 20km transmission distance can be supported using a linear equalizer. In contrast, for MZM and EML, the achievable transmission distances are respectively 20km and 15km using the Volterra equalizer, respectively, and 15km and 10km using linear equalizer, respectively. Moreover, we show that even using the combination of the Volterra equalizer and partial response signaling, the transmission distances of MZM and EML based systems are limited to 30km and 20km.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

In recent years, transmissions for short-haul networks, including datacenter interconnects, mobile fronthaul/backhaul, metro-access, and so forth, have attracted wide-spread interests from both industry and academia [1–3]. Unlike long-haul networks, these short-haul networks are extremely sensitive to cost due to the enormous scale of deployments. Therefore, optical transceivers at low cost are required in these applications, and intensity modulation and direct detection (IM-DD) has been adopted as the mainstream technology [4–6]. In IM-DD systems, directly modulated laser (DML), electro-absorption modulated laser (EML) and Mach-Zehnder modulator (MZM) are major options to build a transmitter [7,8].

Generally, if these three transmitters are operated in links with negligible chromatic dispersion (CD), e.g. at O-band or C-band with dispersion compensation modules, DML is more preferable because of its low cost and small footprint advantages [9–11]. However, in a link at the C-band with high CD, the choice becomes unobvious. On the one hand, since for DML electrical signal is directly applied to its laser cavity, it experiences a larger frequency chirp than EML and MZM, which in the presence of CD can induce severe nonlinear distortions and cause serious degradations on transmission performance [12–14]. This phenomenon is even worse for high-data-rate links as these links can be more sensitive to noise. From this point of view, DML would lead to inferior performance relative to EML and MZM. As a consequence, today it is commonly believed that DML is not preferable in C-band high-speed transmissions in comparison to EML and MZM. On the other hand, in spite of the distortions induced by the frequency chirp, the adiabatic chirp of DML also causes frequency modulation (FM) of optical signals, which is able to fundamentally mitigate the first power fading dip incurred by CD [15,16]. As a result, DML leads to a higher non-faded bandwidth than EML and MZM, which is expected to have a better transmission performance.

Previously, some early works in the 1990’s have demonstrated that the DML can support a transmission distance of more than 100km, but with a data rate of less than 10Gb/s [17]. Recently, some discrete works show that the adoption of DML might lead to a better performance than EML and MZM in high-speed dispersion-unmanaged transmission links with digital signal processing (DSP) [18–22]. For example, in [18] and [19] researchers have demonstrated 26km and 30km transmission of 56Gb/s PAM4 signals using an MZM and EML. Meanwhile, in [21] and [22] we have demonstrated 43km and 15km C-band IM-DD transmissions of 56Gb/s and 100Gb/s PAM4 signals using a DML, respectively. Nevertheless, to the best of our knowledge, there is no direct experimental comparison of the three transmitter schemes in high-speed dispersion-unmanaged fiber links until now, especially in the presence of DSP which is regarded as a key enabler in modern optical communications.

In this paper, we theoretically and experimentally compare the transmission performances of DML, EML and MZM based transmitters in dispersion-unmanaged high-speed systems with DSP. First, a study on the fiber power fading and linear/nonlinear distortions of the three transmitters is presented. We show that the EML and MZM based systems are mainly limited by the power fading effect, whereas the DML based system, with $>\sqrt{2}$higher non-faded bandwidth relative to MZM and positive-chirped EML, is mainly limited by the nonlinear distortions induced the frequency chirp. Accordingly, viable equalization schemes to compensate these distortions are discussed, which includes linear equalizer, simplified nonlinear Volterra equalizer and partial response signaling. Afterwards, experimental comparisons are provided, which include parametric optimizations and evaluation of BER performances under various equalization schemes. We show that 56Gb/s PAM4 signals generated by a DML can achieve a 40km transmission distance to satisfy the extended range-4 (ER4) Ethernet interconnect using a simplified nonlinear Volterra equalizer, and a 20km distance using a linear equalizer. In contrast, for MZM and EML, the achievable transmission distances are respectively 20km and 15km using the Volterra equalizer, and 15km and 10km using the linear equalizer. Moreover, we show that even using the combination of the Volterra equalizer and partial response signaling, the transmission distances of MZM and EML based systems are limited within 30km and 20km.

The remainder of this paper is organized as follows. In Section 2, theoretical analysis is presented and viable DSPs are described. In Section 3, experimental comparison is conducted. Parametric optimizations and evaluation of BER performances under various DSP configurations are provided. In Section 4, other aspects in the application of these transmitters are discussed. Finally, we summarize this work.

