1. INTRODUCTION

In recent years, high-speed data transmission for the demand of high-resolution images/audio, data streaming, and data cloud storage/computing has become an important issue. Transmission speed ranging from 100 to 400 Gbit/s for ethernet has been standardized by IEEE P802.3bs [1]. The required transmission capacity has been increased to the exabyte level, which has also contributed to the rapid pace of Tbit/s data-center technology development.

Artificial intelligence integrated with machine and deep learning technologies will need big-data processing in the future by increasing the amount of data exchanged from devices and networks in data centers [2]. As a result, the servers for data transmission between data centers have become crucial pieces of technology. At the transmitted end, the vertical-cavity surface-emitting laser (VCSEL) has been developed to enhance transmission capacity due to its low threshold bias, high coupling efficiency, wide modulation bandwidth, and cost-effective modulization [3–8]. However, the multimode (MM) VCSEL exhibits a low modulation bandwidth to effectively decrease the entire transmission capacity. In addition, large modal dispersion is induced during transmission to decrease the data rate when an MM VCSEL is used as a transmitter. Although the single-mode (SM) VCSEL has the most broadened modulation bandwidth for obtaining the highest data rate compared with other VCSELs, its emission power when coupled using a fiber is so low that it cannot support long-reach transmission owing to propagation loss during transmission. Based on these trade-offs, the few-mode (FM) VCSEL has become a suitable solution to enhance transmission capacity and distance.

To further improve the transmission capacity in future data centers, the novel fabrication to extend the modulation bandwidth of VCSELs [9,10] and a new data format to increase the spectral efficiency of the transmission system [11,12] have been utilized. Many studies have reported VCSEL-multimode fiber (MMF) transmission with a data rate beyond 50 Gbit/s. For the nonreturn-to-zero on–off keying (NRZ-OOK) data format, Wu et al. successfully demonstrated 50 Gbit/s transmission by using a 25 GHz double-oxide-confined VCSEL to achieve the error-free criterion [13]. In addition, Kuchta et al. used an 850 nm VCSEL to perform NRZ-OOK transmission at 71 Gbit/s [14]. However, most VCSEL-based optical links still utilize MMF as the propagation media. In recent years, graded-index or normal single-mode fibers (SMFs) have been employed to reduce modal dispersion during transmission. Therefore, data rates and transmission distances have been increased. Li et al. employed a graded-index SMF (GI-SMF) to reach 25 Gbit/s NRZ-OOK data carried by an 850 nm VCSEL over 1.5 km transmission [15]. However, the transmission performance of NRZ-OOK data carried by a dual-mode VCSEL between the MMF and SMF links has yet to be compared.

In this work, NRZ-OOK transmission by a dual-mode VCSEL over a 100 m GI-SMF is demonstrated for short-reach data-center applications. A dual-mode VCSEL with higher indium (In) dopant density in the active quantum well region increases the differential gain coefficient to extend the relaxation frequency. In addition, the dopant density improves the modulation bandwidth for obtaining a larger data capacity. The transmission performance of NRZ-OOK data via the dual-mode VCSEL over 100 m OM4 MMF and 100 m GI-SMF is also compared.

2. DESIGN AND FABRICATION OF THE VCSEL DEVICE

In this work, the optical bandwidth and gain of the VCSEL are simulated using Crosslight PICS3D software [16]. Crosslight PICS3D software uses the nonlinear Newton method to solve the current continuity and Schrodinger, Poisson, and other equations to design a VCSEL epitaxial structure with the appropriate material, thickness, and doping. In addition, the Fermi-golden rule and Green function are utilized to simulate the gain of the active region in the VCSEL. The widening of the gain spectrum caused by carrier–carrier and carrier–photon scattering is also considered. In addition, the VCSEL modulation bandwidth can be simulated via commercial software [16] based on the formulas shown in Appendix A. The detailed parameters of the VCSEL structure are listed in Appendix B. Therefore, the simulated optical bandwidth of the VCSEL can be obtained from the frequency modulation response. Figure 1(a) shows the heavy hole and light hole conduction bands of gallium arsenide (GaAs) at different In compositions. Figures 1(b) and 1(c) exhibit the simulated optical bandwidths and D-factors of ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ and ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ VCSEL devices, respectively. An appropriate amount of strain can reduce the mutual influence between sub-bands and split the heavy and light hole conduction bands. In addition, the energy level of the limited hole conduction band can also be reduced. The holes are more evenly distributed in the sub-bands of the valence band, resulting in a lower transparent carrier density. Therefore, a larger gain can be generated. The threshold current is also decreased by properly detuning the strain to improve the performance of the VCSEL. Figures 1(d) and 1(e) show the simulated gain spectra of ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ and ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ quantum well (QW) VCSELs, respectively. The differential gain of the ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ QW VCSEL increases from $1664{\mathrm{cm}}^{-1}$ to $2000{\mathrm{cm}}^{-1}$ compared with that of the ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.88}\mathrm{As}$ QW VCSEL. This 20% enhancement of differential gain can improve the high-speed characteristics of the VCSEL device.

