Open Access
Add to BibSonomy
Abstract
By collimating the single-mode (SM) vertical-cavity surface-emitting laser (VCSEL) at 850 nm with either the OM4 multi-mode fiber (OM4-MMF) or the graded-index single-mode fiber (GI-SMF) with lensed end-face, the directly encoded non-return-to-zero on-off keying (NRZ-OOK) data transmission performance is characterized when tilting the coupling angle with respect to the surface normal of the SM-VCSEL. In comparison with the lensed OM4-MMF and lensed SMF coupling, the lensed OM4-MMF collimator shows a large coupling angle tolerance with the coupling efficiency only degraded by 5% when enlarging the tilted angle from 0° to 10°. In contrast, the lensed GI-SMF collimator attenuates the coupled SM-VCSEL output by more than 50% when tilting the coupling angle up to 10°. For the lensed OM4-MMF coupling, the receivable NRZ-OOK data rate in BtB and after 100-m OM4-MMF cases can achieve 50 Gbit/s with its corresponding BER degraded from 6.5 × 10−10 to 8.8 × 10−10 when enlarging its tilting angle ranged from 0° to 10°. By changing the collimator to the lensed SMF, the decoded BER significantly degrades from 5.8 × 10−5 to 1.2 × 10−1 when coupling and transmitting the NRZ-OOK data at 50 Gbit/s. Owing to the low coupling efficiency via the lensed SMF collimator, the error-free NRZ-OOK data rate under the lensed SMF coupling somewhat decreases to 35 Gbit/s in the BtB link and to 32 Gbit/s after the 100-m GI-SMF link with allowable coupling angle tilted from 0° to 4°. This work confirms the applicability of the lensed MMF or SMF collimator for coupling the SM-VCSEL output with a relatively large tolerance on the tilting angle with respect to the surface normal of the SM-VCSEL.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The requested transmission data rate for optical transceivers in data centers is persistently scaling up owing to the rapid development of network services such as cloud storage/streaming, artificial intelligence, the internet of things, etc. This demand often urges the modulation bandwidth of semiconductor lasers to grow by shrinking their cavity length at the cost of reducing power. The vertical-cavity surface-emitting laser (VCSEL) with an extremely short cavity has emerged as one excellent candidate who exhibits low threshold current [1], low power consumption [2], high modulation speed, and low divergence angle as compared to conventional edge-emitting lasers. However, the multi-mode (MM) VCSEL still suffers from its limited bandwidth during direct modulation and the modal dispersion during the multi-mode fiber transmission [3]. Such drawbacks urge the development of few-mode (FM) [4] or single-mode (SM) VCSEL with a larger bandwidth-distance product and combine the 850-nm quasi-SM or SM-VCSELs [5–8] with the graded-index single-mode fiber (GI-SMF) [9,10] link to serve as the future solution for data-center applications. In addition, the standard SMF is also utilized as a transmission media [11–13].
Hence, Haglund et al. suppressed the oxide-confined aperture to 3 µm to produce a high-bandwidth SM-VCSEL in 2004 [14]. In 2012, Szczerba et al. successfully demonstrated a 25-Gbit/s PAM-4 transmission carried by a quasi-SM-VCSEL with an aperture size smaller than 3 µm over 500-m OM3 MMF [15]. In 2013, Tan et al. utilized the photonic crystal structure to fabricate the SM-VCSEL for transmitting the 25-Gbit/s data over 1-km OM4-MMF [16]. In addition, Safaisni et al. also obtained an SM-VCSEL by using a mode filter to demonstrate the 20-Gbit/s transmission over 2-km MMF in 2014 [17]. In principle, the SM-VCSEL is designed and fabricated by simply decreasing the size of the oxide-confined aperture and reducing the optical field of the VCSEL [18]. Nevertheless, reducing the emission aperture inevitably increases the differential resistance of the VCSEL, which enlarges the reflection coefficient of modulation and the voltage standing-wave ratio (VSWR) to impact the modulation depth (MD) and signal-to-noise ratio (SNR) [19]. In general, these problems can be solved by diffusing heavier zinc dopants into the top distributed Bragg reflector (DBR) mirror for implementing a better ohmic contact with negligible free-carrier absorption [20–23], and by encapsulating a benzocyclobutene (BCB) passivation layer with low capacitance to improve the RC charging/discharging time of the VCSEL [24–26]. Up to now, most of the research efforts were paid on designing and fabricating the SM-VCSEL, whereas seldom discussion was concentrated on the coupling scheme using different kinds of fibers in previous works.
