Experimental study of modulation waveforms for entraining the spikes emitted by a semiconductor laser with optical feedback

Abstract

The entrainment phenomenon, by which an oscillator adjusts its natural rhythm to an external periodic signal, has been observed in many natural systems. Recently, attention has focused on which are the optimal conditions for achieving entrainment. Here we use a semiconductor laser with optical feedback, operating in the low-frequency fluctuations (LFFs) regime, as a testbed for a controlled entrainment experiment. In the LFF regime the laser intensity displays abrupt spikes, which can be entrained to a weak periodic signal that directly modulates the laser pump current. We compare the performance of three modulation waveforms for producing 1:1 locking (one spike is emitted in each modulation cycle), as well as higher order locking regimes. We characterize the parameter regions where high-quality locking occurs, and those where the laser emits spikes which are not entrained to the external signal. The role of the modulation amplitude and frequency, and the role of the dc value of the laser pump current (that controls the natural spike frequency) in the entrainment quality are discussed.

Comparing the dynamics of periodically forced lasers and neurons

“…The signal waveform is sinusoidal in panels (a), (c) and pulsed in panels (b), (d). The ISI values are normalized to the period of the signal, T mod ; therefore, the plateaus seen for ISI/T mod =1, 2, 3, ...reveal the characteristic locking structure of periodically forced excitable systems [58,59] that has been observed experimentally in semiconductor lasers with optical feedback [42,43,60]. In the following, locking n:1 means that the laser, or the neuron, emits a spike every n cycles of the modulation.…”

“…The experimental setup is as described in [42,43]. A semiconductor laser (685 nm Thorlabs HL6750MG with solitary threshold = I 26.62 th,sol mA), has part of its output fed back to the laser by a mirror.…”

“…The intensity time series typically contains more than 10 4 spikes. The ISIs are ΔT i =t i − t i−1 , where t i are the spike times, which were detected using the same method as in [42,43]. First, each time series is normalized to unit variance (the dc value is removed by the amplifier, so the time series has zero mean).…”

“…Specifically, in [38] the circle map was found to qualitatively describe the statistics of a sequence of symbols, known as ordinal patterns (OPs) [40], defined from the laser interspike intervals (ISIs). Follow up studies have analyzed how the statistical properties of the laser spikes are affected by a periodic modulation of the laser current [41][42][43].…”

Investigation of Chaotic and Spiking Dynamics in Mid-Infrared Quantum Cascade Lasers Operating Continuous-Waves and Under Current Modulation

“…Yet, the time interval between these dropouts is not constant. Adding a direct current modulation with a periodic sine forcing makes the spikes appear for a given phase shift of the external frequency modulation corresponding to the entrainment phenomenon [25], [26]. This paper further investigates the nonlinear dynamical features of a mid-infrared QCL operating under optical feedback with continuous-wave operation and, respectively, current modulation.…”