Vertical-cavity surface-emitting lasers with nanostructures for optical interconnects

Abstract

Optical interconnects (OIs) are the only solution to fulfil both the requirements on large bandwidth and minimum power consumption of data centers and high-performance computers (HPCs). Vertical-cavity surface-emitting lasers (VCSELs) are the ideal light sources for OIs and have been widely deployed. This paper will summarize the progress made on modulation speed, energy efficiency, and temperature stability of VCSELs. Especially VCSELs with surface nanostructures will be reviewed in depth. Such lasers will provide new opportunities to further boost the performance of VCSELs and open a new door for energy-efficient OIs.

Key words： optical interconnects (OIs); vertical-cavity surface-emitting laser (VCSEL); subwavelength grating; modulation speed; energy efficiency

Introduction

As more and more devices are connected to the Internet, Internet data traffic grows dramatically and demands increasing performance of data centers as shown in Fig. 1 [ 1]. Especially, cloud computing and big data analysis urge higher data-center performance. Similarly high-performance computers (HPCs) are of steadily increasing interest to provide new levels of computational capability for applications such as geophysical data processing, drug discovery, and climate modeling. The performance of the top 500 supercomputers increases by a factor of 10 every 4 years in the past 20 years [ 2], and it is predicted that supercomputers will reach above 1 exaflops/s in 2020, 20 times higher performance than the current top supercomputer (see Fig. 2). To realize the expected performance of future data centers and HPCs, more communication bandwidth is demanded. Optical interconnect (OI) technology has been proved to be a huge success in the long-distance communication, and has been also deployed in short-reach applications in data centers and HPCs to replace copper-based electrical interconnects [ 3– 8]. Compared with electrical interconnects, OIs have many advantages, for example, broad band, high density, small size, low loss, high power efficiency, and low crosstalk [ 8– 10]. Currently OIs in Datacom and Computercom have been based on multi-mode fibers and vertical-cavity surface-emitting laser (VCSEL) technology, because of low cost, large alignment tolerance, ease of 2D array packaging, and high energy efficiency [ 11– 15]. The wavelength of 850 nm for VCSEL-based links is applied in today’s optical links in Datacom and Computercom, and recently the wavelength range from 900 to 1100 nm and even longer wavelengths is of growing interest [ 16– 26]. This is because there are a large potential for higher speed and efficiency, improved reliability, improved dispersion, higher photodetector responsivity, and backside emission.

Fig.1 Global data center IP traffic growth at a compound annual growth rate (CAGR) of 25% from 2014 to 2019 [1]

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Fig.2 Exponential growth of supercomputing power as recorded by the TOP500 list [2]

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For VCSELs applied in OIs, high speed modulation is an essential requirement to meet the thirsty for permanently increasing bandwidth. As demands for network bandwidth exponentially increase, the size of data centers and HPCs becomes larger and more power is consumed. On the other hand, the heat dissipation in the systems leads to an operating environment for the optical components reaching temperatures of 85°C, even with advanced cooling technologies. Therefore, the VCSELs must be very energy-efficient, and be capable to maintain a high modulation speed at high temperatures without adjusting the operating parameters. In the past few years, VCSELs have achieved numerous and exciting successes in modulation speed, energy efficiency, and temperature stability [ 20– 34]. To further boost the performance of VCSELs for OIs, adopting surface nanostructures to construct nano-scale VCSEL structures is one promising approach. This approach is expected not only to improve the modulation speed, energy efficiency, and temperature stability, but also to realize new functions and can be integrated with planar optical circuits to realize on-chip OIs. In this paper, first the dynamics of VCSELs will be briefly introduced. Then, some basic physics of nanostructures will be given. Finally, the progress of VCSELs with nanostructures will be reviewed, followed by a conclusion.

