This paper introduces a novel semantic communication system that leverages stacked intelligent metasurfaces (SIMs) for image recognition tasks. The system utilizes a diffractive neural network (DNN) architecture to perform complex computations at the speed of light. In the proposed system, a SIM is positioned in front of the transmitting antenna, which directly transmits carrier electromagnetic (EM) waves. The input layer of the SIM is used for source encoding, while the remaining layers form a DNN for semantic encoding. The semantic encoder transforms signals into a unique beam towards the receiving antenna corresponding to the image class. The receiver recognizes the image by probing the magnitude of the received signal across the receiving array. An efficient algorithm is developed to train the transmission coefficients of the SIM's meta-atoms to learn the semantic representation of the image. Extensive numerical results show that the SIM-based DNN achieves over 90% recognition accuracy for image recognition tasks. The system offers advantages such as reduced energy consumption, lower processing latency, and automatic source and semantic encoding as EM waves propagate through the SIM. The paper also presents a detailed system model, channel model, and training process of the DNN, along with simulation results demonstrating the effectiveness of the proposed system. The results show that the recognition accuracy improves with an increase in the number of metasurface layers, meta-atoms, and a shorter propagation distance. The system is capable of focusing information-bearing signals onto the corresponding antenna, enabling efficient image recognition in semantic communications.This paper introduces a novel semantic communication system that leverages stacked intelligent metasurfaces (SIMs) for image recognition tasks. The system utilizes a diffractive neural network (DNN) architecture to perform complex computations at the speed of light. In the proposed system, a SIM is positioned in front of the transmitting antenna, which directly transmits carrier electromagnetic (EM) waves. The input layer of the SIM is used for source encoding, while the remaining layers form a DNN for semantic encoding. The semantic encoder transforms signals into a unique beam towards the receiving antenna corresponding to the image class. The receiver recognizes the image by probing the magnitude of the received signal across the receiving array. An efficient algorithm is developed to train the transmission coefficients of the SIM's meta-atoms to learn the semantic representation of the image. Extensive numerical results show that the SIM-based DNN achieves over 90% recognition accuracy for image recognition tasks. The system offers advantages such as reduced energy consumption, lower processing latency, and automatic source and semantic encoding as EM waves propagate through the SIM. The paper also presents a detailed system model, channel model, and training process of the DNN, along with simulation results demonstrating the effectiveness of the proposed system. The results show that the recognition accuracy improves with an increase in the number of metasurface layers, meta-atoms, and a shorter propagation distance. The system is capable of focusing information-bearing signals onto the corresponding antenna, enabling efficient image recognition in semantic communications.