Ray Tracing Of Spherical Invisibility Cloak Based On Non-linear Transformation

In 2006,the theory of transformation optics was proposed by the physicist Pendry and others,and successfully designed the electromagnetic invisibility device.Since then,the research on the design of various optical devices based on the theory of transformation optics has become a hot topic,which is a new era in the field of electromagnetism.The design of electromagnetic invisibility device has great potential.With people's unremitting efforts in this area,they have made great innovations in theory,the design of invisibility devices has become more and more diverse,and the parameters have become more and more simplified,various optical devices are also produced,such as electromagnetic concentrators,etc.But electromagnetic invisibility device based on the transformation optics theory are generally anisotropic non-uniform parameters,which has brought considerable challenges to practical applications.But in recent years,with the further research in theory and continuous innovation in practice,I firmly believe that in the near future,difficulties will be overcome one by one,and these invisible electromagnetic devices will be applied to real life.Due to the high computational complexity of full-wave numerical simulation of electromagnetic wave propagation at high frequencies,traditional finite difference and finite element methods are no longer applicable.Based on this,the ray tracing method of electromagnetic invisibility device designed by non-linear transformation is studied.Starting from the Maxwell equations,the dispersion relation of the spherical invisibility cloak with non-linear transformation is obtained.By using this dispersion relation and combining with the boundary conditions,the wave vector at the initial time is obtained.Through the transformation optics theory,we obtained the material parameters of the non-linear transformation spherical invisibility cloak,and finally combined the Hamilton equation of motion,the ray tracing of the non-linear transformation spherical invisibility cloak is simulated.We use a similar method to research the relatively simple linear transformation spherical invisibility cloak,and in non-linear transformation and linear transformation of light propagation in spherical invisibility cloak has carried on the contrast experiment,the results show that the non-linear transformation spherical invisibility cloak closer to the boundary,light bending degree of the change,the greater the bending and the light in the linear transformation spherical invisibility cloak level changes smaller;It takes less time for the light coming from the same position to pass out in the non-linear transformation spherical cloak than in the linear transformation spherical cloak.