Developing of a photonic hardware platform for brain-inspired computing based on 5×5 VCSEL arrays
T. Heuser, M. Pflüger, I. Fischer, J. A. Lott, D. Brunner, S. Reitzenstein
DDeveloping of a photonic hardware platform for brain-inspired computingbased on × VCSEL arrays
T. Heuser, M. Pfl¨uger, I. Fischer, J. A. Lott, D. B, and S. Reitzenstein a) Institut fr Festk¨orperphysik, Technische Universit¨at Berlin, Hardenbergstrae 36, 10623 Berlin,Germany. Instituto de F´ısica Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC),Campus Universitat de les Illes Baleares, E-07122 Palma de Mallorca, Spain D´epartement d’Optique P. M. Duffieux, Institut FEMTO-ST, Universit´e Bourgogne-Franche-Comt´e CNRS UMR6174, Besan¸con, France. (Dated: 26 June 2020)
Brain-inspired computing concepts like artificial neural networks have become promisingalternatives to classical von Neumann computer architectures. Photonic neural networkstarget the realizations of neurons, network connections and potentially learning in photonicsubstrates. Here, we report the development of a nanophotonic hardware platform of fast andenergy-efficient photonic neurons via arrays of high-quality vertical cavity surface emittinglasers (VCSELs). The developed 5 × I. INTRODUCTION:
Artificial neural networks and brain-inspired machinelearning concepts have become highly attractive alterna-tives to classical computing based on conventional vonNeumann architectures. These concepts aim at imple-menting functionalities for complex computational taskssuch as fast pattern recognition and real-time learn-ing . Applications include for instance autonomous driv-ing , big data analytics and the prediction of chaoticsystems . At the same time the demand for informationprocessing with these concepts rises, and software-basedneuromorphic solutions implemented on classical compu-tation hardware might soon reach their limits in termsof energy efficiency, speed and latency. Therefore, thedevelopment of energy efficient hardware platforms opti-mized for brain-inspired computing is of crucial impor-tance to support further progress in the field of machinelearning and to enable advanced applications that are outof reach using present day computer architectures.A neural network comprises two fundamental ingre-dients, neurons and network connections. Neurons, usedin a wider sense, nonlinearly map their input informationonto their output, and as such numerous nonlinear pho-tonic components such as semiconductor lasers ,Mach-Zehnder modulators , saturable absorbers orplasmonic devices have been proposed and experimen-tally studied. The promises associated with photonicneural networks are that these components readily en- a) Electronic mail: [email protected] able data-processing rates exceeding 10 GSamples/s ,but even more that they can directly be interfaced withfully parallel photonic networks. Such parallel photonicnetworks typically leverage diffraction , reconfig-urable unitary matrices with Mach-Zehnder arrays and recently, novel 3D-printed waveguides or contin-uous diffraction inside a tailored volume . Combined,such high performance photonic neurons and networkstherefore promise orders of magnitude speed and latencyimprovement and potentially an abolishment of the sig-nificant energy-overheads caused by serial neural networkcircuitry. High-performance, reliable photonic neuronsbuilding upon mature technology such as the surfaceemitting semiconductor lasers we report here are there-fore key in the development of next generation photonicneural networks.In recent years the reservoir computing (RC) concept was one of the neural network concepts accelerat-ing hardware implementations with demonstrations inmechanical , electrical and photonic substrates,where particular photonic implementations promise highcomputation speed and low energy consumption. Onephotonic implementation used commercial vertical cavitysurface emitting lasers (VCSELs) , but it was found thattheir relatively low spectral homogeneity posed funda-mental limitations. An alternative approach envisionedarrays of quantum dot micropillar lasers , whose ultra-dense arrays of hosting hundreds of laser neurons withinless than 0.5 mm is particularly appealing. However,they usually operate under optical pumping at cryogenictemperatures, which hinders real-world applications. Incontrast, VCSEL arrays are of high practical relevance,but upscaling the arrays to more than a few tens of lasers a r X i v : . [ c s . ET ] J un will be challenging. The different approaches of laser-based photonic neural networks have in common that themodulated input signal of an injection laser is fed into anarray of lasers which are mutually connected via diffrac-tive coupling . In this concept a diffractive opticalelement (DOE) spatially multiplexes each laser preciselyat the positions of its neighbors within the array withthe help of an external cavity, as shown schematically inFig. 