Semiconductor lasers, allowing for indispensable science and a wide range of technologies, have become one of the most important enablers of photonics-based technologies . Vertical-cavity surface-emitting lasers (VCSEL), a vital class of semiconductor lasers , specifically, are gaining importance given their form factor and optoelectronic performance for their use as an optical source in high-speed, short-wavelength communications ,  and sensors , , . For instance, in recent years VCSELs have been deployed aside semiconductor diode lasers as the sources in cost-effective fiber links and data center networks , , . This is due to their distinct features, such as high reliability, low cost and high manufacturing yield, low power consumption, seamless packaging, low lasing threshold and operating currents, high-temperature stability, and straightforward fabrication of dense arrays , , . For data-transmission applications, a high modulation bandwidth is desired. The 3-dB bandwidth of the VCSEL is limited by thermal effects, parasitic resistance, capacitance, and nonlinear gain effects (such as relaxation oscillations) , . Thus, with an appropriate design of the active region and RC parasitics, which bypasses the modulation current outside the active region at high frequencies, a high modulation bandwidth can be attained. Optical feedback has proven to increase the modulation bandwidth of VCSELs, owing to an induced photon–photon resonance (PPR) effect , , , . For example, Dalir et al. ,  demonstrated modulation bandwidth enhancement of a VCSEL by adding a single transverse-coupled cavity (TCC) to a primary VCSEL cavity. The underlying principle is to control the delay time in the TCC via an induced slow-light feedback section. However, strong PPR effects suffer comparatively large “kinks” in the light-versus-current (L–I) characteristics indicative of induced laser instabilities due to increased supply currents , , , , . Nonetheless, multiple TCCs (MTCCs) are advantageous to avoid these instabilities in the linear region of the L–I curve. Indeed, this is the common issue in standard (twin) coupled cavities , , , ,  in addition to challenges with respect to optical injection locking .
In this article, we introduce and demonstrate a new design of a VCSEL combining MTCCs, which aims to enhance slow-light optical feedback, thus extending the temporal laser bandwidth (speed) beyond the limit of the relaxation oscillation frequency. In our design, we propose and show that a VCSEL cavity surrounded by MTCCs adiabatically provides direct slow-light feedback from each TCC to the main lasing cavity. Therefore, even if the direct feedback from each cavity is only moderate, it will yet redistribute the optical field density by funneling the slow-light mode into the central cavity, which effectively allows generating sufficient feedback to extend the temporal laser bandwidth (speed). Following this coupled cavity scheme, we show a resulting modulation bandwidth in the 100 GHz range. We validate this novel laser design paradigm by demonstrating a VCSEL design following a hexagonal multi-cavity approach showing a bandwidth of about 45 GHz, which is an about five times improvement over ‘conventional’ VCSEL designs realized on the same wafer. Beyond speed performance, the MTCC paradigm can further be used to increase the laser power output; to achieve high-power at single-mode operation, the Vernier effect in the hexagonal VCSEL can be used to form a wider laser aperture , . Following this design concept, we demonstrate single-mode operation with a high (>30 dB) side-mode suppression (SMSR) and prominent (>45 dB) signal-to-noise ratio (SNR). Finally, optimizing the lattice design, we show extending the laser stability for higher output power by about three times compared with conventional VCSEL fabricated on same epiwafer .
2 Structure and concept
The MTCC VCSEL is designed to promote adiabatic light energy sharing between the coupled cavities relative to the central laser cavity (Figure 1). Even if the feedback strength of each cavity is in a moderate range (∼0.1 THz) , because of its adiabatic design, the laser cavity parametrically accumulates an increased amount of the slow-light portion of the light gain and makes this available for the to-be-modulated cavity. Creating a functional space separation between selective gain and modulation functions is the key to simultaneously achieving high speed and high power in single-mode operation. Furthermore, this design is advantageous by avoiding the optical loss accumulated in the chain of cascaded TCCs .
3 Experimental demonstration of the hexagonal VCSEL
This formulism can predict the MTCC small-signal response as a function of the modulation frequency (Figure 2a); the laser’s intensity modulation (IM), including several PPR effects, shows a speed in excess of 40 GHz, which is about fivefold higher than conventional VCSEL design lacking the MTCC approach. In addition, the corresponding response curve shows a high degree of stability; that is, it is relatively robust against changes in the slow-light feedback (η). The IM response of a conventional VCSEL (η = 0) shows the expected slow (9 GHz) response (Figure 2a) , [, 1935]. For a moderate pump and TCC feedback (Ilaser = 2.5 × Ith = 8 mA and η = 0.12), the IM response exhibits an enhanced carrier to photon resonance (CPR) and multiple PPR before its 3-dB roll-off, which occurs at a bandwidth frequency of 42 GHz (Figure 2a). Increasing the coupling between the inner (modulating) cavity and outer (feedback) cavities exhibit an extended 3-dB roll-off reaching 100 GHz on further increasing the coupling strength to η = 0.45 (Figure 2b) . Note, that an increased coupling strength, normally, adversely affects the stability of the laser; however, some of these can be accounted for using the added degree of freedom given by the MTCC paradigm. As illustrated in Figure 2c, L–I characteristics start displaying ‘kinks’ while the coupling strength increases from η = 0.12 to 0.3.
