We present a deep learning-based method for the automatic extraction of physical parameters from optical spectra and power values of a chirped, tapered, dual-section quantum dot superluminescent diode. The neural network is able to estimate a set of parameters that are capable of reproducing the behavior of the target device with high accuracy

Bardella, Paolo

Carena, Andrea

Curri, Vittorio

Marchisio, Andrea

English

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

17 October 2023POLITECNICO DI TORINORepository ISTITUZIONALEDeep Learning-Driven Extraction of Superluminescent Diodes Parameters / Marchisio, Andrea; Curri, Vittorio; Carena,Andrea; Bardella, Paolo. - ELETTRONICO. - (2023). (Intervento presentato al convegno International Conference onNumerical Simulation of Optoelectronic Devices (NUSOD) tenutosi a Torino (ITALY) nel 18-21 September 2023).OriginalDeep Learning-Driven Extraction of Superluminescent Diodes ParametersPublisher:PublishedDOI:Terms of use:Publisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2982317 since: 2023-09-19T15:16:42ZPolitecnico di TorinoDeep Learning-Driven Extractionof Superluminescent Diodes ParametersAndrea MarchisioPolitecnico di Torinoandrea marchisio@polito.itVittorio CurriPolitecnico di Torinovittorio.curri@polito.itAndrea CarenaPolitecnico di Torinoandrea.carena@polito.itPaolo BardellaPolitecnico di Torinopaolo.bardella@polito.itAbstract—We present a deep learning-based method for theautomatic extraction of physical parameters from optical spectraand power values of a chirped, tapered, dual-section quantum dotsuperluminescent diode. The neural network is able to estimatea set of parameters that are capable of reproducing the behaviorof the target device with high accuracy.Index Terms—Superluminescent diodes, deep learning, param-eter extraction, time-domain traveling wave, quantum dots.I. INTRODUCTIONSuperluminescent diodes (SLEDs) are a prominent solutionfor sources in a wide range of applications, due to their highoutput power and spectral brightness. In particular, chirpedand tapered Quantum Dot (QD) SLEDs are characterized bya large bandwidth, as well as a tunable spectral asymme-try between the two facets [1], which could introduce thepossibility of multiplexing their outputs for flexible tuningof the device output and bandwidth. The characterization ofsuch devices is not straightforward due to the number ofparameters required to properly reproduce the experimentalbehavior in stationary and dynamic conditions, the latter forthe amplification of optical pulses: brute-force approaches toextract these parameters are not recommended because of thehigh computational cost and time of those methods. A muchmore effective approach for the characterization or inversedesign of devices relies on machine learning solutions [2].We hereby present a Deep Learning (DL) approach for theextraction of device parameters of a chirped, tapered, and dual-section QD SLED, starting from its power and spectral data.The accuracy of the Deep Neural Network (DNN) is tested bycomparing the predictions with some reference curves similarto those experimentally reported in [1], here obtained withTime-Domain Traveling Wave (TDTW) simulations.II. REFERENCE DEVICEThe device parameters are presented in [1]. The activematerial contains 10 chirped InAs QD layers: three layers withground state (GS) emission λGS centered at 1243 nm, threelayers with λGS = 1211 nm, and four with λGS = 1285 nm.The device is 6mm long, with an initial 14 µm wide straightridge waveguide (rear of the device), followed by a firsttapered section with a full taper angle of 3◦ and a secondtapered section with a full taper angle of 0.8◦, which isequivalent to a total width of 110 µm at the front facet. At1.875mm from the rear facet, an insulation trench is etched,creating two bias sections that can be driven independently forgreater flexibility.III. TDTW MODEL FOR DATA-SET GENERATIONThe TDTW model [3] takes into account the chirped natureof the active QD material (different layers with differentground state emission wavelengths) and the stimulated emis-sion from the second QD excited state.The carrier dynamics is described by a set of multi-population rate equations (MPREs), which take into accountthe scattering and recombination phenomena graphically sum-marized in Fig. 1. The population dynamics in the conductionand valence bands are assumed to be equivalent (excitonicapproximation) to speed up the simulation. The propagationof the forward and backward field components E± is describedwith two wave equations that, under the slowly varyingenvelope approximation (SVEA), read [4]:1vg∂E±∂t± ∂E±∂z=− 12(α±i (z) + αp)E±(z, t)−−jω0Γxy±(z)2cneffϵ0P±(z, t) + Ssp±(z, t)(1)with vg group velocity, E± progressive and regressive com-ponents of the field, αp plasma losses, ω0 reference angularfrequency, neff effective index. The intrinsic waveguide lossesα±i (z) and the transverse confinement factor Γxy±(z) varywith respect to the position and have different behaviorsdepending on the propagation direction in the tapered structuredue to the weak confinement of the field in the transversedirection. P±(z, t) is the macroscopic polarization, linkedto the stimulated response of the system, while Ssp±(z, t)describes the spontaneous emission process.Finally, boundary conditions are required in order to takeinto account the residual facet reflectivities r0 and rL [5]:E+(t, 0) = r0E−(t, 0) (2)E−(t, L) = rLE+(t, L) (3)The model is solved numerically with a finite differencescheme and it is employed to generate a training data-set forFig. 