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As guided-wave circuits continue to increase in complexity, designing efficient and compact on-chip building blocks for these circuits continues to be a crucial research and development objective for many photonic platforms. Despite this critical requirement, the best-performing devices still require computationally intensive simulations that can take up to days, with no guaranteed results. To address this challenge, we introduce a novel, data-driven, and extremely rapid eigenmode expansion (EME) method for designing compact and efficient integrated photonic devices. In contrast to typical EME, our method models a given waveguide geometry using a pre-calculated dataset of optical scattering matrices and effective indices, therefore easily parallelized to computational accelerators like GPUs. This results in individual device simulation times of 10s of milliseconds, representing a speedup of more than 1000x over traditional methods. We then couple this approach with nonlinear iterative optimization methods and demonstrate the design and optimization of highly efficient nanophotonic devices, including tapers, 3dB splitters, and waveguide crossings within ultra-compact footprints. For all three categories of devices, we verify the response of the final geometry using 3DFDTD simulations and demonstrate state-of-the-art metrics, including below 0.05dB of insertion loss, near-perfect mode matching to the desired output, and broadband operation capabilities of over 100nm. Our unique combination of efficient and physically accurate device simulation methods, together with nonlinear optimization, enables the design of high-performance and ultra-compact photonic building blocks. These capabilities present avenues for developing more complex and previously elusive optical functionalities with unprecedented computational efficiency.
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