  Growing diversity and complexity of on-chip photonic applications requires
rapid design of components with state-of-the-art operation metrics. Here, we
demonstrate a highly flexible and efficient method for designing several
classes of compact and low-loss integrated optical devices. By leveraging a
data-driven approach, we represent devices in the form of cascaded eigenmode
scattering matrices, through a data-driven eigenmode expansion method. We
perform electromagnetic computations using parallel data processing techniques,
demonstrating simulation of individual device responses in tens of milliseconds
with physical accuracies matching 3D-FDTD. We then couple these simulations
with nonlinear optimization algorithms to design silicon-based waveguide
tapers, power splitters, and waveguide crossings with state-of-the-art
performance and near-lossless operation. These three sets of devices highlight
the broad computational efficiency of the design methodology shown, and the
applicability of the demonstrated data-driven eigenmode expansion approach to a
wide set of photonic design problems.
