Silicon scaling continues at an unprecedented speed and the performance of processors doubles each year. To avoid the interconnect bottleneck, the single-channel bit data rate must double every 24 months, whereas the overall bit data rate in the core networking must double every 18 months. The latter scaling law demands a fivefold increase in the number of single channels per link every 10 years. Thus, the pressure on interconnects is growing because of both the bandwidth demand for the single channel and the demand for the bandwidth density per unit space available for interconnects in the module. Presently, according to the Ethernet roadmap, the speed of 106 Gb/s per single channel is expected to be standardized in 2017 for application in single-mode (SM) fiber links. For multimode (MM) fiber (MMF) links, 50 Gb/s per channel is due in 2018. In 2016, the Optical Internetworking Forum has started work on the standardization of common electrical interface at very short reach operating at 112 Gb/s. This speed is expected to mature after 2019 . Modern VCSELs already operate at bit data rates exceeding 160 Gb/s and are able to reach transmission speeds exceeding 150 Gb/s over 100 m of MMF .
Historically, short transmission distances (<150 m) are served by MMF links optimized for 850 nm wavelength. Initially, AlGaAs-based light-emitting diodes are applied and shortly replaced by vertical cavity surface-emitting lasers (VCSELs) at the same wavelength served in combination with MMF optimized for the ultimate modal bandwidth specifically in this wavelength range . IEEE standard requirements underline that for each new standard the installed base must be served and, consequently, 850 nm VCSEL stays in the existing standards. Another IEEE requirement requests a “distinct identity” of the standard solution.
This means that for a given application there is only one solution to be accepted by the industry. The changes are thus possible by extending the bit data rate and keeping the same wavelength and in parallel by extending the wavelength range for high modal dispersion in MMF. Only in this “extending” approach that adjustments are possible. It is expected that the link served by VCSELs will stay in the data center in the foreseeable future. On the contrary, there are solutions served by copper cables, where only the electrical interfaces are defined. In this case, an optical solution may enter the market as active optical cables (AOCs) and any cost- and energy-efficient solution may be applied. Such networks, however, are not reconfigurable, as opposed to standardized optical solutions, which allow the splicing and reconfiguration of the optical fiber links. The target of the present paper is to address the requirements and explain the design tools that can be applied to extend the device performance and the application field.
As discussed above, GaAs-based VCSELs are broadly used in MMF optical data communication links at 850 nm. As the bit data rates are continuously increasing, the copper links are being replaced by VCSELs. In 2006, there existed a great skepticism toward the realization of reliable VCSELs operating at bit data rates significantly exceeding 10 Gb/s . The skepticism was fueled by the experience with standard AlGaAs-GaAs-based VCSELs with guiding GaAs-rich core . The use of InGaAs quantum wells (QW) and quantum dots  in combination with the antiguiding VCSEL concept  has solved the problem of reliable high-speed oxide-confined VCSELs ,  at 850 nm and longer wavelengths. By applying tensile strained wide bandgap layers and the proper use of substrate orientation, potential barriers in the conduction band may be created by preventing leakage of the injected nonequilibrium electrons into the p-doped cladding layers . Presently, the antiguiding VCSEL approach, which allows to increase the oscillator strength of the optical transition  due to the suppressed in-plane modes and an option of ultimately narrow λ/2 cavity, is used by key VCSEL manufacturers.
2 Demands for traditional VCSELs
Although 850 nm VCSELs are shown to be suitable for error-free operation at data bit rates as high as 25 to 50 Gb/s , , , , , there are certain limitations to their operation. At first, VCSEL transmission distance over MMF is limited as each propagating mode has a different time delay. This effect, however, is minimized in modern MMF with precisely graded refractive index. The time delay due to the angle of the mode is compensated by the reduced refractive index, enabling kilometer-scale transmission distances at very high bit rates beyond 50 Gb/s.
A much more severe problem is related to the chromatic dispersion, which is very significant in glass fiber in the spectral range around 850 nm. As the laser emission has a finite spectral width, the short and long wavelength parts of the pulse propagate at different speeds through the fiber, causing the pulse broadening with propagation distance. The chromatic dispersion of the MMF presently represents a major challenge limiting the transmission distance for MM VCSEL to 70 and 100 m for OM3 and OM4 fibers, respectively. The only solution to solve the problem is to apply SM 850 nm VCSEL  enabling kilometer-scale distances at non-return-to-zero (NRZ) operation at 50 Gb/s .