VCSELs for OIs

Dynamics of VCSELs

The dynamical behavior of semiconductor lasers is commonly described in terms of the rate equations [ 35]. The modulation speed of a VCSEL is limited by the intrinsic damping, self-heating, and external parasitics. The intrinsic modulation response of semiconductor lasers can be expressed as the transfer function

(1) {{\displaystyle H}}_{\mathrm{i}}\left(f\right)=A\times {\displaystyle \frac{{{\displaystyle f}}_{\mathrm{r}}^{\mathrm{2}}}{{{\displaystyle f}}_{\mathrm{r}}^{\mathrm{2}}-f^{\mathrm{2}}+\mathrm{j}{\displaystyle \frac{f}{\mathrm{2}\mathrm{\pi }}}\mathit{\gamma }}},

where A is a constant, f_r the relaxation resonance frequency and γ the damping factor.

The relaxation resonance frequency is the oscillation frequency between the carriers and photons through the stimulated emission in the laser cavity. To achieve a high bandwidth, a VCSEL should reach a large relaxation resonance frequency. The relaxation resonance frequency increases with the bias current and can be formulated as

(2) {{\displaystyle f}}_{\mathrm{r}}=D\sqrt{I-{{\displaystyle I}}_{\mathrm{t}\mathrm{h}}},

with D={\displaystyle \frac{\mathrm{1}}{\mathrm{2}\mathrm{\pi }}}\sqrt{{\displaystyle \frac{{\eta }_{\mathrm{i}}\mathrm{\Gamma }{v}_{\mathrm{g}}}{q{{\displaystyle V}}_{\mathrm{a}}}}\times {\displaystyle \frac{{\displaystyle \frac{\partial g}{\partial n}}}{\chi }}} , where I_th is the threshold current, G the optical confinement factor, h_i the internal quantum efficiency, v_g the photon group velocity, V_a the active region volume, ∂g/∂n the differential gain, and c the transport factor.

The damping factor is also a limit to achieve a high bandwidth besides the relaxation resonance frequency. The damping factor increases with the increase of the relaxation resonance frequency and is given as following equation

(3) \gamma =K{{\displaystyle f}}_{\mathrm{r}}^{\mathrm{2}}+{{\displaystyle \mathit{\gamma }}}_{\mathrm{0}},K=\mathrm{4}{\mathrm{\pi }}^{\mathrm{2}}\left({{\displaystyle \tau }}_{\mathrm{p}}+{\displaystyle \frac{ϵ\chi }{{{\displaystyle v}}_{\mathrm{g}}{\displaystyle \frac{\partial g}{\partial n}}}}\right),

where t_p is the photon lifetime and ϵ is the gain compression factor. The damping offset γ₀ is inversely proportional to the differential carrier lifetime.

To achieve a high bandwidth of VCSLs, a large D-factor and reasonable low K-factor are preferred, i.e., high differential gain [ 21– 32], low photon lifetime [ 17, 25, 26, 36, 37], and high confinement factor [ 25, 26, 33, 37]. In the real devices, the relaxation resonance frequency and damping factor do not linearly increase with \sqrt{I-{{\displaystyle I}}_{\mathrm{t}\mathrm{h}}} and {{\displaystyle f}}_{\mathrm{r}}^{\mathrm{2}} , respectively, because of thermal effects [ 12].