1 (a). The output of the system can then be cal-culated from the weighted sum of the lasers’ intensities.This kind of RC system is trainable by adjusting thereadout weights forming the optical output signal .Once such a system is implemented, it promises to per-form machine learning tasks at GHz speed, where theultimatelly bandwith limiting factors are the character-istic dynamical time scales of the lasers, typically on theorder of 10 ps. From a technological point of view, thedependence of laser-based photonic neural networks oninjection locking sets very strict hardware requirementsto the laser array in terms of high spectral homogeneity,polarization alignment and geometric dimensions.Photonic RC based on the diffractive coupling of VC-SELs was realized for the first time in and has provento be indeed a promising and scalable concept of machinelearning. However, the first implementation was basedon commercially available, non-optimized VCSEL arrayswhich limited the performance of the neural network.Here we report on the development of customized 5 × × µ m, which is a factorof 3 smaller than in the individual addressable commer-cial VCSEL arrays . Furthermore, we realized very highand individually tunable spectral homogeneity as well asa well-aligned and stable polarisation characteristic dueto a slightly elliptical cross section of the laser’s aperture.The article is organized as follows. We first describe FIG. 1. (a) Schematic presentation of photonic reservoir com-puting implemented by the diffractive coupling of VCSELs ina dense array, adopted from . technological details of the sample fabrication followed bypresenting the overall laser performance. Then we discussdetails of the performance and limitations of the injectionlocking characteristics. We close with a demonstrationof the spectral tuning capabilities of the individual lasersand an outlook to future work. II. SAMPLE DESIGN AND TECHNOLOGY
The 5 × µ m to meet the maximal dimensionof the RC optics field of view with an area of approxi-mately 1 mm . For the given emission wavelength ofthe VCSELs ( ≈
980 nm) the pitch additionally needs tobe matched precisely with the wavelength dependent op-tical characteristics of the DOE (see Fig.1(a)) . Fur-thermore, the design of the upper p-contacts and theirconnections to larger signal pads (for wirebonding toexternal electrical drivers) facilitates individual address-ability of each laser within the array to allow for biascurrent induced fine-tuning of the emission wavelength(see Fig. 2(b)).The VCSELs are based on a semiconductor het-erostructure consisting of a microresonator with 20.5 (37)Al . Ga . As/GaAs λ/ λ/ . Ga . As layers centeredon optical field intensity nodes forming oxide aperturesduring the VCSEL processing. The fabrication process,shown schematically in Fig.2(a), starts with the realiza-tion of 5 × µ m and a width of 6.5 µ m usingUV lithography and electron beam induced metal depo-sition of 60 nm Cr, 50 nm Pt and a capping of 250 nm Au.Subsequently, the corresponding 5 × µ m the aper-tures were oxidized using an oxidation oven with a 420 ◦ CH O+N atmosphere, a pressure of 50 mbar and an oxi-dation time of around 3 hours and 20 minutes. After theselective thermal oxidation and standard wafer cleaningwe dry etched the larger lower mesas which have a di-ameter of 45 µ m. Next, we deposited and lift-off n-metalground contacts, which consist of a 40 nm Ni Layer fol-lowed by 100 nm of the eutectic alloy Au Ge and afinal capping of a 400 nm Au layer. To improve the longterm stability of the VCSEL arrays, the mesas were thenpassivated and planarized by a 100 nm thick SiN layercreated by plasma enhanced