Another challenge for VCSELs is the need to operate at high speed at extreme temperatures. Making electrical traces on printed circuit board (PCB) for operation at frequencies exceeding 20 GHz is not reasonable due to high electromagnetic (EM) losses and because it requires extreme packaging precision and imposes strict requirements on the quality of glass and copper elements. Consequently, the transceiver subassemblies migrate to the middle of the PCBs with further signal distribution by fiber or through on-board optical waveguides. For low-cost, low-power operation, no active cooling can be provided. This demands high-speed reliable VCSEL operation at elevated temperature. Recently, multilevel coding (PAM4) is being introduced in datacom standards . This adds requirements of low relative intensity noise (RIN) and high linearity of the light-current curves of VCSELs.
To summarize, the targets set for the 850-nm-range VCSELs in modern data communications are as follows:
Narrow lasing spectrum,
Low noise, and
One should note, however, that the design considerations can be self-conflicting, for example, small aperture enables SM operation but is counteracted by low power, low production yield, and high resistance not compatible with driver electronics. On the contrary, large aperture VCSELs (~10 μm) offer high-power operation and high yield and match 50 Ohm electronics but can be heavily MM. To reduce the capacitance, several oxide apertures may be applied; however, the device can become heavily MM. Furthermore, thick aperture VCSELs and multiaperture VCSELs may suffer from fast degradation. VCSELs having a single thin aperture may show better reliability and narrower spectrum but has a higher capacitance, low speed, and beam instabilities due the aperture overheating-induced effects.
In certain cases, due to the inherent properties of the band alignment in the materials system, high effective masses of the charge carriers, and other effects, it is difficult to reach high-speed operation. This may be the case of traditional design InGaAlP VCSELs in the visible spectral range ~630 nm or InGaAlN-based VCSELs emitting in the blue and green spectral ranges. As the visible spectrum range is presently of great interest for visible light communication (VLC), such deficiency needs to be corrected.
3 Novel concepts for VCSELs
3.1 Electrooptically modulated (EOM) VCSELs
Once VCSELs are being employed as light source for silicon photonics chips and integrated circuits, much tougher requirements are being imposed, whereas high-speed modulation should be achieved at low modulation currents. Directly modulated VCSELs can hardly meet this requirements, but EOM VCSELs offer a solution.
The concept of EOM filter section was proposed in Ref. . According to this concept, a vertical cavity EOM device is using resonant interaction between two coupled cavities . The device contains a refractive index tunable element (electrooptical modulator) controlled by an applied voltage, which produces a negative change of the refractive index and a related wavelength shift of the filter cavity resonance. The first EOM VCSEL based on two resonantly coupled cavities was successfully realized in Ref.  (see Figure 1).
Figure 2 illustrates the operation principles of EOM VCSELs. Figure 2A shows a schematic reflectance spectrum of the modulator cavity having a dip at the resonance wavelength of the modulator cavity. The filled circle refers to the lasing wavelength, at which the modulator cavity is not transparent, and laser light does not come out.
Figure 2B refers to the resonance state, in which a bias is applied to the modulator, refractive index is changed, and the reflectivity dip of the modulator cavity is shifted toward the resonance with the VCSEL cavity (a shift from the dashed line to the solid line in Figure 2B). Due to the resonant coupling between both cavities, the field intensity in the modulator cavity is enhanced; thus, the output power is increased.
If the quality factor of the modulator cavity is sufficiently low, no splitting of the cavity modes occurs. Then, there is only one VCSEL-type optical mode having a significant optical confinement factor in the active region of VCSELs.
Figure 2C shows schematically the profiles of the refractive index and electric field strength in the VCSEL optical mode. Figure 2D shows the same profiles in the top part of the device at a larger magnification. A change in the electric field strength between an open state and a closed state of the device is significant only in the modulator cavity and in the top distributed Bragg reflector (DBR) and is negligible in the rest of the device, including the active medium of the VCSEL. This fact ensures that the state of the active medium (e.g. the photon density) remains the same whether the modulator is open or closed for the laser light. Note that the light intensity is proportional to the square of the electric field; thus, the contrast in the electric field strength at the device output in Figure 2D corresponds to the extinction ratio of approximately 3 dB.
