Implementing time-delayed feedback in optoelectronic circuits allows one to uncover the rich physics and application potential of nonlinear dynamics. Important feedback effects are, for instance, the generation of broadband chaos, or laser self-pulsing. We explore the effect of optoelectronic feedback in an ultracompact microlaser–microdetector assembly operating in the regime of cavity quantum electrodynamics (cQED). This system is used to generate self-pulsing at MHz frequencies in the emission of a microlaser, which is qualitatively explained by a rate equation model taking cQED effects into account. The results show promise for exploring chaos in ultracompact nanophotonic systems and for technological approaches toward chaos-based secure communication, random number generation, and self-pulsed single photon sources on a highly integrated semiconductor platform.
© 2017 Optical Society of America
Semiconductor lasers undergoing feedback are known to demonstrate rich nonlinear dynamics and have provoked much research in the fields of chaos, synchronization, and secure communication [1–3]. The manifestations of feedback can be either detrimental or beneficial to device performance. For instance, optical feedback caused by reflections at facets is known to cause data distortion in laser-based optoelectronic communication ; on the other hand, low optical feedback levels can be exploited, e.g., to reduce laser linewidths  and pulse jitter for better signal integrity . In particular, optoelectronic feedback, where the laser light is converted to an electrical signal that incoherently modulates the carrier density within the laser , allows one to explore routes to chaotic dynamics . It has also had a significant technological impact as it has been shown to be useful for the suppression of bistabilities in directly modulated semiconductor lasers .
Micropillar lasers based on quantum dots (QDs) exhibit low threshold currents thanks to their small mode volumes and high -factors, and can serve as excellent testbeds for studying feedback effects on lasing at ultralow light levels in the cavity-quantum electrodynamic (cQED) regime . Apart from generating light, electrically contacted QD-micropillars can also be applied to detect photons in the single-QD regime of cQED , making them applicable as photodetectors for on-chip quantum optical experiments [12–14].
In this report, we present interdisciplinary work in which we combine the above-mentioned fields in an ultracompact optoelectronic feedback scheme, which is based on a monolithically integrated microlaser–microdetector assembly. Here, an electrically driven whispering gallery mode (WGM) micropillar laser creates photocurrent within negatively biased QD micropillar detectors displaced 15 μm from the WGM microlaser. The extracted photocurrent is amplified within a 2 MHz bandwidth, and fed back to the microlaser. This feedback leads to a significant modification of the laser behavior over a certain range of laser bias currents. Clear indications of feedback influencing the laser emission are observed, such as undulations in the input–output (IO) curve, and periodic pulsing of the laser’s optical output. To describe the observed effects, we apply a rate equation model with temperature-induced gain changes and a stochastic noise source. The fact that feedback effects can be observed at MHz frequencies opens attractive avenues of research into nonlinear dynamics and may also lead to new insights into slow-timescale chaos. Future applications in quantum optics such as on-chip triggering of single-photon sources can also be foreseen.
A schematic of the sample layout is shown in Fig. 1(a). The larger, 8 μm diameter WGM micropillar laser is monolithically integrated on the same chip as a group of five surrounding micropillars with a smaller diameter (2 μm) which, when reverse-biased, serve as photodetectors . The assembly of five detector-pillars was chosen to increase the photocurrent generated by the central WGM microlaser. The five photodetectors form a semicircle contacted in parallel with each other [one shown in Fig. 1(a) for clarity], and the active region of the detectors lies within the same plane as the radial WGM laser emission . The radial separation between the microlaser and the photodetectors is 15 μm. This geometrical configuration leads to a rather low detection efficiency, which in combination with the external amplifier is nevertheless sufficient to observe pronounced feedback effects in our proof-of-principle work. The lasers and detectors are constructed from a planar microcavity structure grown by molecular-beam epitaxy on an n-doped (100)-oriented GaAs substrate. A single layer of self-organized InGaAs QDs (area density ) is embedded within a pin-doped distributed Bragg reflector (DBR) cavity. For more details on the DBR layer design and the device processing we refer to . Individual gold contacts are evaporated onto the p-doped upper part of the micropillar cavities for electrical pumping of the lasers and extraction of the photocurrent from the detectors .
