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Dynamics of a Micro-VCSEL Operated in the Threshold Region Under Low-Level Optical Feedback

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Dynamics of a Micro-VCSEL Operated in the Threshold Region Under Low-Level Optical Feedback 1 Dynamics of a micro-VCSEL operated in the threshold region under low-level optical feedback Tao Wang, Xianghu Wang, Zhilei Deng, Jiacheng Sun, Gian Piero Puccioni, Gaofeng Wang, and Gian Luca Lippi Abstract—Semiconductor lasers are notoriously sensitive to quality, ease of integration and single-longitudinal mode emis- optical feedback, and their dynamics and coherence can be sion. In addition, they are less sensitive to optical feedback significantly modified through optical reinjection. We concentrate than their edge-emitting counterparts, rendering them more on the dynamical properties of a very small (i.e., microscale) Vertical Cavity Surface Emitting Laser (VCSEL) operated in attractive in many applications, in spite of their polariza- the low coherence region between the emission of (partially) tion sensitivity on which have focussed most of the optical coherent pulses and ending below the accepted macroscopic reinjection investigations (cf., e.g., [8], [9], [10], [11]). Our lasing threshold, with the double objective of: 1. studying the work focuses on the basic understanding of operation regimes feedback influence in a regime of very low energy consump- of very small devices which, in the future, could be used tion; 2. using the micro-VCSEL as a surrogate for nanolasers, where measurements can only be based on photon statistics. for transmissions and interconnects (e.g. datacenter applica- The experimental investigation is based on time traces and tions [12], [13]). Thus, we look at the dynamics of VCSELs radiofrequency spectra (common for macroscale devices) and due to non-polarization-selective feedback [14], [15], [16]. An correlation functions (required at the nanoscale). Comparison overview of the phenomenology observed in VCSELs with of these results confirms the ability of correlation functions to optical feedback can be found in [17]. satisfactorily characterize the action of feedback on the laser dynamics. Numerical predictions obtained from a previously VCSELs themselves are at the origin of laser miniatur- developed, fully stochastic modeling technique provide very close ization with the first design of a vertical semicounductor agreement with the experimental observations, thus supporting cavity [18], [19], which later branched along several inde- the possible extension of our observations to the nanoscale. pendent directions (e.g., photonic-crystal-based devices [20]). Index Terms—Semiconductor micro-VCSEL, optical feedback, The very low threshold and low power dissipation typical coherence, correlation functions, nonlinear dynamics. of nanolasers promise breakthroughs in a broad palette of applications [21], which, for our purposes, cover light sources for all-optical chips [22], data centers [23], [12], [13] and I. INTRODUCTION AND OBJECTIVES quantum information [24], [25], [26], [27]. However, their Optical communications have been the prime mover behind extremely small photon numbers render an in-depth character- the investigation of optical feedback on the emission properties ization quite challenging. Thus, aside from a couple of older of semiconductor lasers, due to the extreme sensitivity of investigations [28], [29] (even at the single-photon level [30]), edge-emitting devices to even very low reinjection levels (e.g., only recently have concerted efforts surfaced, covering opto- from fiber ends [1]). The noise and coherence properties, as electronic feedback [31] or external light feedback both in well as the emitter’s dynamical stability, are thus modified, microcavities [32], [33], [34] and in photonic-crystal-based with detailed features depending on whether the reinjected Fano-lasers [35], [36]. light fraction carries phase information [2], [3] (coherence Aiming at future on chip and datacenter applications, which length Lc > Lf , Lf feedback length) or whether only the require extremely low power consumption, we concentrate reinjected photon fraction counts [4], [5] (Lc < Lf ). The large on the investigation of feedback on the emission at bias number of investigations dedicated to the study of feedback current levels in the region between the first light emission is reviewed in different papers, depending on the scope: for and the traditional threshold [37], where we have shown that instance, optical transmission systems [6] or understanding it is possible to obtain reliable pulse generation at lower energetic costs [38]. Our objective is threefold: understanding arXiv:1907.00145v1 [physics.optics] 29 Jun 2019 the dynamical features of semiconductor lasers with optical reinjection [7]. the dynamical influence of feedback on a small (mesoscale) Developed in