Optical Analog Computing Without Fourier Setups

Optical computing uses light to carry information and exploits propagation of light for computing purposes,which has been of interests for many decades due to its potential of performing computation at high speed and low power consumption.Specifically,optical analog computing in the spatial domain operates on the electric field distribution on the plane perpendicular to the beam propagation direction,and so that is massively parallel in nature as compared to the conventional digital electronic computation.Traditionally,such computing uses bulky 4f systems of lenses and filters based on Fourier optics.In recent years,the developments of nanophotonics and fabrication technique enable optical analog computing with wavelength-scale and even subwavelength-scale devices,which provide the possibility of miniaturization and integration of optical computing systems.This thesis focuses on the optical analog computing of spatial differentiation,which is a prominent example of optical computing and is useful for edge detection in image processing.In this thesis,we design and realize different types of spatial differentiators based on excitation of surface plasmon polariton(SPP),spin Hall effect of light(SHEL)and the topological effect in optical transfer functions.These differential operators have linear transfer functions in the wavevector space with respect to the spatial frequencies,and so that can perform the nonlocal filtering to the incident beams directly in the wavevector space,without the need for optical Fourier transform.Moreover,we use these proposed nonlocal differentiators for image processing and biological phase imaging:we directly apply the devices in the image space of deployed imaging systems to perform real-time edge detection of input images and differential contrast imaging as well as further phase retrieval of observed phase objects.Specifically,we realize longitudinal one-dimensional(1D)differentiation by exciting the SPPs at a metal-dielectric under critical coupling condition,where the differentiation operation originates from the destructive interference between the directly reflected field by the interface and the leakage filed from the excited SPPs.The metal film of the device has a thickness of 50 nm,which is a very simple structure and can be fabricated on a large scale.We also realize a generalized transverse 1D differentiation based on the SHEL,which only relies on light reflection process at an optical planar interface,independent of material composition or incident angles.The SHEL-based differentiator can utilize the polarization as one more degree of freedom and hence enables image processing on vectorial fields.Furthermore,by introducing a longitudinal spatial dispersion effect into the SHEL-based differentiation,we propose an adjustable differentiator with tunable differentiation direction and bias.We take advantage of the adjustability of the differentiator for differential contrast imaging and phase retrieval of phase objects.At last,we establish a connection between topological optics and analog computing,based on which we generate a transfer function with a nonzero topological charge to perform two-dimensional differentiation,i.e.,gradient computation.Being topologically protected,the device has a certain level of robustness with respect to parameter variations and correspondingly has a broad spectral bandwidth.