Figure 3 shows a top view of the fabricated hexagonal VCSEL and the calibrated 45 GHz small-signal measurement test setup. This top emitting VCSEL structure is grown by metal organic chemical vapor deposition on an n+ substrate. The epitaxial structure consists of 35 pairs of Si-doped bottom Al0.16Ga0.84As/Al0.9Ga0.1As distributed Bragg reflector (DBR), whereas the cavity consists of three 70 Å, In0.3Ga0.7As–GaAs quantum wells, and a top 24-period DBR mirror. Inductively coupled plasma etched the mesa into a semiconductor heterostructure, and its etch size was selected to be 2 µm larger than the active diameter (mesa diameter and oxidation time optimization). The aperture mesa diameters used are 3.5 μm wide to ensure single transverse mode operation with a lower threshold current. The inner cavity is an RF-modulated VCSEL with the six identical outer cavities adiabatically coupled to the center cavity, thus providing parametric and selective slow-light feedback. The end interface of each feedback cavity acts as a perfect mirror in the lateral direction, supporting the lateral optical light coupled back into the inner one .
However, the TCC-based VCSEL design has two fundamental challenges; (i) a typical limitation of the VCSEL with only a single TCC requires a strong slow-light coupling coefficient to enhance the modulation, and (ii) the TCC(s) add parasitic nonlinearity which reduces the modulation performance , , , .
To mitigate or entirely avoid both of these limitations, we propose and show that rather than relying on a single cavity, a MTCC design induces direct slow-light feedback from each TCC, thus enhancing feedback and relaxing coupling coefficient requirements. The small-signal frequency response (S21) of the VCSEL was obtained by generating a low power modulating signal with a vector network analyzer. The output modulated intensity from the inner (laser) cavity with a fixed current is then collected via a single-mode fiber, whereas each of feedback cavities is operated at 2 mA. A high-speed photodetector (PD) collects the VCSEL’s RF output and compares it with the original modulating source. The IM response showed enhanced CPR and multiple PPR before its 3-dB roll-off. The 3-dB roll-off of the MTCC-enhanced laser exceeds the conventional design by about fivefold compared with a conventional VCSEL fabricated on the same epiwafer (Figure 4a). While the conventional VCSEL being driven at Iconventional = 7 mA, which is the maximum power before it saturates, our designed VCSEL is just operated at 8 mA for the inner cavity with surrounding cavities driven at constant current of 2 mA below threshold bias current. Even at this level, our 3-dB roll-off is beyond the PD limit (>45 GHz). Figure 4b depicts the measured L–I curve for our MTCC VCSEL with an effective aperture size of 3.5 × 25 µm2, and a conventional VCSEL fabricated on the same epitaxial wafer with an aperture size of 3 × 3 µm2. Interestingly, this hexagonal VCSEL drives more current even beyond the conventional limitation (>7 mA), the output power linearly increases to about 5.5 mW, which is almost triple that of its conventional counterpart. It is also, important to mention that the threshold current of our hexagonal VCSEL can be further reduced via optimization of the oxide layer structure close to conventional VCSEL. Thanks to the Vernier effect in the MTCC VCSEL, even with such a large oxide aperture, a single-mode operation with SMSR of >30 dB (7 dB higher than a conventional VCSEL design)  and SNR of >45 dB are obtained (Figure 4c). Note, that to obtain a coupling of η ∼ 0.45 (which potentially provide a 3-dB roll-off ∼100 GHz), one can design oxide-free VCSELs recently reported by Deppe .
In conclusion, we propose a novel design of a 980 nm VCSEL adiabatically and laterally coupled to six hexagonal feedback cavities. Succeeding this approach, we demonstrate a fivefold higher 3-dB roll-off laser modulation bandwidth (>45 GHz limited by the experimental setup) compared with a noncoupled, conventional design.
This coupled hexagonal VCSEL paradigm shows single-mode operation with SMSR > 30 dB, which is 7 dB higher than a conventional VCSEL fabricated on the same epiwafer. Furthermore, with an SNR of >45 dB, the peak output power of 5.5 mW is about triple as high compared with the conventional design. Further bandwidth enhancement for the VCSEL with MTCC is the need for a strong slow-light coupling into the modulating cavity. For example, to obtain η ∼ 0.45, it is possible to provide a roll-off of 3 dB–100 GHz. This device concept opens up new opportunities and fields of use ranging from data-comm, to sensing, automotive, and photonic artificial intelligence systems.
