Self-Configuring Universal Linear Optical Component

We show how to design an optical device that can perform any linear function or coupling between inputs and outputs. This design method is progressive, requiring no global optimization. We also show how the device can configure itself progressively, avoiding design calculations and allowing the device to stabilize itself against drifts in component properties and to continually adjust itself to changing conditions. This self-configuration operates by training with the desired pairs of orthogonal input and output functions, using sets of detectors and local feedback loops to set individual optical elements within the device, with no global feedback or multiparameter optimization required. Simple mappings, such as spatial mode conversions and polarization control, can be implemented using standard planar integrated optics. In the spirit of a universal machine, we show that other linear operations, including frequency and time mappings, as well as non-reciprocal operation, are possible in principle, even if very challenging in practice, thus proving there is at least one constructive design for any conceivable linear optical component; such a universal device can also be self-configuring. This approach is general for linear waves, and could be applied to microwaves, acoustics and quantum mechanical superpositions

Fundamental Limit to Linear One-Dimensional Slow Light Structures

Using a new general approach to limits in optical structures that counts orthogonal waves generated by scattering, we derive an upper limit to the number of bits of delay possible in one-dimensional slow light structures that are based on linear optical response to the signal field. The limit is essentially the product of the length of the structure in wavelengths and the largest relative change in dielectric constant anywhere in the structure at any frequency of interest. It holds for refractive index, absorption or gain variations with arbitrary spectral or spatial form. It is otherwise completely independent of the details of the structure's design, and does not rely on concepts of group velocity or group delay

Why optics needs thickness

We show why and when optics needs thickness as well as width or area. Wave diffraction explains the fundamental need for area or diameter of a lens or aperture to achieve some resolution or number of pixels in microscopes and cameras. Now we show that, if we know what the optics is to do, even before design, we can also deduce minimum required thickness. This limit comes from diffraction together with a novel concept called "overlapping non-locality" C that can be deduced rigorously just from the mathematical description of what the device is to do. C expresses how much the input regions for different output regions overlap. This limit applies broadly to optics from cameras to metasurfaces, and to wave systems generally