Advanced optical materials: catenary function meets electromagnetic wave

Kdsps catenary is a common curve in nature which is commonly used in free hanging chains power transmission lines cobwebs cable bridges arches. There are two types of catenary hyperbolic cosine function (ordinary catenary) logarithmic cosine function (usually called equal strength catenary). The study of its mechanical properties can be traced back to three centuries ago. At the end of the 20th century it was recognized that the mechanical properties of catenary structures may contribute to the construction of large optical microwave mirrors. In the past two decades with the development of nanofabrication characterization numerical modeling technology the research of sub wavelength scale catenary optics has gradually emerged. There are three main applications of

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catenary functions in subwavelength Electromagnetics: firstly the hyperbolic cosine form of catenary function is a special solution of wave equation the catenary light field generated by the coupling of near-field evanescent wave can compensate the attenuation of high spatial frequency evanescent wave which has been applied in super-resolution imaging. Secondly the sub wavelength structure with catenary shape is one of the ideal choices for generating geometric phase. It has been used to construct various functional hypersurfaces such as monolithic hyperlens with large field of view perfect orbital angular momentum Bessel beam Airy beam generator. In addition it is found that the dispersion curves of many capacitive superstructures have the characteristics of equal intensity catenary function which provides a mathematical physical model for predicting the optical electromagnetic properties of superstructures.

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