1. Scheme of the considered levels and the scattering and recombinationphenomena that affect them.TABLE IINVESTIGATED PARAMETERS AND CORRESPONDING RANGES.Parameter Range Parameter Range Parameter RangeProgr. losses α+i [cm−1] 2.2 –5.0 GS gain gGS [10−16 cm2 eV] 0.2 –0.6 GS Auger rec. time τGSAug [ns] 0.1 –5.0Regr. losses α−i [cm−1] 0.3 –2.4 ES1 gain gES1 [10−16 cm2 eV] 0.3 –0.8 ES1 Auger rec. time τES1Aug [ns] 0.1 –5.0Injection efficiency ηi [ ] 0.5 –0.8 ES2 gain gES2 [10−16 cm2 eV] 0.4 –1 ES2 Auger rec. time τES2Aug [ns] 0.1 –5.0DL. This is achieved by randomly generating combinations ofthe nine target parameters shown in Table I, as they play afundamental role in the definition of the static and dynamicalbehavior of SOA. The parameters’ values are randomly gen-erated according to a uniform distribution over the associatedranges, listed in Table I, the only additional constraint beingthat gES2 > gES1 > gGS . For each parameter set, the rearcurrent is fixed to IR = 100mA, while the front current IF ischanged from 1A to 5A. A single simulation lasts 5 ns. Eachentry in the data-set contains the front and rear facet spectra(102 equally spaced points each) and the front and rear facetaverage output powers for the five current combination. Dueto the high computational cost, training is done on a data-set of 1000 samples (60% training, 20% validation, and 20%testing).IV. DEEP LEARNING SCHEMEThe deep neural network (DNN) used for parameter ex-traction is developed in TensorFlow™ with the Keras API.It is a single fully connected DNN that employs the ADAMoptimizer, with step-decaying learning rate, and Leaky ReLUas activation of the layers. To prevent overfitting, batch nor-malization and L2 regularization are considered. To maximizethe accuracy of the prediction, different combinations ofhyperparameters are evaluated during the training process. Inparticular, we tested multiple values of number of hiddenlayers ([2, 3, 4, 5, 6, 7]), number of neurons per layer ([20, 30,50, 100]) and batch size ([10, 20, 50, 100, 150, 200]). Duringthis optimization process, early stopping is implemented toprevent overfitting and to speed up the process itself. Twocombinations of hyperparameters are selected since they areable to minimize the loss (mean squared error) and the averageerror of the predictions on the test set, defined as∆e =1NN∑i=1Xi −XtargiXtargi(4)where N = 9 is the number of target parameters, Xtargi is thevector of values for the i-th parameter of the test set, and Xiis the vector of associated predictions. We selected 3 hiddenlayers, 100 neurons per layer, and 50 batch size (minimumloss) and 5 hidden layers, 100 neurons per layer, and 100batch size (minimum average error). Finally, the referencecurves are fed to the trained networks and their predictions areaveraged for better accuracy (model averaging). The obtainedparameters are simulated once again with the TDTW solverin order to compare the spectra and output powers.V. RESULTS DISCUSSIONFig. 2 shows the comparison of the reference spectra (solidlines) and those obtained by simulating the extracted parame-Fig. 2. Comparison of the reference and predicted spectra.ters (circles), at different values of front section current. Thepredicted parameters yield spectral curves that are in goodagreement with the target. Indeed, they are characterized bythe same spectral components with very similar profiles, witha limited decrease in accuracy at larger currents. In general,due to the limited size of the data-set, the predicted normalizedcurves present a lower peak at λ = 1240 nm with respect tothe reference cases; we expect to solve this issue by increasingthe size of the data-set.VI. CONCLUSIONSWe proposed a DL approach to the extraction of parametersfrom the spectral data of superluminescent diodes. Whileaccuracy improvements can be achieved by increasing thenumber of entries in the data-set, the proposed DNN is ableto extract a set of nine parameters that reproduce the behaviorof the target device, thus providing an accurate starting pointfor studying the device dynamic behavior in the presence ofexternal optical pulses.REFERENCES[1] A. F. Forrest et al., “Wide and tunable spectral asymmetry between narrowand wide facet outputs in a tapered quantum-dot superluminescent diode,”Optics express, vol. 28, no. 2, pp. 846–859, 2020.[2] Y. Xu et al., “Interfacing photonics with artificial intelligence: an innova-tive design strategy for photonic structures and devices based on artificialneural networks,” Photon. Res., vol. 9, no. 4, pp. B135–B152, Apr 2021.[3] A. Marchisio et al., “Time-domain travelling-wave analysis of semicon-ductor optical amplifiers based on chirped quantum dot materials,” inCLEO proceedings, 2023.[4] M. Rossetti et al., “Time-domain travelling-wave model for quantum dotpassively mode-locked lasers,” IEEE Journal of Quantum Electronics,vol. 47, no. 2, p. 139 – 150, 2011, cited by: 66.[5] A. F. Forrest et al., “Numerical and experimental characterization ofchirped quantum dot-based semiconductor optical amplifiers,” in NUSODproceedings, 2021, pp. 17–18.

Deep Learning-Driven Extraction of Superluminescent Diodes Parameters

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Deep Learning-Driven Extraction of Superluminescent Diodes Parameters

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