The authors thank Dr. Gernot Pomrenke, Dr. Luke Graham and Dr. Chung-Yi Su for their fruitful discussions.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: Air Force Office of Scientific Research (AFSOR) Small Business Innovation Research (SBIR) Program (FA9550-19-C-0003) Naval Research Electronic Warfare Program (N00014-19-1-2595).
K. Iga, “Surface-emitting laser-its birth and generation of new optoelectronics field,” IEEE J. Sel. Top. Quant., vol. 6, pp. 1201–1215, 2000. https://doi.org/10.1109/2944.902168.
G. de Valicourt, G. Levaufre, Y. Pointurier, et al., “Direct modulation of hybrid-integrated InP/Si transmitters for short and long reach access network,” J. Lightwave Technol., vol. 33, pp. 1608–1616, 2015. https://doi.org/10.1109/jlt.2015.2396297.
S. Kajiya, K. Tsukamoto, and S. Komaki, “Proposal of fiber-optic radio highway networks using CDMA method,” Proceedings of ICUPC ‘95 – 4th IEEE International Conference on Universal Personal Communications, Tokyo, Japan, vol. 1995, pp. 496–500, 1996. https://doi.org/10.1109/ICUPC.1995.497058.
K. Iga, “Vertical-cavity surface-emitting laser: it’s conception and evolution,” Jpn. J. Appl. Phys., vol. 47, pp. 1–10, 2008. https://doi.org/10.1143/jjap.47.1.
C. P. T. McPolin, J.-S. Bouillard, S. Vilain, et al., “Integrated plasmonic circuitry on a vertical-cavity surface-emitting semiconductor laser platform,” Nat. Commun., vol. 7, p. 12409, 2016. https://doi.org/10.1038/ncomms12409.
A. Larsson, “Advances in VCSELs for communication and sensing,” IEEE J. Sel. Top. Quant., vol. 17, pp. 1552–1567, 2011. https://doi.org/10.1109/jstqe.2011.2119469.
M. Z. Alam, I. D. Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science, vol. 352, pp. 795–797, 2016. https://doi.org/10.1126/science.aae0330.
R. Rodes, M. R. Rodes, M. Mueller, et al., “High-speed 1550 nm VCSEL data transmission link employing 25 GBd 4-PAM modulation and hard decision forward error correction,” J. Lightwave Technol., vol. 31, pp. 689–695, 2013. https://doi.org/10.1109/jlt.2012.2224094.
C. Choi, L. Lin, Y. Liu, and R. T. Chen, “Performance analysis of 10-µm-thick VCSEL array in fully embedded board level guided-wave optoelectronic interconnects,” J. Lightwave Technol., vol. 21, pp. 1531–1535, 2013. https://doi.org/10.1109/JLT.2003.812162.
F. Koyama, “Recent advances of VCSEL photonics,” J. Lightwave Technol., vol. 24, pp. 4502–4513, 2006. https://doi.org/10.1109/jlt.2006.886064.
R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers, Berlin, Springer, 2012, p. 557–577.
L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, vol. 218, Hoboken, John Wiley & Son, 2012, p. 260.
C. Wilmsen, H. Temkin, and L. A. Coldren, Vertical-cavity Surface-Emitting Lasers: Design, Fabrication, Characterization, and Applications, vol. 24, United Kingdom, Cambridge University Press, 2001.
C. Chen and K. D. Choquette, “Analog and digital functionalities of coupled cavity surface emitting lasers,” J. Lightwave Technol., vol. 28, pp. 1003–1010, 2010. https://doi.org/10.1109/jlt.2010.2041747.
A. Paraskevopoulos, H. J. Hensel, W. D. Molzow, et al.., in OFC Conference and the National Fiber Optic Engineers Conference, paper PDP22, 2006.
P. Westbergh, J. S. Gustavsson, B. Kögel, Å. Haglund, and A. Larsson, “Impact of photon lifetime on high-speed VCSEL performance,” IEEE J. Sel. Top. Quant., vol. 17, pp. 1603–1613, 2011. https://doi.org/10.1109/jstqe.2011.2114642.
P. Bardella, W. W. Chow, and I. Montrosset, “Design and analysis of enhanced modulation response in integrated coupled cavities DBR lasers using photon–photon resonance,” Photonics, vol. 3, p. 4, 2016. https://doi.org/10.3390/photonics3010004.
H. Dalir and F. Koyama, “29 GHz directly modulated 980 nm vertical-cavity surface emitting lasers with bow-tie shape transverse coupled cavity,” Appl. Phys. Lett., vol. 103, p. 091109, 2013. https://doi.org/10.1063/1.4820149.
