Research On The Application Of PT Symmetry-based Wireless Sensing System In Stone Heritage Conservation

In recent years,non-Hermitian quantum theory has received academic attention as a complement to the traditional Hermitian quantum theory.In 1998,Bender and Boettcher showed that non-Hermitian quantities satisfying Parity-Time（PT）symmetry can have real eigenvalues in specific parameter intervals.Since then,the study of PT symmetry in optical systems has been carried out to construct symmetric systems and realize the Exceptional Point（EP）by adjusting the effective imaginary part of the electromagnetic parameters or introducing losses and gains,which leads to many novel physical phenomena.In particular,the eigenvalues of non-Hermitian systems have a 1/Nth order dependence on the perturbation around EP（N is the non-Hermitian simplicity order of EP）,which can greatly improve the sensing sensitivity compared to the conventional linear dependence.The photonic artificial microstructure is a natural non-Hermitian system.The multivariable electromagnetic modes of the artificial microstructure can be used to modulate the electromagnetic wave transport and light-matter interaction,and the conditions of the non-Hermitian system are satisfied due to the mutually coupled resonant modes within the system that interact with the incident waves and the presence of material dissipation.In this paper,based on the non-Hermitian physics and photonic artificial microstructure platform,we study the high-precision wireless detection system of rock weathering degree and apply it to the conservation of stone relics in Yungang Grottoes.Under the weathering disease of the rocks of the Yungang Grottoes,the Si O₂ content in the composition of the grotto sandstone gradually increases and the Al₂O₃ and K₂O content gradually decreases as the weathering depth increases.Therefore,we used Si O₂,Al₂O₃,and K₂O as the main factors to characterize the different weathering depths of the grottoes,and rocks with different Si O₂（Al₂O₃/K₂O）content ratios were prepared as samples to simulate the actual samples under different weathering depths.At the same time,since the samples of lithic artifacts with different weathering degrees have different mineral compositions,they will have different dielectric constants.As the degree of weathering deepens,the different proportions of minerals contained will lead to changes in the dielectric constants of weathered rock samples.Therefore,for the detection of a certain kind of rock sample,the perturbation can be provided by the change of dielectric constant.During the complex change of weathering composition,the change of dielectric constant is very small,that is,the change of perturbation term is very subtle,and the wireless sensing system designed by PT symmetry and EP principle can reflect the very small change of perturbation term by the obvious frequency splitting amount.For the above designed stone artifact samples of the Yungang Grottoes,we designed a second-order EP wireless sensing system.The system is composed of four coils,i.e.,two resonant coils and two non-resonant coils,and a parallel plate capacitor is introduced into the system to place the detection samples.The incident wave is used as the effective gain of the system,and by adjusting the coupling distance between the coils,the system achieves a PT symmetry EP.After the EP is reached,samples with different constituent contents are placed into the system as perturbations for detection.The results show that when the system is near the second-order EP,the amount of perturbation of samples with different constituent contents has a relationship with the system frequency offset of 1/2order,which improves the sensitivity of detection compared with the conventional passive wireless sensors.Finally,the fitted relationship between the main constituent content of the cave sandstone and the resonant frequency was obtained by analyzing the results,and the weathering depth of the cave can be successfully predicted using the fitted curve.