EOM VCSELs allow drive currents to demonstrate electrical bandwidth up to 60 GHz  and are suitable for analog modulation at 20 GHz , . Recently, on-off keying (OOK) at 10 Gb/s has been demonstrated in a two-section EOM device  (see Figure 3).
EOM VCSELs are presently most suitable for analog modulation due to a relatively low modulation amplitude at moderate (~1 V) modulation voltage. However also in digital transmission both NRZ and return to zero (RZ) (Figure 3) modulation formats are realized. In certain cases for large signal modulation, RZ can provide better bit-to-error ratio due to the overshoot effect revealed in the devices with a residual absorption in the modulator section.
The vastly growing application of VCSELs as light sources in red, green, and blue visible spectral ranges in VLC is challenging due to the specific properties of materials used for the corresponding light sources. The technology developed for GaAlAs/GaAs-based 850 nm VCSELs cannot be one-to-one transferred to a different type of materials. Red VCSELs based on InGaAlP materials suffer from the lack of high barriers for nonequilibrium electrons and hence of poor temperature stability. Operation under high current density leads to strong overheating and hence deteriorates lasing. Nitride-based green and blue VCSELs have very different material properties compared to GaAlAs-based devices. All these show a necessity to employ an alternative technology for fast VCSELs in the visible range. EOM VCSELs offer a good opportunity.
3.2 Passive cavity VCSEL
A significant problem of modern laser diodes used in data transmission is the temperature dependence of the lasing wavelength. As the refractive index of the semiconductor material changes with temperature, the VCSEL wavelength shifts, making uncooled applications in dense wavelength division applications impossible without active cooling and applying wavelength control tools through dielectric reference filters with calibrated temperature stable wavelength.
There exists, however, a much simpler approach, namely, applying a passive cavity laser. In such a laser, the active medium is placed in a semiconductor DBR, whereas the resonant cavity is passive. Such an approach allows, for example, placing the active medium into a bottom semiconductor DBR and forming both the resonant cavity and the top DBR of dielectric materials. Such type of device may lase at a wavelength that is stable upon temperature .
A possibility of a device with a high temperature stability of the wavelength in dielectric resonant cavities and also a weak negative temperature shift of the resonance wavelength (approximately −0.02 nm/K) was demonstrated in Ref. .
The vertical profiles of the reflective index and optical field intensity are shown in Figure 4A. Although the optical confinement factor of the lasing mode in the active medium is reduced approximately three times with respect to a conventional VCSEL, the device shows good performance, with the L-I curves at different apertures depicted in Figure 4B and the spectrum shown in the insert. In spite of the three thick oxide aperture layers, SM or quasi-SM operation is observed up to aperture diameters of ~6 μm.
Another advantage of the passive cavity VCSEL is related to the option of processing of photonic crystal directly in the cavity (Figure 6), drastically increasing the oscillator strength due to the Purcell effect, by far overcompensating the losses related to the moderately reduced optical confinement factor.
There are many recent developments in the passive cavity VCSEL field. Etching away an In0.49Ga0.51P sacrificial layer and having air gap acting as the passive cavity allowed the electrostatic tuning of the VCSEL wavelength in a 15 nm spectral range . Having a grating introduced into the passive dielectric VCSEL cavity acting also as an in-plane waveguide enabled the effective grating coupling of the vertical lasing into the transverse direction turning the light into the waveguide direction . In Ref. , using the SiO2/Ta2O5/Si waveguide-attached VCSEL concept, a high potential of the passive cavity VCSEL for high-speed data transmission is demonstrated. Although the optical field maximum is placed in the dielectric cavity layer and the optical field is significantly stretched to enable thick intracavity contact region, the -3dB modulation bandwidth in excess of 11 GHz is realized and 20 Gb/s error-free transmission at very small received power (−8 dBm) is demonstrated.
For the proper waveguide grating and the passive cavity design engineering, one can enable wavelength-stabilized waveguide lasing using in-plane distributed feedback (DFB) effect with active semiconductor DBR allowing the activation and amplification of the waveguide emission through the grating-induced mixing of the vertical and lateral modes.
3.3 Single fundamental mode VCSELs for high-speed operation
The goal of error-free transmission over a long distance through MMF using SM VCSELs becomes mandatory. The high performance of optical links based on SM VCSELs is achieved due to the lack of modal and chromatic dispersion.
