| Anderson was the first to demonstrate that electron transport is suppressed in a disordered lattice using a straightforward model.The electrical characteristics of a substance are insulated by semiconductor doping,this phenomenon later called Anderson localization.The so-called Anderson localization occurs when an electron conducts in a conductor that contains impurities,numerous impurity scattering causes the amplitude and phase of the electron wave to shift and interfere with one another,and the original extended state becomes the local state.The research focus started to broaden to include optics,acoustics,microwave,condensed matter physics,photonic crystals,and other domains as Anderson localization phenomenon was recognized as a wave effect.While having developed more recently than electron localization,photon localization has a much greater research advantage.The most evident characteristic is that as optical technology advances quickly,the benefits of visualization become increasingly clear.Also,researchers are noticing clear localization phenomena in a variety of optical systems.Transverse disordered waveguides,plasma structures,photonic crystal structures,and microcrystalline suspensions can all be utilized to investigate photon localization.The transverse disordered waveguide is a very effective one,which was first proposed by De Raedt et al.The transverse refractive index of the structure is randomly distributed while the longitudinal structure remains uniform.Research demonstrate that sufficiently large one-dimensional and two-dimensional transverse disordered systems can always satisfy the localization criteria of Ioffe-Regel.Due to the lateral multiple random scattering,the incident beam will not be diffused and will instead move along the longitudinal direction with a constrained beam radius.Compared with ordinary optical fiber,it is characterized by disordered waveguide structure without fixed mode,and the field is highly localized within the cross section.The structure is equivalent to the all-pass system in the spatial frequency domain and the common optical fiber is equivalent to the resonant band-pass system.Any point on the cross section can be used as a channel for optical signal transmission.Transverse disordered systems have the ability to directly transfer optical images for use in the fields of biology and medicine,in addition to significantly increasing the capacity for information transmission.Research on transverse disordered waveguides is mainly restricted to theory and numerical modeling.Effective numerical simulation computation tools are crucial because statistical analysis is required,particularly for disordered systems.Finite difference time domain(FDTD)offers a high computational accuracy as a general electromagnetic field simulation algorithm,but its application to large-size optoelectronic devices is constrained by its high storage requirements and lengthy simulation operating times.In a disordered lattice with impurities,the Schrodinger equation can be solved to determine the distribution of the electron wave function.We can model the wave equation using the paraxial approximation and then numerically solve the related field distribution in each cross section of the transverse disordered waveguide by taking into account the analogous process of electron localization to photon localization.The evolution of the electromagnetic field in transverse disordered waveguides can be computationally simulated using the beam propagation algorithm(BPM),allowing for the observation of the transition of the beam from the extended state to the localized state.In transverse disordered waveguides with large refractive index contrast,the vector characteristics of electromagnetic wave can no longer be ignored.It is necessary to evaluate the error of the disordered model under various structural parameters in order to choose the appropriate simulation parameters,such as transverse grid size and longitudinal step size,in order to construct the transverse electric field distribution accurately and increase computational efficiency.For the disordered waveguide structures with random transverse refractive index distribution and large refractive index contrast on the subwavelength scale,the conventional three-dimensional full-vector BPM is easy to diverge and no longer applicable.To solve these problems,the existing numerical calculation methods should be improved.The main research work and innovation of this dissertation as follows:(1)The simple model of electron localization,localization theory and scaling theory,coherent backscattering and transverse photon localization are introduced.In order to analyze typical transverse disordered waveguide structures numerically,a paraxial approximation-based model is developed.The numerical model is iterated,and the propagation characteristics of the beam in the transverse disordered waveguide are computed using the BPM implicit algorithm.(2)Investigations on the evolution of electromagnetic wave propagation in two-dimensional transverse disordered waveguides include the transition from the initial extended state to the ultimate localized state;The findings of the numerical simulation demonstrate that the structural parameters,such as refractive index contrast,feature size,and fill-fraction,are the primary factors impacting the localized intensity.With the increase of refractive index contrast,the effective width of the beam tends to be stable.When the refractive index contrast exceeds certain threshold,the vector characteristics need to be considered.The optimal fill-fraction is 50%and greater than or less 50%will reduce the scattering intensity.will reduce the scattering intensity.Finally,the effects of refractive index contrast on optical image transmission quality in disordered waveguides are compared and analyzed.(3)Block numerical modeling was carried out based on conventional 3D full vector BPM.It can not only reduce the demand for computing resource storage,but also further relax the longitudinal propagation step size with sufficient computing accuracy.At the same time,it is not easy to diverge when there is a large refractive index contrast.The algorithm is based on the idea that the transverse refractive index of the disordered waveguide structure has random distribution and the large quasi-sparse matrix can be used for block inversion calculation.In order to accurately construct the transverse electric field distribution,the meshes on the cross section must be very fine.Large quasi-sparse matrices will be introduced when using the finite difference method to approximate partial differential equations,and inverse operation will take excessive computational resources,which will have an impact on the effectiveness of the operation.The algorithm can be used as an efficient and reliable numerical calculation tool to deal with the disordered waveguide structures with random index distribution and large refractive index contrast.(4)The mode characteristics of transverse disordered waveguides based on Anderson localization are analyzed.The localized modes in guide modes are separated effectively and as the research object which are no longer affected by input source and cladding structure.After mode decomposition,the whole localization evolution process can be clearly analyzed.The localization strength is effectively measured by the average effective width of the localized modes.Finally,the influence of different structural parameters,including refractive index contrast and fill-fraction,on the localization strength is studied.And the variation trend of localization length is given. |
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