## 2. Analysis of DML, EML and MZM based dispersion-unmanaged transmissions

#### 2.1 Theoretical comparison of fiber channel response

In IM-DD transmissions, since the modulated optical signal is double sideband, the two sidebands will experience different phase variations due to CD. Consequently, at certain frequencies, the two sidebands have opposite phases, thereby producing fiber power fading after square-law direct-detection. According to [23], the fiber response for IM-DD transmission is given by

^{2}/km at 1550nm for standard single mode fiber (SSMF).$f$and$L$are signal frequency and fiber length, respectively.

From Eq. (1), we know that ${H}_{IM\leftrightarrow PM}$plays a key role to characterize the fiber response with different transmitters. First, for MZM in a pull-push operation, the optical signal is purely intensity modulated with no phase modulation. In this case, no frequency chirp exists and${H}_{IM\leftrightarrow PM}$is 0. Then, for EML, due to the dependence of refractive index on the applied electrical signal, the change in the optical intensity is accompanied by the phase modulation (PM), which causes transient frequency chirp. The transient chirp is represented by$\Delta f=\frac{\alpha}{4\pi}(\frac{1}{P(t)}\frac{dP(t)}{dt})$, where$P(t)$is the output optical power, and $\alpha $is the linewidth enhancement factor which is exactly${H}_{IM\leftrightarrow PM}$, i.e${H}_{IM\leftrightarrow PM}=\alpha $. Lastly, for DML, the frequency chirp not only includes the phase modulation by the transient chirp as in EML, but also the frequency modulation (FM) by the adiabatic chirp. As a result, the frequency chirp of DML is represented by

Next, we study the frequency responses using the transfer functions in Table 1. Figure 1(a) plots the responses of a 20km fiber link in the three transmission systems, and in each of them we observe several frequency dips. For MZM, it is apparent that the first frequency dip emerges when $\theta $ is $\frac{\pi}{2}$, i.e.

Accordingly, we can calculate that the first frequency dip of a 20km fiber in MZM based transmission is at 13.6GHz.For EML, the first frequency dip occurs when $\theta $ is $\frac{\pi}{2}-{\mathrm{tan}}^{-1}\alpha $, i.e.

Typically, $\alpha $of EML varies depending on the applied bias voltage on the electro-absorption modulator (EAM) as will be illustrated later. When$\alpha $is positive ${B}_{EML}$ is reduced, and when $\alpha $is negative${B}_{EML}$ is enhanced. Here in Fig. 1(a), the response of the EML based system is plotted when$\alpha $is 0.5, which is also the value at the bias voltage in the following experiments. Accordingly, we can calculate that the first frequency dip of the EML based system emerges at 11.4GHz, which can also be observed in Fig. 1(a).For DML, the responses caused by the transient chirp and adiabatic chirp are respectively noted as ${H}_{tst}$ and ${H}_{adb}$in Table 1, and we plot them in Fig. 1(b). If ${H}_{tst}$and ${H}_{adb}$ are regarded independently, two phenomena can be observed in Fig. 1(b): (1) with the transient chirp only, the response curve is similar as that of MZM and EML, but the first frequency dip is at a much lower frequency (~6.1GHz) due to a larger positive value of $\alpha $; (2) with the adiabatic chirp only, the first frequency dip is at 0GHz. However, the overall response in Fig. 1(b) shows that the two frequency dips can be compensated when the transient and adiabatic chirp interact with each other. Specifically, both the 6.1GHz dip in${H}_{tst}$and the 0GHz dip in${H}_{adb}$disappear in the overall response. Nevertheless, the second dip in${H}_{tst}$and the second dip in${H}_{adb}$still remain, and they are the major factors influencing the fiber response of the DML based system. Since ${\mathrm{tan}}^{-1}\alpha $ is smaller than$\frac{\pi}{2}$, the second dip in ${H}_{tst}$ is always higher than the second dip in${H}_{adb}$. Therefore, we have

#### 2.2 CD-induced Distortions

In order to find out the desired DSP for the performance comparison, it is necessary to investigate the distortions in the MZM, EML and DML based transmissions. Here, we only focus on the chirp and CD induced distortions, and ignore electrical/optical components nonlinearity, signal-to-signal beating noise and fiber nonlinearity.

For MZM, frequency chirp does not exist, and the direct detected signal is purely distorted by the power fading effect as mentioned earlier. Similar to the inter-symbol interference (ISI) caused by other system bandwidth limitations, this effect can be partially addressed by linear equalizers.