H. Dalir and F. Koyama, “High-speed operation of bow-tie-shaped oxide aperture VCSELs with photon–photon resonance,” Appl. Phys. Express, vol. 7, p. 022102, 2014. https://doi.org/10.7567/apex.7.022102.
Z. Gao, S. T. M. Fryslie, B. J. Thompson, P. Scott Carney, and K. D. Choquette, “Parity-time symmetry in coherently coupled vertical cavity laser arrays,” Optica, vol. 4, pp. 323–329, 2017. https://doi.org/10.1364/optica.4.000323.
S. T. M. Fryslie, M. P. T. Siriani, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photonics Technol. Lett., vol. 27, pp. 415–418, 2015. https://doi.org/10.1109/lpt.2014.2376959.
Z. Feng, F. Yang, X. Zhang, et al., “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep., vol. 8, p. 13135, 2018. https://doi.org/10.1038/s41598-018-31381-x.
H. Dave, P. Liao, S. T.-M. Fryslie, et al., “Digital modulation of coherently-coupled 2 × 1 vertical-cavity surface-emitting laser arrays,” IEEE Photonics Technol. Lett., vol. 31, pp. 173–176, 2019. https://doi.org/10.1109/lpt.2018.2888806.
C. Xu, W. E. Hayenga, H. Hodaei, D. N. Christodoulides, M. Khajavikhan, and P. LiKamWa, “Enhanced modulation characteristics in broken symmetric coupled microring lasers,” Opt. Express, vol. 28, pp. 19608–19616, 2020. https://doi.org/10.1364/oe.394830.
H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science, vol. 346, pp. 975–978, 2014. https://doi.org/10.1126/science.1258480.
M. A. Miri, P. LiKamWa, and D. N. Christodoulides, “Large area single-mode parity-time-symmetric laser amplifiers,” Opt. Lett., vol. 37, pp. 764–766, 2012. https://doi.org/10.1364/ol.37.000764.
N. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled semiconductor lasers subject to optical injection”, Sci. Rep., vol. 8, p. 109, 2018. https://doi.org/10.1038/s41598-017-18379-7.
M. Li, N. Zhang, K. Wang, J. Li, S. Xiao, and Q. Song, “Inversed Vernier effect based single-mode laser emission in coupled microdisks,” Sci. Rep., vol. 5, p. 13682, 2015. https://doi.org/10.1038/srep13682.
H. R. Ibrahim, M. Ahmed, and F. Koyama, in 24th Microoptics Conference (MOC), Japan, 2019, pp. 300–301.
E. Heidari, H. Dalir, M. Ahmed, M. H. Teimourpour, V. J. Sorger, and R. T. Chen, in Proc. SPIE 11286, Optical Interconnects 2020 XX, p. 112861B.
H. Dalir and F. Koyama, “Bandwidth enhancement of single-mode VCSEL with lateral optical feedback of slow light,” IEICE Electron. Express, vol. 8, pp. 1075–108, 2011. https://doi.org/10.1587/elex.8.1075.
M. Ahmed, A. Bakry, M. S. Alghamdi, H. Dalir, and F. Koyama, “Enhancing the modulation bandwidth of VCSELs to the millimeter-waveband using strong transverse slow-light feedback,” Opt. Express, vol. 23, pp. 15365–15371, 2015. https://doi.org/10.1364/oe.23.015365.
R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quant. Electron., vol. 16, pp. 347–355, 1980. https://doi.org/10.1109/jqe.1980.1070479.
X. Gu, M. Nakahama, A. Matsutani, M. Ahmed, A. Bakry, and F. Koyama, “850 nm transverse-coupled-cavity vertical-cavity surface-emitting laser with direct modulation bandwidth of over 30 GHz,” Appl. Phys. Express, vol. 8, p. 082702, 2015. https://doi.org/10.7567/apex.8.082702.
K. Iga, in Proc. SPIE 11263 (VECSELs) X, 2020, p. 1126302.
H. Dalir, Y. Takahashi, and F. Koyama, “Low-voltage, high-speed and compact electro-absorption modulator laterally integrated with 980-nm VCSEL,” Opt. Express, vol. 22, pp. 25746–25755, 2014. https://doi.org/10.1364/oe.22.025746.
K. Iga, F. Koyama, and S. Kinoshita, “Surface emitting semiconductor lasers,” IEEE J. Quant. Electron., vol. 24, pp. 1845–1855, 1988. https://doi.org/10.1109/3.7126.
M. Bayat and D. G. Deppe, “Laser characteristics for VCSELs for 77 K and 4 K optical data applications,” IEEE J. Quant. Electron., vol. 56, pp. 1–6, 2020. https://doi.org/10.1109/jqe.2020.2967783.