Fig. 2: Experimental architecture.
a The input vector \({A}_{N}\) is encoded in the time domain using an EOM as a train of optical pulses which are injected into the fiber through a circulator. Rayleigh scattering (described by a series of complex reflectivity coefficients, \(\widetilde{{r}_{i}}\)) provides distributed feedback and the backscattered field, \(\widetilde{{C}_{M}}\), is then recorded on a photodetector, providing a non-linear response. b The distributed scattering process can be described using a space-time diagram which tracks the position of each pulse as it travels through the fiber. The pulses (shown in different colors for clarity) are partially reflected by Rayleigh scattering centers with varying complex reflectivity as they propagate down the fiber. As a result, the backscattered field contains randomly weighted contributions from each input pulse (i.e. each element in the input vector). c The distributed scattering process can be expressed as the multiplication between a complex transfer matrix \({B}\) and the input vector \(A\). d An example pulse train representing the SONAR data discussed in the SVM section and e the resulting RBS pattern. The inset in e shows a magnified view of the RBS pattern. EOM electro-optic modulator, SVM support vector machine, ADC analog-to-digital converter, Det photodetector, RBS Rayleigh backscattering.
