Research progress on topological states and applications in optical waveguide arrays
Topological insulators have been a novel area of research since the integer quantum Hall effect was proposed.The concept of topology was soon introduced to the field of photonics and attracted a lot of research attention due to the unique ability of light manipulation.Research on topological edge states,Anderson localization,and other interesting topological properties have been conducted in different systems.Topological photonic insulators,constructed on various platforms,have the advantages of high integration,robustness to external disorders under topological protection,and exhibit wide application prospects in light sensing,communications,and quantum computing.Optical waveguide arrays,with their properties of simple fabrication and fine structure,are one of the ideal platforms for studying topological photonics.Due to the similarity between the Schrodinger equation and the paraxial equation,topological properties can be visualized through light dynamics.In addition,a new type of Floquet topological insulator can be realized through space modulation in the z direction.In experiments,by changing the parameters of the waveguide arrays,such as refractive index,waveguide spacing,and waveguide configuration,the light field in waveguide arrays can be flexibly controlled within the tight-binding model.In addition,space modulation in the z direction and manipulation of non-Hermitian and nonlinear effects in waveguide arrays can realize novel topological photonic insulators.In this paper,we mainly focus on topological photonic insulators constructed using optical waveguide arrays and review recent experiments realized in different dimensions,covering the following aspects.First,we introduce the coupled-mode theory,which is the basis of topological photonics in waveguide arrays.We also describe the common fabrication methods of optical waveguide arrays,such as ultrafast laser direct writing and E-beam lithography,and we analyze the advantages and disadvantages of these methods.Second,some typical topological experiments in one and two dimensions are introduced,discussing the topological phase transition and the bulk-edge correspondence in different models based on waveguide arrays.Most of the experiments have been realized in straight waveguides;however,recent research has found that helical waveguides are also useful.The z-reversal symmetry of the system can be broken by changing the shape of the waveguide in the z direction,revealing new topological properties.Third,we review non-Hermitian effects in topological waveguide arrays.Non-Hermitian modulation can be achieved by introducing gain and loss in waveguides.In experiments,loss can be easily introduced through spatial modulation or artificial additional loss,while gain is more difficult to achieve.Finally,we discuss the application potential of topological photonic insulators in waveguide arrays.In short,topological photonic insulators with novel light control properties are one of the interesting branches of condensed matter physics,which has application potential in many fields.Through this review,we hope to gain a comprehensive understanding of topological photonics in optical waveguide arrays and inspire future applications in topological optical waveguide array devices.
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