In this work, the lensed MMF and SMF coupling efficiency for the collimation of the SM-VCSEL output is compared to each other, and the effect of tilted-angle coupling on the SM-VCSEL delivered NRZ-OOK transmission performance is declared. By using either the lensed OM4-MMF or the lensed SMF for coupling the 850-nm SM-VCSEL at different tilting angles, this work initially compares the essential output characteristics such as the output power, the coupling ratio, and the mode partition noise (MPN) under different tilting angles of coupling. The NRZ-OOK data streams carried by the SM-VCSEL under the lensed OM4-MMF and lensed SMF coupling with different tilted angles in the BtB and 100-m graded-index SMF (GI-SMF) are compared in detail.
2. Description of device design and fabrication
The design of the SM-VCSEL with a top-view microscopic photograph shown in Fig. 1 is described below. First of all, a bottom DBR mirror comprised of 25-pair undoped binary AlAs/GaAs DBRs was designed to ensure efficient heat transport from the active region to the substrate. The other 8-pair n-doped Al0.9Ga0.1As/Al0.12Ga0.88As DBRs were added for generating the n-type ohmic contact.
Fig. 1. The top-view microscopic photograph of the SM-VCSEL (left) after connected with the G-S microwave coplanar transmission-line probe (middle). The light illumination of the SM-VCSEL (right).
The active region consisted of 5-pair strained InGaAs/AlGaAs quantum wells (QWs). The photoluminescence (PL) peak was designed at 835 nm. In addition, the QW active region was enclosed in the λ/2 cavity for high differential gain and low transparency carrier density. The oxidation layer was composed of 2 Al0.98Ga0.02As oxidized layers for electrical and optical confinements to suppress the high-order transverse modes and narrow the spectral width of VCSELs. The 4 deep-oxidized Al0.96Ga0.04As layers were grown for parasitic capacitance reduction. The top DBR mirror included 14-pair p-doped Al0.12Ga0.88As/Al0.9Ga0.1As layers. A thick heavily p-doped GaAs cap layer was grown for current spreading and p-type ohmic contact. Then, the Ti/Pt/Au multilayers were deposited for p-type metal contact. A cylindrical mesa with vertical profiles and smooth etched surfaces was formed by an inductively coupled plasma etching (ICP-RIE) system with an optimized recipe to minimize scattering loss and ensure accurate etching depth. An N2-H2O flowing furnace system at 465°C was employed for the 2.5-µm oxide aperture formation. In this work, the designed SM-VCSEL consists of a 2.5-µm aperture surrounded by oxidized layers, which does not undergo the Zn-diffusion or the surface relief processes. The control of the transverse modes in this VCSEL is mainly governed by the relatively small size of the oxidation-confined aperture, which is approached via reducing the active volume and increasing the mode spacing (Δλ) to support highly single-mode lasing. Afterward, the multi-layered Au/Ge/Ni/Au metallic film was evaporated for n-type metal contact. Finally, the low-k dielectric materials of the BCB monomers were applied on the VCSEL for the planarization and passivation between p- and n-type contacts. Moreover, an optimized coplanar waveguide (CPW) structure is also employed to minimize the extrinsic parasitic capacitance. This SM-VCSEL incorporates an enhanced thermal design and extends the maximal relaxation oscillation frequency and rollover current. These advantages mitigate the problem of the high series resistance for the SM-VCSELs. Afterwards, the SM-VCSEL was connected with the ground-signal (G-S-G) microwave coplanar transmission-line probe, and its output power was coupled by using the lensed MMF or SMF collimator for transmission data analysis.
3. Results and discussion
3.1 Optical properties of the lensed MMF- or SMF-coupled SM-VCSEL at different tilting angles
Figure 2(a) shows the light-current-voltage (L-I-V) curve of the SM-VCSEL. Under the 4.5-mA operation, the SM-VCSEL exhibits the maximal output power of 0.57 mW with a corresponding dP/dI slope of 0.17 W/A. In addition, the differential resistance at 4.5 mA is obtained as 277 Ω from the V-I curve. Owing to the mismatching between the SM-VCSEL and commercial microwave instruments, the reflection coefficient, return loss, and voltage standing wave ratio of the SM-VCSEL operated at 4.5 mA are obtained as 0.69, 3.2 dB, and 5.5, respectively. From Fig. 2(b), the SM-VCSEL exhibits the single transverse mode as the bias current operates between 1 mA and 4 mA.
