Spatial Differentiators And Ising Model For Optical Analog Computing

In optical analog computing in spatial domain,the information is loaded on the wavefront of spatial optical field and the computing processes are realized during the optical spatial interference.Such analog computing devices and systems,benefiting from the parallelism of optical spatial interference processes,outperform their electronic counterparts in higher speed,lower power consumption,larger bandwidth and better scalability.Optical analog computing devices and systems are suitable for solving various real-world problems in science and engineering.Specifically,the optical spatial differentiators are promising in real-time and high-throughput image processing,and the optical Ising machines are useful for computing tasks such as combinatorial optimization problems.In this Thesis,the method of spatial mode coupling and interference is studied for designing optical spatial differentiators with resonant nanostructures.The goal guiding the device designing is to realize the required spatial spectral transfer functions for spatial differentiations.An analytical theoretical model,the coupled-mode theory,is developed for describing the spatial mode coupling and interference processes in resonant structures,from which the transfer functions can be derived out further.Thus the coupled-mode theory connects the detailed physical processes in nanostructures and the optical responses of the devices.Guided by the coupled-mode theory for '2 resonances-1 port' systems,a 2nd-order spatial differentiator working in the terahertz(THz)region is proposed based on the graphene surface plasmon polaritons.The requirement for realizing the 2nd-order spatial differentiation is the‘critical coupling condition'.The proposed differentiator has large spatial bandwidth and is ultracompact.It is useful for real-time imaging applications in THz security detections.Guided by the coupled-mode theory for‘1 resonance-2 ports'systems,a 1st-order spatial differentiator with multiple working wavelengths is proposed based on the waveguide modes.The requirement for realizing the multiple-wavelength-1st-order spatial differentiation is the'background diffraction condition'.The device simultaneously operates both spatial differentiation at 4 wavelengths and demultiplexing during light diffraction.The proposed device demonstrates image processing such as edge detection for a synthetic three-dimensional optical field,where 4 images are loaded in the wavelength-division-multiplexed form.In this Thesis,an optical Ising machine in spatial domain is proposed based on the spatial phase modulation method.Here,the spin configurations are loaded on the wavefront of collimated beams in a space-division-multiplexed way through phase modulation,and coupling between spins are enabled by the spatial interference in the Fourier optics system.By introducing the gauge transformation processes,the coupling strengths between spins are programmable through phase modulation.Such spatial optical Ising machines demonstrate good scalability and can be used for solving the combinatorial optimization problems,where nearly accurate solution of the number-partition problem is demonstrated for number sets with 400 elements.