Concepts of SM VCSEL are all based on generating higher external or internal losses for higher-order transverse modes compared to the fundamental transverse mode. For high-speed VCSEL, a critical issue is to ensure SM operation at moderate oxide aperture sizes up to high current densities and to enable high modulation bandwidth.
In the following subsections, we discuss the applications of nanophotonics for designing SM VCSELs. We show that the three-dimensional (3D) modeling of EM fields provides a perfect match to the experimental data.
3D modeling is extensively used to simulate all properties of the structures to optimize its performance before prototyping and to reach specific design goals. Such exact modeling is even more important as already minor changes in layer thicknesses on a scale of a few nanometers can strongly alter the device performance.
The 3D simulations of EM fields discussed in the present paper are performed using the finite element software package based on full vector Maxwell’s equations (JCM Wave) in combination with custom-designed MATLAB software package. The details of the numerical method were presented in Ref. . The refractive indices of materials for the simulation were taken from Ref. . We present here several examples of nanoengineering.
3.3.1 Leaky VCSELs
SM operation in oxide-confined VCSELs can be achieved via the proper engineering of the optical modes in VCSELs , enabling the preferential lateral leakage of high-order modes.
Usually, the leakage effect is considered for light propagation in a waveguide layer attached to a layer with a larger refractive index (n). In this case, the optical field distribution of the fundamental optical mode propagating in the waveguide does not match the optical field distribution of the light propagating in an adjacent layer parallel to the waveguide as the wavelength of the light in the crystal is smaller in the high refractive index medium. However, one can match the optical field distribution of the waveguide mode, on the one hand, and a light wave propagating in an adjacent layer at certain angle with respect to the waveguide layer. Once the k-vector component in the propagation direction is reduced, the periodicity of the optical field oscillation in the cladding layer increases, matching the periodicity of the waveguide mode. The overlap integral of these two modes at the interface can be consequently high if the nodes of the two optical fields match. Thus, the leakage of the optical mode from the waveguide becomes allowed. On the contrary, such leakage is prohibited if the medium surrounding the waveguide has a lower refractive index. Then, there may be no matching modes at any angle, as already the mode propagating parallel to the interface in the low-n medium has a larger spatial periodicity than the fundamental waveguide mode. All the other modes in the surrounding medium have further increased spatial periodicity of their optical field at the interface. The nodes of the optical fields cannot match the nodes of the fundamental mode of the waveguide and the overlap integral is zero.
For the short vertical cavity resonators, such consideration should be modified as there are only a limited number of the nodes in the region where the optical field intensity has a maximum. Thus, in cases where the intensity of the modes in the surrounding area is highly distorted compared to the undistorted core region, the overlap integral of the inner and outer modes at the interface region may become nonzero even if the number of the nodes and their periodicities are different. Such a mismatch in the optical fields exists in each oxide-confined VCSEL due to the field distortion caused by the oxidized layer having an approximately twice smaller optical thickness compared to the AlAs layer; consequently, the phase of the mode is shifted. In a standard oxide-confined VCSEL, the effect is strong only at small apertures and is usually referred to as “diffraction loss”. Such loss is the most important for the high-order modes, which exhibit optical field intensity maxima shifted closer to the boundary of the aperture region. Thus, all thick oxide-confined VCSELs lase in the fundamental mode at small (~1–2 μm) aperture diameters.
However, one can intentionally engineer the specific resonant mode in the oxidized part, which is highly distorted by the oxidation-induced refractive index change and due to this effect has a high overlap integral with the VCSEL mode in spite of a different number and a different periodicity of the nodes of the related optical fields. The VCSEL cavity mode then can transform at the interface into the related mode in the oxidized part and can leak outside of the cavity region similar to the case of a leaky waveguide design.
In the devices discussed below, the lateral leakage of the optical mode from the nonoxidized core to the oxidized periphery is realized due to a coupling of the vertical profile of the optical mode in the VCSEL core region with another optical mode in the periphery region, whereas this coupling can be enhanced using a duo-cavity VCSEL structure. This approach allows leaky VCSELs to be fabricated in a way fully compatible with the standard oxide-confined VCSEL technology without additional processing steps. Such design realized for 850 nm VCSEL enables SM operation of VCSELs with aperture diameters of up to 5 μm or above depending on the aperture region design.
In Ref. , it is shown that a 3D simulation of the EM field allows an accurate prediction of the specific features in the far-field pattern of the laser emission. To visualize this effect, Figure 7 shows a cross-section of the VCSEL with simulated optical fields.