 

Fig. 1. (a) Heavy hole and light hole conduction band at different indium compositions. Optical bandwidths of (b) ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ and (c) ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ QW VCSELs. D-factors of (d) ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ and (e) ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ QW VCSELs. Simulated gain spectra of (f) ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ and (g) ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$ QW VCSELs.

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The structural epitaxy, patterning fabrication, and the top and cross-sectional view images of the designed dual-mode VCSEL are shown in Fig. 2. Figure 2(a) shows a cross-sectional view of the dual-mode VCSEL structure; Fig. 2(b) exhibits a top-view SEM image of the dual-mode VCSEL device. Figure 2(c) shows a cross-sectional SEM image of the Zn-diffusion region in the VCSEL device. The epitaxial VCSEL wafer in this study was fabricated by the following processes. A semi-insulating GaAs substrate is grown using a metal–organic chemical vapor deposition system. The short resonant cavity ($\lambda /2$) reduces the transient time of its internal carriers and increases its confinement factor. Multiple pairs of oxide layers on the two primary oxide apertures formed by selective wet oxidation reduce the parasitic capacitance. The active region consists of three 6.5 nm ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.92}\mathrm{As}$ QW layers separated by 8 nm ${\mathrm{Al}}_{0.37}{\mathrm{Ga}}_{0.63}\mathrm{As}$ barriers. After In doping, the stress formation and the increased differential gain achieve high bandwidth characteristics.

 

Fig. 2. (a) Schematic illustration of the fabricated dual-mode VCSEL structure. (b) Top-view SEM image of the fabricated VCSEL. (c) Cross-sectional SEM image of the Zn-diffusion region in the device.

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Considering the impact of the parasitic effects, benzocyclobutene (BCB) with a low dielectric constant under a radio frequency (RF) electrode is used to reduce electrode capacitance. In addition, the doping concentrations of 33-pair $\mathrm{n}$-type and 20-pair $\mathrm{p}$-type distributed Bragg reflectors are also improved to reduce parasitic resistance. A graded distribution form is designed to reduce the energy band difference of the heterogeneous junction. For the Zn-diffusion process, ${\mathrm{SiO}}_2$ is utilized as a hard mask to achieve mode suppression. The diffusion depth and aperture are about 1 and 4 μm, respectively.

3. EXPERIMENTAL SETUP

The experimental setup for performing NRZ-OOK transmission carried by the dual-mode VCSEL over 100 m SMF and 100 m OM4 MMF links is shown in Fig. 3(a). NRZ-OOK data with a pseudorandom binary stream (PRBS) length of $2^{17}-1$ was generated by an arbitrary waveform generator (AWG, Keysight M8194A) with an analog bandwidth of 45 GHz and a sampling rate of 120 GSa/s. The electrical NRZ-OOK data generated from the AWG was amplified via a microwave amplifier (Anritsu, AH54147A) with an analog bandwidth of 50 GHz and a gain of 20 dB. Then, the NRZ-OOK data stream and a direct current (DC) bias current were combined using a bias-tee (Anritsu, V250) with an analog bandwidth of 65 GHz. The size of the dual-mode VCSEL is $300\mathrm{\mu m}\times 225\mathrm{\mu m}$, as shown in Fig. 3(b). The combined signal was injected into the dual-mode VCSEL by a 40 GHz ground-signal (GS) microwave probe (GGB 40A-GS-125-DP) with a pitch interval of 125 μm. Figure 3(c) shows the GS probe touching the dual-mode VCSEL device to deliver the bias current and NRZ-OOK data. The dual-mode VCSEL emits light as the electrical signal is injected into the device via the GS probe, as shown in Fig. 3(d). The VCSEL output was collected by a lensed OM4-MMF with a core diameter of 50 μm, as shown in Fig. 3(e). In this work, the lensed MMF segment is customized by using the Corning OM4-MMF with its core/cladding size of 50/125 μm, spot size of 20 μm, and radius of curvature of 45 μm. The GI-SMF is SMF-28(R) Ultra fiber made by Corning Incorporated. A 100 m GI-SMF or 100 m OM4 MMF was used to create the short-reached transmission. After 100 m SMF or 100 OM4 MMF transmission, the optical NRZ-OOK data transmitted by the dual-mode VCSEL was received by a photoreceiver (Newport, 1484-A-50) with an analog bandwidth of 22 GHz to perform the optical-to-analog conversion. Finally, the converted data was analyzed via a digital serial analyzer (DSA, Tektronix 8300), wherein the $Q$-factor was directly measured and analyzed by built-in software.

