Surface states in the one-dimensional model of a crystal with an arbitrary potential at the boundary

The approximate formula for the number of surface states and the approximate equation for its energy values has been obtained for the model of a one-dimensional semi-infinite crystal with an arbitrary potential at the boundary and the Kronig-Penney-type potential inside the crystal.     

Density of states of a one-dimensional disordered photonic crystal

An analytic theory of the density of states in one-dimensional disordered photonic crystals is proposed. It is shown that the problem of the density of optical modes can be reduced in the small dielectric contrast approximation to solving a generalized Fokker-Planck equation for the distribution function of the logarithmic derivative of the electric field (the wave phase). The exact analytic solution and density-of-states asymptotics deep in the band gap of the photonic crystal and close to the band gap edge are derived. The results obtained agree well with the empirical relations derived earlier from numerical experiments.     

含负折射率材料并具有零平均折射率的半无限一维光子晶体的表面态

用传输矩阵方法和Bloch定理,从理论上分析以色散介质为背景,由正负折射率材料组成的半无限一维光子晶体的表面态,发现以色散介质为背景,在满足平均折射率等于零的情况下,第一层厚度变化时,表面态将会在较大频率范围内显著变化。讨论了同一入射角度下不同频率的表面态的电场分布情况,结果表明：远离带边的表面态局域长度较小。     

Surface states/modes in one-dimensional semi-infinite crystals

Analytical expressions on how the eigenvalue of an existing surface state/mode in one-dimensional semi-infinite periodic systems depends on the boundary location and the boundary condition are obtained, by using a Sturm-Liouville theory approach. The obtained equations are verified by numerical calculations. A direct consequence of the results obtained is that the termination of the periodicity at a boundary τ in a semi-infinite periodic system does not always cause a surface state/mode in a specific band gap.     

Surface Tamm states in a photonic crystal slab with asymmetric termination

The reflection and transmission spectra of a finite thickness 2D photonic crystal slab (PCS) based on macroporous silicon are investigated. Periodic photonic crystal region is separated from air by homogeneous silicon interfacial layers. These interfacial layers at the silicon/air boundary being defects of the photonic crystal lattice, define the properties of surface Tamm states in the photonic stop‐bands (PSBs). It is demonstrated experimentally and theoretically that the reflection spectra of a structure with different thicknesses of the interfacial layers on both sides of the PCS depend on the illuminated side. At the same time, the transmission spectra are identical for both light directions in agreement with the reciprocity principle. Analysis shows that the dependence of the reflection spectrum on the side of light entrance is due to scattering losses in the real structure. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明:在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Zone folding induced tunable topological interface states in one-dimensional phononic crystal plates

In previous literature, the realization of topological interface state in one-dimensional periodic system is strongly relied on the tedious parameter adjustment to search for the Dirac cone. In this paper, based on a strategy of zone folding, multiple topological interface modes for the shear horizontal guided waves in one dimensional phononic crystal plate are investigated by using finite element method and eigenmode matching theory, in which the Dirac points are formed by simply making the unit cell double. Significantly, by simply contracting or expanding the stubs can bring the topological phase transition. Furthermore, the topological phase transition is further achieved by varying the height of the stubs. The proposed designs will be more convenient to be applied in real engineering.     

色散负折射特异介质的1维光子晶体缺陷态

在1维光子晶体中引入色散负折射特异介质,分析了其介电常数和磁导率在微波区（1～10 GHz）与频率的关系。分别对以色散负折射介质为缺陷的正折射率介质光子晶体及以正折射率介质为缺陷的正负折射率介质光子晶体进行了数值仿真,得出了均匀平面电磁波在正入射和斜入射时的透射谱。结果表明：在介电常数和磁导率均为负值的不同禁带中,分别出现了单、双缺陷模。利用透射谱的这一特点,可实现单、双通道滤波。     

Surface Tamm states in one-dimensional photonic crystals containing anisotropic indefinite metamaterials

Silica-based Yb 3+-doped glass is prepared by non-chemical vapor deposition.The drawn photonic crystal fiber(PCF) has a strong absorption at 976 nm and emission wavelength of approximately 1 037 nm.The intensity and spectral lineshape of the near infrared(NIR) luminescence of the Yb3+-doped PCF are recorded and discussed in terms of excitation power,excitation wavelength,fiber length,and Yb3+ ion concentration.The emission intensifies as the excitation power and Yb3+ ion concentration increase.The intensity of the shorter wavelength side of the luminescence spectrum decreases as the length of the PCF increases.     