For EML, in addition to the power fading effect, it also suffers from nonlinear distortion, which is mainly caused by the dependence of chirp parameter$\alpha $ on the applied electrical voltage: a higher instantaneous voltage produces a larger$\alpha $. To show the variation of$\alpha $, we experimentally measure the small signal response of a 40km fiber link under various static EAM bias voltages using a vector network analyzer. With the first frequency dips of these responses, we calculate the chirp factor$\alpha $ according to the transfer function in Table 1, and plot them in Fig. 2(a). The EAM modulation curve is also plotted. It is easy to figure out that, if we consider each of the three eyes of PAM4 as small signals, the three eyes will have different chirp factor$\alpha $. Therefore, they experience different power fading effects. Consequently, the EML-based multi-level signal after CD shows an unequally-spaced eye diagram as will be illustrated in Section 3.2, which are essentially nonlinear distortions.

For DML, the interplay between the adiabatic chirp and CD is also a nonlinear distortion. Previously, such distortions have been theoretically analyzed to be composite second-order distortions [12]. Figure 2(b) gives an intuitive illustration of such distortions. The directly modulated PAM symbols with different intensity levels have different optical frequencies, and thus they travel with different velocities due to CD. Therefore, the eye diagram after fiber transmission manifests an eye skewing effect. For this reason, PAM symbols with different intensity levels have different inter-symbol interference (ISI) contributions to their adjacent symbols, which is a nonlinear distortion. In addition, the overlap of adjacent symbols due to CD also causes nonlinear beating noise after direct detection, which is also a nonlinear distortion.

From above analysis, we summarize the main limiting factors of the three transmitters in Table 2. For both MZM and EML, the main limiting factor is the bandwidth insufficiency caused by power fading. Also, the nonlinear distortion caused by the non-uniform transient chirp effect can further worsen the performance of EML. For DML, the main limiting factor is the chirp-induced nonlinear distortions, and the fiber power fading is not a major issue compared with DML and EML.

#### 2.3 Digital signal processing schemes

Next, we discuss the desired DSP for the three systems. First, to address the power fading effect, one of the simplest methods is to use a linear feedforward equalizer (FFE) to compensate the frequency response. Nevertheless, when CD is too large such that the frequency response of the fiber channel is too poor, it is impossible to use an FFE to compensate the sharp cut-off dips incurred in MZM or EML based transmissions. One efficient solution is to adopt the bandwidth-saving partial response (PR) signaling [24], which has been actively studied in recent years [25,26]. In this method, controllable ISI is introduced by shaping the duration of each signal pulse from one symbol period to multiple periods, which can compress the signal bandwidth by multiple folds. In this work, we consider a particular version of PR signaling – duobinary (DB)-PAM4, in which the duration of each PAM4 symbol is shaped to two symbol periods, resulting in 7-level signals. To implement DB-PAM4, we can directly recover the PAM4 sequence by a subtraction operation at the receiver side, i.e.${a}_{k}={c}_{k}-{a}_{k-1}$, where${a}_{k}$ is the current recovered PAM4 symbol, ${a}_{k-1}$ is the preceding recovered PAM4 symbol and ${c}_{k}$ is the received 7-level DB-PAM4 symbol. However, error propagation is unavoidable in this method, since the decoding procedure requires the information of former symbols. To address this problem, an alternative method is to adopt precoding at the transmitter side, which is carried out as

where ${b}_{k}$ is the PAM4 symbol after precoding. After transmission and post-DSP, the received signal ${c}_{k}$ is naturally shaped to 7-level DB-PAM4, which is then recovered to PAM4 bySecond, to mitigate the nonlinear distortions, Volterra equalization is widely adopted [27]. Conventionally, if we only consider the first and second order kernels, the Volterra equalizer is given by

## 3. Experiments

In this section, we present the experimental comparisons with different equalization schemes and various transmission distances. The setup and parameter optimization of the experiment are firstly given. Then, we measure and compare the fiber channel responses of the three IM-DD systems. After that, we compare the achievable transmission distance with different equalization schemes as discussed in Section 2.1, which includes linear FFE, and simplified nonlinear Volterra equalizer, as well as their PR signaling counterparts. Note that since the 3dB bandwidth of the employed DML is only 16.8GHz while that of the EML and MZM is more than 30GHz, we choose a data rate of 56Gb/s to make transceiver bandwidth not a limiting factor.