Fig. 2. (a) The L-I-V curve, (b) bias-dependent optical spectra, and (c) bais-dependent frequency responses of the SM VCSEL.
Figure 2(c) shows the electrical-to-optical (E-O) frequency response of the SM-VCSEL under different bias currents. When the bias current enlarges from 1.5 mA to 4.5 mA, the SM-VCSEL exhibits its 3-dB modulation bandwidth from 10.8 GHz to 13.4 GHz and 6-dB modulation bandwidth from 18.5 GHz to 21.8 GHz. Enlarging the bias current to 4.75 mA maintains the same 3-dB and 6-dB modulation bandwidths of the SM-VCSEL.
To understand the effect of the tilting angle of the lensed OM4-MMF on the coupling power efficiency, the angle between the lensed fiber and the vertical line is measured as the work platform is selected as the horizontal plane. The coupling angles between the lensed fiber and the horizontal line are measured as 3° and 0°, respectively. Figure 3 shows the photographs, coupling spectra, and P-I curves for the SM-VCSEL collected by the lensed fiber with the coupling angles of 13° and 0°. From the optical spectra, the peak wavelengths obviously keep the same as 847 nm. However, different peak powers are respectively observed as -5.7 dBm and -5.1 dBm for the coupling system with coupling angles of 13° and 0°. In addition, the maximal output powers of the SM-VCSEL collected by the lensed fiber with the coupling angles of 13° and 0° are respectively obtained as 0.46 mW and 0.56 mW with the corresponding dP/dI slopes of 0.13 W/A and 0.17 W/A. That indicates that the power loss of the SM-VCSEL collected by the lensed fiber with the coupling angle of 13° is measured as 18% as compared to that with the coupling angle of 0°. A similar phenomenon for the dP/dI slope is also observed. This power difference between the coupling system with different coupling angles is originated from the mismatch of the optical field between the lensed fiber and the SM-VCSEL. Because only one transverse mode exists in the SM-VCSEL, the area of the optical mode field is relatively small. As the coupling angle increases, the overlap between the mode field and the effective working area of the lensed fiber will gradually decrease. This phenomenon also reduces the coupling efficiency and the peak power. From the abovementioned discussion, the coupling angle of 0° is determined as the best operating condition.
Fig. 3. The photographs, coupling spectra, and P-I curves for the SM-VCSEL collected by the lensed fiber with the coupling angles of (a) 13° and (b) 0°.
The performance of the SM-VCSEL collected by different fiber coupling systems with different coupling angles is shown in Table 1. For the lensed OM4-MMF coupling system with different coupling angles, the output power of the SM-VCSEL keeps the same in the BtB and 100-m GI-SMF cases. In the BtB case, the output power of the SM-VCSEL is measured as 0.56 mW. However, the mismatch of the core diameter causes a huge coupling loss between the lensed OM4-MMF and 100-m GI-SMF to 78.6% with a low output power of 0.12 mW. This low output power is not enough to support the basic data transmission requirement. To solve the problem of coupling loss, the lensed SMF is used because of the same core diameter as the GI-SMF. Owing to the smaller core diameter for the lensed SMF, the effective working area of the lensed SMF is small as compared to the lensed OM4-MMF. Therefore, the mismatch between the lensed SMF and the VCSEL optical field becomes serious to cause power degradation as the coupling angle increases. Furthermore, the power collected from the lensed SMF is lower than that from OM4-MMF for all coupling-angle conditions in the BtB case. For the GI-SMF transmission, the lensed SMF exhibits its advantage with a small coupling loss of 8% to make the output power beyond 0.2 mW for the data transmission.
Table 1. The collected power of the SM-VCSEL collimated with different fiber at different coupling angles.