chemical vapor deposition(PECVD) and spun-on benzo-cyclo-butene (BCB) poly-mer, respectively. The polymer is reopened selectivelyusing a further UV lithography and a (CF +O )-RIE FIG. 2. (a) Schematic overview of the sample fabrication process as described in section 2. (b) Microscope images of thefinished VCSELs and the fully wirebonded and mounted array. plasma etching step to again obtain access to the p- andn-contacts. Finally, fabrication is completed by a furtherUV lithography and metallization process forming largersignal contact areas to connect the individual VCSEL p-contacts with their intended signal pads. These square-shaped signal pads with side lengths between 100 and200 µ m are placed on larger areas of the semiconductormaterial formed in parallel with the mesa etching. Thesesignal pads are electrically isolated to the semiconduc-tor material by an initially 500 nm thick SiO layer alsodeposited by PECVD and shaped by wet-chemical etch-ing using buffered oxide etch (BOE). The thickness ofthe SiO layer is reduced to a remaining thickness of 200to 300 nm during the BCB polymer opening plasma RIEetching process.An important aspect of our customized VCSEL de-sign is the slightly elliptical cross-section of the VC-SELs which ensures tight polarization alignment whichis important for the envisioned RC application. The in-tentional ellipticity stabilizes the laser polarization andaligns it throughout the array to improve the efficiencyof optical injection and mutual diffractive coupling of theVCSELs. The elliptical shape was imposed to the upper(smaller) mesa, which also influences the shape of theoxide aperture that in turn has impact on the opticalmode confinement. We applied only moderate ellipticaldistortions with the long mesa axis being about 0.3 µ m(1 %) larger than the short axis. The goal is to controlthe polarization axis of the lasers’ strong mode withoutdegrading the overall emission properties. III. BASIC EMISSION PROPERTIES OF A × VCSELARRAY
In this section we present the emission properties ofan exemplary 5 × µ EL) emission spectra, the input-output characteristics and the polarization control. Theoptical characterization of the laser array was performedon a two-needle contact stage integrated into a high-resolution µ EL setup. The two freely movable needlesallow us to address individual lasers, whose emission was collected by a microscope objective with a numericalaperture (NA) of 0.4 placed in front of the x-y-movablesample stage. The signal was directed to a spectrometerwith 0.75 m focal length equipped with an IR-enhancedSi-CCD camera providing a spectral resolution of 30 µ eV( ≈ λ /2-plates and linear filters inthe detection path enable polarization resolved measure-ments. The emission power of individual VCSELs wasmeasured with a power meter placed in the detectionpath behind the microscope objective.An exemplary µ EL spectrum of VCSEL (column 1—row 5) recorded at an injection current of 750 µ A (2.2x I th ) is presented in Fig. 3(a). We observe multimodeemission with dominating signal from the fundamentaltransverse cavity mode at 977.8 nm and weaker emissionof the next higher lateral mode component at 977.3 nm.This multimode behavior is typical for most of the VC-SELs inside this array. Some devices, such as VCSEL(4—4) in Fig. 2(a), feature single mode emission withside-mode suppression ratios better than 10 dB. Figure3(b) shows the input-output characteristics of VCSEL(1—5). From the light output curve we infer a thresholdcurrent of (352.2 ± µ A and in the double-logarithmicpresentation of the fundamental mode intensity (inset)we observe a smooth s-shape transition, where we ex-tract a β -factor of 0.32 % by fitting the data with theequation from . The maximum emission power is ob-served at about 2.8 mW (at a pump current of 15 mA),which means that the available optical power range meetsthe requirements of photonic neural networks .Moving on to the characteristics of the whole array, weplot the output power as function of the injection currentfor all 25 devices in linear scale in Fig. 3(c). All lasersare functional and show very similar laser characteris-tics with an average threshold current of (368 ± µ A.Additionally, we observe an average slope efficiency of(0.359 ± FIG. 3. (a) µ EL emission spectra