Figure 7A and B shows a cross-section of the simulated electric field intensity of the fundamental mode and the first excited optical mode of an oxide-confined AlGaAs-based leaky VCSEL. The fundamental mode (HE11) has the maximum intensity in the center and the excited mode (HE21) reaches the maximum intensity close to the edge of the oxide layer, which leads to higher leakage losses of the excited mode. Higher leakage losses can be observed through a higher intensity of the in-plane leakage through the second cavity.
Emitted laser light that propagates through the second cavity parallel to the surface can be used in the engineering of photonic integrated circuits (PICs), for example, by the coherent coupling of two or more devices for beam steering . Another important feature of the emission pattern is an angular peak in the far-field pattern related to a specific tilted emission over the VCSEL surface at ~35° to 37°, which was verified in a series of far-field experiments.
VCSEL, according to this design, was manufactured and tested. One can observe that at high current densities, during MM operation, narrow lobes at ~35° angles related to the leakage process arise, which correspond fairly accurately to the predictions of the simulation (Figure 8).
The VCSEL has demonstrated quasi-SM operation up to high current densities and is able to operate at high-speed at and above 32 Gb/s (Figure 9).
It should be emphasized that the leakage process can be sensitive to the diameter of the oxide aperture, a parameter that is controlled with a certain precision in a large volume production.
Figure 10 demonstrates the modeled oscillatory behavior of the mode lifetimes and confinement factors as a function of the aperture diameter. Such an oscillatory behavior is associated with the characteristic wave vectors of the modes.
It depends on the DBR periodicity, the aperture diameter, and the direction from the center of the active cavity to the particular place in the device where leakage occurs, similar to the planar waveguide with micrometer-scale scatters . As the diameter of the aperture changes, the reflectance of the mode from the oxide layers and therefore the leakage losses also change, differently for the fundamental mode and the excited modes.
The best SM performance is expected at the apertures, for which the lifetime ratio of the fundamental mode and the excited modes is the highest. In the design studied, the highest leakage of the excited mode occurs for the aperture diameter of ~4.5 μm.
In general, adding the leaky loss may negatively affect the threshold current of the device. For a proper design, engineering the leakage effect makes it possible to achieve a strong leakage for the high-order transverse modes but a minimized one for the VCSEL fundamental mode. If the leakage effect for the fundamental mode is also significant, the threshold current can be increased. However, as VCSELs operate typically at 10- to 20-fold currents above the threshold, an increase of 10% to 20% may be not significant. Furthermore, thermal effects caused by resistive losses and free carrier absorption tend to increase the refractive index in the center of the aperture region and further shift the fundamental mode toward the center and away from the oxide-confined aperture boundaries, further reducing the leakage for the fundamental mode. For the proper evaluation of the effect at practical current densities, a detailed modeling of the temperature distribution and the impact of this distribution on the optical modes are to be considered.
To conclude, we have demonstrated that a significant improvement in the VCSEL spectral quality is possible without any need in additional processing steps and only through the advanced epitaxial design of the VCSEL. 3D modeling has shown good agreement with the experimental data and thus can be used in the future to optimize the characteristics of VCSELs.
3.3.2 VCSEL with intermixing-induced confinement of optical modes
Another promising way to manufacture SM VCSELs is the impurity-induced intermixing of semiconductor alloy materials.
Impurity diffusion-induced intermixing is the concept of intermixing the III-V layered semiconductor materials by the generation of high concentration of charged point defects (mostly group III atoms at interstitial positions) . In the GaAs-AlAs materials system, the intermixing is normally realized by a processing step, including the mask-patterned Zn diffusion applied from the top of the semiconductor. Then, beneath the openings in the mask, the layered structure of the DBR with alternating alloy composition transforms, forming a homogeneous alloy. Selective intermixing can be also achieved by the masked annealing of the structure allowing vacancy diffusion into the nonprotected areas and by selective ion implantation followed by high-temperature annealing.
Zn diffusion can be employed for the on-wafer tuning of the VCSEL emission wavelength to realize wavelength-separated chip arrays from the same wafer .