State of the art of VCSELs for OIs

For a high differential gain, compressively strained InGaAs quantum wells (QWs) are commonly employed in the wavelength range from 850 to 1200 nm [ 11– 18, 20– 24]. Shallow surface etching has been adopted to tune the photon lifetime to enhance the modulation bandwidth but introduces mirror losses as shown in Fig. 3 [ 36]. However, Bimberg’s group at TU Berlin experimentally showed that a short laser cavity, for example, l/2-cavity, can greatly enhance the confinement factor to 5.1% from 3% in a 3l/2-cavity without degrading other parameters [ 37, 38]. Figure 4 shows that there is a maximum peak of the field intensity distribution at the QWs region for the l/2-cavity compared with the 3l/2-cavity. At the same time, a short cavity means a low photon lifetime resulting in a low K-factor [ 37]. The reported highest speed of 71 Gbps for VCSELs was achieved with a l/2-cavity [ 17]. For the energy efficiency, Bimberg’s group reported the record lowest energy efficiency of 56 fJ/bit dissipated energy with a 3.5-µm VCSEL, as shown in Fig. 5 [ 28]. It has been shown that a small oxide aperture help to achieve a high energy efficiency because of the single mode operation and large mode spacing [ 28, 33, 34]. To improve the temperature stability, the wavelength of the laser cavity resonance is detuned from the gain peak wavelength in the laser design [ 39]. The gain peak has a shift rate of 0.396 nm/K for In_0.21Ga_0.79As/GaAs_0.88P_0.12 QW system, whereas the cavity resonance wavelength shifts to longer wavelengths with a rate of 0.061 nm/K. Thus the cavity resonance wavelength is positioned at the longer wavelength side of the gain curve at room temperature in the design, as shown in Fig. 6(a). Figure 6(b) shows that at 85°C error-free data transmission at 46 Gbit/s has been achieved for 980-nm VCSELs [ 31], and 50 Gb/s error-free data transmission at 90°C for 850-nm VCSELs [ 32].

Fig.3 (a) Output optical power versus current density for 11-µm oxide aperture VCSELs with different etch depths at 25°C. Inset: close-up of the threshold region; (b) measured small-signal modulation response at currents for maximum bandwidth for 11-µm oxide aperture VCSELs with different etch depths at 25°C [36]

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Fig.4 Comparison of the refractive index and simulated optical field intensity distribution inside the previous VCSEL structure with a 3l/2 cavity (a) and inside the new VCSEL structure with a l/2 cavity (b) [37]

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Fig.5 BER against received optical power of VCSELs with oxide-aperture diameters of 3.5, 4, and 5 µm operating at 25 Gbit/s at bias currents yielding maximum energy efficiency [28]. BER: bit error ratio; EDR: energy-to-data ratio; HBR: heat-to-bit rate ratio

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Fig.6 (a) Peak gain wavelength of a single In_0.21Ga_0.79As/GaAs_0.88P_0.12 QW/barrier active region and the etalon resonance wavelength of our 980 nm VCSEL versus temperature for gain-to-etalon wavelength offsets fixed at 300 K at 0, - 15, and - 25 nm relative to the peak QW gain [39]; (b) large-signal modulation measurements of multimode oxide-confined 980 nm VCSEL at 50 and 46 Gbit/s at 25°C and 85°C, respectively [31]. OM2: optical mode 2; MMF: multimode fiber; NZR: non-return-to-zero; PBRS: pseudo random binary sequence

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VCSELs with HCGs

To push the performance of current VCSELs for OIs to a high level, nanostructures like high-contrast subwavelength gratings (HCGs) can be integrated to VCSELs due to the unique physics. Here we focus on one-dimensional (1D) HCGs. Two-dimensional (2D) HCGs (also called photonic crystal slabs) also can serve as broadband reflectors based on Fano resonance, and have been comprehensively reviewed elsewhere [ 40].

Physics of HCG reflector for VCSELs

HCG reflectors are also termed as photonic crystal mirrors or guided-mode resonant reflectors [ 41– 47]. The grating bars composed of the high-index material in the HCG are fully immersed in the low-index medium, e.g., air, resulting in a high index contrast. The grating period is in the near-wavelength regime, between the wavelengths in the high-index material and in the low-index material. Figure 7 that shows the first two waveguide array modes with real propagation constants in infinite HCGs have a p-phase difference at the output plane and cancel each other causing a nearly 100% reflection [ 48]. When the first two modes are very closely located in the spectrum, a high-reflectivity broad band is realized [ 48]. There are other explanations for the high-reflectivity broad band of HCGs based on the Fano resonance or guided-mode resonance [ 43– 47]. Thus, a broadband and high-reflectivity HCG can serve as a reflector and replace a part or full of the top distributed Bragg reflector (DBR) to construct a HCG-VCSEL [ 41– 55]. Experimentally, HCG-VCSELs show a good mode selectivity and polarization control even for large oxide apertures [ 52– 57].

