1. Introduction

Vertical cavity surface emitting lasers (VCSELs) based on GaAs/AlGaAs structures are broadly applied in data communication links via multimode fibers (MMF) operating at 850 nm at distances <~100 m. To match a steady increase in processor performance, the single channel bit data rate must approximately double every two years. On–board signaling rate is presently ~56 Gb/s, while the next standard of 112 Gb/s is under development. At such rates copper links are too power consuming and expensive due to extremely tough processing tolerances and are being replaced by optical solutions, even for very short distances. VCSELs have critical advantages due to low power consumption and cost. However, there existed a great skepticism towards a possibility of reliable VCSEL operation significantly above 10 Gb/s [1]. The experience with standard AlGaAs/GaAs–based VCSELs with a waveguiding GaAs–rich core [2] appeared to be negative. An anti–waveguiding VCSEL (A–VCSEL) design concept [3], aimed to increase the oscillator strength for the vertical cavity mode [4] and suppress the highly undesirable in–plane emission, led to high–speed performance up to very high temperatures [5]. Reliable high–speed multiple aperture oxide–confined VCSELs, both at 850 nm [6] and at longer wavelengths [7] were demonstrated. It was reported in [8], that presently the A–VCSEL approach is broadly used by the industry.

Furthermore, recently there emerged a significant interest in single–mode (SM) VCSELs for extended distance transmission over multimode fiber for applications in data centers and high performance computers. To achieve single–mode operation optical leakage effects were introduced more recently [9–11]. An optimized duo cavity epitaxial structure further processed by a standard processing scheme for oxide–confined VCSELs favors high lateral leakage losses of high–order transverse modes thus promoting single–mode lasing in the fundamental transverse mode up to the aperture diameter of ~5 µm. Modeling of the current–induced and infrared absorption–induced heating effects confirmed the robustness of single–mode operation versus overheating [12]. Remaining issues in this approach are a moderately reduced optical confinement factor due to a duo cavity design and an increased threshold current density caused by some leakage of the fundamental mode. A different approach using a combination of Zn diffusion–induced alloy intermixing in a part of Ga_1–xAl_xAs–based distributed Bragg reflector (DBR) and of oxide relief in partially oxidized aperture layers (and formation of air gaps) [13,14] demonstrated sustainable single–mode operation in the entire range of injection currents. However, two different types of apertures, namely oxide–confined/air gap–confined aperture and Zn diffusion–confined aperture render technology more complex and require optimized relation between their diameters to achieve high–speed operation. Modeling [15] demonstrated that partially intermixed DBRs result in lateral leakage of transverse optical modes, which explains single–mode operation and at the same time emphasized an increased threshold current due to some leakage of the fundamental mode. It was also suggested in [15] that single mode operation could be achieved by Zn diffusion–induced intermixing of the DBRs only, without any oxide–confined or air gap–confined apertures.

Single–mode operation at bit data rates 54 Gb/s in non–return–to–zero (NRZ) format and at oxide–confined apertures of a diameter ~5 µm was realized at high yield, and error–free data transmission was achieved over a distance 2.2 km [16] due to alleviation of chromatic dispersion related signal distortions, which otherwise is a limiting factor in modern MMF. Most recently data transmission beyond 160 Gb/s (DMT format) was demonstrated [17].

2. Concept of anti–waveguiding VCSEL

The radiative recombination probability of an electric dipole can be affected by varying the refractive index of the medium to which the photon is emitted. Multilayer structures open broad possibilities in redistribution of the oscillator strength, increase in differential gain and suppression of the parasitic modes. The straightforward approach to improve VCSEL performance is related to an anti–waveguiding design [3] with the cavity region having a lower refractive index compared to the average refractive index of the DBRs (Fig. 1(e)). In conventional VCSELs, the cavity is typically formed of a material with a higher refractive index (Fig. 1(a)). In such a structure in–plane waveguide modes are possible. It is known that VCSEL structures behave as low–threshold high–performance in–plane lasers, if processed in stripe laser geometry. In a standard high–speed oxide confined VCSEL design with relatively small deep–etched VCSEL mesa, two types of in–plane confined modes, which do not penetrate into the DBRs, are possible. High quality factor (high–Q) modes are associated with the etched mesa, which is typically small enough to reduce the parasitic capacitance. Low–Q modes are associated with the oxide–confined aperture [18].

