Onset of Lasing in Small Devices: The Identification of the First Threshold through Autocorrelation Resonance

Abstract

A simple technique for identifying the onset of coherent emission in mesoscale lasers, which makes use of a small-amplitude modulation added to the pump, is introduced. The optimal modulation frequency is obtained from the radio-frequency power spectrum of the unperturbed laser emission. The identification of the lasing onset rests on the appearance of a resonance in the experimentally measured zero-order autocorrelation function (g (2) (0)) plotted as a function of the pump rate. Numerical proof is provided in support of the autocorrelation resonance. The intrinsic simplicity of this technique and its inherent compatibility with photon counting makes it an excellent tool for certifying the onset of laser emission independent of the laser cavity volume. Recently published measurements of g (2) (0), obtained in nanolasers, support the extension of this technique to nanoscale devices.

Exploration of VCSEL ultra-low biasing scheme for pulse generation

“…Increasing slightly the bias point, i b = 1.15mA (i.e., ≈ 8% above threshold [23]), we end up with an optimal condition, where we can consistently obtain regular pulses which, while displaying some residual variability, can be well identified with the help of thresholding: setting a threshold at, for instance, 50% of the average peak level we can confirm the presence of a pulse per modulation period. During the modulation, the laser is still brought temporarily below threshold, but only for a time τ bt ≈ 0.25ns.…”

“…The modulation amplitude is chosen in such a way as to obtain the most effective pulse generation with minimal amplitude (cf. below for evidence and [23] for spectral analysis). The choice of a sinusoidal modulation originates from its spectral purity, which allows for reliable results without the need for special probes.…”

“…We first present the laser response for a small set of biasing choices, identifying the optimum condition, then analyze it. Thanks to previous work [23], which allows us to identify the threshold for coherent emission, we know for this device that the latter is placed at i b = 1.06mA. The laser response (input-output or L-L curve) is displayed in the upper part of Fig.…”

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

“…This is probably due to reliance of the numerical scheme on the photon number, while the field's phase progressively gains relevance in the gradual transition towards coherent laser emission. Nonetheless, the scheme's validity in the fully incoherent regime promises to provide insights into the feedback dynamics at the smallest laser scales [45].…”

“…Fig 3(a) shows the rf spectrum at i = i th : peaks appear at the external cavity repetition frequency (∆ν ec ≈ 0.23 GHz) and its harmonics, where the third one, located close to an intrinsic "resonance" in the spiking (cf. [37], [44], [45] for its interpretation), presents a somewhat stronger amplitude and slightly narrower peak, but no additional feature (as in the free-running case [44]).…”