Matrix Method Of Planar Optical Waveguide And Simulation Of Silicon Waveguide Coupling

Integrated optics is an interdiscipline that integrates optoelectronics,optical waveguide theory,laser technology and microelectronics.It mainly studies and develops versatile,stable and reliable Optical integration system and hybrid optoelectronic integration system that are needed in optical communication,optical information processing,photonic computers and optical sensing.In the integrated optical path,the key element that connects the discrete components is the optical waveguide.The planar optical waveguide is a very important waveguide model in integrated optics,whose field distribution of both the radiation mode and the guided-mode is relatively simple,and it is also the basic unit of various complex optical waveguides.Therefore,in this thesis we proposed a novel method based on Matrix theory to study the transmission mode of planar optical waveguides.Meanwhile,the miniaturization of the light source is very important for the integrated optical path,and a single-chip light source on the chip is absolutely necessary for the optical interconnection.Therefore,this thesis put forward a design method for coupling edge-emitting lasers to silicon waveguides.Moreover,the coupling of optical fibers and nano-scale optical waveguides is a fundamental problem in the chip interconnection in integrated photonics.Thus,a design method was proposed in this thesis for coupling the optical fiber to the silicon waveguide using the plasmonic waveguide.The main researches are as follows:Firstly,the matrix method of the planar optical waveguide was studied.Planar optical waveguides,also known as two-dimensional planar optical waveguides,can be viewed as a multi-layer stack.When a plane wave shines in a layered medium,reflection and transmission occur at each layer boundary,so the complex amplitudes of the forward and backward waves can be represented through the matrix method and the transfer matrix is written,too.In the guided-mode,the two-dimensional waveguide has only output on the boundary,and there is no input,which means the evanescent wave exists in both the first layer(cover layer)and the last layer(substrate layer).At this time,the complex element of the transfer matrix D = 0,and we can obtain the effective refractive index in the guided-mode.Moreover,when the light is reflected and refracted on the surface of the medium,the continuity boundary condition can also be determined based on the Fresnel equation,and consequently,the electric field and magnetic field distribution of light waves are also obtained.Finally,the matrix method is applied to all types of two-dimensional planar optical waveguides,including multi-layer step-index dielectric waveguides,gradient-index waveguides,slot waveguides and plasmonic waveguides.The transverse electric(TE)mode and transverse magnetic(TM)mode of light transmitting are studied respectively.And in the application process,it was proved that the matrix method is consistent with the electromagnetic theory of the optical waveguide.The matrix method is effective for two-dimensional planar optical waveguide mode solutions and is versatile and suitable for all types of two-dimensional planar optical waveguides.Meanwhile,the matrix method is simple,so it is easier to write the transfer matrix of the two-dimensional planar optical waveguide in the guidedmode to obtain its effective refractive index.Through analyzing all elements in a matrix,the matrix method can be used to further study transmitting characteristics of light in a planar optical waveguide.The further development of the matrix method can be used to analyze other fluctuations such as electromagnetic waves,acoustic waves and elastic waves.Secondly,a coupler design method for butt-coupling of edge-emitting lasers and inverted-cone silicon waveguides was proposed.The influence of the inevitable gap,lateral and vertical offset in the fabrication and installation of the coupler on the coupling efficiency was fully considered to optimize the coupler design to obtain the best coupling efficiency.Two edge-emitting lasers were selected in this thesis: InGaAsP/InP edge-emitting laser diode and Ge/Si oxide edge-emitting laser diode.We found that the coupling losses of edge-emitting laser diode and dielectric silicon waveguide mainly came from reflection,bottom leakage and side leakage.Reflection and bottom leakage varied significantly with gap offset,lateral offset and vertical offset,while leakage on both sides was not obvious.Air gap had the most obvious effect on coupling efficiency,which can be solved by gap filling method.This butt-coupling design was insensitive to the polarization: both TE and TM modes achieve high coupling efficiency.The maximum coupling efficiency of the InGaAsP/InP edge-emitting laser diode-coupled TE mode was 91.9%,and the maximum coupling efficiency of the TM mode was 90.4% The maximum coupling efficiency of the Ge/Si oxide-emitting laser diode TE mode was 86.5%,and the maximum coupling efficiency of the TM mode was 86.1%.Those results showed that the design of this coupler was very effective to solve the coupling problem caused by the large difference of refractive index and size difference between laser and silicon waveguide.In this thesis,the support vector machine was also used to analyze the coupling efficiency.Firstly,the three optimization methods,such as leave-one method,genetic algorithm and particle swarm optimization algorithm,were used to optimize the parameters of the support vector regression models to make them more stable and optimal.Then,the support vector machine model was used to predict the coupling efficiency.The three coupling variables,air gap,lateral offset and longitudinal offset,which may affect the coupling efficiency,were analyzed for maximum coupling efficiency optimization,factor sensitivity and interaction of factors.This provided a good guiding role in the design and optimization of the coupler model.Lastly,in the research of the coupling between the optical fiber and the silicon waveguide,this thesis proposed the coupling method of the tapered plasmonic waveguide and the inverted cone silicon waveguide by using the characteristics of the plasmonic waveguide.It was found in the research that the plasmonic waveguide had a good constraint on the light transmission.As the size of the tapered plasmonic waveguide changes,the modulus of the light changes.The modulus from the input end matched to the fiber was directly increased from 1 to 3,then the modulus was reduced to 2 and 1,and the output end was well coupled to the silicon waveguide.This kind of coupler design can solve the problem of large size difference and refractive index mismatch between optical fiber and silicon waveguide.We further studied the influence form the gap,lateral offset and vertical offset upon coupling efficiency.The simulation results showed that the coupler design had good alignment tolerance and flexibility,and was suitable for manufacturing,easy to assemble and realize.The maximum coupling efficiency of the coupler we got was 86.8%,with the effective length about 25μm,and it had better spectral characteristics.Similarly,we also used support vector machine modeling to study the influences of three input factors of air gap,lateral offset and vertical offset on coupling efficiency.The model data showed that the maximum coupling efficiency of the coupler can reach 89% when the air gap,lateral offset and vertical offset were optimized.At this optimal position,the sensitivity and factor interaction were analyzed.This optimization model and the simulation data of the coupler can be mutually verified,and can be also used to guide relevant experiments.As a result,the blindness of experiments was greatly reduced,and thereby a lot of manpower,material resources,financial resources and time were saved.