Figure 4(a) shows the photographs of lensed OM4-MMF and lensed SMF with respective core diameters of 50 µm and 9 µm. With using the lensed MMF and SMF for coupling the emission from the VCSEL, the output power and coupling ratio under different coupling-angle conditions are shown in Fig. 4(b) and Fig. 4(c). The maximal output power of the VCSEL collected by the lensed OM4-MMF with a coupling angle of 0° is obtained as 0.56 mW. As the coupling angle increases to 6°, the output power starts to decrease. When the coupling angle further enlarges to 8°, the output power exhibits an antilogarithm decay to 0.46 mW. By setting the coupling angle to 13°, the output power reduces to 82% output power by the lensed OM4-MMF with a coupling angle of 0°. For the lensed SMF with a thinner core diameter, the output power for the coupling angle at 0° is obtained as 41% output power for the lensed OM4-MMF. In addition, the output power also degrades by an antilogarithm function with a larger decaying slope. When the coupling angle increases to 10°, the output power decreases to 0.11 mW as only 47% output power by the lensed SMF with a coupling angle of 0°. The difference between the coupling ratios for the lensed OM4-MMF and the lensed SMF is originated from the different core diameters.
Fig. 4. The (a) photographs, (b) output powers, and (c) coupling ratios of both lensed SMF and lensed MMF under different coupling-angle conditions.
In principle, the best working condition of the lensed fiber is obtained when the Gaussian beam emitted from the VCSEL totally coincides with the focal point of the lensed fiber. The coincidence level seriously affects the coupling results. Using the lensed SMF with a smaller core diameter and a smaller radius of curvature causes the mismatch between the Gaussian beam and the focal point of the lensed fiber. In addition, increasing the coupling angle can induce a more serious mismatch. For the lensed OM4-MMF, the larger core diameter allows a greater tolerance of the output power for the coupling angle variation. There is no collimation lens but just the lensed OM4-MMF or GI-SMF used in this work. For the lensed OM4-MMF, it exhibits a numerical aperture (NA) of about 0.2, a spot size of about 20 µm, a working distance of about 30-40 µm, The acceptance angle of the OM4-MMF is estimated as 2×Sin-1(0.2)≈23°. For the lensed GI-SMF, it exhibits a numerical aperture (NA) of about 0.13, a spot size of about 3-4 µm, a working distance of 15 µm, and the acceptance angle is estimated as ≈14.9°. As the divergent angle of the SM-VCSEL is about 11°, the larger spot size and acceptance angle of the lensed OM4-MMF can cover the whole emission area of the SM-VCSEL and favor more coupled power, whereas the lensed GI-SMF reveals a higher coupling loss as its spot size relatively close to the emission area of the SM-VCSEL with an oxide surrounded aperture size of 2.5 µm. As the tilting angle of the lensed MMF/SMF increases, the coupling cross-section will transfer from a circular spot with an area of πr2 to the elliptical spot with an area of 0.25πr2cosθ with r and θ respectively denoting the spot radius and the titling angle. The coverage area between the cross-correlated fields of the lensed MMF/SMF and the SM-VCSEL shrinks with increasing the tilting angle. That is, the lensed GI-SMF suffers from a larger coupling loss owing to a smaller cross-correlated area between two optical fields, which becomes more sensitive to the tilting angle with a smaller tolerance when compared to the lensed OM4-MMF used in this work. The MPN performances of the SM-VCSEL collected by the lensed OM4-MMF and lensed SMF coupling with different coupling angles are also discussed and shown in Fig. 5. To change the coupling angle, an optical fiber holder with the tunable inclination adjustment is used. In Fig. 5(a), the MPN of the SM-VCSEL for the lensed OM4-MMF coupling keeps stable below -135 dBc/Hz when the coupling angle increases from 0° to 4°.
Fig. 5. The MPN of the SM-VCSEL for the (a) lensed MMF and (b) lensed SMF coupling with different coupling angles.
Moreover, the MPN also remains almost unchanged in the lensed SMF coupling case, but Fig. 5(b) reveals that the overall noise power level is somewhat smaller than -140 dBc/Hz as obtained in the lensed SMF coupling case, which is mainly attributed to the weaker coupling of high-order transverse modes as well as the power originated from the mode overlapping region when using the lensed SMF. In principle, the MPN is caused by the multi-mode characteristic and mode competition of the VCSEL [27–29]. For the MM VCSELs, the different coupling angles may cause the incomplete collection of the optical modes. For the lensed SMF with a smaller core diameter, all the optical modes are hard to be completely collected. In this work, the SM-VCSEL only offers a single optical mode. Therefore, the multi-mode characteristic and mode competition do not exist in the SM-VCSEL. As a result, the SM-VCSEL collected by both lensed OM4-MMF and lensed SMF coupling under the different coupling angles shows a stable MPN. The power level of the overall MPN for the SM-VCSEL is dependent on the output power. Therefore, the average noise power of the SM-VCSEL for lensed OM4-MMF coupling is larger than that for the lensed SMF coupling.
