The transmission properties of a one-dimensional defective photonic crystal have been investigated using the transfer matrix method. A layer of graphene-based hyperbolic metamaterial whose optical axis is tilted with respect to the interface is taken as a defect. It is shown that two kinds of the defect modes can be found in the band gaps of the structure for TM-polarized waves. One kind is created at the frequency range in which the principle elements of the effective permittivity tensor of the defect layer have the same signs. The frequency of this kind of defect mode is independent from the orientation of the optical axis of the defect layer. The other one is created at the hyperbolic dispersion frequency range. Such a defect mode appears due to the anisotropic behavior of the defect layer and its frequency strongly depends on the orientation of the optical axis. Unlike the conventional defect modes, the magnetic field of this defect mode is localized around the defect layer.

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Seeking operative terahertz (THz) devices has always stimulated considerable attention. Of particular interest is the THz beam splitter. Here, a tunable THz polarizing beam splitter (PBS) is proposed based on a graphene-embedded quarter-wave stack with a central defect layer of air. The spectral performance of the structure is investigated by the transfer matrix method. It is found that the electromagnetic waves can be decomposed into two separate polarized waves at incident angles greater than the critical angle. Furthermore, it is shown that a new kind of Brewster angle is found at the low THz frequencies due to the existence of the graphene nano-layers. The appearance of this angle which we call it the graphene induced Brewster angle results in the separation of TM-and TE-polarized waves at the low THz frequencies (f < 2 THz) in addition to the high THz region. It is shown that the working frequency range of PBS can be easily tuned by adjusting the width of the defect layer of air and also by tuning the chemical potential of graphene nano-layers via a gate voltage. The analysis of the proposed PBS is confirmed by the Finite Element Method (FEM) simulations that were performed with the commercial software COMSOL 5.2. Our investigations also reveal that the high transmission extinction ratio (> 200 dB) for TM waves with frequency f < 2 THz is achieved by increasing the chemical potential to 0.5 eV. Moreover, this structure can exhibit extremely high extinction ratio for TE waves with high THz frequencies. Finally, the degree of polarization equals to one is reported for the PBS proposed here. This structure offers the opportunity to realize a high-efficiency PBS with very high extinction ratios at the broadband THz frequency.

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Based on the transfer matrix theory, I realize a nearly perfect wavelength-selective absorption of near-IR waves in a one-dimensional defective photonic crystal, $$(AB)^ND(BA)^M$$ ( A B ) N D ( B A ) M , containing a vanadium dioxide (VO$$_2$$ 2 ) phase transition layer as a defect. Firstly, the effect of the period numbers, N and M, on the absorption spectrum is studied to achieve a perfect absorption peak. It is shown that optimal period numbers of the structure to maximize the absorption peak are N = 7 and M = 16. Our results also indicate that a narrow-band, almost perfect absorption is achieved due to the symmetry of the structure with respect to VO$$_2$$ 2 . Also, the absorption amount of the considered structure is about 50 times larger than that of a free-standing VO$$_2$$ 2 . Furthermore, the absorption peak value and resonant wavelength can be continuously tuned while VO$$_2$$ 2 transits from semiconductor to metal phase at 340 K temperature. In addition, how different parameters such as the polarization and incident angle affect the absorption spectra is discussed. Finally, the nonlinear absorption spectra of the structure are graphically demonstrated beside the linear case. The current system can be applied in designing practical tunable optical devices such as IR sensors, limiters, and switches.