#### 3.1 Experimental setup

Figure 3 depicts the experimental setup. At the transmitter, the original PAM4 symbols are generated offline with periodic 21504 bits. For the DB-PAM4 transmission case, PR signaling pre-coding is conducted according to Eq. (7). Then, the signal is pulse-shaped by a raised cosine filter with a roll off factor of 1 at two samples per symbol (sps), and fractionally up-sampled by 5/4 to match the 70GS/s sampling rate of the arbitrary waveform generator (AWG) and generate a data rate of 56Gb/s. After that, pre-emphasis is adopted to compensate the bandwidth insufficiency caused by the AWG and electrical amplifier (EA). Before the data sequence is loaded into the AWG, an arcsine pre-distortion is adopted to compensate the sine modulation curve of MZM. For EML and DML, we optimize the RF parameters which will be discussed in Section 3.2. After the AWG, the electrical signal is amplified by an EA (SHF806E) and attenuated by an electrical attenuator, before being applied to modulate the three electrical-to-optical devices. The detailed parameters of the three devices are listed in Table 3. Note that in this study we only focus on distributed feedback Bragg (DFB) DML, although some other options such as vertical cavity surface emitting laser (VCSEL) and Fabry-Parot laser diode (FPLD) are also in the category of direct modulation. After transmission over standard single mode fiber (SSMF), the optical signal is first attenuated by a variable optical attenuator (VOA), and then detected using a PIN-TIA (trans-impedance amplifier) (Picometrix, 35GHz bandwidth). A real-time oscilloscope (RTO) with a sampling rate of 160GS/s is employed to digitize the received signal. In the receiver-side offline processing, we adopt either a linear FFE or a nonlinear Volterra equalizer both operated at 2 sps to compensate the distortions. Note that in the DB-PAM4 transmission case, the FFE and Volterra equalizer are designed to recover the signal to DB-PAM4 with 7 levels, which is further decoded back to PAM4 by the subsequent modulo-4 PR decoding according to Eq. (8). Finally, BER is calculated.

#### 3.2 Parameter optimization

In order to achieve a better transmission performance, the parameters of DML and EML are optimized. For DML, both the bias (output optical power) and Vpp are optimized because they are key parameters to influence the frequency chirp according to Eq. (3). For EML, only the EAM bias is optimized with fixed Vpp.

First, we optimize the DML based transmission system. BER performances with a linear FFE under various Vpp and output power are measured in Fig. 4. Figure 4(a) plots the influence of Vpp in the back-to-back (BtB) case and 20km case, in which the DML output optical power are respectively 10dBm and 11dBm, and the received optical power into PIN-TIA are fixed at −2dBm. For the BtB case, it is clear that the increase of Vpp always reduces the BER in this case, which is mainly attributed to the increased extinction ratio. On the other hand, for the 20km case, the BER first decreases and then increases as the Vpp increases from 1.1V to 1.5V. As a result, the optimal Vpp is found to be ~1.25V. The increase in the BER from 1.25V to 1.5V Vpp is caused by the increased adiabatic chirp as inferred from Eq. (3), which can aggravate the nonlinear distortions and induce severer eye skewing effect as shown in Fig. 4(a). For other transmission distances, the optimal Vpp are listed in Table 3.

Then, Fig. 4(b) shows the influence of DML output power in the BtB case and 20km case, in which the Vpp are respectively set as 1.6V and 1.25V, and the received optical power into PIN-TIA is −2dBm. For the BtB case, the BER is reduced with the increase of the output power, which is caused by the saturation effect of DML. However, for the 20km case, the BER first decreases and then increases when the output power increases from 10dBm to 13dBm. The decrease part is due to the suppressed transient chirp according to Eq. (3), while the increase part is due to the saturation effect. As a result, the optimal output power for 20km is 11dBm. For the other transmission distances, the optimal output power is listed in Table 3. Note that although the extinction ratio is sacrificed due to the increased output power and decreased Vpp, the performance can be improved after transmission, attributed to the FM-to-amplitude modulation (AM) conversion caused by the interaction between the adiabatic chirp and CD [29].

Next, we optimize the bias voltage of EML. As plotted in Fig. 5, we measure the BER under various bias voltages for BtB and 10km cases, where the received powers are respectively set as −10dBm and −2dBm. For the BtB case, it is shown that the BER increases as we increase the negative bias voltage from 1.1V to 1.4V. This is because the center of the linear modulation region of EML is at ~1.15V as shown in Fig. 2(a). Increasing the bias higher than this voltage causes clipping effect, which makes the eye diagram unequally-spaced as shown in Fig. (5). In contrast, the 10km transmission case exhibits a completely different phenomenon. When the bias voltage is at the linear modulation point of ~1.1V, the eye diagram is unequally-spaced. This is because that the EAM has a non-uniform chirp feature depending on the applied electrical signal as discussed in Fig. 2(a). In particular, the upper eye with a lower negative voltage has positive frequency chirp, whereas the lower eye with a higher negative voltage has negative frequency chirp. When such signal experiences positive CD, the upper eye will suffer from severer power fading effect than the lower eye, thereby resulting in unequally-spaced eye diagrams. In contrast, as we increase the bias voltage, the nonlinear modulation curve and the non-uniform frequency chirp counteract with each other, which helps generate equally-spaced eye diagrams as shown in Fig. 5, meanwhile reducing the BER. Consequently, we adopt 1.35V as the optimal bias voltage. Note that this voltage is used for all distances here, because we find optimization in other distances does not give significant improvement.