at an injection current of 353, 750 and 758 µ A and (b) emission power (integrated over allcavity modes) as function of the current of one laser within the VCSEL array. The inset shows the Gaussian fit intensity of thefundamental mode, fitted with equation from . (c) Emission power of all VCSELs within the 5 × × ± µ A demonstrating high polarization control due to the slightly elliptical cross-sectionof the devices. sion powers and indicates a slight spatial inhomogeneityin the oxidation process.Well-defined polarization properties of the VCSELs arecrucial for the target application of the array in photonicRC. We therefore recorded the linear polarization at abias current of (700 ± µ A and plotted the correspond-ing angular dependence of the emission in Fig. 3(d) for alldevices within the 5 × µ m (1 %). Indeed, the standard devia-tion of the polarization orientation has a value of 1.5 ◦ andthe maximum angle difference between two polarizationsis only 2.8 ◦ . Noteworthy, in reference measurements wealso investigated the polarization dependence of deviceswith nominally circular mesa shape and smaller ellipticityof 0.15 µ m. Here, we observed differences in the polar-ization orientation of up to 26.9 ◦ and 15.3 ◦ , respectively.This comparison highlights the importance of introduc-ing a suitable ellipticity for efficient polarization controlof the emission.Overall, the presented lasing performance of the inves-tigated 5 × IV. INJECTION LOCKING
The envisioned implementation of photonic RC isbased on the diffractive coupling of the lasers of the VC-SEL array and of injection locking to the external infor-mation injection laser . In this section we study opticalinjection locking exemplarily for one laser of the 5 × FIG. 4. (a) 2D intensity map of VCSEL emission under optical injection by an external tunable laser for a bias current of1.2 mA and an injected power of 0.87 mW. (b) Relative emission frequency of the VCSEL acting as slave laser as a functionof the master laser detuning. (c) Power dependent measurement of the boundaries of the locking area. (d) Injection powerdependent locking range for different injection currents.
VCSEL, where we study a tuning range of about 0.2 nm(60 GHz). The joint emission of the master laser with aninjection power of 870 µ W and the VCSEL is presentedin the 2D intensity plot of Fig. 4(a) for a bias currentof 1.2 mA (corresponding to a slave power behind theobjective of 288 µ W). We observe pronounced frequencylocking to the injection laser, identified by the strongly(by up to a factor of 6 in relation to the master emission)increased joint intensity of the two lasers, in a detun-ing range of about -8 GHz to about 5 GHz, where thedetuning is defined as the difference between the mas-ter laser’s frequency and the frequency of the consideredmode of the VCSEL (emitting at 977.896 nm). Lineshapefitting of the emission modes allows us to determine thecorresponding emission frequencies relative to the soli-tary slave frequency and to plot them as function of themaster-slave detuning. This is depicted in Fig. 4(b). Us-ing this evaluation we are able to extract the lockingrange ∆ which is (12.7 ± : − ν Slave Q (cid:114) P Master P Slave (cid:112) α < ∆ < ν Slave Q (cid:114) P Master P Slave , (1)where ν Slave is the resonance frequency and Q is the cav-ity Q -factor of the slave laser. α describes the linewidthenhancement factor and P Master /P Slave is the opticalpower ratio between master and slave laser. To obtaininsight into the underlying physics, we studied the evo-lution of the locking range’s upper and lower boundaryas function of (cid:112) P Master /P Slave for four different VCSELbias currents, as shown in Fig. 4(c). We observe a sys-tematic increase of the locking range and its asymmetrywith both, increasing (cid:112) P Master /P Slave and increasingbias current. Here, the dependence of the locking rangeon the bias current is attributed to a bias current de-pendent pre-factor ν Slave /Q in Eq. (1). While ν Slave ishardly influenced by the current (apart of a temperatureinduced red-shift of 142.6 GHz in the relevant currentrange), a negative correlation between the decreasing ef-fective Q -factor and the VCSEL’s bias current may be themain reason for the observed current induced increaseof the locking range. This current induced decrease ofthe Q -factor can be explained by enhanced optical lossesmost probably due to heating of the VCSEL’s opticalcavity.We further determined the injection locking range fora wide range of master/slave power ratios from about 0.2to 8 and plotted the results in Fig. 3(d), again for fourdifferent bias currents. The maximum locking range isabout 20 GHz (80 µ eV) for the applied injection pow-ers and bias currents. The experimental values are wellapproximated by a linear dependence as expected fromEq.