The explosive growth in computational demands of artificial neural networks has spurred research into optical neural networks. However, most existing work overlooks the co-design of software and hardware, resulting in challenges with data encoding and nonlinear activation in optical neural networks, failing to fully leverage the potential of optical computing hardware. In this work, we propose a nonlinear optical processing unit (NL-OPU) based on the nonlinear response of Mach-Zehnder modulators (MZMs) for an optical Kolmogorov-Arnold network (OKAN), which bypasses the challenges related to linear data representation and nonlinear activation execution in optical neural networks. In proof-of-concept experiments, an OKAN and a multilayer perceptron (MLP) with cosine activation are all implemented on our intelligent accelerator to handle RF signal modulation format recognition. Compared to MLPs, OKAN significantly improves training convergence speed and recognition accuracy, indicating that OKAN is a more suitable neural network model for our optical hardware. This work highlights the great significance of software and hardware co-development in optical intelligent computing and provides a feasible approach.