#### 3.3 Fiber power fading comparison

To verify the theoretical analysis presented in Section 2, we experimentally measure the frequency responses of a 20km fiber using offline data and plot them in Fig. 6. For MZM, the first power fading dip is shown to be at 13~14GHz, which is consistent with the theoretical results in Fig. 1(a). This also indicates that the MZM we adopt here is in push-pull operation with nearly zero frequency chirp. For EML, the frequency of the first fading dip is at ~11GHz. Such decreased bandwidth in comparison to MZM is because that the EML biased at 1.35V has a positive chirp factor $\alpha $ of ~0.5, which shifts the dip to a lower frequency in comparison to the MZM-based system according to Eq. (5). For DML, the response curve is shown to be quite different from that of MZM and EML. On the one hand, the fading dip appears at ~20GHz, which is more than $\sqrt{2}$ times of MZM as analyzed in Section 2. In this case, the power fading of the DML based system is no longer the dominant limiting factor in comparison to the EML and MZM based systems. On the other hand, owing to the adiabatic chirp, the frequency response of the DML system presents a rising trend from zero frequency to ~15GHz, which is also consistent with the theoretical analysis and expected to provide a performance gain.

#### 3.4 Performance comparison using a linear equalizer

Figure 7 shows BER performances using the linear equalizer. The parameters of the three transmitters are chosen according to Table 3, and the tap number of the FFE is set to 101, which is sufficient to achieve an optimal performance for each case. The eye diagrams under the BtB case and the maximum distance case are also inserted. For DML, BER performances under distances from 0km to 43km are plotted in Fig. 7(a). Obviously, as the transmission distance increases, the BER gets higher, and the maximum distance under the HD-FEC limit of 3.8 × 10^{−3} is found to be 20km. Also, compared with the BtB case, the eye diagram of the 20km case manifests a skewing effect, which is caused by the interaction between the adiabatic chirp and CD as previously discussed. On the other hand, for EML and MZM, the maximum distances are respectively found to be 10km and 15km, which are much shorter than DML. The performance inferiority of the EML and MZM systems is reasonable if we recall their fiber channel responses, where the first frequency dips are respectively located at ~20GHz, ~16GHz and ~19GHz for the DML, EML and MZM systems at 20km, 10km and 15km, respectively. This result also reveals that the power fading effect introduced in the EML/MZM based systems causes a far more serious problem than the nonlinear distortions introduced in the DML based system. The required tap number of the three transmitters are also analyzed in Fig. 7(e) when the transmission distance is 20km. It is shown that when the FFE has more than 31 taps, the BER of all the three systems reaches a floor, and the DML based system always shows more than an order of magnitude BER superiority. Therefore, the equalization complexity of the corresponding systems can be reasonably low.

#### 3.5 Performance comparison using a nonlinear equalizer

Then, we compare the BER performance using the simplified Volterra equalizer of Eq. (10), in which the tap number of the first and second order kernels are respectively set to 101 and 19, and the second order kernels with product terms larger than 5 intervals are truncated ($P=5$). The results are plotted in Fig. 8. For DML, a significant performance improvement is observed in comparison to the results with the linear equalizer in Fig. 7(a). Particularly, the maximum achievable distance under the HD-FEC can be extended to ~40km, which can satisfy the ER4 requirement in the Ethernet standard [30]. Also, it is observed that the eye skewing effect which exists when using a linear equalizer is well suppressed. However, for EML and MZM, the improvement is shown to be much less than DML, and the achievable distance are respectively 15km and 20km, which are only half of the DML based system. The reason of such a significant improvement in the DML based system is that the main limiting factor of the DML based system is the nonlinear distortions caused by the interaction between frequency chirp and CD, which can be mostly mitigated by the nonlinear equalizer, whereas the main limiting factor of the EML and MZM based systems is the power fading effect, which cannot be overcome by the nonlinear equalizer. At last, because the 2nd order kernels occupy a major complexity of the equalizer, the BER versus the 2nd order tap number under 20km distance is plotted in Fig. 8(e). It is observed that the DML shows a significant improvement over the other two transmitters even when the 2nd order tap number is only 5.

