# Parallel Extreme Learning Machines Based on Frequency Multiplexing
## 2 Experimental System  
### Experimental Setup  
Our experimental setup is depicted in Figure 1. The light sources are three continuous wave lasers that are tunable in the C-band; we fix their wavelengths at values of \(\lambda_{1}=1546.0\) nm, \(\lambda_{2}=1550.8\) nm, and \(\lambda_{3}=1555.7\) nm. These wavelenghts are chosen so that the frequency combs they generate do not overlap. The three sources are injected into a single optical fiber through a set of isolators and combiners; the laser output powers are set in such a way as to obtain a total optical power of approximately 9 dBm at the output of the coupling system. PM\({}_{1}\) and PM\({}_{2}\) are two phase modulators exploited respectively to generate the combs and mix their lines. Both modulators are driven by the same periodic Radio Frequency (RF) signal at frequency \(\Omega/2\pi=16.96860\) GHz. The electrical input of each phase modulator is processed by an RF amplifier (A\({}_{1}\) for PM\({}_{1}\) and A\({}_{2}\) for PM\({}_{2}\)). These two amplifiers provide two different fixed gains, hence PM\({}_{1}\) and PM\({}_{2}\) are driven by two different RF powers: 20 dBm and 30 dBm respectively. The effect of periodic phase modulation is more easily described by the dimensionless number \(m=\frac{\pi V}{V\pi}\), where \(V\) is the amplitude of the electrical signal and \(V\pi\) is the characteristic voltage of the phase modulator. In our setup, \(m_{1}\approx 7.78\) and \(m_{2}\approx 2.18\). \(\Omega\) defines the spacing of comb lines and its exact value is not important as long as it does not drift significantly during the experiment. The settings are such that PM\({}_{1}\) approximately generates a 30-line comb out of each light source (see Figure 2a). The periodic phase modulation effect is described in detail in Section 2.2, where we provide a description of the setup in terms of electric fields. For a review on electro-optic frequency comb generation, see [26]. The programmable spectral filters, SF\({}_{1}\) and SF\({}_{2}\), are two Finisar Waveshapers, models 1000 and 4000, respectively. SF\({}_{1}\) is employed to inject inputs in the network by setting the proper attenuation on each comb line, while SF\({}_{2}\) is employed to retrieve outputs, redirecting properly filtered combs on the photodiodes PD\({}_{1}\) and PD\({}_{2}\). The nominal bandwidth resolutions of the filters SF\({}_{1}\) and SF\({}_{2}\) are 20 GHz and 10 GHz, respectively, which should be enough to resolve a single comb line since the comb spacing is determined by \(\Omega\). Nevertheless, we measured a slight crosstalk effect between two lines filtered by SF\({}_{1}\) (which is, in any case, not expected to influence performances; see [19]). Figure 1: Scheme of the experimental setup. Red lines represent optical connections, green lines represent data connection to and from the computer, and blue lines represent RF connections. A\({}_{1}\) and A\({}_{2}\) represent two RF amplifiers. The first Phase Modulator, PM\({}_{1}\), generates a frequency comb out of each line in the spectrum of the light source, \(E^{\text{source}}\). The first programmable Spectral Filter, SF\({}_{1}\), encodes input features in these combs, thus generating the input layer \(E^{\text{in}}\) (or the set of input layers, in the case of parallel operations). The filter shape loaded onto SF\({}_{1}\), \(F^{\text{in}}\), is calculated according to the features to be encoded. The second Phase Modulator, PM\({}_{2}\), mixes the components of \(E^{\text{in}}\), thus generating the hidden layer \(E^{\text{hidden}}\) (or the set of hidden layers, in the case of parallel operations). The second programmable Spectral Filter, SF\({}_{2}\), is employed for the readout and can apply two different filter shapes (\(F^{\text{out},\ 1}\) and \(F^{\text{out},\ 2}\)) to its two outputs, generating \(E^{\text{out},\ 1}\) and \(E^{\text{out},\ 2}\). The photodiodes PD\({}_{1}\) and PD\({}_{2}\) measure the total intensities in \(E^{\text{out},\ 1}\) and \(E^{\text{out},\ 2}\), respectively.