(1). Again, the scaling factor, i.e. the slope of thelines, increases with the injection current from 5.2 GHzto 16.8 GHz per applied square-root power-ratio.The impact of the obtained injection locking resultson the application of our VCSEL arrays in photonic RCcan be assessed by taking the related laser power budgetinto account. In the RC concept based on diffractivelycoupled VCSELs, the signal of the input injection laserwith an optical power of typically 100 mW is distributedby a DOE to the individual lasers within the array. As-suming an equal distribution of the available power toall 25 VCSEL we obtain an injection power of 4 mW perlaser. Extrapolating the fitted data in Fig. 4(d), and un-der the conservative assumption that only 50% of thispower (i.e. 2 mW) is effectively injected into the laser,we estimate an available locking range of 18.8 - 24.8 GHz(75 - 102 µ eV), depending on the bias current. This lock-ing range is an important number for the technologicaloptimization of the VCSEL array’s spectral homogene-ity which needs to match at least this range to allow forefficient photonic RC . V. SPECTRAL HOMOGENEITY OF VCSEL ARRAYEMISSION
After having obtained a detailed characterisation ofthe input-output and injection locking properties of thefabricated VCSELs, we now turn towards the spectralhomogeneity of the 5 × ≈
25 GHz (110 µ eV).To evaluate the spectral homogeneity of the 5 × ± µ A. Fig. 5(a) shows a 2D presentation of theassociated, color coded emission wavelengths, with eachsub-square being associated with one laser located inthe given row and column of the array. We observe avariation of laser wavelengths throughout the array from977.719 nm to 977.831 nm, i.e. with a maximum differ-ence of 0.112 nm (145.2 µ eV, 35.12 GHz), leading to anaverage wavelength of 977.77 nm with a standard devia-tion of only 0.033 nm (42.4 µ eV). This high spectral ho-mogeneity is attributed to the high-quality sample pro-cessing and to the fact that the processed sample stemsfrom the center of the wafer where the resonance wave-length of the planar microresonator is almost indepen-dent of the position. Interestingly, the wavelength varia-tion in the array is low enough that the majority of the lasers in the array are already inside the spectral rangeneeded for efficient injection locking, hence even for uni-form bias currents the realized 5 × × µ A (difference maximum tominimum: 630 µ A) for a target wavelength of 977.8 nm
FIG. 5. (a) Intrinsic spectral distribution of the VCSEL’s fundamental mode wavelength at an constant bias currents of(0.70 ± ± ± ± to 110 µ A (420 µ A) for a wavelength of 978.6 nm, whilethe associated deviation of the emission power increasesfrom 73 µ W (240 µ W) to 160 µ W (700 µ W). These num-bers show that each wavelength in the given range canbe reached by adjusting the bias current of the individuallaser, while keeping the resulting variation of the emis-sion power in an acceptable range well below the typicalinjection power. In this regard also the relative devia-tion of the laser power compared to the average poweris of interest and is presented in Fig. 5(d) as well (greenclosed circles). In contrast to the absolute values for theassociated power, the relative maximum power deviationreaches its maximum of 0.42 at low target wavelengthsand is decreasing with longer wavelengths to about 0.13,as the average output power of the array is increasing.Overall, the measurements of the tuning abilities haveshown that the fabricated array allows us to compensateany spectral inhomogenities of the array and align thelasers to achieve a globally injection-locked state. Con- sidering all the discussed data we find that a low tar-get tuning wavelength is the most beneficial regime foroperating the VCSEL