In Ref. , VCSELs with shallow Zn diffusion and oxide relief were studied. One of the VCSEL designs had a 6 μm intermixing-induced aperture formed by shallow 2-μm-deep Zn intermixing of the top DBR. The oxide-relief aperture had a much larger diameter of 17 μm and thus did not contribute to the optical confinement. A single transverse mode VCSEL operation up to 22 mA was demonstrated and no signs of excited transverse modes were revealed within the noise level (dynamic range of three orders of magnitude).
In Ref. , the leakage in VCSELs subject to selective Zn diffusion has been modeled. The structure modeled is the conventional VCSEL device with a 3λ/2 cavity described in Ref.  but without selectively oxidized apertures. Instead of applying Zn-induced intermixing of the top DBR, the active region and a part of the bottom DBR were modeled (Figures 11 and 12).
The Zn diffusion profile enters the n-doped bottom Al0.15Ga0.85As-Al0.9Ga0.1As DBR having a bandgap in the range from 1.66 to 2.13 eV. Consequently, at the onset voltage of 1.45 V, the carriers are injected only into the non-intermixed QW material. The QWs are laterally surrounded by ~50% AlGaAs material that prevents the leakage of carriers. Thus, carrier injections occur in both vertical and lateral (transverse junction) directions .
The fundamental mode in both cases has the maximum intensity located in the center of the VCSEL. One can see that the Zn diffusion-induced intermixing is capable of achieving good confinement of the optical mode (Figure 11).
The excited mode leaks into the alloy-intermixed material stronger than the fundamental mode. In this case, the lifetime of the fundamental mode is two times higher than that of the first excited mode (Figure 12).
Experimental results on data transmission with VCSELs with intermixing-induced confinement are very promising , but the reliability of such devices needs to be carefully checked. The simulations show that an efficient mode selection in the emission spectrum can be achieved even at very large aperture diameters.
From Figure 13 one can see that the lifetime of the first modes of the VCSEL with intermixing-induced confinement differs strongly from the oxide-confined case. The lifetime is shorter due to drastically increased losses, and it increases upon increasing aperture diameter.
The lifetime ratio of the first two modes, which is connected to the SM behavior of the VCSEL, is much higher for the device with the intermixing-induced confinement of the optical modes because the high-order modes leak much more efficiently into the periphery. It varies with the intermixing depth slightly, but in general the trend is stable, which gives a big advantage for the processing robustness of these VCSELs as there is no requirement for a precise control of the intermixing depth.
Thus, a device with a 4.5 μm aperture diameter and an intermixing depth of 4.3 μm from the surface of the VCSEL has the ratio of the lifetimes of the fundamental mode and the excited mode equal to 2.4.
It is conceivable that a special design can be created that will further increase confinement and simultaneously improve the leakage in the intermixing-confined VCSELs. Detailed experimental studies on recently manufactured devices will be published elsewhere.
4 Impact of the mode composition on the data transmission distance in the MMF
The persistent demand in high-speed optical solutions for the Datacom market has led to a large progress on 850 nm VCSEL-based interconnects during the last years. The use of directly modulated VCSELs as inexpensive reliable light sources with wide bandwidth and low-energy consumption, together with the use of p-i-n photodetector-based receivers and MMF, are key to achieve low-cost fast optical interconnects.
High-speed 850 nm VCSEL solutions have been successfully proven in standards as Fibre Channel, Ethernet, or Infiniband with serial lines in the range of 25 to 28 Gb/s. The data rates aimed for the next generation of aforementioned standards are 50 and 100 Gb/s per wavelength, which give rise to 200 and 400 Gb/s through parallel optics or wavelength division multiplexing (WDM). Despite the limitation of the actual 850 nm VCSEL technology, with the maximum reported 3dB bandwidth of 28 GHz , recent studies show the feasibility of optical interconnects operating at 50 Gb/s and well beyond using OOK modulation.
To face higher-speed requirements, attention is focused on the increase of the spectral efficiency through high-order modulation formats, such as pulse-amplitude modulation (PAM), discrete multitone modulation (DMT), or carrierless amplitude/phase modulation (CAP). Even if these modulation schemes allow the application of direct modulation and p-i-n detection, drawbacks of increased system complexity and higher power consumption of the related electronics have to be considered.
A significant research effort has been dedicated to extend the data rate and the reach of the 850 nm VCSEL-based optical links. Several remarkable transmission experiments have been reported on this topic. In this section, we briefly review the different approaches of the investigations, focusing on those studies that have demonstrated single-lane solutions at data rates of 50 Gb/s and beyond.
