Slit Shear Waves in a Quasi PT-Symmetric Piezoelectric Heterostructure Near the Mode Degeneracy Point

The propagation of slit shear waves in a quasi-symmetric structure of piezoelectrics of the 4mm symmetry class has been theoretically studied. It has been shown that taking into account the unequal level of loss and gain in piezoelectrics results in either intersection, touching, or convergence of two modes at the point of their degeneracy (singular point) in the shear wave spectrum. It has been found that the intersection of the mode spectra occurs only in the case of equal loss and gain magnitudes (a PT-symmetric structure). Based on this, it is concluded that using the pattern of the spectra near a singular point, it is possible to determine the level of imbalance of gain and loss in piezoelectric waveguides. As in the case of a purely PT-symmetric structure, the frequency dependence of the amplitude at an exceptional point of a quasi PT-symmetric structure (with a rather small difference in loss and gain levels) exhibits a very narrow peak, which opens up the possibility of creating hypersensitive sensors based on them. Thus, it has been shown that even at unequal loss and gain levels in piezoelectrics (a quasi PT-symmetric structure), it is possible to obtain a structure with all the characteristics of a PT-symmetric structure.