Figure 1(b) illustrates the setup used for the optoelectronic feedback experiment. The photocurrent generated by the microlaser within the group of detectors was extracted, amplified, and fed back to the laser. The sample was held at 15 K within a liquid helium-flow cryostat. A forward bias voltage was applied to the WGM microlaser. The microlaser’s stray light scattered from the detectors in the vertical direction was collected by an objective and analyzed with a micro-electroluminescence (μEL) spectroscopy setup with a spectral resolution of 85 μeV. The transimpedance amplifier (TA) with a bandwidth of 20 MHz delivered a variable detector bias voltage to the detectors, which served to extract the photocurrent (0.2–0.3 μA per pillar on average at a laser current of 188 μA) generated by the microlaser under continuous-wave operation (see below for more details). To increase the signal-to-noise ratio (SNR) in measuring photocurrents and to exclude external radio frequencies from the circuit, we limited the measurement bandwidth to 2 MHz by a low-pass filter (LP) with a stopband attenuation >60 dB. The preamplified, filtered signal was passed through a larger-gain voltage amplifier (VA) with a 200 MHz bandwidth, with the overall amplification of the circuit being and a maximum output voltage from the VA of 2.75 V peak-to-peak. This amplified voltage was then coupled back into the WGM microlaser through a bias-T (BT) with a high-pass cutoff frequency of . The VA has a second output, which allowed us to monitor the amplified time-varying photocurrent signal in real time with an oscilloscope (OSC) that has a 2-GHz bandwidth. The two-stage external amplifier configuration was designed with the best SNR achievable and was necessary because, in the present device design, the photocurrent alone was not sufficient to modify the gain directly. The TA has an input-referred noise density of at 20 MHz measured with a 40 pF input capacitance, which is the total estimated capacitance of our sample and cabling within the cryostat. The effective round-trip time of the feedback circuit was measured to be .
We first characterized the emission properties of the integrated device without feedback. The laser was driven in forward bias and scattered light was collected and analyzed with a μEL spectroscopy setup (see  for details of the setup). Figure 2(a) shows the IO curve of an 8 µm-diameter WGM laser obtained by fitting the µEL spectra with a Voigt function. The onset of lasing is evidenced by the sudden drop in the emission linewidth (full width at half-maximum, FWHM) of the laser mode to the setup’s spectral resolution limit. A linear fit to the integrated intensity of the laser mode yields a threshold current of 40 μA at 4.3 V. An exemplary spectrum of the single-mode microlaser driven at 240 μA is shown in the inset of Fig. 2(a).
Next, we investigate the microlaser–microdetector system in the feedback configuration outlined in Fig. 1(b). The feedback consists of a positive voltage coupled into the laser via the p-contact. The corresponding photocurrent was detected by the TA and passed as an amplified voltage to the laser through the BT. The bias voltage on the detectors, and thus the dark current, remained constant during the recording of each data set. The electrical coupling between the laser and the detector via the common substrate was found to be negligible. The photocurrent as a function of detector bias under constant laser current is shown in Fig. 2(b). The dotted line indicates the bias for the optoelectronic feedback experiment. In the presence of feedback, the behavior of the microlaser is markedly different to the case without feedback. This is highlighted in Fig. 2(c) by a comparison between the IO characteristics of the laser mode with feedback (light red circles) and without feedback (solid black circles) below DC threshold . In semi-logarithmic scaling, pronounced undulations in the integrated intensity of the laser mode can be seen as the bias laser current is increased in the presence of optoelectronic feedback. These undulations are indicative of nonlinear modulation of the laser current due to feedback. The increased laser-mode visibility at such low bias currents can be attributed to the following: spontaneous emission-induced photocurrent is converted to a time-varying voltage delivered to the laser which, together with electronic noise, has an initial peak-to-peak magnitude of 900 mV at and . Consequently, it modulates the laser current and leads to laser emission even below the nominal DC threshold current. Further, there is a blue shift in the QD gain maximum under AC and DC excitation. Figure 2(d) demonstrates this with the appearance of the laser mode at 1.448 eV in the laser spectrum at DC bias currents as low as 4.8 μA, far below the DC threshold value of 40 μA.
