An integrated neural network and optimization framework for the inverse design of optical devices

The inverse design of optical devices that exhibit desired functionalities as well as the solution of complex inverse problems are becoming essential research directions in modern optical engineering. Recent advancements in computation algorithms, machine learning architectures and optimization methods offer efficient means to deal with complex photonics problems with a large number of degrees of freedom. In this thesis, I present our work on developing an integrated framework for the inverse design of diffractive optical elements and nanophotonic media with tailored optical responses. In the first part of our work, we introduce the design of single-layer diffractive optical devices that extend conventional imaging functions to include dual-band multi-focal microlenses for multi-band imaging, modulated axilenses for ultracompact spectrometers, and hyperuniform phase plates for lensless imaging systems. We design these diffractive elements based on Rayleigh-Sommerfeld scalar diffraction simulations. We also fabricate them using scalable lithography and experimentally characterize their predicted diffraction and imaging performances. While we successfully validated our designs, we also identified the fundamental limitations and challenges of single-layer diffractive devices. In order to address these problems, in the second part of the work we introduce a novel and flexible approach for the inverse design of diffractive optical elements based on adaptive deep diffractive neural networks (a-D2NNs). In particular, we demonstrate two-layer dual-band multi-focal devices that exceed the efficiency limit of traditional single-layer devices and we leverage the powerful a-D2NN inverse design platform to engineer systems with targeted spectral lineshapes and focusing point-spread functions. Moreover, we apply a-D2NNs to the inverse design of ultracompact spectrometers and demonstrate nanometer-range spectral resolution for 100 micron-size devices that can be fabricated using conventional lithographic procedures. Finally, we apply the a-D2NNs approach to the design of hyperuniform scalar random fields that we have introduced as novel lensless imaging systems with modulated transfer functions that produce enhanced image quality compared to state-of-the-art phase plates based on the Perlin noise. We additionally show that a-D2NNs can be used to efficiently design different classes of hyperuniform random media that are currently being explored for a number of optical applications. In the third part of my thesis, we propose and develop a deep learning framework for solving inverse photonics problems by employing physics-informed neural networks (PINNs). We solve the non-local effective medium problem for finite-size metamaterials and address losses and radiation effects. Furthermore, we apply PINNs to solve the invisible cloaking inverse problem beyond the quasi-static limit. Finally, we develop a general PINN framework for inverse retrieval of optical parameters based on near-field data information. Based on our approach, we show the successful retrieval of the electric and magnetic optical parameters (i.e., non-local permittivity and permeability functions) of two-dimensional and three-dimensional scatterers in the presence of absorption losses. Additionally, we demonstrate the application of the inverse PINN design to the scanning near-field microscopy technique under localized excitation and in the presence of noise. In the last part of our work, we couple adjoint optimization methods with the rigorous multiple scattering theory of cylinder arrays (i.e., two-dimensional generalized Mie theory) for the inverse design of small-size, photonic structures, called “photonic patches”, that achieve different functionalities with optimal efficiencies. Specifically, we present the inverse design of photonic patches that angularly shape incoming radiation and that focus light intensity over Fresnel-zone distances (~ 10μm) with engineered spectral lineshapes, enhanced local density of states and resonance quality factors