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A theoretical investigation is presented for nematic liquid crystal photonic bandgap fibers (LCPBGFs), in which the rotation angle of liquid crystal's director n could be arbitrarily controlled by external electric field. Based on the investigation on the polarization effect of photonic bands, we propose two orthogonal polarization-dependent bandgap maps to describe the mode guiding behavior. The symmetry properties analysis of photonic band structure reveals that the bandgap map of LCPBGFs is approximately independent of the rotation angle of director. The guiding properties of LCPBGFs including the position and width of high transmission windows, single-mode single-polarization or ultrahigh birefringence guiding, confinement loss, and coupling loss are investigated. Specifically, the high loss peaks due to the coupling between guided mode and polarization-dependent photonic bands will greatly narrow the transmission windows of the LCPBGFs. The polarization axis of the guided mode is determined by the rotation angle of the director, which could be controlled by external electric field.