 

Fig. 3. (a) Experimental setup for NRZ-OOK transmission carried by the fabricated dual-mode VCSEL in BtB and 100 m GI-SMF links. (b) Top-view microscopic photograph of the VCSEL chip. (c) Top-view microscopic photograph of the GS microwave probe touching the VCSEL chip. (d) Top-view microscopic photograph of the VCSEL chip light-emission. (e) Top-view microscopic photograph of the lensed fiber probe collecting the light-emission of the VCSEL chip.

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In this work, the bit-error ratio (BER) of the NRZ-OOK data is measured using commercial software (Tektronix, 80JARB and 80SJNB) [17]. According to this software, the average BER is obtained from the BERs of the horizontal and vertical bathtub curves. The measured signal-to-noise ratio (SNR) is given by the commercial analyzer software (DSA8300 with option 80SJNB), which follows the definition by the ratio of the signal difference between the 1- and 0-levels relative to the noise at both levels obtained by [18,19],

In detail, two transmission routes are defined at the beginning, as shown in Fig. 4. The first route ($H_{\mathrm{total}}$ with VCSEL and channel responses) contains all elements added into the measured transmission channel between the AWG and the DSA, whereas the second route ($H_{\text{channel}}$ with channel response only) contains only the microwave elements between the AWG and DSA. Then, two transfer functions in the frequency region for the two transmission circuits are defined as

 

Fig. 4. Schematic diagrams of the measured and simulated system in the pre-emphasis process.

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To compensate the channel response at the very beginning by delivering a pre-emphasized amplitude function of $V_{\mathrm{preemphasis}}(f)$ from the AWG for convenience, the pre-emphasized transfer function of $H_{\mathrm{preemphasis}}(f)$ must be extracted from the measured $H_{\text{channel}}(f)$ and $H_{\mathrm{total}}(f)$ functions. $V_{\mathrm{preemphasis}}(f)$ is written as

During the experiments, the pre-emphasized AWG output function in the frequency domain is generated by multiplying the original AWG output amplitude function with the $H_{\mathrm{preemphasis}}(f)$ function, which is the reciprocal channel response function obtained by performing the fast Fourier transform:

4. RESULT AND DISCUSSION

A. Basic Characteristics of the Dual-Mode VCSEL

Figure 5(a) shows the power-to-current ($P-I$) curve and $\mathrm{d}P/\mathrm{d}I$ slope of the dual-mode VCSEL. This dual-mode VCSEL exhibits a threshold current of 0.72 mA and a maximal optical output power of 2.2 mW @ 8 mA before saturation via the lensed MMF. In addition, the corresponding $\mathrm{d}P/\mathrm{d}I$ is 0.35 W/A above the lasing threshold. From Fig. 5(a), a small variation in $\mathrm{d}P/\mathrm{d}I$ at the biased current, ranging between 1.44 and 5 mA, indicates the linear modulation response. Biasing the dual-mode VCSEL between 5 and 8 mA increases its power by 0.8 mW; however, the power saturation slightly decreases the $\mathrm{d}P/\mathrm{d}I$, sacrificing the modulation throughput. The distinct rollover of the $P-I$ curve occurs when biasing the dual-mode VCSEL beyond 8.5 mA. Here, the Auger effect increases the nonradiative scattering and reduces the quantum efficiency. From the voltage-to-current ($V-I$) curve and the differential resistance ($\mathrm{d}V/\mathrm{d}I$) of the dual-mode VCSEL operated at 25°C, shown in Fig. 5(b), the differential resistances of $218\mathrm{\Omega }$ @ 5 mA and $115\mathrm{\Omega }$ @ 8 mA are obtained.

 

Fig. 5. (a) $P-I$ and $\mathrm{d}P/\mathrm{d}I$ responses. (b) $V-I$ and $\mathrm{d}V/\mathrm{d}I$ responses of the dual-mode VCSEL.

