| With the advent of the post-Moore’s Law era,photon-based information transmission and processing chips have garnered widespread attention due to their advantages such as high integration,fast response speed,and low energy consumption.However,the defects and errors introduced during the manufacturing process of integrated photonic chips seriously limit the further improvement of their performance.Building upon optimized manufacturing processes,topological photonic states,thanks to their robust transmission properties protected by geometric structures,have opened new avenues in principle for enhancing chip performance,and topological photonics has provided new means for photon manipulation.Among these,optical waveguide arrays fabricated using femtosecond laser direct writing technology have become a crucial platform for studying topological photonics due to their high fabrication flexibility and design freedom.In recent years,researchers have utilized the high-precision true 3D processing capabilities of femtosecond laser direct writing technology to precisely control waveguide parameters and array structures,enabling the construction of a series of topological models and the observation of novel physical phenomena in various optical systems including Hermitian,non-Hermitian,non-Abelian,and nonlinear systems.This has laid a solid foundation for in-depth exploration of the physical mechanisms behind topologically protected transmission and the design of robust optical transmission devices,holding significant potential for practical applications.This thesis is built upon the utilization of femtosecond laser direct writing technology to create topological waveguide array structures within glass.It focuses on conducting a series of theoretical and experimental studies concerning the transmission of light within these waveguide arrays,with a particular emphasis on localized transmission characteristics.By establishing a femtosecond laser processing system and optimizing the fabrication process,precise control over the morphology,performance,and spatial arrangement of the waveguides has been achieved,enhancing the ability to construct topological models using waveguide arrays.Through theoretical and experimental investigations into the light transmission properties within the topological waveguide array,methods have been explored for qualitatively demonstrating the behavior of topologically protected transmission of light,as well as quantitatively describing topological edge states and behaviors near phase transition points.These findings provide feasible approaches for interpreting new physical effects in subsequent topological models and also pave the way for innovative strategies in the development of robust optical transmission devices in the future.The main research content and innovative aspects of this thesis include:1.To meet the requirements for designing and evaluating the fundamental parameters of topological waveguide arrays,several setups were constructed:a femtosecond laser processing system and optical waveguide coupling testing systems.These setups enabled the manipulation and analysis of basic parameters such as morphology,birefringence,and spatial distribution of the glass waveguides.Two optimized fabrication schemes for femtosecond laser direct writing of low-birefringence,high cross-sectional circularity waveguides were proposed.These schemes employed cylindrical lenses and slits to shape the laser beam,effectively reducing birefringence induced by the waveguide structure.The fabricated polarization-independent directional coupler quantum interference exhibited visibility exceeding 95%.Building upon this foundation,a method using low-power misalignment-assisted lines was introduced to further adjust local stress,effectively compensating for weak stress-induced birefringence.The achieved level of birefringence in the fabricated waveguides was reduced to the order of 10-9,representing one of the lowest values reported to date.A demonstration was conducted using equidistant waveguide arrays fabricated from low-birefringence waveguides,showcasing insensitivity to light polarization during transmission.This demonstration provides an experimental approach for exploring the optical transmission characteristics and underlying physical principles of topological waveguide arrays.2.The study investigated the optical transmission characteristics and corresponding topological phase transition behavior of a one-dimensional topological waveguide array based on the Su-Schrieffer-Heeger（SSH）model.The complete dynamic process of light propagation in the waveguide array was experimentally measured,demonstrating both ballistic transport in topologically trivial systems and localized transport in topologically nontrivial systems.Two key physical quantities characterizing topological phase transitions,survival probability and localization length,were introduced.Analytical relationships for these quantities were theoretically derived and experimentally validated.Survival probability was utilized to describe the topological phase diagrams of the lattice with odd and even numbers of sites in the topological waveguide arrays,providing the topological phase transition boundaries and explaining their dimerization dependence.Furthermore,survival probability was employed to extract the universal class,critical exponent,defining the topological phase transition in the vicinity of the critical point.This allowed for a quantitative interpretation of critical behavior near the topological phase transition point.The experimental results were consistent with theoretical expectations,providing a comprehensive understanding of the topological phase transition behavior in the studied system.3.The research focused on the optical transmission characteristics of（quasi）three-dimensional topological waveguide arrays based on the extended Su-Schrieffer-Heeger（SSH）model,taking into account the influence of next-nearest-neighbor interactions.The study also analyzed the impact of next-nearest-neighbor interactions on the topological edge states in the system.Utilizing the three-dimensional writing capability of femtosecond laser processing technology,spatial"Z"-shaped waveguide array structures were fabricated to fulfill the experimental requirements for observing observable interactions between next-nearest-neighbor waveguides.The study examined the effects of next-nearest-neighbor interactions on the optical transmission characteristics.Experimental observations included localized light transport in topologically nontrivial systems and delocalization phenomena influenced by next-nearest-neighbor interactions.The theoretical analysis of survival probability and experimental extraction yielded the topological phase transition boundaries of the system,elucidating the boundary of the photon bandgap opening and closing under the influence of next-nearest-neighbor interactions.These results were in line with theoretical expectations.4.The research focused on the optical transmission characteristics of quasi-periodic one-dimensional waveguide arrays based on the Fibonacci sequence.It explored the quantum walk behavior of classical light simulating single photons and analyzed the influence of quasi-periodic modulation on quantum walks.Using the versatile shaping capability of femtosecond laser processing technology,waveguide arrays with different sizes（effective refractive indices）were constructed to satisfy both the quasi-periodic modulation rule for propagation constants and coupling coefficients.The study theoretically and experimentally demonstrated random and localized quantum walks in periodic and quasi-periodic waveguide arrays,illustrating their complete dynamic evolution processes.By introducing Kerr nonlinearity-induced refractive index changes,the experiment achieved significantly enhanced localization of quantum walk in quasi-periodic waveguide arrays.This showcased the pronounced impact of weak optical nonlinear effects on the optical transmission characteristics of the system. |
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