We present a deep learning approach using an optical neural network to predict the fundamental modal indices $neff$ in a silicon (Si) channel waveguide. We use three inputs, e.g., two geometric and one material properties, and predict the $neff$ for transverse electric and transverse magnetic polarizations. With the least number (i.e., $33$ or $43$) of exact mode solutions from Maxwell’s equations, we can uncover the solutions which correspond to $103$ numerical simulations. Note that this consumes the lowest amount of computational resources. The mean squared errors of the exact and the predicted results are . Moreover, our parameter ranges are compatible with current photolithography and complementary metal–oxide–semiconductor (CMOS) fabrication technology. We also show the impacts of different transfer functions and neural network layouts on the model’s performance. Our approach presents a unique advantage to uncover the guided modes in any photonic waveguides within the least possible numerical simulations.