Analysis of tunable bandgaps in liquid crystal-infiltrated 2D silicon photonic crystals

We present a theoretical study on two-dimensional photonic crystals composed of silicon and the E7 liquid crystal. We analyze how the optical axis orientation of the liquid crystal influences the photonic bands and bandgaps, for the case when the Maxwell equations can be decoupled into the TE and TM modes. We consider two different structures, a triangular lattice of E7 liquid crystal cylinders in a silicon background and a triangular lattice of silicon cylinders in an E7 liquid crystal background. The effect of the liquid crystal anisotropy on the geometry of the irreducible Brillouin zone allows us to propose a simplified way to calculate the photonic bandgaps. Results show that the bandgap width and center frequency have a 60° periodicity for both structures. Using the plane-wave expansion method, we determined the maximum bandgap and the optimal radius of the cylinders for each structure. Finally, for the second structure, we propose an optical switch with a 50% duty cycle. These structures can be applied to design tunable photonic devices.     

二维光子晶体点群对称对不可约布里渊区的影响

采用平面波展开法,研究了二维光子晶体点群对称对不可约布里渊区的影响。在单柱体二维光子晶体单胞中增加一个柱体,设计成不同点群对称操作数的对称结构,计算了最低5条能带的本征频率值在第一布里渊区的分布图。结果表明:在计算二维光子晶体的能带结构时,如果光子晶体的点群对称操作数为n,所取的不可约布里渊区应为整个第一布里渊区的1/n。     

Plasmonic Zener tunneling in metal-dielectric waveguide arrays

We elucidate in this Letter plasmonic Zener tunneling (PZT) in metal-dielectric waveguide arrays (MDWAs) by using numerical simulations and theoretical analyses. PZT in MDWAs occurs at the waveguide entrance and wherever the beam completes Bloch oscillations, because the bandgap between the first and second bands is minimal at the center of the first Brillouin zone. This feature significantly differs from that of optical Zener tunneling in dielectric waveguide arrays. The dependence of the simulated tunneling rate on the gradient of the relative permittivity of the dielectric layers correlates with the tunneling theory, thus confirming the occurrence of PZT in MDWAs.     

关于第n布里渊区体积等于倒格子原胞体积的证明

通过证明Wigner-Seitz原胞的体积等于原胞体积,说明第一布里渊区体积等于倒格子原胞体积;对于第n布里渊区和第n-1布里渊区建立保长同胚映射证明两者体积相等.     

各向异性金刚石结构的光子晶体

基于平面波展开法,理论分析了填充率、介质各向异性的程度对单轴金刚石结构三维光子晶体禁带的影响.结果表明,当填充率和介质各向异性取合适的值,单轴各向异性金刚石结构光子晶体存在着完全带隙.介质各向异性的引入使该晶体的带隙变窄甚至完全关闭.在各个布里渊区域里,带隙率和带隙宽度随介质各向异性程度的变化而变化.各向异性的引入为调整光子禁带提供了一种方法.     

Lattice-vibrational symmetry of ZnP2 and ZnAs2 in the monoclinic system

The vibrational representation is decomposed into irreducible representations in the symmetry points of the Brillouin zone. The selection rules are found for a one-phonon IR absorption and Raman scattering of light. In the IR absorption, 17 frequencies are active with polarization along the second-order axis and 16 frequencies are active with a perpendicular polarization. There are 36 frequencies active in the Raman scattering. The basis vectors of the normal vibrations are found for symmetry points of the Brillouin zone and the nature of the long-wave vibrations is investigated. The decomposition of the direct product of irreducible representations is found (selection rules).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 75–78, May, 1976.The authors thank G. F. Karavaev and N. V. Kudryavtsev for consultations.     

Momentum-dependent energy losses in core level photoemission spectra of poorly conducting metals

Angular resolved photoemission spectra of 5d core levels from Bi111 exhibit a component which is split off in energy by approximately 200 meV. The energy as well as the spectral width and relative intensity of the split off structure are strongly modulated by the final state electron momentum k(perpendicular) and k||, resembling the periodicity of the surface and bulk Brillouin zone. The data can be explained by a k-dependent energy loss function Im[-1/epsilon(k)(omega)] composed of indirect and direct interband transitions from various parts of the bulk Brillouin zone.     