Fig.7 (a) Schematic of the HCG; (b) double-mode solution exhibiting perfect cancellation at the HCG output plane leading to 100% reflectivity [48]. Λ: grating period; S: width of the grating bar; a: width of the air gap; TE: transverse electric; TM: transverse magnetic

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For the HCG design, the structure parameters can be optimized by rigorous coupled wave analysis (RCWA) [ 58] and analytical methods [ 48]. These two methods consider that HCGs are with an infinite size and the incident wave is an infinite plane wave. The infinite-size HCG model is useful to rapidly search the parameters of HCGs. However, in the real devices the reflectivity is reduced caused by the finite HCG size [ 59], which increases the threshold current causing a low energy efficiency of VCSELs. Especially, the finite-size incident wave can excite the guided modes in the HCG by the higher-order angular components. The excited guided mode reduces the reflectivity and enhances the transmission as shown in Fig. 8(a) [ 60]. On the other hand, the excited guided mode can redirect the incident wave into the in-plane direction (see Fig. 8(b)), which provides the chances for the integrated optical sensor and for integration with planar optical circuits [ 61, 62]. Therefore, it is indispensable to calculate the finite-size HCG by finite difference time domain method after choosing HCG parameters using RCWA or analytical methods in designing HCG reflector.

Fig.8 (a) Reflectivity spectra for different HCG sizes with a fixed-size (4 mm, 1/e width of the Gaussian source) Gaussian source under normal incidence [60]; (b) mode field in finite-size HCG with a 4-mm Gaussian incident wave [61]; (c) guided mode with even symmetry with a 4-mm Gaussian incident wave [61]

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HCGs also show a strong ability to confine the field besides the feature of the high-reflectivity broad band. The energy penetration length of HCGs is much smaller than that of DBRs as shown in Fig. 9 [ 63]. The low energy penetration length brings a large confinement factor [ 64]. The small mode volume is very helpful to enhance the Purcell factor to reduce the carrier lifetime for a larger available modulation bandwidth and higher energy efficiency [ 32, 33]. In HCGs, the phase penetration length related to the photon lifetime can be tuned by the structure parameters without degrading the reflectivity, not like the shallow surface etching method [ 36, 65]. Thus due to the enlarged confinement factor in HCG-VCSELs and the optimum photon lifetime with a high reflectivity introduced by HCGs to VCSELs, HCG-VCSELs are expected to achieve a high relaxation resonance frequency, low damping factor, and low threshold current, which is very helpful for high-speed modulation and energy-efficient operation.

Fig.9 Energy penetration depths for HCG, 2D photonic crystal slab, and DBR [63]

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Progress of HCG-VCSELs

The first electrical HCG-VCSEL was realized with a sub-milliampere threshold current and single-mode and polarization-selective operation at 850 nm range as shown in Fig. 10 [ 52]. Later 1060-nm and 1550-nm HCG-VCSELs were developed [ 55, 56]. Also tunable HCG-VCSELs were developed for fast tuning because of the compact HCG mirrors [ 53]. The maximum f_{-3 dB} bandwidth is 7.8 GHz, which is limited by the parasitic capacitance, and an error-free data transmission at 10 Gb/s was demonstrated at 1550 nm [ 66].

