Research in the field of dielectric metasurfaces has recently enabled wavelength-scale thickness flat optical elements that promise to reduce the form factor of existing optical elements in addition to providing a platform for implementing new optical functionalities. This new class of optical elements has been used for point spread function engineering, holography, adapting freeform optics to a flat surface, and polarization optics. These diverse functions are allowed by the large numbers of modifiable degrees of freedom that characterize these large, coupled arrays of optical scatterers. In this talk I will present the two major research directions I have been involved with: silicon nitride-based optics for producing visible wavelength optics such as lenses and freeform optics and computational electromagnetic inverse methods to use these degrees of freedom for the optimization and design of metasurfaces with user-defined functionalities. In addition, I will discuss the current state of metasurface research and how these works fit into this greater context.
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