## 1 Introduction
In this work, we present numerical results concerning a \"deep\" five-layer Photonic Spiking Convolutional Neural Network (PSCNN), realized with the help of two-section (gain-absorber) VCSEL photonic neurons. The proposed configuration is a photonic adaption of a software based Spiking Convolutional Neural Network (SCNN) capable of feature extraction [36]. Although software based SCNNs emulate the performance of their biological counterparts, they cannot exploit their full potential as they are equally as power hungry as typical convolutional neural networks and are subjected to latencies. The realization of a hardware version of the proposed network will alleviate these restrictions and in turn permit feature extraction from more complex images. Moreover, by exploiting the nanosecond refractory period of VCSELs, a time-multiplex scheme is incorporated, aiming to map spatial information to the temporal domain; meaning that different pixels' contrasts are processed by the same neurons and are mapped to spike latency. Therefore, the number of physical neurons is reduced from 2020 nodes for a typical five-layer network [36] to only 62, resulting in a 96.93% decrease. Following this lead, processing speed is tunable; from the multi-Mframe/s scale, where physical neurons are equal to the effective neurons, to the Kframe/s rate by proportionally decreasing the number of physical neurons. Taken to the extreme, the processing speed can be reduced to an application related frame-rate (e.g., 120 frame/s), in turn resulting in a tremendous decrease in the physical neuron count. In this work, the time-multiplexed PSCNN multilayer network is evaluated by tackling a basic image processing task that consists of classifying monochrome images representing digital digits. Contrary to previous approaches, the training in our case is based on purely unsupervised spike dependent plasticity (STDP) [37], which could, in future implementations, alleviate the need for complex offline processing and offer a photonic friendly solution [38]. Numerical simulations, through the help of a graphic processor unit (GPU) accelerator, provide evidence regarding the relationship between systematic amplitude variations in the target images and classification errors. Summarizing, this work provides the first, according to our knowledge, investigation of a full-scale PSCNN that simultaneously merges approaches such as: multiple convolutional layers for feature extraction, unsupervised STDP as training technique, time multiplexing of incoming signals so as to reduce neuron count and finally retina-ganglion-cell based structures so as to replace costly digital processing with a bioinspired process. This work is organized as follows. In Section 2, the methods used are presented in detail. In particular, we presented the numerical model used to simulate VCSEL's neural operation and analyzed the structure and operation of every layer of the proposed network during training and inference mode. In Section 3, we present the numerical results from our network and analyze the impact of noise, processing time and actual number of neurons on our network's performance. Moreover, a detailed comparison between our work and other VCSEL networks is presented.