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These differential resistances cause modulated signal reflection and reduce the throughput efficiency. As the characteristic impedance is typically set to $50\mathrm{\Omega }$, large differential resistance causes the high impedance mismatch to enlarge the reflection coefficient, which results in a huge signal reflection induced between the dual-mode VCSEL and the data-stream generator. The reflection coefficient ($\mathrm{\Gamma }$) is defined as $(Z_{\mathrm{VCSEL}}-Z_{\mathrm{RF}})/(Z_{\mathrm{VCSEL}}+Z_{\mathrm{RF}})$, where $Z_{\mathrm{VCSEL}}$ and $Z_{\mathrm{RF}}$ represent the impedance of the VCSEL and the characteristic impedance, respectively. As an example, a reflection coefficient of 0.39 for the dual-mode VCSEL operating at 8 mA is better than that of 0.63 operating at 5 mA. In principle, the return loss (RL) and voltage standing wave ratio (VSWR) are defined as $-20\log |\mathrm{\Gamma }|$ and $(1+\mathrm{\Gamma })/(1-\mathrm{\Gamma })$, respectively. After calculating these values, the dual-mode VCSEL operated at 8 mA exhibits an RL of 8.1 dB and VSWR of 2.27. The smaller reflection coefficient promotes better modulation efficiency, which improves the SNR and effectively reduces the microwave power consumption of the encoding data stream caused by the impedance mismatch.

To connect the dual-mode VCSEL chip with the fiber link for analysis, two kinds of optical fiber coupling schemes were employed. The first optical coupling scheme uses only the lensed OM4-MMF (with the 100-m OM4-MMF for transmission), whereas the second scheme combines the lensed OM4-MMF (with the 100 m GI-SMF for transmission). Figures 6(a) and 6(b) show the coupled optical powers and spectra of the dual-mode VCSEL received by the lensed OM4-MMF in the BtB and 100 m GI-SMF conditions, respectively. Compared with the first scheme shown in the upper inset of Fig. 6(a), with only the lensed OM4 MMF link, the second scheme in Fig. 6(b), with the lensed OM4 MMF $+$ 100 m GI-SMF link, changes not only the coupling efficiency but also the coupled-mode number. From the coupled optical powers and spectra obtained from the two schemes shown in Fig. 6, the whole dual-mode VCSEL lasing spectrum is coupled out, with a coupled power as high as 2.2 mW obtained at the lensed MMF end-face for transmission. As observed before transmission, the dual-mode VCSEL emits two main peaks at 851.8 and 853.4 nm with respective powers of $-2.7$ and $-7.8\mathrm{dBm}$. The spectrum of the VCSEL coupled to the MMF has a total output power estimated to be $-1.5\mathrm{dBm}$. The spectrum of the VCSEL coupled to the GI-SMF has a total output power of $-6.9\mathrm{dBm}$ and two main modes at $-8.2$ and $-12.6\mathrm{dBm}$. The power difference of 5.4 dB between the MMF-to-MMF and MMF-to-SMF schemes correlates to a coupling loss of 6 dB. Moreover, the optical spectrum of the dual-mode VCSEL exhibits only two principal modes at 851.8 and 853.4 nm.

 

Fig. 6. Coupling powers and optical spectra of the dual-mode VCSEL received by the lensed OM4-MMF in (a) BtB and (b) 100 m GI-SMF conditions.

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As the lensed OM4 MMF connects with the 100 m SMF, the coupling power of the dual-mode VCSEL significantly decreases to 0.6 mW with a coupling efficiency of 0.26. That is due to the core diameter mismatch between the lensed OM4-MMF ($D_{\mathrm{core}}=50\mathrm{\mu m}$) and the SMF ($D_{\mathrm{core}}=9\mathrm{\mu m}$). Figure 7 shows the optical spectra of the VCSEL operated under different bias currents at the lensed MMF and lensed MMF $+$ GI-SMF outputs. After MMF $+$ GI-SMF coupling, the fundamental mode of the VCSEL survives, whereas the high-order-mode peaks of the VCSEL diminish after passing through the 100 m GI-SMF. Indeed, we cannot exclude the situation that the side modes with attenuated peak power merge into the noise background of the optical spectral analyzer.

 

Fig. 7. Optical spectra of the VCSEL operated under different bias currents at lensed MMF (top) and lensed MMF + GI-SMF (bottom) outputs.

