## 3 Results and Discussion
Overall, the physics of the process present a new research direction for analytical treatment, as well as improved understanding of the signal-signal dynamic processes inside the cavity, in particular, for the design of new generating and processing regimes in lasers. The transfer function is identical when increasing or decreasing the input power; it is below the conversion power value at which the mode-locking is destroyed (this value is defined by the cavity parameters of the processing laser; here it is 120 mW). The proposed technology has a characteristic spiking response with a power threshold and exhibits non-linear behaviour dependent on the input signal power, mimicking biological neurons. The mode-locking effect in fibre lasers is known to enable processing over ultra-short timescales. As the first demonstration of the laser design, we used an Er-doped fibre as a gain medium for illustration purposes as it is one of the most accessible, low cost and well-studied doped-fibre types, thus achieving an ms-order response time (see Figure 4a). Depending on the relaxation time of the gain medium, it is possible to achieve higher processing speeds targeting ultra-fast processing, which can also benefit from the fibre-based Echo state network architecture (FESNA) [22; 25; 26], potentially enabling THz-bandwidth processing. Moreover, the system offers an additional advantage of non-linear spectral re-shaping dependent on the input signal power similar to biological neurons, which may generate spikes with a frequency dependent on the input excitation. Here the spectral width of the output pulse has a distinct two-branch non-linear response depe  
Figure 4: **(a)** The spectrum width of the output signal as the input signal power generated by the seed (left) laser is varied by the VOA; **(b)** the spectrum before the threshold at 5.742 \(\upmu\)W input power (here the red dotted line represents Gaussian fitting) with the spectral width 6.83 nm; **(c)** the spectrum after the threshold at 139 \(\upmu\)W input power and the corresponding spectral width 5.33 nm. (see Figure 4a). The two-branch dependency of the spectrum on the input power is due to the transition between two operating regimes, as explained above, namely:  
(i) below the threshold - the non-linearity is small and the output signal spectrum width equals that of the _eigen-signal_, i.e., the signal when the (right) laser operates without the input signal; (ii) above the threshold - for larger non-linearity, the input signal becomes dominant and the output spectrum width equals the width of the _input signal_ spectrum. The distinct gap in the spectrum width in Figure 4a is due to the rapid switch between two regimes. The spectrum is captured via a Yokogawa optical spectrum analyzer (AQ6370D) and calculated at a 3 dB pulse width using Gaussian fitting. The spectrum can be compared before the threshold plotted in Figure 4b at 5.742 \(\mu\)W input power (here, the red dotted line represents Gaussian fitting) with the corresponding spectral width 6.83 nm and the spectrum after the threshold plotted in Figure 4c with 139 \(\mu\)W input power and the corresponding spectral width 5.33 nm. The results plotted here are for the 20 mW pump power of the processing laser. With further increase in the pump power the general trends in the amplitude transfer function and the value of the threshold remain the same, while the spectrum width transfer function becomes more step-like and the drop value increases drastically. However, increase in the pump value above 50 mW leads to a multi-pulsing regime. In this work, we focus on single-pulsing only--the emergence of complex dynamics in a multi-pulsing regime will be the subject of further work. Thus, the proposed technology can lead to a new type of neural coding. In particular, depending on the input power, the spectrum width can be modulated with clearly defined power-dependent regimes with a threshold. Thus, information can be encoded in the spectrum width. This is similar to rate coding.