Despite various optical realizations of convolutional neural networks (CNNs), optical implementation of nonlinear activation functions and pooling operations are still challenging problems. In this regard, this paper proposes an optical saturable absorption nonlinearity and its atomic-level model, as well as two various optical pooling operations, namely optical average pooling and optical motion pooling, by means of 4f optical correlators. Proposing these optical building blocks not only speed up the neural networks due to negligible optical processing latency, but also facilitate the concatenation of optical convolutional layers with no optoelectrical conversions in-between, as the significant bottlenecks of implementing photonic CNNs. Furthermore, the proposed optical motion pooling layer increases the translation invariance property of CNNs, avoiding the inclusion of all corresponding translated images for the training procedure, and hence, increases the training speed of the neural network. The classification accuracy of the proposed optical convolutional layer is evaluated as the first layer of a customized version of AlexNet architecture, named as OP-AlexNet, for classification of Kaggle Cats and Dog challenge, CIFAR-10, and MNIST datasets, as 83.76%, 72.82%, and 99.25%, respectively, by using optical average pooling.