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The frequency responses of the dual-mode VCSEL operated under different bias currents are shown in Fig. 8. For the frequency response measurement, the peak-to-peak amplitude of the RF signal is set to 2.2 V. When setting the DC bias current to 8 mA, the obtained DC voltage is 4.2 V. The original response of optical receiver is specified in a datasheet without executing any advanced signal pre-emphasis for compensating the channel response. By employing a discrete channel bandwidth pre-emphasis algorithm, the overall response of the whole transmission system, including the dual-mode VCSEL, the transmission channel, and the optical receiver, is measured for feedbacking amplitude and phase pre-compensation node to the generator node by node. Afterward, all the responses of microwave and optical components except for the dual-mode VCSEL are calibrated for obtaining the net response of the dual-mode VCSEL. According to the response of the dual-mode VCSEL, the modulation bandwidth of the dual-mode VCSEL is obtained eventually. When the bias current increases from 2 to 5 mA, the 3 dB bandwidth of the dual-mode VCSEL extends from 13.7 to 25.1 GHz. The corresponding relaxation oscillation peak also extends from 8.6 to 18.5 GHz. By further increasing the bias current to 8 mA, the 3 dB bandwidth of the dual-mode VCSEL is enhanced to 28 GHz. In addition, the relaxation oscillation peak gradually disappears. However, the 3 dB bandwidth slightly suppresses to 27.5 GHz when the dual-mode VCSEL is operated at 9 mA. This degradation of the 3 dB modulation bandwidth of the dual-mode VCSEL is mainly attributed to declined frequency response with increasing DC bias current. Zn diffusion can significantly reduce the resistance of the top DBR layer to decrease the RC time constant. This decreased RC time constant extends the 3 dB modulation of the dual-mode VCSEL.

 

Fig. 8. Frequency response of the dual-mode VCSEL under different biasing currents.

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B. NRZ-OOK Transmission Carried by the Dual-Mode VCSEL

Figure 9 shows the eye diagrams of NRZ-OOK transmission carried by the dual-mode VCSEL with and without the pre-emphasis process for the BtB case. Without executing the pre-emphasis process, the eye diagrams of the NRZ-OOK transmission at 50, 53, and 56 Gbit/s become blurred, with degraded SNR owing to the distortion caused by the finite transmission channel response. From the eye diagrams, the SNR of the NRZ-OOK transmission is measured between 5.7 and 5.8 dB as the data rate changes from 50 Gbit/s to 56 Gbit/s. This is because the bandwidth limitation of the dual-mode VCSEL hardly supports NRZ-OOK transmission with a data rate beyond 50 Gbit/s. Therefore, the corresponding BER is also degraded from $2.6\times {10}^{-2}$ to $2.7\times {10}^{-2}$, which fails the telecom standard (BER of ${10}^{-9}$) as the data rate increases to 56 Gbit/s. However, the pre-emphasis process compensates for the frequency response of the overall system to significantly improve the data rate during transmission. After the pre-emphasis process, the SNR of NRZ-OOK transmission at 50 Gbit/s is 18 dB with a corresponding BER of $9.8\times {10}^{-16}$, which passes the datacom standard (BER of ${10}^{-12}$). When the data rate increases to 56 Gbit/s, the SNR of NRZ-OOK transmission is slightly degraded to 17 dB. The corresponding BERs of NRZ-OOK transmission at 53 and 56 Gbit/s are $8.3\times {10}^{-15}$ and $1.2\times {10}^{-13}$, respectively, which still pass the telecom standard. The pre-emphasis process is further utilized to test the transmission limitation of NRZ-OOK transmission carried by the dual-mode VCSEL.

 

Fig. 9. Eye diagrams of NRZ-OOK transmission carried by the dual-mode VCSEL in the BtB case with and without the pre-emphasis process under data rates of 50, 53, and 56 Gbit/s.

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Figure 10(a) shows eye diagrams of NRZ-OOK transmission carried by the dual-mode VCSEL at data rates ranging from 61 to 69 Gbit/s. When the data rate increases from 61 to 69 Gbit/s, the eye diagrams become blurred due to the bandwidth limitation of the dual-mode VCSEL. Moreover, the bandwidth limitation also contributes to the increased rise/fall times from 6.9 to 10.1 ps. In Fig. 10(a), the peak-to-peak jitter broadens from 1.28 to 1.76 ps when the data rate enlarges from 61 to 69 Gbit/s. The eye width of the NRZ-OOK data is suppressed from 7.53 to 5.9 ps as the data rate increases to 69 Gbit/s. In addition, the amplitude of the NRZ-OOK data is decreased from 168 to 135 mV when the data rate increases from 61 to 69 Gbit/s. This is because the pre-emphasis process sacrifices more power at the low-frequency region to compensate for that at the high-frequency region under higher data-rate operation. In addition, the $Q$-factor of the NRZ-OOK transmission is also degraded from 4.5 to 3.0 dB when the data rate increases from 61 to 69 Gbit/s. Figure 10(b) summarizes the received SNR and decoded BER performance of NRZ-OOK transmission carried by the dual-mode VCSEL at data rates between 61 and 69 Gbit/s. Because of the bandwidth limitation of the dual-mode VCSEL, the SNR of the NRZ-OOK data is degraded from 16.5 to 12.1 dB with a decaying rate of $-0.55\mathrm{dB}/\mathrm{GHz}$ as the data rate increases from 61 to 69 Gbit/s. In addition, the obtained BER enlarges above ${10}^{-12}$ to fail the error-free condition for the datacom standard when the data rate increases beyond 61 Gbit/s.