3.2 NRZ-OOK transmission carried by the lensed MMF- or SMF-coupled SM-VCSEL
Under a direct encoding of 50-Gbit/s NRZ-OOK data stream, the received eye diagrams using lensed MMF and SMF at normal (0°) and tilted (10°) coupling schemes are compared with one another in Fig. 6. Owing to the better overlapping between the Gaussian beam from the VCSEL and the focal point of the lensed fiber for the lensed fiber with the larger core diameter, the lensed OM4-MMF exhibits a greater tolerance for the coupling angle variation. When the coupling angle increases to 10°, the amplitude of the eye diagram for the 50-Gbit/s NRZ-OOK data stream decreases from 60 mV to 56 mV with only 7% amplitude degradation to decrease the SNR from 15.6 dB to 15.4 dB. This phenomenon also increases the corresponding BER from 6.5×10−10 to 8.8×10−10 to pass the telecom standard. For the lensed SMF coupling, the amplitude of the eye diagram for the 50-Gbit/s NRZ-OOK data stream exhibits a significant 70% amplitude loss when the coupling angle enlarges to 10°.
Fig. 6. The eye diagram of the 50 Gbit/s NRZ-OOK data stream carried by the SM-VCSEL for both lensed OM4-MMF and lensed SMF coupling with different coupling angles.
In addition, the serious distortion of the eye diagram is observed to reduce the SNR from 11.8 dB to 1.3 dB and degrade the BER from 5.8×10−5 to 0.12. Therefore, the small tolerance of the transmission performance for the lensed SMF coupling with different coupling angles is easily observed because of the 3.7-dB coupling loss for the lensed SMF coupling.The eye diagrams of the NRZ-OOK data streams carried by the SM-VCSEL for different fiber combinations with various coupling angles are shown in Fig. 7. In Fig. 7(a), the eye diagrams of the 50 Gbit/s NRZ-OOK data are similar for the lensed OM4-MMF coupling with different coupling angles in the BtB case.
Fig. 7. The eye diagrams and BERs of the NRZ-OOK data with different data rates carried by the SM-VCSEL for the (a) lensed OM4-MMF, (b) the lensed SMF, and (c) the lensed SMF + 100-m GI-SMF coupling with different coupling angles.
As the coupling angle varies from 0° to 4°, the eye diagrams of the NRZ-OOK data stream are almost the same. The corresponding BER and SNR are respectively obtained as 6.5×10−10 and 15.6 dB to pass the telecom standard. In Fig. 7(b), the eye diagram for the lensed SMF coupling in the BtB case exhibits a smaller amplitude as compared to that for the lensed OM4-MMF coupling owing to the difference of the output power between the lensed OM4-MMF and lensed SMF. The lower output power also affects the allowable NRZ-OOK data rate to pass the telecommunication standard. The allowable data rate is decreased to 35 Gbit/s with a BER of 1.8×10−10 and an SNR of 16 dB. When the coupling angle changes from 0° to 4°, the transmission performance of the NRZ-OOK data is almost fixed. After coupling the VCSEL power from lensed SMF to GI-SMF, the allowable data rate still reduces to 32 Gbit/s even though the coupling loss is smaller than 10%. As the coupling angle changes from 0° to 4°, the transmission performance is also stable with a BER of 9.8×10−10 and an SNR of 15.6 dB, as shown in Fig. 7(c). Although the output power changes for the lensed SMF coupling with varying the coupling angles, the transmission performance is not changed owing to the small power variation by detuning the coupling angle from 0° to 4°. Therefore, the data transmission can keep stable with a slightly decreased data rate for the lensed SMF + 100-m GI-SMF link. These results exhibit one of the advantages of the lensed SMF + 100-m GI-SMF link. For the lensed OM4-MMF + 100-m GI-SMF transmission, the coupling loss is too large to carry out data transmission.
