Study Of Continuous Zero Refraction Effects Based On Two-dimensional Photonic Crystals

In recent years,two-dimensional photonic crystal models composed of pure dielectric materials have been widely used in the theoretical and experimental research of zero refractive materials,due to their low loss characteristics.However,the emergence of special degenerate states of the energy bands,a necessary and insufficient condition for achieving near zero refractive index in photonic crystals,is mostly accidental.In response to the accidental zero refraction in two-dimensional photonic crystals,this paper systematically conducts research on the continuous zero refractive effects and the optimized structure design of non-accidental zero refractive index,and has achieved the following research results:(1)Regarded the accidental dispersion of photonic bands in traditional two-dimensional photonic crystals,a design method for an air-hole photonic crystal model under transverse magnetic(TM)polarization is proposed,which leads to the continuous zero refraction effects independent on refractive index parameters.Firstly,based on the analysis of traditional models,it is found that a small change in structural parameters of only 6 ‰ or background material refractive index parameters of only 0.14 can cause the special dispersion phenomenon of photon energy bands to disappear,leading to the interruption of zero exponential behavior.The numerical simulation results show that in the redesigned air hole model,continuous zero refractive index can be achieved when the refractive index parameter varies between 2.4 and 4,breaking the accidental properties of zero refractive index in traditional photonic crystals.(2)Regarded the accidental dispersion of photonic bands in isotropic zero-index two-dimensional photonic crystals when structural parameters change,a design method for an air-ring photonic crystal model under transverse electric(TE)polarization is proposed,which leads to the continuous zero refraction effects independent on structural parameters.This method achieves sustained triple degeneracy of photonic bands,as the structural parameter combinations continue to change.The numerical simulation results show that continuous degenerate states represent continuous zero refractive indices,breaking the limitations of fixed structural parameter combinations on the fabrication of two-dimensional photonic crystal zero refractive optical devices.(3)Regarded the accidental dispersion of photonic bands in isotropic zero-index photonic crystals when both refractive index parameters and structural parameters change,a design method for an air-ring photonic crystal model under both TM and TE polarizations is proposed,which leads to the continuous zero refraction effects independent on both parameters.It has been proven that the triple degeneracy required for the zero refractive effect is not related to the order of bands.The theoretical results indicate that,unlike previous designs,special dispersion of the energy band can always exist,when the refractive index and radius of the internal dielectric column are at a large range,whether under TM or TE polarizations.It can also achieve triple degenerate states composed of high-order energy bands,achieving continuous zero index behavior with almost constant operating frequency.(4)Regarded the accidental dispersion of photonic bands in anisotropic zero-index photonic crystals when both refractive index parameters and structural parameters change,a design method for an air-hole photonic crystal model with low rotational symmetry under TM polarization is proposed,which leads to the continuous zero refraction effects independent on refractive index parameters,which is robust to changes in structural parameters.The results of simulation and numerical calculation show that the two redesigned low symmetry structures,based on a high symmetry refractive-index independent structures,can achieve sustained zero index anisotropy of refractive index parameters in the range of 3 to 6.7.Moreover,small changes in structural parameters will not lead to the disappearance of special optical transmission effect,providing ideas for stable and efficient directional transmission waveguides.