 

Fig. 1 Comparison of 1λ waveguiding ((a)–(d)) and λ/2 anti–waveguding ((e)–(h)) VCSEL designs. Red: refractive index profile, blue: vertical profile of the longitudinal VCSEL mode, green: vertical profile of the in–plane waveguiding mode. (a), (e): general model structures; (b), (f): profiles of practical structures close to the resonance cavity; (c), (g): profiles in the entire structures in the aperture region; (d), (h): profiles in the entire structures in the oxidized region.

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Figures 1(b)–1(d) focus on a practical conventional 1λ–cavity design, which also shows the refractive index profile introduced by multiple quantum well (QW) active region (AR). In addition to the vertical cavity mode (blue), the fundamental waveguide mode of the multilayer structure (the lowest order in–plane mode) is plotted (green) versus the vertical coordinate. Figures 1(b) and 1(c) show that the optical field of the in–plane mode in the active region is stronger than the field of the vertical mode. One should emphasize that the selective oxidation of the aperture layers does not affect the in–plane mode, which persists also outside the aperture region at the oxidized periphery (Fig. 1(d)).

Figures 1(f)–1(h) show the refractive index profile for a practical λ/2–cavity device (close to that of [19]). Figures 1(f) and 1(g) depict the vertical profiles of the refractive index, of the vertical cavity mode (blue) and of the in–plane mode (green) in the aperture region. Contrary to Figs. 1(b), (c), the optical field strength of the in–plane mode is suppressed and is now approximately the same as the vertical cavity mode. Figure 1(h) refers to the oxidized periphery of the VCSEL. Remarkably, the fundamental in–plane mode is shifted away from the cavity region into the bottom DBR. The optical field strength of the in–plane mode in the active region is about 3 times lower than that of the vertical mode. Then the intensity (~|E|²) of the in–plane mode in the active region is an order of magnitude lower than the intensity of the vertical mode. Thus, the in–plane propagation of the emission originating in the cavity is suppressed. Consequently, the defect–rich region under the partially oxidized aperture layers and at the mesa sidewalls are not populated by photogenerated nonequilibrium carriers, which would otherwise cause generation of dislocations and their fast propagation. Furthermore, the in–plane mode has significant losses due to leakage into the substrate. Thus, the practical λ/2–cavity devices are indeed A–VCSELs, in which parasitic modes are strongly suppressed and the oscillator strength of the vertical mode is enhanced compared to the conventional VCSEL. One should also note that even multiple QWs having a high refractive index do not destroy the basic anti–waveguiding properties of the A–VCSEL.

3. Transverse mode selection in thin–aperture A–VCSEL

The concept of A–VCSEL enables effective selection of the optical modes in the vertical direction, rendering the vertical (longitudinal) VCSEL mode favorable and suppressing the in–plane modes. A further design step is needed to suppress high–order transverse modes associated with the longitudinal VCSEL mode. The approach suggested in [9–11] is based on a duo–cavity VCSEL where partially oxidized aperture layers promote effective leakage of the transverse optical modes formed in the non–oxidized core of the device to the oxidized periphery, whereas the modes leak to the continuum of the tilted modes associated with the second cavity. This effect is robust versus current–induced heating of the device as the current–induced thermal lens localizes the fundamental mode stronger than the high–order ones thus enhancing the advantage of the fundamental mode.