 

Fig. 10. (a) Eye diagrams and (b) BER and SNR of NRZ-OOK transmission carried by the dual-mode VCSEL in the BtB case with the pre-emphasis process under different data rates (between 61 and 69 Gbit/s).

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The dual-mode VCSEL successfully transmits NRZ-OOK data at 61 Gbit/s with a corresponding BER of $6.8\times {10}^{-12}$. Because the SNR of the NRZ-OOK data decreases and degrades the BER performance when increasing the data rate, the allowable data rate is enlarged to 63 Gbit/s with a BER of $9.9\times {10}^{-10}$, which passes the telecom standard with a BER of ${10}^{-9}$. As the data rate further increases to 69 Gbit/s, the BER of the NRZ-OOK data decays to $2.6\times {10}^{-5}$. Therefore, this dual-mode VCSEL can transmit NRZ-OOK data with data rates of 56 Gbit/s for the datacom standard and 63 Gbit/s for the telecom standard in the BtB case. This transmission performance provides an opportunity for achieving the IEEE 802.3cm standard. After optimizing NRZ-OOK transmission in the BtB case, the NRZ-OOK transmission carried by the dual-mode VCSEL over the 100 m GI-SMF with pre-emphasis is also demonstrated. Figure 11 shows eye diagrams of NRZ-OOK transmission carried by the dual-mode VCSEL in the BtB and 100 m GI-SMF links under different data rates for comparing transmission performance. As the data rate increases from 50 to 51 Gbit/s, the SNR of the NRZ-OOK data after 100 m GI-SMF transmission is decreased from 17.3 to 14.1 dB with a corresponding $Q$-factor reduction from 4.5 to 3.6. This phenomenon also contributes to the degraded BER from $9.1\times {10}^{-14}$ to $2.2\times {10}^{-7}$. The penalty of the allowable data rate to pass the telecom standard results in 13 Gbit/s between the BtB and 100 m GI-SMF transmission conditions. Such a large penalty is mainly due to the coupling loss at the lensed OM4 MMF/GI-SMF interface and the propagation loss during transmission. Because of the bandwidth limitation for the dual-mode VCSEL, the SNR of the NRZ-OOK data is degraded from 16.5 to 12.1 dB with a corresponding decaying rate of approximately $-0.55\mathrm{dB}/\mathrm{GHz}$ when the data rate increases from 61 to 69 Gbit/s.

 

Fig. 11. Eye diagrams of NRZ-OOK transmission carried by the dual-mode VCSEL in BtB and 100 m GI-SMF cases under different data rates.

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For a parametric comparison, key parameters of the received eye diagram obtained from the NRZ-OOK data at different coupling fiber schemes are summarized in Table 1. Table 1 also exhibits the key parameters of the pre-emphasized NRZ-OOK data stream before and after 100 m GI-SMF transmission under the allowable data rate to pass the telecom standard. Under the criterion of the telecom standard, the allowable data rates of NRZ-OOK transmission carried by the dual-mode VCSEL are 63 Gbit/s in the BtB case and 50 Gbit/s over the 100 m GI-SMF link.

Table 1. Key Parameters of Pre-emphasized NRZ-OOK Data Carried by the Dual-Mode VCSEL before and after 100 m GI-SMF Transmission