Symmetry of lattice vibrations of hexagonal Cu2Te

The vibrational representation is expanded in terms of irreducible representations at the principal symmetry points of the Brillouin zone. Selection rules are found for single-phonon IR absorption, Raman scattering, and Mandel'shtam-Brillouin scattering of light. In IR absorption, a single frequency is active for light polarized parallel to the sixth order axis and a single frequency for perpendicular polarization. Five frequencies are active in Raman scattering of light. Expansions of the direct product of irreducible representations (selection rules) are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 45–48, November, 1981.     

Bandgap tuning in armchair MoS(2) nanoribbon

We report on the first-principles calculations of bandgap modulation in armchair MoS(2) nanoribbon (AMoS(2)NR) by transverse and perpendicular electric fields respectively. In the monolayer AMoS(2)NR case, it is shown that the bandgap can be significantly reduced and be closed by transverse field, whereas the bandgap modulation is absent under perpendicular field. The critical strength of transverse field for gap closure decreases as ribbon width increases. In the multilayer AMoS(2)NR case, in contrast, it is shown that the bandgap can be effectively reduced by both transverse and perpendicular fields. Nevertheless, it seems that the two fields exhibit different modulation effects on the gap. The critical strength of perpendicular field for gap closure decreases with increasing number of layers, while the critical strength of transverse field is almost independent of it.     

二维复式声子晶体中基元配置对声学能带结构的影响

研究了二维复式声子晶体中基元配置对其声学能带结构的影响,发现当声子晶体的基元配置改变时,声子晶体的不可约布里渊区也会改变,而且部分能带的极值不再在高对称线上.特别地,在某些基元配置下,不可约布里渊区扩大为整个第一布里渊区.因此,对于对称性较高的复式晶格声子晶体,可用通常的方法得到能带结构,而对于对称性较低的复式晶格结构声子晶体,只有采用对整个第一布里渊区进行研究的方法,才能获得可信的能带结构及带隙.     

Investigation the effect of lattice angle on the band gap width in 3D phononic crystals with rhombohedral(I) lattice

In this paper, the propagation of acoustic waves in the phononic crystal of 3D with rhombohedral(I) lattice is studied theoretically. The crystal composite constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of Brillouin zone. In the present work, we have investigated the effect of lattice angle on the band structure and width of the band gap rhombohedral(I) lattice in the irreducible part of the first Brillouin zone and its planes separately. The results show that more than one complete band gape are formed in the four planes of the irreducible part. The most complete band gaps are formed in the (111) plane and the widest complete band gap in (443) with an angle greater than 80 \(^{\circ }\) . So, if the sound passes through the (111) and (443) planes for the lattice angle close to 90 \(^{\circ }\) , the crystal phononic displays the excellent insulation behavior. Moreover, in the other planes, the lattice angle does not affect on the width and the number of band gaps. Also, for the filling fraction 5 %, the widest complete band gap is formed. These results are consistent with the effect of symmetry on the band gap width, because the (111) plane has the most symmetry.     

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.     

布里渊区与倒格子原胞

用简单数学方法就体心立方晶格和面心立方晶格证明了三维情况下布里渊区体积等于倒格子原胞体积．同时提出证明高阶布里渊区与简约布里渊区体积相等的一种简捷方法．     

Zero-point energy of some cubic metals

A screened shell phenomenological model has been used for the estimation of the zero-point energies of four alkali, three noble and six b.c.c. transition metals. The calculated values are compared with the reported values. It has been found that a good phenomenological model along with a consideration of proper number of wave vectors in the irreducible ($\text{1}\text{48}$) part of the Brillouin zone, can yield satisfactory results.     

石墨烯纳米带的制备与电学特性调控

石墨烯由于其独特的晶体结构展现出了特殊的电学特性,其导带与价带相交于第一布里渊区的六个顶点处,形成带隙为零的半金属材料,具有优异的电子传输特性的同时也限制了其在电子学器件中的使用.因而科研人员尝试各种方法来打开其带隙并调控其能带特性,主要有利用缺陷、应力、掺杂、表面吸附、结构调控等手段.其中石墨烯纳米带由于量子边界效应和限制效应,存在带隙.本综述主要介绍了制备各类石墨烯纳米带的方法,并通过精确调控其细微结构,从而对其进行精确的能带调控,改变其电学特性,为其在电子学器件中的应用提供一些可行的方向.     

