Multilayered analog optical differentiating device: performance analysis on structural parameters

Analogy optical devices with the function of mathematical computation have recently gained strong research interests due to the potential application as accelerating hardware in traditional electronic computers. The performance of these wavefront-processing devices is primarily decided by the accuracy of the engineered angular scattering spectra usually using artificial optical structures. In this paper, we address this issue through the performance analysis of an analog second-order optical differentiator made of dielectric (Si-SiO2) multilayer films that enable analytical discussions and also a combined design. The performance could be optimized according to the Fourier spectrum width of the incident light whose wavefront represents the input function. Based on this, we propose different optical differentiating devices that work for different wave input conditions. Rescaling of the Fourier spectrum intensity is suggested to enhance the fabrication and measurement error tolerance of the device. The minimum number of multilayers is also discussed in order to improve the practical feasibility. The current results are thought instrumental in guiding the design and implementation of analogy optical computation devices.