Why optics needs thickness

This Science paper (D. A. B. Miller, “Why optics needs thickness,” Science 379, 41-45 (2023)) shows why and when optical systems need thickness as well as width or area. Understanding this thickness matters as we try to make ever thinner cameras or exploit the emerging possibilities of nanophotonics and flat optics, such as metasurfaces.

We have understood for some time why wave diffraction forces area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. Surprisingly, we have not understood fundamentally whether optics also needs some minimum thickness. This paper demonstrates that if we know what the optics is to do, even before design, we can also deduce the minimum required thickness.

This limit comes from diffraction combined with a concept called overlapping nonlocality C that can be deduced rigorously from just the mathematical description of what the device is to do. C expresses how much the input regions for different output regions overlap. The limit can be understood quite intuitively in some simple cases. A modal approach based on singular-value decomposition gives a rigorous approach for a wide range of cases. This limit applies broadly to optics, from cameras to metasurfaces, and to wave systems generally.

This work is also presented in the talk

“Shrinking optics – why optics needs thickness and how much it needs,” (Invited), 53rd Winter Colloquium on the Physics of Quantum Electronics Snowbird, Utah, January 11, 2023