In amplitude shift-keying modulations (ASK), digital data are represented as variations in amplitude of the carrier wave based on the data to be sent. The NRZ OOK is the simplest and most common ASK format. Frequency and phase remain constant, whereas two different amplitude levels are used to represent the logical values 0 and 1, without a 0 being forced after each 1.
Figure 14 shows the effective data rate vs. MMF transmission length for OOK , , , , , . To date, the highest serial data rates demonstrated error-free (BER<1E-12) using OOK are 71 Gb/s over 7 m , 64 Gb/s over 57 m , and 60 Gb/s over 107 m . These results were obtained using two-tap feed forward equalization (FFE) at both the transmitter and the receiver sides. Comparable results of 57 Gb/s back-to-back (BTB), 55 Gb/s over 50 m, and 43 Gb/s over 100 m are presented in Ref.  without equalization circuits, therefore minimizing the link complexity.
With 850 nm VCSEL-based links demonstrated to operate at 50 Gb/s OOK, the next challenge is the extension of link distances to 1 to 2 km to satisfy the enormous growth of modern data centers during the last decades. As the transmission distance increases, modal and chromatic dispersion in MMF deteriorate the transmission quality, seriously limiting the maximum linking distance under such high transmission data rates. The effects of dispersion can be efficiently mitigated by decreasing the number of VCSEL modes traveling through the fiber. Thus, the signal spectral width is shrunk and the number of excited modes in the MMF is reduced. Figure 15 shows the influence of dispersion on 25 Gb/s eye diagrams for MM and SM VCSELs at different OM4 MMF lengths.
This approach is studied in Refs  and , where SM VCSELs are used. Error-free transmission under the consideration of forward error correction (FEC) (BER <3.8E-3), at an effective data rate of 50 Gb/s over 1 km and 2.2 km MMF, is demonstrated in Refs  and , respectively. In this case, decision feedback equalization (DFE) techniques are only used at the receiver side. For 850 nm VCSEL-based links, 118.8 Gb/s km is the highest bit rate distance product (BRDP) reported up to date .
These results confirm dispersion as the most limiting factor on determining the maximum possible transmission length, instead of the output power of VCSELs, which for SM-VCSELs is significantly lower than for MM-VCSELs.
Due to its low complexity, PAM is the preferred solution for the next-generation optical interconnects. Instead of transferring 1-bit information using two values of 1 or 0 in one time slot like OOK, the N-PAM signal transfers one symbol of log2(N) bits information in one time slot using N amplitude values.
PAM has dual advantages of maintaining the signal bit rate while increasing the data transfer capacity and the spectral system efficiency. As a disadvantage, the smaller distance between levels in PAM signals reduces the strength against intersymbol interference (ISI) and causes a degraded signal-to-noise-ratio (SNR), which results into a power penalty compared to OOK systems.
Laser RIN plays a more important role than thermal noise and photodetector shot noise in the total noise of optical interconnects. Therefore, low RIN VCSELs are essential to achieve high-speed operation, especially when high-order modulations as PAM or DMT are used.
The coexistence of stimulated and spontaneous emission in a laser leads to random fluctuations of the optical power. RIN describes the intensity of these fluctuations relative to the average optical power level. For VCSELs, RIN level decreases upon increasing the bias current. However, high currents in MM VCSELs produce the excitation of spurious modes, resulting in mode competition and mode partition noise.
More severe RIN requirements are expected for the next-generation optical standards due to the introduction of higher-order modulations. SM-VCSELs can satisfy these exigencies, thanks to the absence of mode competition and mode-selective coupling, which limit the noise performance of MM-VCSELs. The 50 Gb/s 4-PAM optical eye diagram of low RIN SM-VCSEL is shown in Figure 16 without equalization or pre-emphasis used.
PAM and multicarrier modulations as DMT or CAP typically need a large dynamic range to operate, which makes them more vulnerable to the nonlinear characteristic of VCSELs compared to OOK. For this reason, linear behavior around the operating point must be guaranteed.
The most significant transmission studies on PAM and 850 nm VCSELs are gathered in Figure 17, which shows the effective data rate vs. MMF transmission length reported in Refs , , , , , , , , , , , .