Next, we analyze the dynamics of the laser mode-emission under optoelectronic feedback. Figures 3(a) and 3(b) show the experimental and simulated feedback-induced amplifier output time traces, respectively, while panels (c) and (d) show their respective fast-Fourier transforms within the bandpass of the setup. In Fig. 3(a), the laser bias was increased in 0.5 V steps (values of relative to the DC threshold shown above each waveform) while the detector bias was held constant at . When the laser is biased at , the amplitude of the VA output is peak-to-peak. As the relative bias current increases to 0.03, the laser mode becomes visible in the emission spectrum and subsequent photocurrent amplification becomes strong enough to generate self-sustained pulses in the amplifier output with a maximum amplitude of at . The slow pulses in Fig. 3(a) vary in amplitude and yet are very regular in separation with a period of at , increasing with the relative bias current to at . This kHz envelope contains a faster oscillation at a frequency close to , corresponding to the time required for pulses of laser light to be converted into photocurrent, processed by the electronics and passed back into the laser. This is evidenced by the second dominant frequency at 1.54 MHz (corresponding to ) appearing in the power spectrum of Fig. 3(c), becoming significant only after the onset of lasing. This frequency becomes more prominent as the laser bias is increased throughout the series until it falls off accompanied by the vanishing of the kHz-envelope. Long time-scale periodicity as well as chaos can emerge simultaneously in optoelectronic feedback systems , although the electronic bandwidth of our setup (2 MHz) precludes the observation of any dynamics on the timescale of the relaxation oscillations (GHz). Chaotic pulsing of semiconductor lasers under optoelectronic feedback has also been observed at much slower timescales compared to the relaxation-oscillation frequency when an additional bandwidth limitation is introduced to the feedback signal [8,17]. Here, however, we observe an additional prominent oscillation at a few kHz, which cannot be explained by the bandpass filtering of the feedback signal. Instead, we attribute this slow dynamic timescale to thermal effects, which are known to have characteristic timescales on the order of μs, and which have previously been shown to induce slow dynamics in semiconductor lasers . The origin of this microsecond timescale pulsing is attributed to the thermal shift of the gain spectrum and the related dynamical change of as the current in the laser varies. Ohmic heating due to such voltage pulses was verified to cause the laser mode to shift by 100 μeV, which is related to a temperature change of about 20 K . A bi-exponential decay was measured in a separate experiment to explore the dynamical features of this dependence.
To describe the optoelectronic feedback dynamics in our integrated microsystem, we used a rate-equation model to simulate the IO characteristics and dynamics of the WGM laser mode emission under optoelectronic feedback. Our theoretical description goes beyond existing optoelectronic feedback models by including temperature-induced gain changes as dynamic variables. The model consists of the following equations:1(b) and represents the effective round-trip time of the signal from photodetector to microlaser. is the cavity photon lifetime, and the effective carrier lifetime includes the carrier scattering time of the refilling from reservoir states. The dimensionless fit parameters determine the rates at which the temperature is driven by the photon number, and the two timescales and are of a bi-exponential dependence with which the gain recovers. The timescales were experimentally determined by a time-resolved detection of the cavity mode’s energy, which is indicative of the local temperature of the microlaser. Spontaneous emission is included by the stochastic normalized Gaussian white noise source , and is the spontaneous emission coupling factor. The value of the parameters used in the simulations are displayed in Table 1. The dynamic simulations shown in Figs. 3(b) and 3(d) are found to qualitatively reproduce the experimental current dependence, i.e., the appearance of a slow kHz modulation within a small current range. The slow modulation is found to disappear when neglecting the temperature change in the model, clearly showing the importance of thermal effects in the observed dynamics. The discrepancy between experiment and simulation in the injection current values for which the dynamics set in is partly explained by the reduction in threshold under DC and AC excitation compared to the purely DC case as discussed above, which was not taken into account.
In conclusion, optoelectronic feedback using a QD-based, monolithically integrated microlaser-microdetector assembly has been realized and investigated experimentally as well as theoretically. Self-pulsing of the microlaser was observed over a narrow range of laser biases, and the system was modeled with rate equations in dependence of cavity photon number, charge carrier number, and a temperature dependence of the microlaser gain qualitatively reproducing the experimental results. We find that the inclusion of thermal effects is necessary to describe the observed μs-modulation of the laser output under feedback. With further development, our platform could be employed for diverse applications such as tuning the external cavity geometry to match the laser excitation, forming an integrated resonant detection device with a higher efficiency, and potential use for in situ monitoring. Integration of amplifier electronics on the same chip would comprise a truly self-contained, on-chip feedback system for compact chaotically secure communication  or for an array of self-pulsed single-photon sources when using one or more external micropillars as a quantum light emitter instead of as a photodetector. A network of nonlinear oscillators could also be conceived to study complex nonlinear dynamics . Further work is required to optimize the contact layout and reduce parasitic capacitances for an increase in bandwidth to compete with other feedback schemes using a wholly off-chip detection method. Additional improvements can be made to the detector geometry to increase the extracted photocurrent, and deformed resonator geometries such as the limaçon of Pascal can be exploited for laser emission preferentially in the direction of the detectors .
European Research Council (ERC) (615613); Deutsche Forschungsgemeinschaft (DFG) (RE2974/9-1, SCHN1376/1-1, CRC787).
We thank M. Emmerling for sample preparation.
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