4. Conclusion
The NRZ-OOK data transmitted by the 850-nm SM-VCSEL with various collimation scenarios using either OM4-MMF or GI-SMF lensed coupler under different tilted angles are analyzed for data center applications. The coupling power ratio is decreased by enlarging the tilting angle with revealing an antilogarithm-function trend, as attributed to the serious mismatch of the optical field between the Gaussian beam of the VCSEL and the focal point of the lensed fiber. Employing the lensed OM4-MMF shows the decreasing output power with a slower decaying slope and a greater tolerance to the tilting-angle variation as compared to the lensed SMF. In the BtB case, the OM4-MMF coupling obtains a higher power of 0.56 mW because of the larger core diameter regardless of its tilting angle from 0° to 4°. The SM-VCSEL output power coupled by using the lensed SMF collimator is only 0.23 mW under exactly vertical coupling, which slightly reduces to 0.21 mW. When enlarging the tilting angle of coupling up to 10°, the lensed OM4-MMF collimator shows a large coupling angle tolerance with the coupling efficiency only degraded by 5%. but the lensed SMF collimator attenuates the coupled SM-VCSEL output by more than 50%. When directly encoding the SM-VCSEL with the NRZ-OOK data transmission in the OM4-MMF, the receivable NRZ-OOK data rate in BtB and after 100-m OM4-MMF cases can achieve 50 Gbit/s with its corresponding BER degraded from 6.5 × 10−10 to 8.8 × 10−10 when enlarging its tilting angle ranged from 0° to 10°. By changing the collimator to the lensed SMF, the decoded BER significantly degrades from 5.8 × 10−5 to 1.2 × 10−1 when coupling and transmitting the NRZ-OOK data at 50 Gbit/s. Owing to the low coupling efficiency via the lensed SMF collimator, the error-free NRZ-OOK data rate somewhat decreases to 35 Gbit/s in the BtB link for decoding the BER of 1.8×10−10 with a receiving SNR of 16 dB, which further decreases to 32 Gbit/s with corresponding BER and SNR of 9.8×10−10 and 15.6 dB after passing through the Lensed SMF + 100-m GI-SMF link with allowable coupling angle tilted from 0° to 4°. The performance of the receiving BER versus the allowable data rate reveals almost unchanged when varying the titled angle of coupling from 0° to 4°, indicating that the transmission performance is not affected by the coupling angle no matter using lensed MMF or SMF collimator under the small coupling angle variation. This work confirms the applicability of the lensed MMF or SMF collimator for coupling the SM-VCSEL output with a relatively large tolerance on the tilting angle with respect to the surface normal of the SM-VCSEL.
Funding
Ministry of Science and Technology, Taiwan (MOST 109-2221-E-002-184-MY3, MOST 110-2124-M-A49-003-, MOST 110-2221-E-002-100-MY3, MOST 110-2224-E-992-001-).
Acknowledgment
Chih-Hsien Cheng is supported by International Research Fellow of Japan Society for the Promotion of Science (Postdoctoral Fellowships for Research in Japan (Standard)) with a grant number of 20F20374.
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.
References
1. P. Westbergh, R. Safaisini, E. Haglund, B. Kögel, J.S. Gustavsson, A. Larsson, M. Geen, R. Lawrence, and A. Joel, “High-Speed 850 nm VCSELs with 28 GHz modulation bandwidth operating error-up to 44 Gbit/s,” Electron. Lett. 48(18), 1145–1147 (2012). [CrossRef]
2. H. E. Li and K. Iga, “Vertical-Cavity Surface-Emitting Laser Devices,” Springer Series in Photonics (Springer, 2003), Vol. 6.