array as a reservoir system, al-though the range of choice here is limited by the ge-ometric dimensions of the array pitch and the DOEcharacteristics . On the one hand the main advan-tage of low target wavelengths is an overall low outputpower level, which reduces the energy footprint. Con-sidering a bias current of 0.76 mA the average emissionpower of the lasers in the array is about (178 ± µ W.Together with the spectral homogeneity in this case ofabout 42 µ eV, as estimated above, one can determinewith the data from Fig. 4(d) a needed injection power ra-tio of about 3.4 and with that a power consumption forthe injection locking for one VCSEL of about 0.609 mW.Together with typical bias voltages of about 2 V the to-tal power consumption for one VCSEL would be about2.1 mW, and about 45 mW for the complete array. Withthis we estimate the energy needed for one induced non-linear transformation with a value of only 104 fJ per VC-SEL and 2.6 pJ for the complete array, while consideringa modulation bandwidth of the nonlinear transformationof up to 20 GHz . On the other hand, the major costfor operating at low bias currents and wavelengths is arelatively large distribution of output powers comparedto the average value, which leads to a wider distributionof the applied power ratio. While this is indeed a slightcomplication for achieving the locking state, this disad-vantage is partly mitigated by the low increase in thelocking range, which makes this regime most suitable forthe locking operation. VI. SUMMARY
In summary, we presented a photonic hardware plat-form consisting of a tailored high quality VCSEL laserarrays developed for the realization of next generation op-tical neural network concepts, i.e. for reservoir comput-ing (RC). Main challenges for such applications are theoptical injection locking operation as well as to achievethe strict requirements for the spectral homogeneity ofthe laser elements in the array. To meet these goals, wespecifically adapted our VCSEL array design. First, wechose an elliptical mesa design which managed to alignthe polarization of the VCSEL emission to a standarddeviation of only 1.52 ◦ . Secondly, a contact design toindividually control each laser inside the array was cho-sen to create a post fabrication wavelength tuning abilityvia the injection current, where we use the temperatureinduced resonance shift of the lasers to meet the spectralrequirements of optical injection locking and coupling.Overall, the fabricated 5 × ± µ A. Also thespectral position of the fundamental LP01 mode emissionwith an average value of 977.77 nm with a standard devi-ation of 0.033 nm (42.4 µ eV) give evidence that the arrayshows excellent intrinsic spectral homogeneity in the caseof constant bias currents around (700 ± µ A. Investi-gations of the injection locking range in dependence ofthe injected optical power revealed an additional depen-dence of the locking range on the bias current. Consider-ing realistic injection conditions for RC experiments wefound locking ranges between (18.8 - 24.8 ± µ eV), depending on the bias current. These lockingranges are suitable to use the array as a reservoir evenfor constant pumping conditions. Additionally, the in-dividual contact design provides the flexibility to easilyspectrally align the lasers inside the array with tuningranges over a several nm. The consequences of differenttuning regimes were discussed and as a result, we suggesta low tuning wavelength, which promises a low consump-tion per VCSEL of only about 100 fJ at a bandwidth of20 GHz. Ongoing work focuses on the application of thefabricated arrays in reservoir computing setups to exploretheir reservoir computing performance and their poten-tial for further applications in the brain-inspired comput- ing field. Finally, combining with novel integrated andscalable photonic networks based on 3D printed photonicwaveguides has high potential to enable fully integratedphotonic neural networks based on this technology in thefuture. VII. ACKNOWLEDGEMENTS
The research leading to these results received fundingfrom the Volkswagen Foundation via the project ”Neuro-QNet”. Additionally, the German Research Foundationsupported this work via the Collaborative Research Cen-ter CRC 787.
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