Error-free (BER<1E-12) 4-PAM operation at 60 Gb/s BTB as well as 50 Gb/s over 50 m and 40 Gb/s over 100 m MMF are demonstrated in Ref.  without the use of equalization or FEC. However, a proper combination of these techniques can help to extend both data rate and transmission distance. Effective 70 Gb/s BTB operation is proven in Ref.  using 5-tap FIR offline equalization at the receiver and separated FEC coding for most significant bit (MSB) and least significant bit (LSB).
A high modal bandwidth OM4-MMF with partial modal-chromatic dispersion compensation (MCDC) properties is used in Ref.  to mitigate the effects of dispersion. The 100 and 200 m transmission is reached at effective 58.4 and 56.7 Gb/s, respectively. The 5-tap minimum mean square error (MMSE) equalization and FEC were used for the 100 m case, whereas 7-tap DFE and a stronger FEC were used for the 200 m transmission.
The highest data rates for 4-PAM direct modulation of 850 nm VCSEL were reported in Refs , . Effective 104 Gb/s over 100 m is demonstrated in Ref.  applying FIR and 16-states MLSE equalization at the receiver together with FEC. The use of an SM-VCSEL with very low RIN of −155 dB/Hz to minimize the effects of dispersion and ISI allows 600 m transmission at effective 83.7 Gb/s in Ref. , where also 104 Gb/s BTB and 100 Gb/s over 100 m are demonstrated under the consideration of FEC. Root-raised-cosine filtering and DFE are used at the receiver. The same setup is used in this paper for record data rate on 8-PAM, effective 83.7 Gb/s over 100 m MMF.
DMT modulation has been presented as an alternative solution to OOK and PAM for short-reach optical interconnects. Widely used in Digital Subscriber Line (DSL) applications, DMT is a baseband version of the orthogonal frequency division multiplexing (OFDM). DMT splits the available bandwidth into a large group of subcarriers, each of which uses an independent quadrature amplitude modulation (QAM) form.
Despite the more complex implementation and higher power consumption compared to OOK and PAM, DMT offers an enhanced spectral efficiency and adaptability to the link characteristics using power and bit loading. DMT direct modulation of 850 nm VCSELs has been investigated by different research groups in Refs , , , .
The aforementioned benefits of SM-VCSELs are again employed in Ref.  obtaining the highest data rate reported up to date for this approach. Error-free transmission considering FEC (BER<3.8E-3) is proven effective at 111.6 Gb/s BTB and 109.7 Gb/s over 100 m and 104.1 Gb/s over 300 m MMF. The 255-subcarrier DMT signal used is generated using bit power loading, inverse fast Fourier transform (IFFT) at a size of 512, and addition of a 10 cyclic prefix to each symbol. Demodulation consists of Volterra nonlinear equalization, FFT window synchronization, cyclic prefix removal, FFT operation, MIMO channel estimation, and data recovery.
A novel approach based on multi-CAP modulation, well-known for being standardized in several DSL variants, was for the first time studied for direct modulation of 850 nm VCSELs in Ref. . The modulating signal is divided in 10 different bands, each of which is mapped into a different symbol constellation and it is conditioned through upsampling, orthogonal CAP filtering, and power loading. Demodulation is carried out at the receiver through orthogonal matched CAP filtering, downsampling, DFE, and k-means algorithm.
A comparison of the performance between SM-VCSEL and MM-VCSEL shows that better results are obtained for the SM-VCSEL case. Error-free transmission under FEC consideration (BER<3.8E-3) is achieved at effective 100 Gb/s over 100 m and 79 Gb/s over 1 km MMF. Figure 18 shows the received electrical spectrum of the multi-CAP signal together with the constellation diagram of each band for 107.5 Gb/s transmission over 100 m MMF.
To conclude, we underline that the history of VCSELs may be only starting. The high speed, high temperature stability, high energy efficiency, low noise, and high linearity of GaAs-based VCSELs make them attractive components for application in data networks at bit data rates exceeding 150 Gb/s per channel.
High-speed devices have high potential for VLC, particularly in the red spectral range, in silicon photonics, and in sensing as flash source for 3D cameras with extreme spatial resolution. To serve these goals and match the growing demands in bandwidth and integration opportunities, significant changes in the design have been proposed.
We have shown that the highest speed and longest transmission distance results for various transmission formats could be obtained with SM and quasi-SM VCSELs. We have also discussed the design concepts that will potentially play a big role in their fabrication.
The work on high-speed (>25 Gb/s) VCSELs presented in this paper has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement 666866.
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