#### 3.6 Performance of MZM and EML using partial response signaling

Since the main limiting factor of the EML and MZM based systems is the power fading rather than the nonlinear distortions, it is beneficial to study their performances when using bandwidth-saving PR signaling (DB-PAM4) in order to provide a fairer comparison. Here the results of PR signaling with both the linear and nonlinear equalizers are presented. Figure 9 plots the BER performance with the linear FFE. For EML and MZM, it is observed that the maximum supported distances are respectively 15km and 20km, which shows an increase in comparison to the condition without PR signaling in Figs. 7(b) and 7(c). Nevertheless, if these results are compared with DML without PR signaling in Fig. 7(a), they still show inferior performances. In particular, the BER of DML using only a linear equalizer is less than 10^{−3}, whereas the BER of EML and MZM using the combination of PR signaling and linear equalizer are still larger than 10^{−3}. In addition, by comparing Fig. 9 and Fig. 7(b)-7(c), one can also observe that the PR signaling causes an increase in BER at short transmission distances. For example, at −6dBm received power in the BtB case, the BER using only the linear equalizer is less than 10^{−5}, while the BER using the combination of PR signaling and linear equalizer is ~10^{−3}. The increase in the BER using the PR signaling is because the PR signaling with 7 decision levels requires a higher signal-to-noise ratio (SNR).

Similarly, Fig. 10 plots the BER performance with the combination of PR signaling and the simplified Volterra equalization. It is shown that 20km and 30km distances are finally achieved for EML and MZM using this equalization scheme. However, if we also compare them with the result in Fig. 8(a) where only Volterra is adopted for DML (without PR signaling) again, we can find a worsen performance of EML and MZM. For example, at a 30km distance, the DML simply using Volterra can achieve a BER of ~2 × 10^{−4}, whereas the EML and MZM using both PR signaling and Volterra are respectively ~3 × 10^{−2} and ~3 × 10^{−3}.

## 4. Discussion

When implementing these transmitters in short-reach transmissions, there are some other factors needed to be considered. First, if we aim at achieving optimal transmission performance for each distance, the RF parameters of DML needs to be optimized for each distance as discussed in Section 3.2, which may raise some difficulties in practical deployment. Nevertheless, as indicated by Fig. 4, even if we use fixed high output power and low Vpp for all distances, we can still achieve a BER well below the HD-FEC over all of them. In other words, the high output power and low Vpp optimized for long distance scenarios can also be applied to the BtB case with a higher but acceptable BER. Second, the bandwidth of commercial devices is another important factor in the selection of transmitter components. Generally, due to the modulation dynamics, the DML usually has a smaller bandwidth than EML and MZM. The common bandwidth of DML is 20~30GHz, while that of MZM and EML is 30GHz~40GHz. Also it was reported that the state-of-art bandwidth of DML can be 55GHz [31], while EML can be up to 100GHz [32]. This fact might be a limitation for the application of DML. Third, in some scenarios such as optical access networks, we might require the transmitter to have a high launch power to produce a high power budget, which will induce fiber nonlinearities. In these scenarios, the DML will further show its superiority as the optical spectrum of DML is more spread due to the frequency chirp, which can significantly decrease the optical power at certain optical frequencies and reduce fiber nonlinearities [33].

## 5. Summary

In this paper, we have given a detailed study on the performances of DML, EML and MZM based systems in dispersion-unmanaged high-speed links with DSP. We show that the available non-faded bandwidth in a DML based system is >$\sqrt{2}$ of EML and MZM based systems, attributed to the frequency modulation from DML adiabatic chirp. We illustrate that the EML and MZM are mainly limited by this fiber power fading, and DML is mainly limited by nonlinear distortions. Accordingly, we adopt linear equalization, nonlinear diagonally-pruned Volterra equalization and PR signaling to compensate these distortions. In the experimental comparison, we first conduct a detailed parametric optimization of the output power and Vpp of DML as well as the bias voltage of EML. Then, with these optimized parameters, we compare the transmission performances of the three transmitters. The maximum transmission distances are collected in Table 4. In particular, we show that, 56Gb/s PAM4 signals with a DML can achieve a 40km transmission distance using the simplified Volterra equalizer, and a 20km transmission distance using linear equalizer. On the contrary, for MZM and EML, the achievable transmission distances are respectively 20km and 15km using the Volterra equalizer, and 15km and 10km by using linear equalizer. Moreover, we show that even using the combination of the Volterra equalizer and partial response signaling, the transmission distances of MZM and EML are limited within 30km and 20km. To conclude, we believe the performance superiority of DML presented in this paper provides a valuable reference for the transmitter implementation in DSP-enabled C-band high-speed short-reach transmissions.

## Funding

This work was supported by National Natural Science Foundation of China (NSFC) (61431009, 61521062).

