Our research team work in the field of development and study of advanced photonic sources, emitting in the near and middle infrared NIR/MIR windows, and in the THz range.

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**Non-conventionnal coherent light states based on III-V nanotechnology for photonic applications**

We are putting a lot of work in the design, the realization and the deep study of Vertical External-Cavity Surface Emitting Lasers, strengthening innovative semiconductor-based nanostructures. This laser source is compact, wavelength-flexible (NIR/MIR), widely tunable, highly coherent, with an high optical power, allowing the generation of classical laser-states (TEM00, single frequency and polarization state) and outperforming the other technologies.

This design also proves a high potential for the generation of new coherent optical states : spectrally modeless broaband laser, Vortex laser, dual-mode laser, spatially modeless degenerated laser for 3D spatial-temporal localized structures ...

This work goes hand in hand with a long standing expertise in optical instrumentation, in free space and guided optics configurations, namely allowing the study of the laser coherence and of the laser emission noise.

Once this state-of-the-art device is perfectly packaged, and taking into account a very successful technological transfer we managed, many applications are targeted : high resolution spectroscopy, velocimetry, inertial sensor, ...

**Metrology : Amplitude & Frequency Noise - Lineshape - Linewidth **

The metrology of the linewidth classically relies on the so-called heterodyne set-up: the beams of two identical lasers are superimposed spatially, and the frequency of the lasers is adjusted to generate a beating at a frequency which is low enough to be observable with radio-frequency (RF) instrumentation. The resulting beam then falls on a photodetector that generates a beat-note in the radio-frequency domain which is in turn analyzed thanks to a sweeping (superheterodyne) RF spectrum analyzer, see figure below.

Unfortunately, these spectrum analyzers do not allow to study easily the time dependency of the linewidth, because of the time required to sweep across the RF spectrum, which cannot usually be quicker than 1 ms in practical cases. There is an additional problem: using this device, the data obtained cannot be considered to be a snapshot of the laser spectrum, because all the points of such spectrum are not evaluated accurately at the same time due to the sweeping of the resolution filter.

This comes from the fact that acquisitions obtained with this kind of analyzer assume that the spectrum remains stable during the whole sweeping, which is not true with laser lines perturbed by technical noise sources. Thus, the profile acquired is distorted by the highly non-linear transfer function of the spectrum analyzer, loosing accuracy on the spectral shape itself. For that reason, such linewidth can only be given in statistical terms over repeated measurements, such as average value and standard deviation.

**Due to these metrological limits, the experimenters try to estimate the laser linewidth from frequency noise measurements**. It is an interesting idea because thanks to a frequency noise spectrum, as illustrated below, on can pinpoint the characteristic time associated with each noise source and obtain much more information than with a single-shot heterodyne measurement.

Nevertheless, the different known measurement techniques to get this frequency spectrum require quite complex set-ups and are not so easy to calibrate accurately. Secondly, the computation of the linewidth thus requires approximations that can lead to inaccurate results.

Furthermore, it is today possible to acquire the heterodyne beat-note in the time domain thanks to the emergence of high-speed data acquisition systems at quite low cost (compared to RF spectrum analyzers). This beat-note contains obviously all the noise information traditionally obtained by indirect ways. We use modern widespread data acquisition systems (high performance samplers) and numerical signal analysis, see illustration below, to perform a more accurate and more powerful study of the beat-note obtained with the heterodyne set-up, and enabling to overcome the various drawbacks of the standard method.

Our approach consists in performing numerical processing to the acquired time-domain beat-note signal in order to extract the phase fluctuation information in terms of power spectral density and linewidth. The associated theoretical description is summarized in the figure below, that displays the attainable physical quantities as well as the mathematical relationships that exist between them. The numerical acquisition of the time-domain beat-note is the central entry point. These mathematical relationships are not new and are very well understood in the signal analysis literature. However, in the context of laser study, they are generally taken as a pure theoretical basis and not used in practice under their numerical form in order to be applied directly on recorded signals: this is precisely what we propose here.

For more details, see our last article describing our state-of-the-art metrology :

N. Von Bandel et al., *Time-dependent laser linewidth : beat-note digital acquisition and numerical analysis*, Optics Express, 24, 24, pp 27961-27978, Nov. 2016.