The complex symmetric dielectric tensor of a monoclinic crystal cannot be diagonalized by a space rotation operation in general, which poses a serious difficulty in analyzing the propagation of electromagnetic fields in monoclinic crystals so far. This propagation issue is discussed in a general case without using the index ellipsoid scheme. It is found that, when incident waves travel along the mirror plane normal or 2-fold rotation axis of monoclinic crystals, two eigenmodes following specific dispersion relations are elliptically polarized with the same ellipticity and chirality but have spatially orthogonal elliptical principal axes. The frequency independent features are the unique manifestation of the crystal symmetry. Using polarization sensitive terahertz time-domain spectroscopy and our developed data analyzing and processing methods, three complex permittivity tensor elements for a monoclinic crystal BaGa4Se7 are straightforwardly extracted and the properties of the two eigenmodes are characterized in full. It is also interesting that the spectral components beyond 1.7 THz show a very high refraction index (>10) and low dissipation during propagation, which suggests that the bulk phonon-polariton waves may be excited and effectively propagate in the crystal, resulting from the coherent phonon excitations by the incident terahertz waves. Our results may promote to develop novel terahertz devices based on polariton excitation and propagation in monoclinic crystals.
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