Fig.10 Schematic of a HCG-VCSEL; (b) power-current-voltage curve of a HCG-VCSEL. The inset shows the polarization-resolved output power plotted in dB scale [52]

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HCG reflectors are a kind of resonant structures, very different from DBRs, and the reflection phase can be tuned while keeping a high reflectivity [ 65]. By adjusting the HCG parameters like period and duty cycle, different wavelengths of HCG-VCSELs on a single wafer can be simultaneously achieved [ 67]. Therefore, HCG-VCSEL array with multiple uniformly spaced wavelengths can be constructed on a single HCG-VCSEL wafer for wavelength-division multiplexing (WDM) which provides a promising way to increase the aggregate bandwidth of a single fiber. Optically pumped HCG-VCSEL arrays were reported with double silicon-based HCGs as reflectors for dense WDM at 1.55 µm [ 68]. A GaAs-based HCG filter array with different resonance wavelengths were demonstrated targeting the application in electrically pumped HCG-VCSEL arrays as shown in Fig. 11 [ 69]. SiN-based HCGs were developed for WDM at 850 nm [ 70].

Fig.11 (a) Scanning electronic microscopy (SEM) image of GaAs-based HCG; (b) reflectivity spectra of HCG-based filter array [69]

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VCSELs have been the most successful light sources for short-reach interconnects, from ~1 m for module-to-module interconnects to several hundred meters for rack-to-rack interconnects. For future very-short-reach (meters to centimeters), ultrashort-reach (centimeters to millimeters), and even on-chip OIs, VCSELs are still promising light sources because of high energy efficiency, high modulation speed even at 85°C with a low thermal resistance. Thus one ongoing effort is to integrate VCSELs with planar optical circuits. Several approaches have been proposed and demonstrated like using 45° gold mirror [ 71] and grating coupler [ 72] for conventional VCSELs integrated with waveguides in the package level. These optical structures can transfer the vertical emitting light into the in-plane waveguides. Integrating a VCSEL structure with a waveguide in the design or fabrication phase makes the chip more compact. Inserting a diffraction grating into the top or bottom DBR can extract power to the in-plane waveguide [ 73, 74]. Vertical coupling was also proposed to extract light from a FP microcavity composed of double HCG mirrors to a Si waveguide [ 75]. Very recently, HCGs have been proposed to replace the DBR as reflectors, and at the same time to route the emitting light into the in-plane waveguides [ 76, 77]. This approach also brings a low thermal resistance for the devices. Figure 12 shows an optically-pumped hybrid vertical-cavity laser with lateral emission into a silicon waveguide using a silicon HCG at 1.5 μm [ 78]. The potential modulation speed was predicted up to 100 Gbit/s. For the short wavelength range, SiN-based HCGs were proposed to serve as reflectors and extract the light into the in-plane SiN waveguide because SiN is transparent from 600 to 1100 nm [ 70].

Fig.12 (a) Schematic of the Si-VCSEL; (b) fundamental mode profile of the Si-VCSEL; (c) SEM image of the Si-VCSEL sample seen from the top [78]

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Conclusions and prospects

VCSELs for high-speed and energy-efficient optical links progress rapidly, and numerous achievements have been made in the past few years. VCSELs will continue to be the dominant light sources for Datacom, Computercom, and consumer links including short-reach OIs, and penetrate chip-to-chip and even on-chip OIs. Worldwide research from academic institutions as well as industrial companies is continuing to make efforts to enhance the energy efficiency, modulation speed, and temperature stability. Nanostructures with unique properties will play a critical role here. Future research in the areas of fundamental physics, new structures, and new technology will lead VCSELs to bit rates of>100 Gb/s at room temperature or even at 85°C, and an energy efficiency of<10 fJ/bit.

Acknowledgements

We gratefully acknowledge the German Research Foundation (DFG) for funding via the collaborative research center 787 and the Alexander von Humboldt Foundation for supporting Anjin Liu by a Postdoctoral Research Fellowship. We thank W. Hofmann, G. Larisch, Hui Li, J. A. Lott, P. Moser, and P. Wolf for helpful discussion. Anjin Liu also gratefully acknowledges the support from Chinese Academy of Sciences (CAS) Pioneer Hundred Talents Program.

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