the 1980’s and 1990’s, Vertical Cavity Surface laser at ultra-low bias (i.e., below the traditional thresh- Emitting Lasers (VCSELs) have become the most widespread old) where the deterministic dynamics mixes with stochastic coherent light sources thanks to their versatility, good beam behaviour [39]; testing the predictive capabilities of fully stochastic modeling [40]; and probing the second-order (zero- T. Wang, X. Wang, Z. Deng, J. Sun and G. Wang are with School of delay) autocorrelation as a suitable dynamical indicator. This Electronics and Information, Hangzhou Dianzi University, Hangzhou, 310018, last point aims at validating, on a micro-VCSEL [41], the China, e-mail: [email protected] G. P. Puccioni is with Istituto dei Sistemi Complessi, CNR, Via use of the only technique currently usable to characterize Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy, e-mail: gian- nanolasers, the target devices for datacom applications. [email protected] The need for photon statistics to investigate nanolaser G. L. Lippi is with Universite´ Coteˆ d’Azur, Institut de Physique de Nice (INPHYNI), UMR 7010 CNRS, 1361 Route des Lucioles, F-06560 Valbonne, behaviour (including their threshold properties) comes from France, e-mail: [email protected] the lack of available detectors with sufficient sensitivity and, 2 simultaneously, electrical bandwidth to obtain a full charac- terization of the laser output. The extremely low photon flux (typically at the sub-nW, or even pW level) renders interfer- ometry challenging for routine tests. Thus, photon statistics becomes the obvious choice, given that it possesses both the necessary time response and optical sensitivity. However, since it only provides statistical information, the identification of the emission features must be based on models, or – as is the case with our present proposal – on the comparison with other techniques. A discussion on the pertinency of microlaser investigations to learn about nanolaser behaviour and comparison between linear measurements and photon statistics can be found in [41]. II. EXPERIMENTAL DETAILS AND OBSERVATIONS The experimental setup is shown in Fig. 1. The laser is a Fig. 1. Schematic illustration of the experimental design: LD, semiconductor VCSEL 980 (Thorlabs), designed for LAN data transmission laser diode (VCSEL); BS, beam splitter; M, dielectric mirror; PD, fast photodetector. The semiconductor micro-VCSEL is temperature stabilized at at 2.5 Gb/s [42], electrically supplied by a stabilized current 25◦C, powered by a commercial dc power supply (Thorlabs LDC200VCSEL) source (Thorlabs LDC200VCSEL), temperature-stabilized by with resolution 1µA and accuracy ±20µA. a home-made controller to better than 0.1◦C, with estimated β ≈ 10−4 [37]. The nominal threshold current declared by the Manufacturer [42] is typically ith ≈ 2:2mA, but can be as fied photodetector (Thorlabs PDA8GS, 9:5GHz bandwidth), high as ith;max = 3:0mA for some devices, while the maxi- to avoid backreflected contributions coming from the latter. mum operating current is imax = 10mA with corresponding The electrical signal from the photodetector is digitized by maximum laser output Pmax ≈ 1:85mW. The laser emits on a LeCroy Wave Master 8600A oscilloscope (6GHz analog a single polarization until a pump current value i ≈ 2:5mA bandwidth – acquiring 1 × 106 points in all measurements). (corresponding to the limit of the range we investigate) with a The data are stored in a computer through a GPIB interface rejection ratio of approximately 24 dB (spontaneous emission controlled in Python. The second-order autocorrelation func- is, of course, isotropic). Additional technical information can tion is numerically computed from the data trace acquired by be found in the Supplementary Information section of [37]. the linear detector, as in [37]. Comparison between the coherence properties of this de- Fig. 2 shows, in double-logarithmic scale, the average laser vice [37] and the manufacturer’s specifications suggest a output in the presence of the external cavity (squares) for consistency between the maximum specified threshold current different values of the pumping current, compared to the same value and the threshold for laser coherence, since the latter is response in the absence of feedback (circles). The error bars attained close to ith;max [37]. However lasing emission, in the are computed from the fluctuations in the measured signals. In form of partially coherent spikes, can already be obtained from the absence of feedback, emission from the laser in the form i ≈ 1:26mA [37], thus providing an interesting pumping range of irregular bursts has been observed for i = 1:26mA [37], below the coherence threshold where the influence of feedback thus we choose this bias point as reference (ith = 1:26mA on coherence buildup can be tested, and opening potential new hereafter) to normalize
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