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Figure 12 shows eye diagrams of NRZ-OOK data transmitted by the dual-mode VCSEL in the BtB, 100 m GI-SMF, and 100 m OM4 MMF cases. To achieve the demand for an intra-data-center application, the permissible data rate is reduced to 50 Gbit/s to perform the BtB, 100 m GI-SMF, and 100 m OM4 MMF transmission. BERs of the NRZ-OOK data are below the BER criterion of the telecom standard (${10}^{-9}$) in both 100 m GI-SMF and 100 m OM4 MMF cases. In the SMF case, the dual-mode VCSEL can deliver 50 Gbit/s NRZ-OOK data with a BER of $9.1\times {10}^{-14}$, an SNR of 17.3 dB, and a $Q$-factor of 4.5. For the 100 m OM4 MMF transmission, the BER, SNR, and $Q$-factor are degraded to $7.6\times {10}^{-10}$, 15.7 dB, and 4.1, respectively. Although the mismatch of the core diameter between the lensed MMF and the GI-SMF causes huge coupling loss, which affects the transmission performance, the transmission performance in the 100 m GI-SMF case is better than that in the 100 m OM4 MMF case. This is because the larger modal dispersion in the OM4 MMF also induces more serious deterioration during transmission, even though the coupling loss is as small as 9% between the lensed MMF and the OM4 MMF. The related transmission parameters of NRZ-OOK data carried by the dual-mode VCSEL in the BtB, 100 m GI-SMF, and 100 m OM4 MMF cases are summarized in Table 2. Apparently, the modal dispersion induced by the OM4-MMF degrades the transmitted data waveform. This phenomenon also causes an enlarged timing jitter and large rise/fall times. Eventually, the received SNR for the 100 m OM4 MMF case is decreased to cause BER degradation by more than four orders of magnitude compared with the transmission performance in the 100 m GI-SMF case. From the above-mentioned discussion, the transmission performance of short-reach data-center transmission is mainly attributed to the modal dispersion.

 

Fig. 12. Eye diagrams of 50 Gbit/s NRZ-OOK data carried by dual-mode VCSEL in BtB, 100 m OM4 MMF, and 100 m GI-SMF cases.

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Table 2. Key Parameters of NRZ-OOK Data Stream Carried by the Dual-Mode VCSEL before and after the SMF Link with the Pre-emphasis Process

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In summary, Fig. 13 and Table 3 reveal the developing benchmarks for the data rate of NRZ-OOK transmission versus the oxide aperture and modulation bandwidth of the VCSEL. As early as 2011, IBM used a SiGe-based laser driver IC to drive a VCSEL to perform 20 Gbit/s NRZ-OOK transmission over 200 m [21]. In 2012, Johnson et al. directly modulated a VCSEL to demonstrate 30 Gbit/s NRZ-OOK transmission under the datacom standard [22]. Moreover, Westbergh et al. developed a high-speed VCSEL with the highest modulation bandwidth of 30 GHz for delivering NRZ-OOK data with the highest data rate of 57 Gbit/s [23–27]. At the same time, Muting et al. demonstrated NRZ-OOK transmission with the highest data rate of 40 Gbit/s using a VCSEL with a modulation bandwidth of 21 GHz [28,29]. Feng et al. also utilized a VCSEL with a modulation bandwidth of 29.2 GHz to achieve a data rate of 57 Gbit/s for NRZ-OOK transmission [30,31]. In addition, Shi and coworkers further developed a single-mode VCSEL with 29 GHz bandwidth to perform NRZ-OOK transmission at 54 Gbit/s [32–34]. For comparison, Table 3 summarizes the transmission performance of NRZ-OOK data carried by VCSELs in previous studies [21–44]. To date, this study presents error-free NRZ-OOK transmission carried by a dual-mode VCSEL with data rates of 50, 53, and 56 Gbit/s that obtain corresponding BERs of $2.6\times {10}^{-15}$, $3.9\times {10}^{-12}$, and $2.3\times {10}^{-11}$, respectively, which pass the criterion of the telecom standard. The highest data rate of 61–69 Gbit/s is achieved by using a dual-mode VCSEL for data center applications. After the pre-emphasis process, the dual-mode VCSEL carries the NRZ-OOK data stream at 66 Gbit/s in this work. For error-free data transmission that passes the telecom standard, the allowable data rate is 63 Gbit/s.

 

Fig. 13. Benchmarks of data rate versus (a) oxide aperture and (b) modulation bandwidth for high-speed VCSELs reported in previous work.

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Table 3. Benchmarks of Data Rate versus Oxide Aperture and Modulation Bandwidth for High-Speed VCSELs Reported in Previous Works

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A comparison of the coupled power and encoded bandwidth of optical data streams delivered by SM, FM, and MM VCSELs over SMF or MMF transmission is summarized in Table 4 [10,14,15,26,35,43–54]. A parametric comparison reveals that the FM-VCSEL can provide a higher encoding bandwidth than the MM-VCSEL for data transmission over MMF. The FM-VCSEL can also deliver a larger coupling power than the SM-VCSEL and benefit from better SNR and BER at the same encoding data rate. A transmission channel range within several hundred meters for short-reached data centers has been executed by the VCSEL-MMF link over one decade.

