The design of an optimal controller for soft robotic manipulators has gained increasing attention due to their deformability and adaptability in dynamic environments. However, obtaining an accurate dynamic model for soft robotic arms is challenging due to the practically infinite number of degrees of freedom. This study presents a novel approach that uses a deep Koopman-based modeling method to tackle these challenges. The proposed approach integrates an encoder-decoder structure within a deep learning framework to approximate the finite-dimensional observable function of the Koopman operator. A key aspect of the proposed method is the construction of state transition matrices in the observable space to reduce computational complexity through a set of real and complex eigenvalue pairs. Subsequently, a linear quadratic regulator (LQR) is designed using the learned deep Koopman model for optimal set-point regulation tasks. The experimental results validate the effectiveness of the proposed approach.