Moving forward with multilayer metastructures - simple design of complex optics

I propose a simple and progressive way of designing and fabricating complex multilayered optics, even as we scale to large numbers of layers. The approach relies on successive layers of two-by-two blocks in which light only flows in the forward direction. It exploits a proposed trapezoidal architecture that can also support self-configuration in programmable structures, with the desired linear function or matrix set up using input vectors that correspond to the matrix rows, without any iteration other than successive single-parameter power maximizations. A key required component is a layer of 2 by 2 beamsplitters. The approach can support functions corresponding to a broad range of banded diagonal matrices. Example applications include a camera that also measures phase gradients and the direct convolution of a line of inputs with a kernel based on wavelets.