3. C.-T. Tsai, C.-Y. Peng, C.-Y. Wu, S.-F. Leong, H.-Y. Kao, H.-Y. Wang, Y.-W. Chen, Z.-K. Weng, Y.-C. Chi, H.-C. Kuo, J. J. Huang, T.-C. Lee, T.-T. Shih, J.-J. Jou, W.-H. Cheng, C.-H. Wu, and G.-R. Lin, “Multi-Mode VCSEL Chip with High-Indium-Density InGaAs/AlGaAs Quantum-Well Pairs for QAM-OFDM in Multi-Mode Fiber,” IEEE J. Quantum Electron. 53, 2400608 (2017). [CrossRef]
4. H.-Y. Kao, Y.-C. Chi, C.-T. Tsai, S.-F. Leong, C.-Y. Peng, H.-Y. Wang, J. J. Huang, J.-J. Jou, T.-T. Shih, H.-C. Kuo, W.-H. Cheng, C.-H. Wu, and G.-R. Lin, “Few-mode VCSEL chip for 100-Gb/s transmission over 100 m multimode fiber,” Photonics Res. 5(5), 507–515 (2017). [CrossRef]
5. R. Safaisini, K. Szczerba, P. Westbergh, E. Haglund, B. Kögel, J. S. Gustavsson, M. Karlsson, P. Andrekson, and A. Larsson, “High-Speed 850 nm Quasi-Single-Mode VCSELs for Extended-Reach Optical Interconnects,” J. Opt. Commun. Netw. 5(7), 686–695 (2013). [CrossRef]
6. C.-H. Cheng, C.-C. Shen, H.-Y. Kao, D.-H. Hsieh, H.-Y. Wang, Y.-W. Yeh, Y.-T. Lu, S.-W. Huang Chen, C.-T. Tsai, Y.-C. Chi, K.-S. Kao, C.-H. Wu, H.-C. Kuo, P.-T. Lee, and G.-R. Lin, “850/940-nm VCSEL for optical communication and 3D sensing,” Opto-Electron. Adv. 1, 180005 (2018). [CrossRef]
7. H.-Y. Kao, C.-T. Tsai, S.-F. Leong, C.-Y. Peng, Y.-C. Chi, J. J. Huang, H.-C. Kuo, T.-T. Shih, J.-J. Jou, W.-H. Cheng, C.-H. Wu, and G.-R. Lin, “Comparison of single-/few-/multi-mode 850 nm VCSELs for optical OFDM transmission,” Opt. Express 25(14), 16347–16363 (2017). [CrossRef]
8. H.-Y. Kao, C.-T. Tsai, S.-F. Leong, C.-Y. Peng, Y.-C. Chi, H.-Y. Wang, H.-C. Kuo, C.-H. Wu, W.-H. Cheng, and G.-R. Lin, “Single-mode VCSEL for pre-emphasis PAM-4 transmission up to 64 Gbit/s over 100–300 m in OM4 MMF,” Photonics Res. 6(7), 666–673 (2018). [CrossRef]
9. K. Li, X. Chen, J. E. Hurley, J. S. Stone, and M.-J Li, “High data rate few-mode transmission over graded-index single-mode fiber using 850 nm single-mode VCSEL,” Opt. Express 27(15), 21395–21404 (2019). [CrossRef]
10. M.-J. Li, K. Li, X. Chen, S. K. Mishra, A. A. Juarez, J. E. Hurley, J. S. Stone, C.-H. Wang, H.-T. Cheng, C.-H. Wu, H.-C. Kuo, C.-T. Tsai, and G.-R. Lin, “Single-Mode VCSEL Transmission for Short Reach Communications,” J. Lightwave Technol. 39(4), 868–880 (2021). [CrossRef]
11. D. Vez, S. G. Hunziker, R. Kohler, P. Royo, M. Moser, and W. Bächtold, “850 nm vertical-cavity laser pigtailed to standard singlemode fibre for radio over fibre transmission,” Electron. Lett. 40(19), 1210–1211 (2004). [CrossRef]
12. J. Nanni, J.-L. Polleux, C. Algani, S. Rusticelli, F. Perini, and G. Tartarini, “VCSEL-Based Radio-Over-G652 Fiber System for Short-/Medium-Range MFH Solutions,” J. Lightwave Technol. 36(19), 4430–4437 (2018). [CrossRef]
13. I. Papakonstantinou, S. Papadopoulos, C. Soos, J. Troska, F. Vasey, and P. Vichoudis, “Modal dispersion mitigation in standard single-mode fibers at 850 nm with fiber mode filters,” IEEE Photonics Technol. Lett. 22(20), 1476–1478 (2010). [CrossRef]
14. Å Haglund, J. S. Gustavsson, J. Vukŭsić, and P. Modh, “Single Fundamental-Mode Output Power Exceeding 6 mW From VCSELs With a Shallow Surface Relief,” IEEE Photon. Technol. Lett. 16(2), 368–370 (2004). [CrossRef]
15. K. Szczerba, P. Westbergh, J. Karout, J. S. Gustavsson, Å. Haglund, M. Karlsson, P. A. Andrekson, E. Agrell, and A. Larsson, “4-PAM for High-Speed Short-Range Optical Communications,” J. Opt. Commun. Netw. 4(11), 885–894 (2012). [CrossRef]