Here we extend another approach to the effective selection of the transverse modes suggested in [20] and introduce two thin apertures, having a thickness significantly smaller than λ/4, in the two nodes of the longitudinal mode closest to the anti–waveguiding cavity, on the p–side. A cylindrically–symmetric A–VCSEL structure is modeled, and optical modes are sought in the approximation of linearly polarized LP modes, without and with taking into account the impact of heating (see modeling details in [12]). Solution of the current continuity equation yields the electric current profile. Heat conductivity equation gives the temperature profile including as the two sources both Joule heating and infrared absorption of the optical modes by free carriers in the doped semiconductor layers. For practical doping levels used in the VCSELs and moderate currents (up to 10 mA) the contribution of the infrared absorption to the overheating is about 3 times stronger than that of the Joule heating. Figure 2(a) represents the cross–sectional profiles of the fundamental LP₀₁ and the high–order LP₁₁ transverse optical modes calculated for the aperture diameter 4 µm. The high–order mode LP₁₁ turns out to be the most dangerous high–order mode, as was also shown earlier for a different approach [12] to single–mode VCSELs. At zero current, the LP₀₁ mode is localized within the aperture, whereas the LP₁₁ mode is strongly shifted to the periphery outside the aperture. Thus, the fundamental mode has a strong advantage in optical confinement factor in the active region inside the aperture. Upon current increase, the localization of both modes inside the aperture becomes stronger. The effect is more pronounced for the LP₁₁ mode, which is initially not localized. Figure 2(b) displays the ratio of the optical confinement factors of the modes LP₁₁ and LP₀₁ versus aperture radius at currents 0 mA, 10 mA and 20 mA. A low value of this ratio means strong discrimination of the modes ensuring single–mode operation of the VCSEL. It follows from Fig. 2(b) that the mode discrimination at current 10 mA persists at the aperture radii smaller than, say, 2.5 µm (diameter up to 5 µm, the current density for this diameter being ~50 kA/cm²).

 

Fig. 2 (a) Modeled cross–sectional profiles of the intensity of the fundamental (LP₀₁) and the high–order (LP₁₁) transverse modes in an A–VCSEL with thin aperture layers at injection current 0 and 10 mA. Increase in current enhances localization of the high–order mode within the aperture. (b) Ratio of the optical confinement factors of two transverse modes versus aperture radius at different currents.

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In Fig. 3 we show the measured lasing spectra of the devices with the aperture radii of 1 µm (a) and 3 µm (c). In Figs. 3(b) and 3(d) an increase in the spacing between the fundamental and the first high–order modes is shown for the devices with the aperture radii of 1 µm (b) and 3 µm (d).

 

Fig. 3 Measured lasing spectra of quasi–Single–Mode 850 nm VCSELs with the aperture radius of 1 µm (a) and 3 µm (c) (diameters 2 µm and 6 µm). An increase in the spectral separation between the fundamental and the first high–order modes upon current is shown for the devices with the aperture diameter of 2 µm (b) and 6 µm (d).

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One can conclude from Fig. 3 that the spectral separation between the modes initially rapidly increases upon current and then saturates once the lateral extension of the both optical modes becomes predominantly defined by the enhancement of the refractive index in the aperture region caused by overheating. An increase in the absolute value of the spectral shift with current occurs at a much higher pace as compared to the large aperture devices as also predicted by modeling. The absolute values of the shifts corresponding to ~10 mA currents are by a factor of two higher than the predicted ones. We note, however, that at high current closer to roll over the wall plug efficiency decreases and at the same nominal current the heat dissipation is significantly higher, such that a mismatch by a factor of ~1.5 can be expected. One should also refer to the uncertainties in thermal conductivity coefficients in the materials, doping compensation, residual potential modulation at the interfaces of the DBRs and non–ideal heat sinking to the holder.

One should emphasize drastically different locations of the fundamental LP₀₁ and of the high–order LP₁₁ transverse optical modes (within and outside the aperture) depicted by their cross–sectional profiles of Fig. 2(a) at zero current. Such different locations is a specific and a targeted feature of a VCSEL with thin apertures placed in the nodes of the longitudinal field. On the contrary, for a conventional VCSEL, the calculated cross–sectional profiles of the fundamental and a high–order mode (see, e. g., Fig. 1 of [15]) demonstrate that both those modes are localized within the aperture. The optical confinement factors of those modes as well as of a large number of other modes are approximately the same [20], even without taking thermal effects into account.

4. Data transmission with A–VCSEL

The persistent demand on high–speed optical solutions for the datacom market requires the data rate and reach increase of the 850 nm VCSEL–based optical links. Whereas 28 Gb/s VCSEL–based products are already commercially available, the data rates aimed for next generation standards are 50 Gb/s and 100 Gb/s per wavelength, which gives rise to 200 Gb/s and 400 Gb/s through parallel fiber lanes or wavelength division multiplexing (WDM).

