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In general, the photonic crystal (PC) is a periodical optical structure, but there are some studies considering aperiodic structures. If we insert a defect layer into a one-dimensional periodic PC to break its translational symmetry order (TSO), some peaks, called defect modes, appear in the transmittance spectrum. The defect layer thickness governs the frequencies of these defect modes but almost does not affect the other part of the spectrum. The discovery of quasi-crystals tells us that not only the TSO but also other orders can produce Bragg diffraction. It is well known that triadic Cantor set (TCS) PCs, which lack TSO but have a self-similar symmetry order (SSO), still exhibit narrow transmission peaks. In this work, we try to break the SSO in TCS PCs and find the resulting optical phenomena, where single-negative materials and dielectrics are chosen as the constituents of PCs. The study method is the transfer matrix method, and the calculation results show that the background intensity of the transmittance spectrum rather than the frequency of peaks obviously periodically changes with the break of SSO. It follows that the SSO does have physical meaning, and not only the transmission peaks but also the background should be treated as a significant optical property.

We theoretically study the one-way absorption in two 1D defective asymmetric photonic crystals, air/(DB) N A(BD) M /air and air/(DB) N A(BD) M A(DB) N A(BD) M /air, where A and B are dielectrics, D is the semiconductor, n-InSb, and N, M are stack numbers with N≠M. It is revealed that their absorption spectra exhibit one-way properties. We also find that the number of one-way absorption peaks depends on the symmetry and number of defect layers, which are similar to the defect modes in the transmittance spectra of the usual symmetry photonic crystals. Additionally, effects of the incident angles for both TE and TM waves on the one-way feature are also presented. At a large incident angle, the TE wave is almost reflected, whereas the TM wave can have a partial absorption.

We theoretically study wave properties for one-dimensional defective asymmetric photonic crystals, air/(AB) M G(BA) N /air, air/(AQ) M G(QA) N /air, and air/(BQ) M G(QB) N /air, where A is a lossy epsilon-negative material, B is a lossy mu-negative material, G and Q are dielectrics with different refractive indexes, and M and N are stack numbers with M≠N. Special attention has been paid to their absorption spectra. It is found that at certain frequencies the absorption can exhibit unidirectional properties. Our calculated results show two kinds of unidirectional absorption peaks. One is a single absorption peak whose frequency depends on the thickness of defect layer G. For the other peaks, its frequency does not change when the defect layer's thickness changes. In addition, in the second kind of peaks, the peak numbers for forward and backward propagation are different, that is, there are (M-1) absorption peaks for forward propagation, while there are (N-1) absorption peaks for backward propagation. When the two kinds of unidirectional absorption peaks are merged, some new peaks appear, and both forward and backward propagation will have (M+N-1) absorption peaks.

The ferroelectric material KTaO 3 (KTO) has a very high refractive index, which is advantageous to the photonic crystal (PC) design. KTO polycrystalline crystal has a high extinction coefficient. In this work, we perform a theoretical study of the transmission properties of a PC bandpass filter made of polycrystalline KTO at terahertz (THz) frequencies. Our results show that the defect modes of usual PC narrowband filters no longer exist because of the existence of the high loss. We provide a new PC structure for the high-extinction materials and show that it has defect modes in its transmittance spectra, providing a possible bandpass filter design in the THz region.

In this work, we propose a filter structure using a one-dimensional ferroelectric-dielectric periodic multilayer, air/[(ABA) N s C] Np (ABA) N s /air, where N s and N p are the two numbers of periods. Here, B is a dielectric material of SiO 2 , C is the same as B with a different thickness, and A is taken to be a ferroelectric material Ba 55 Sr 45 TiO 3 +30%Mg 2 SiO 4 , whose dielectric constant is very high (ϵ=439 at 10 GHz). The results show that the transmittance spectra have N s -channel groups at microwave frequencies and these groups can be classified into two types. The first type has only one channel group with N p narrower channels. The other has N s -1 groups, each of which has N p +1 broader channels. In this filter structure the group number and channel number of each group can be determined simply by changing N s and N p .

In this work, the photonic band gap (PBG) structure in a one-dimensional ferroelectric photonic crystal (PC) is theoretically investigated. We consider a PC, air/(AB) N /air, in which layer A is a dielectric of MgO and layer B is taken to be a ferroelectric of Ba 0.55 Sr 0.45 TiO 3 (BSTO). With an extremely high value in the dielectric constant in BSTO, the calculated photonic band structure at microwave frequencies exhibits some interesting features that are significantly different from those in a usual dielectric-dielectric PC. First, the photonic transmission band consists of multiple and nearly discrete transmission peaks. Second, the calculated bandwidth of the PBG is nearly unchanged as the angle of incidence varies in the TE wave. The bandwidth will slightly reduce for the TM mode. Thus, a wide omnidirectional PBG can be obtained. Additionally, the effect of the thickness of the ferroelectric layer on the PBG is much more pronounced compared to the dielectric layer thickness. That is, the increase of ferroelectric thickness can significantly decrease the PBG bandwidth.

A fractal multilayer structure made of two dielectric materials can exhibit photonic bandgap (PBG). In this work, with the use of this PBG, we study the transmission properties of periodic triadic Cantor set structures. The results indicate that the structure can be used to design multichannel filters with channel number equal to N-1 for a given number of periods, N. In addition, the channel frequencies can be designed at will. The considered structure provides another new type of design for a tunable multichannel filter.