16. M. P. Tan, S. T. M. Fryslie, J. A. Lott, N. N. Ledentsov, D. Bimberg, and K. D. Choquette, “Error-Free transmission over 1-km OM4 multi-mode fiber at 25 Gb/s using a single mode photonic crystal vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett. 25(18), 1823–1825 (2013). [CrossRef]
17. R. Safaisini, E. Haglund, P. Westbergh, J. S. Gustavsson, and A. Larsson, “20 Gbit/s data transmission over 2 km multimode fibre using 850 nm mode filter VCSEL,” Electron. Lett. 50(1), 40–42 (2014). [CrossRef]
18. R. Michalzik and K. J. Ebeling, “Generalized BV diagrams for higher order transverse modes in planar vertical-cavity laser diodes,” IEEE J. Quantum Electron. 31(8), 1371–1379 (1995). [CrossRef]
19. M. H. Macdougal, J. Geske, C. K. Lin, A. E. Bond, and P. D. Dapkus, “Low resistance intracavity-contacted oxide-aperture VCSELs,” IEEE Phot. Techn. Lett. 10(1), 9–11 (1998). [CrossRef]
20. I. Harrison, H. P. Ho, B. Tuck, M. Henini, and O. H. Hughes, “Zn diffusion-induced disorder in AlAs/GaAs superlatttices,” Semicond. Sci. Technol. 4(10), 841–846 (1989). [CrossRef]
21. Y. J. Yang, T. G. Dziura, T. Bardin, S. C. Wang, and R. Fernandez, “Continuous Wave Single Transverse Mode Vertical-Cavity Surface-emitting Lasers Fabricated by Helium Implantation and Zinc Diffusion,” Electron. Lett. 28(3), 274–276 (1992). [CrossRef]
22. J.-W. Shi, C.-C. Chen, Y.-S. Wu, S.-H. Guol, and Y.-J. Yang, “High power and high-speed Zn-diffusion single fundamental-mode vertical cavity surface-emitting lasers at 850 nm wavelength,” IEEE Photon. Technol. Lett. 20(13), 1121–1123 (2008). [CrossRef]
23. H.-Y. Kao, C.-T. Tsai, Y.-C. Chi, C.-Y. Peng, S.-F. Leong, H.-Y. Wang, C.-H. Cheng, W.-L. Wu, H.-C. Kuo, W.-H. Cheng, C.-H. Wu, and G.-R. Lin, “Long-Term Thermal Stability of Single-Mode VCSEL Under 96-Gbit/s OFDM Transmission,” IEEE J. Sel. Top. Quantum Electron. 25, 1500609 (2019). [CrossRef]
24. N. Suzuki, H. Hatakeyama, K. Fukatsu, T. Anan, K. Yashiki, and M. Tsuji, “25-Gbps operation of 1.1-µm-range InGaAs VCSELs for high-speed optical interconnections,” in Optical Fiber Communication Conference (OFC) (2006), paper OFA4.
25. W. Hofmann, N. H. Zhu, M. Ortsiefer, G. Bohm, J. Rosskopf, L. Chao, S. Zhang, M. Maute, and M. C. Amann, “10-Gb/s data transmission using BCB passivated 1.55 µm InGaAlAs-InP VCSELs,” IEEE Photon. Technol. Lett. 18(2), 424–426 (2006). [CrossRef]
26. C.-Y. Huang, H.-Y. Wang, C.-H. Wu, W.-C. Lo, C.-T. Tsai, C.-H. Wu, M. Feng, and G.-R. Lin, “Comparison on OM5-MMF and OM4-MMF Data Links With 32-GBaud PAM-4 Modulated Few-Mode VCSEL at 850 nm,” J. Lightwave Technol. 38(3), 573–582 (2020). [CrossRef]
27. J. Y. Law and G. P. Agrawal, “Mode-partition noise in vertical-cavity surface emitting lasers,” IEEE Photonics Technol. Lett. 9(4), 437–439 (1997). [CrossRef]
28. L.-G. Zei, S. Ebers, J.-R Kropp, and K. Petermann, “Noise Performance of Multimode VCSELs,” J. Lightwave Technol. 19(6), 884–892 (2001). [CrossRef]
29. W.-C. Lo, W.-L. Wu, C.-H. Cheng, H.-Y. Wang, C.-T. Tsai, C.-H. Wu, and G.-R. Lin, “Effect of Chirped Dispersion and Modal Partition Noise on Multimode VCSEL Encoded With NRZ-OOK and PAM-4 Formats,” IEEE J. Sel. Top. Quantum Electron. 28, 1500409 (2021). [CrossRef]