Despite the bandwidth limitation (<30 GHz) of the actual 850 nm–VCSEL technology, the recent studies demonstrate the feasibility of optical interconnects operating at 50 Gb/s and beyond, using on–off keying (OOK) modulation [16]. In order to face higher speed requirements, focus is made on the increase of the spectral efficiency through the high order modulation formats, such as pulse–amplitude modulation (PAM), discrete–multitone modulation (DMT) or carrierless amplitude/phase modulation (CAP). The use of these modulation formats allows the application of direct modulation and direct detection. However, in terms of VCSEL requirements, it necessitates high–linearity and low–noise VCSELs compared to those used for OOK modulation.

Regarding the impact of the mode composition on the MMF data transmission, single–mode A–VCSELs present significant advantages versus conventional multimode VCSELs as employment of the single–mode devices mitigates the impact of chromatic dispersion enabling longer transmission distances, as shown in [21].

Figure 4 combines the most remarkable transmission experiments over MMF using single–mode A–VCSELs developed by VI Systems, and an overview of different modulation formats is given. To date, the highest serial data rates demonstrated for 850 nm VCSEL were achieved through the use of DMT modulation: 161 Gb/s over 10 m, 152 Gb/s over 300 m and 135 Gb/s over 550 m were reported in [17].

 

Fig. 4 Gross data rate versus multi–mode fiber transmission distance for directly modulated single–mode A–VCSEL using different modulation schemes. Note: All above mentioned data transmission studies achieved error–free transmission with forward error correction (FEC).

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Data rates close to 100 Gb/s were also demonstrated applying other modulation formats. 4–PAM 112 Gb/s back–to–back (BTB) operation, 108 Gb/s over 100 m and 90 Gb/s over 600 m were demonstrated, while 90 Gb/s over 100 m was achieved using 8–PAM [22,23]. An approach based on multi–CAP modulation was studied in [24] allowing 112.5 Gb/s, 107.5 Gb/s, 102.5 Gb/s and 85 Gb/s over 0 m, 100 m, 200 m and 1 km, respectively.

Moreover, single–mode A–VCSELs also demonstrated their feasibility to extend the link distances to 1–2 km in order to satisfy the enormous grow in size of modern datacenters during the last decades. Non–return–to–zero (NRZ) 54 Gb/s over 2.2 km MMF was achieved in [16], resulting in a bit–rate distance product (BRDP) of 118.8 Gb/s · km, to the best of our knowledge the highest BRDP reported up to date.

Besides, the development of advanced OM5 fiber allowing high modal bandwidth in the spectral range 840–950 nm motivated research in VCSELs at wavelengths beyond the previously accepted for short reach applications.

50 Gb/s NRZ open eye diagrams for 850 nm and 910 nm SM–VCSELs up to 1200 m OM5 MMF transmission distance are shown in Fig. 5(a). These results were obtained without equalization and pre–emphasis. The corresponding bathtub curves for each wavelength and fiber length were extrapolated from jitter and noise analysis of the eye pattern [25], and the bit error rate (BER) is displayed in Fig. 5(b). Error–free 50 Gb/s NRZ transmission up to 1200 m OM5 is demonstrated for both wavelengths under assumption of different FEC thresholds.

 

Fig. 5 Study of 50 Gb/s NRZ data transmission links for 850 nm and 910 nm directly modulated SM–VCSELs at different OM5 MMF lengths. (a) Eye diagrams. (b) Bathtub curves.

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5. Conclusions

To conclude, we have proposed and developed advanced design concepts of the VCSELs, addressing both longitudinal and transverse optical modes. Applying an epitaxial structure having an anti–waveguiding cavity in the vertical direction leads to a strong suppression of parasitic in–plane optical modes, which supports a high modulation bandwidth. Using thin aperture layers located in the nodes of the longitudinal field of the lasing mode results in a strong suppression of high–order transverse modes and in single transverse mode lasing. Modeling including thermal effects demonstrates that single–mode lasing persists up to the aperture diameter 5 µm and current density ~50 kA/cm². A combination of advantages gives rise to record speed record distance data transmission based on such device, wherein the error–free transmission over 2.2 km at 54 Gb/s using NRZ format as well as the transmission at 160 Gb/s using DMT format have been achieved.