Research On Silicon-based Integrated Transformation Optics Theory And Devices

Silicon photonics plays a critical role in optical communication,optical computing,optical sensing,quantum information,quantum computing,and etc.Passive optical devices are the basis of large-scale silicon optical circuits,but there are several difficulties in design and simulation,such as the multiple modes bend/crossing and the loss or leakage from periodic sub-wavelength structure.Therefore,new design theory and simulation methods are demanded.Transformation optics utilizes coordinate transformation to manipulate light propagation.According to the theory of transformation optics,through deforming the simple prototype,some multimode optical devices with low loss and low crosstalk can be designed.On the other hand,transformation optics can be applied in electromagnetic field simulation.The perfect matching layer can be achieved by complex coordinate transformation,which simplifies the weak form for the complex band calculation of the photonic crystals.The research results and contributions of this thesis are summarized as the followings:Firstly,the basic theory of transformation optics is studied.The required basic knowledge of the curvilinear coordinate is summarized in detail,and the equations of transformation optics are strictly deduced.The explanation for conformal mapping simplifying the requirements of optical medium is demonstrated.Various conformal mapping methods are reviewed and compared.Secondly,through bending a multimode straight waveguide using conformal mapping,a multimode bend waveguide capable of supporting six modes is designed.By adjusting the index of the straight waveguide prototype along the propagation direction,the index of multimode bend waveguide was restricted in an achievable range.Simulated by two-dimensional COMSOL,the transmission efficiency from TE₀ to TE₅ mode are all above94.43%.Thirdly,an artificial boundary conformal mapping method is proposed.By deforming the Maxwell fisheye lens,a multimode waveguide star crossing capable of supporting 3modes and 4 crossing channels is realized.Simulated by 3D FDTD,in the wavelength range from 1308 nm to 1702 nm,for TE₀,TE₁ and TE₂ mode,all the losses are lower than-1.14dB,and all the crosstalks are lower than-21 dB.The device was fabricated on silicon-on-insulator wafer by gray-scale electron beam lithography.The measured transmission efficiencies are all higher than-2.68 dB,and the crosstalks are all lower than-19.5 dB.The procedures of the grayscale electron beam lithography are mentioned.The development and etching characteristics of PMMA photoresist are studied quantitatively.And the multi-layer layout in the experiment is presented.Fourthly,a perfect matching layer achieved by complex coordinate transformation and associated with weak form is applied for calculating the complex band of the photonic crystals.Based on this,a lossy sub-wavelength waveguide is designed.By changing its size,the loss coefficient can be changed in the range from 0 to 0.052,and it has been successfully applied to on-chip non-Hermit photonics experiments.Utilizing this method,a chirped focusing subwavelength grating coupler is also designed.Simulated by 3D FDTD,the center wavelength is 1553.1 nm,the maximum coupling efficiency is 56.1%(-2.51 dB),and the 3dB bandwidth is 51 nm.Fifthly,in order to improve the fabrication tolerance of the asymmetric directional coupler used in the experiment,the design theory of shortcut to adiabaticity for directional coupler is studied.A TE₂ mode asymmetric coupler with high tolerance is designed.By 3D FDTD simulation,for the waveguide width variation from-25 nm to 15 nm,the efficiencies are all above-1 dB,and the crosstalks are all below-40 dB.Through experiments,for the waveguide width variation from-6 nm to 40 nm,the efficiencies are all above-3 dB,and the crosstalks are all below-26.4 dB.