## References

**1. **K. Zhong, X. Zhou, J. Huo, C. Yu, C. Lu, and A. P. T. Lau, “Digital signal processing for short-reach optical communications: a review of current technologies and future trends,” J. Lightwave Technol. **36**(2), 377–400 (2018). [CrossRef]

**2. **D. Sadot, G. Dorman, A. Gorshtein, E. Sonkin, and O. Vidal, “Single channel 112Gbit/sec PAM4 at 56Gbaud with digital signal processing for data centers applications,” Opt. Express **23**(2), 991–997 (2015). [CrossRef] [PubMed]

**3. **H. Xin, K. Zhang, H. He, W. Hu, and M. Zhang, “Fidelity enhancement in high-data-rate digital mobile fronthaul with sample bits interleaving and unequally-spaced PAM4,” Opt. Express **25**(5), 5559–5570 (2017). [CrossRef] [PubMed]

**4. **M. Xiang, Q. Zhuge, Z. Xing, K. Zhang, T. M. Hoang, F. Zhang, and D. V. Plant, “Experimental study of performance enhanced IM/DD transmissions based on constellation switching,” Opt. Express **26**(12), 15480–15489 (2018). [CrossRef] [PubMed]

**5. **J. Shi, J. Zhang, N. Chi, Y. Cai, X. Li, Y. Zhang, Q. Zhang, and J. Yu, “Probabilistically shaped 1024-QAM OFDM transmission in an IM-DD System,” in Optical Fiber Communication Conference (OFC) (2018), paper W2A.44. [CrossRef]

**6. **X. Pang, O. Ozolins, S. Gaiarin, M. I. Olmedo, R. Schatz, U. Westergren, D. Zibar, S. Popov, and G. Jacobsen, “Evaluation of high-speed EML-based IM/DD links with PAM modulations and low-complexity equalization,” in Proceedings of European Conference on Optical Communication (ECOC) (2016), Paper W.4.P.1.

**7. **F. Chang and S. Bhoja, “New paradigm shift to PAM4 signalling at 100/400G for cloud data centers: a performance review,” in Proceedings of European Conference on Optical Communication (ECOC) (2017), paper W.1.A.5. [CrossRef]

**8. **D. V. Plant, M. Morsy-Osman, and M. Chagnon, “Optical communication systems for datacenter networks,” in Optical Fiber Communications Conference (OFC) (2017), paper W3B.1. [CrossRef]

**9. **F. Gao, S. Zhou, X. Li, S. Fu, L. Deng, M. Tang, D. Liu, and Q. Yang, “2 × 64 Gb/s PAM-4 transmission over 70 km SSMF using O-band 18G-class directly modulated lasers (DMLs),” Opt. Express **25**(7), 7230–7237 (2017). [CrossRef] [PubMed]

**10. **K. Zhang, Q. Zhuge, H. Xin, Z. Xing, M. Xiang, S. Fan, L. Yi, W. Hu, and D. V. Plant, “Demonstration of 50Gb/s/λ symmetric PAM4 TDM-PON with 10G-class optics and DSP-free ONUs in the O-band,” in Optical Fiber Communication Conference (OFC) (2018), paper M1B.5. [CrossRef]

**11. **Y. Gao, J. C. Cartledge, S. S.-H. Yam, A. Rezania, and Y. Matsui, “112 Gb/s PAM-4 using a directly modulated laser with linear pre-compensation and nonlinear post-compensation,” in Proceedings of European Conference on Optical Communication (ECOC) (2016), paper M.2.C.2.

**12. **E. Bergmann, C. Kuo, and S. Huang, “Dispersion-induced composite second-order distortion at 1.5 μm,” IEEE Photonics Technol. Lett. **3**(1), 59–61 (1991). [CrossRef]

**13. **B. G. Kim, S. H. Bae, H. Kim, and Y. C. Chung, “DSP-based CSO cancellation technique for RoF transmission system implemented by using directly modulated laser,” Opt. Express **25**(11), 12152–12160 (2017). [CrossRef] [PubMed]

**14. **C.-C. Wei, H.-L. Cheng, and W.-X. Huang, “On adiabatic chirp and compensation for nonlinear distortion in DML-based OFDM transmission,” J. Lightwave Technol. **36**(16), 3502–3513 (2018). [CrossRef]

**15. **K. Zhang, H. He, H. Xin, W. Hu, S. Liang, D. Lu, and L. Zhao, “Chirp-aided power fading mitigation for upstream 100 km full-range long reach PON with DBR DML,” Opt. Commun. **407**, 63–68 (2018). [CrossRef]

**16. **H. Kim, “High-speed optical transmission system using 1.55-um directly modulated lasers,” in Proceedings of International Conference on Optical Instruments and Technology (ICOIT) (2017).