Table 4. Comparison of the Coupled Power and Bandwidth of SM, FM, and MM VCSELs in SMF or MMF Transmission

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Table 5. Simulation Parameters for the Proposed 850 nm VCSEL

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Table 6. Simulation Parameters for p-Type Distributed Bragg Reflectors

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Table 7. Simulation Parameters for Multiple Quantum Wells

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Table 8. Simulation Parameters for n-type Distributed Bragg Reflectors

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To extend the coverage between intra- and inter-data centers with the same link from 500 m to 10 km in the future [55], an MMF may induce extremely large modal dispersion, degrading the transmission performance, and either the SMF-28 or the GI-SMF is considered as a replacement for transmission distance expansion. In the comparison between the GI-SMF and MMF, the GI-SMF exhibits lower propagation loss and modal dispersion than those for the MMF at 850 nm [56]. In addition, the GI-SMF has higher modal bandwidth than the MMF [56]. Therefore, the BER performance of VCSEL delivered data under GI-SMF transmission is better than that under MMF transmission, even though the GI-SMF at 850 nm also provides ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes. Recently, SMF or GI-SMF transmission by FM or SM VCSELs has been demonstrated [15,50–52]. A transmission distance of several kilometers can be achieved. In this work, the lensed MMF is employed to receive as much VCSEL data power as possible, and the GI-SMF is added for less dispersion than the MMF for distant transmission. Such a coupling architecture provides an alternative approach for future intra-data-center applications, as coupling loss between the MMF and SMF can be effectively decreased. In 2016, Lavrecik et al. used the five-tap feed-forward equalizer (FFE) filter to optimize each bit rate and the nine-tap RC pulse shape filter at the transmitter to reduce the spectral occupancy for obtaining the 90 and 102 Gbit/s two-level pulse-amplitude modulation (PAM-2) transmission over 50 m OM5 MMF at the error-free and KP4 criteria [57]. In addition, the same group employed the time-domain raised cosine and static five-tap FFE filters to optimize the response at the transmitter and receiver, individually, for the 168 Gbit/s PAM-4 transmissions over 50 m OM5 MMF [58,59]. In this work, the discrete-bandwidth pre-emphasis algorithm is simplified to pre-compensate for the whole channel response to take over the advanced data optimization from the previous reports. When combined with the artificial intelligence decision for pre-emphasizing the NRZ-OOK transmission in this work, the computing time of the machine learning procedure can be effectively suppressed for improving the bit rate and time lag in the future.

5. CONCLUSION

In summary, high-speed NRZ-OOK transmission at different bit rates and coupled output with lensed OM4 MMF or OM4 MMF + GI-SMF schemes using a dual-mode VCSEL device is demonstrated for future intra- and inter-data-center applications. By using the lensed OM4-MMF to collect the VCSEL output, the dual-mode VCSEL chip shows a threshold current of 0.72 mA and output power of 2.2 mW at 8 mA before saturation with a differential quantum efficiency of 0.38. When the In-dopant density in the active QW region is increased from ${\mathrm{In}}_{0.08}{\mathrm{Ga}}_{0.88}\mathrm{As}$ to ${\mathrm{In}}_{0.12}{\mathrm{Ga}}_{0.88}\mathrm{As}$, the differential gain coefficient is increased from 1664 to $2000{\mathrm{cm}}^{-1}$. In addition, the 20% enhancement of differential gain also improves the high-speed characteristics of the dual-mode VCSEL. At highly biased conditions (with $I_{\mathrm{bias}}>{10I}_{\mathrm{th}}$), the dual-mode VCSEL only exhibits two obvious transverse modes. In addition, the coupled VCSEL output for the lensed OM4 MMF + 100 m GI-SMF coupling scheme shows a lower power coupling ratio of 0.26 and a smaller $\mathrm{d}P/\mathrm{d}I$ of 0.35. During the performed analysis, a data waveform pre-emphasis operation was performed to compensate for the transmission channel response. In the BtB case, the pre-emphasized NRZ-OOK data carried by the dual-mode VCSEL at 50, 53, and 56 Gbit/s exhibits corresponding BERs of $2.6\times {10}^{-15}$, $3.9\times {10}^{-12}$, and $2.3\times {10}^{-11}$. The permissible NRZ-OOK data rate is increased up to 69 Gbit/s after executing the waveform pre-emphasis process. The dual-mode VCSEL guarantees error-free NRZ-OOK transmission with a $\mathrm{BER}<{10}^{-9}$ at 63 Gbit/s. For 69 Gbit/s NRZ-OOK transmission, the received BER of less than $2.6\times {10}^{-5}$ is still lower than the forward-error correction criterion. When the OM4 MMF (1 m) + GI-SMF (100 m) link is used for future inter-data-center transmission, the transmission rate of pre-emphasized NRZ-OOK data is 51 Gbit/s with a BER of $2.2\times {10}^{-7}$ and an SNR of 14.1 dB.