Magnetooptik und elektronische Struktur der magnetisch ordnenden Europiumchalkogenide

The absorption coefficient and the interband Faraday rotation of EuS, EuSe and EuTe thin films have been measured as function of the photon energy (1–6 eV), the temperature (2.7–300 K) and the applied magnetic field (0–11.5 kOe). In addition a magnetic field modulation technique has been developed, with a resolution of 2 ? 10^?4 deg. This allows the measurement of the Faraday rotation in fields of only 100 Oe, which is important for metamagnetic samples with low critical fields. A Kramers-Kronig transformation of the Faraday rotation leads to the circular dichroism and from these two quantities and the optical constants the off-diagonal elements of the conductivity tensor have been computed. From a comparison of this experimental result with values obtained from a modified atomic model, we deduce the character of the involved transitions and the spin polarization of the occupied ground states (4f ⁷,p(anion)). In addition the ratio of exchange splitting to band width of the empty 5d final state can be evaluated. The fine structure of the first main peak is discussed in terms of Kasuya's coupling scheme between the 4f ⁶ multiplett and the excited 5d electron. In the antiferromagnetic EuTe the temperature dependence of the Faraday rotation does not follow the net magnetization of the sample for all photon energies, but some transitions show a “ferromagnetic” behavior. This is interpreted in Slater's model of the magnetic Brillouin zone.     

Optical properties and temperature dependence of critical transitions in ZnSe

The dielectric function of ZnSe has been deduced from ellipsometric measurements between 20 K and 380 K. is analysed around each critical point with the standard critical point model. The variations of the different parameters characterising each transition with temperature are presented and analysed. The temperature coefficients of the energies of the critical transitions are given. is essentially governed by the Coulomb interaction near the fundamental gap. Thanks to the high binding energy of the exciton and the low spectral width of the ellipsometer, the fundamental state of the exciton is found completely separated from the first excited states and the continuum at low temperature. In return the strong transition E₁ near the L points of the Brillouin zone can be described equally well with a 2D or an excitonic transition. Received 5 February 1999 and Received in final form 15 June 1999     

Experimental observation of optical bandgaps for surface electromagnetic waves in a periodically corrugated one-dimensional silicon nitride photonic crystal

Dispersion curves of surface electromagnetic waves (SEWs) in 1D silicon nitride photonic crystals having periodic surface corrugations are considered. We experimentally demonstrate that a bandgap for SEWs can be obtained by fabricating a polymeric grating on the multilayered structure. Close to the boundary of the first Brillouin zone connected to the grating, we observe the splitting of the SEW dispersion curve into two separate branches and identify two regions of very low group velocity. The proper design of the structure allows the two folded branches to lie beyond the light line in a wide spectral range, thus doubling the density of modes available for SEWs and avoiding light scattering.     

Forward mode coupling and bandgap formation in magnonic crystals

The bandgap formation for magnetostatic surface spin waves (MSSW?s) is numerically simulated in a lateral magnetic superlattice. It is found that, while the bandgaps opened at Brillouin zone edges is an intrinsic property of the periodic lattice, the exact mechanism of their formation can be revealed by incorporating a real source of MSSW excitation into the system. The obtained results uncover that the bandgaps arise due to the coupling between the MSSW?s travelling away from the excitation source (forward modes). This behavior differs from that provided by Bragg diffraction, which is the well-established mechanism for bandgap formation in periodic lattices.     

Apparently complex high-pressure phase of gallium as a simple modulated structure

The phase of gallium GaII, with symmetry C222(1) and 104 atoms per unit cell, has been recently reported as an example of structural complexity under high pressure. It is shown here that this phase is a simple modulated distortion of an average structure of Fddd symmetry with all atoms structurally equivalent. The modulation can be described with only 4 parameters and satisfies symmetry properties described by a centrosymmetric superspace group. The structural distortion is dominated by a frozen transversal mode associated with a single irreducible representation of Fddd, with a wave vector on the line Q, at an edge of the Brillouin zone. The average structure can be related with an hcp configuration through simple sliding of hcp layers, reminiscent of the hcp-bcc Bürgers mechanism.