**17. **J. Binder and U. Kohn, “10 Gbit/s-dispersion optimized transmission at 1.55 μm wavelength on standard single mode fiber,” IEEE Photonics Technol. Lett. **6**(4), 558–560 (1994). [CrossRef]

**18. **C. Chen, X. Tang, and Z. Zhang, “Transmission of 56-Gb/s PAM-4 over 26-km single mode fiber using maximum likelihood sequence estimation,” in Optical Fiber Communications Conference (OFC) (2015), paper Th4A.5. [CrossRef]

**19. **F. Karinou, N. Stojanovic, C. Prodaniuc, and Q. Zhang, “Experimental demonstration of an electro-absorption modulated laser for high-speed transmissions at 1.55-μm window using digital signal processing,” Photonics **4**(1), 9 (2017). [CrossRef]

**20. **M. Kim, S. Bae, H. Kim, and Y. C. Chung, “Transmission of 56-Gb/s PAM-4 signal over 20 km of SSMF using a 1.55-μm directly-modulated laser,” in Optical Fiber Communication Conference (OFC) (2017), paper Tu2D.6. [CrossRef]

**21. **K. Zhang, Q. Zhuge, H. Xin, M. Morsy-Osman, E. El-Fiky, L. Yi, W. Hu, and D. V. Plant, “Intensity directed equalizer for the mitigation of DML chirp induced distortion in dispersion-unmanaged C-band PAM transmission,” Opt. Express **25**(23), 28123–28135 (2017). [CrossRef]

**22. **H. Xin, K. Zhang, Q. Zhuge, L. Yi, H. He, W. Hu, and D. V. Plant, “Transmission of 100Gb/s PAM4 signals over 15km dispersion-unmanaged SSMF using a directly modulated laser in C-band,” in Proceedings of European Conference on Optical Communication (ECOC) (2018) (accepted).

**23. **L. A. Neto, D. Erasme, N. Genay, P. Chanclou, Q. Deniel, F. Traore, T. Anfray, R. Hmadou, and C. Aupetit-Berthelemot, “Simple estimation of fiber dispersion and laser chirp parameters using the downhill simplex fitting algorithm,” J. Lightwave Technol. **31**(2), 334–342 (2013). [CrossRef]

**24. **P. Kabal and S. Pasupathy, “Partial response signaling,” IEEE Trans. Commun. **23**(9), 921–934 (1975). [CrossRef]

**25. **X. Xu, E. Zhou, G. N. Liu, T. Zuo, Q. Zhong, L. Zhang, Y. Bao, X. Zhang, J. Li, and Z. Li, “Advanced modulation formats for 400-Gbps short-reach optical inter-connection,” Opt. Express **23**(1), 492–500 (2015). [CrossRef] [PubMed]

**26. **N. Eiselt, D. Muench, A. Dochhan, H. Griesser, M. Eiselt, J. J. V. Olmos, I. T. Monroy, and J.-P. Elbers, “Performance comparison of 112-Gb/s DMT, Nyquist PAM4, and partial-response PAM4 for future 5G ethernet-based fronthaul architecture,” J. Lightwave Technol. **36**(10), 1807–1814 (2018). [CrossRef]

**27. **N. Stojanovic, F. Karinou, Z. Qiang, and C. Prodaniuc, “Volterra and Wiener equalizers for short-reach 100G PAM-4 applications,” J. Lightwave Technol. **35**(21), 4583–4594 (2017). [CrossRef]

**28. **E. Batista and R. Seara, “On the performance of adaptive pruned Volterra filters,” Signal Processing **93**(7), 1909–1920 (2013). [CrossRef]

**29. **D. Mahgerefteh, Y. Matsui, X. Zheng, and K. McCallion, “Chirp managed laser and applications,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1126–1139 (2010). [CrossRef]

**30. **L. Spiekman, “Extended range 100 gigabit ethernet,” in Proceedings of International Conference on Transparent Optical Networks (ICTON) (2016), paper Th.A5.1.

**31. **Y. Matsui, R. Schatz, T. Pham, W. A. Ling, G. Carey, H. M. Daghighian, D. Adams, T. Sudo, and C. Roxlo, “55 GHz bandwidth distributed reflector Laser,” J. Lightwave Technol. **35**(3), 397–403 (2017). [CrossRef]

**32. **O. Ozolins, X. Pang, M. I. Olmedo, A. Kakkar, A. Udalcovs, S. Gaiarin, J. R. Navarro, K. M. Engenhardt, T. Asyngier, R. Schatz, J. Li, F. Nordwall, U. Westergren, D. Zibar, S. Popov, and G. Jacobsen, “100 GHz externally modulated laser for Optical interconnects,” J. Lightwave Technol. **35**(6), 1174–1179 (2017). [CrossRef]

**33. **Z. Li, L. Yi, W. Wei, M. Bi, H. He, S. Xiao, and W. Hu, “Symmetric 40-Gb/s, 100-km passive reach TWDMPON with 53-dB loss budget,” J. Lightwave Technol. **32**(21), 3389–3396 (2014).