Surface states on the (100) plane of a sphalerite-type crystal

The surface states of an ideal (100) plane of a sphalerite-type crystal were studied in the one-electron approximation; both the plane formed by electronegative atoms (>0) and that consisting of electropositive atoms (<0) were investigated. The interpretation of surface states whose energy lies in the gap is the same as for the diamond-like lattice. The influence of electro-negativity or electropositivity of the surface on the position of these states in the gap was investigated and possible consequences of these states joining one of the energy bands of volume states were pointed out. The results of this paper can be used to discuss correlation effects on the (100) plane of a diamond-like crystal.     

Defect mode properties in a one-dimensional photonic crystal

Based on the transfer matrix method (TMM), the interaction of electromagnetic waves with one-dimensional (1D) defective photonic crystal in ultraviolet (UV) frequency region had been studied. With the calculated transmittance characteristics in the wavelength domain, it can be found that the defect mode can be generated within the photonic band gap (PBG) at the central wavelength. Also the effects of many parameters such as the angle of incidence, the state of polarization and the defect layer thickness have been taken in account. A significant effect in generating multiple defect peaks within the PBG has been illustrated.     

Omnidirectional reflection from a one-dimensional photonic crystal

We demonstrate that one-dimensional photonic crystal structures (such as multilayer films) can exhibit complete reflection of radiation in a given frequency range for all incident angles and polarizations. We derive a general criterion for this behavior that does not require materials with very large indices. We perform numerical studies that illustrate this effect.     

Donor and acceptor-like electronic states in a one-dimensional semiconductor

Donor and acceptor-like electronic states were observed near the conduction and valence band, respectively, in a semiconducting single-wall carbon nanotube using scanning tunneling microscopy and spectroscopy. They are observed to be, spatially, at the same location and spread within a few nm. Their physical origin is suggested as locally formed excessive and deficient number of electrons per a closed carbon network.     

Polariton dynamics of a one-dimensional gyrotropic magnetic photonic crystal in a dc electric field: II. Surface waves

Localization and dispersion of collective magnetic TE and TM polaritons are analyzed for a semi-infinite, one-dimensional, magnetic photonic crystal of the compensated antiferromagnetic-nonmagnetic dielectric type in the presence of orthogonal magnetic and electric fields. The case where easy magnetization axis is orthogonal to the external electric field is considered.     

Graphene-based one-dimensional photonic crystal

A novel type of one-dimensional (1D) photonic crystal formed by an array of periodically located stacks of alternating graphene and dielectric stripes embedded into a background dielectric medium is proposed. The wave equation for the electromagnetic wave propagating in such a structure is solved in the framework of the Kronig-Penney model. The frequency band structure of the 1D graphene-based photonic crystal is obtained analytically as a function of the filling factor and the thickness of the dielectric between the graphene stripes. The photonic frequency corresponding to the electromagnetic wave localized by a defect of the photonic crystal formed by an extra dielectric placed in the position of one stack of alternating graphene and dielectric stripes is obtained.     

Wave propagation in a one-dimensional photonic crystal with metamaterial

This paper deals with the study of the transmission of electromagnetic waves through a one-dimensional multilayer periodic structure consisting of alternating slabs of negative- and positive-index media. It also focuses on the behavior of the transmission with the angle of incidence for both polarizations. The proposed structure works as a tunable p-polarization filter i.e. a filter which completely blocks the s-polarized wave but partially allows the p-polarized wave to pass through it for an angle of incidence greater than 20 ^°. For angles of incidence less than 50 ^° the structure works as a tunable edge filter.