Contour of the attenuated length of an evanescent wave at constant frequency within a band gap of photonic crystal

The plane wave method is normally applied to determine the eigenfrequency of a two-dimensional (2D) photonic crystal. A slight change to this eigenvalue equation makes the wave number its eigenvalue providing a direct means to determine the attenuated length of the evanescent modes at the frequency within the photonic band gap. The contour of the length of attenuation of the evanescent modes in a square lattice can be determined using the proposed wave number eigenvalue equation. The wave number eigenvalue equation for the two-dimensional (3D) photonic crystal can also be obtained using a derivation similar to that for the 2D photonic crystal. Possible applications of the proposed calculation-method are presented.     

Extension of the radiation spectrum method for the reflection calculation at the end of a strongly guiding optical waveguide

In this work we extend the radiation spectrum method (RSM) with evanescent modes to use it for the calculation of the reflection coefficient at the end of a strongly guiding dielectric waveguide. The extension is made by considering the coupling between the radiation (or evanescent) modes at both sides of the optical discontinuity. To insure the convergence of the method, this extension is achieved analytically. Using this technique, we show that for small guide width, the generation of evanescent modes results in a complex reflection coefficient. The magnitude and the phase of the reflection coefficient are calculated and compared with the simple theory of the effective index as well as the finite difference time domain (FDTD) technique. The spectra of the transmitted and reflected fields are also obtained.     

Interaction of interface plasmons and longitudinal optical phonons in a multilayer structure

The interaction between two-dimensional interface plasmons and longitudinal optical phonons in multilayer structures is analysed in this communication. The dispersion relations for the mixed modes are obtained for periodic boundary conditions in the direction normal to the layer planes. The energy gap between the two bands of mixed modes can be seen in the density of states ?_k(ω) at fixed k parallel to the layers. ?_k(ω) also exhibits singularities at the band edges characteristics of the one-dimensional periodic array of parallel layers.     

Transmission mode of one-dimensional phononic crystal based on coupling of total evanescent waves

In order to obtain the transmission properties of one-dimensional phononic crystal under total evanescent waves, we design structure model. Basing on the basic acoustic wave equations and boundary condition as well as the Bloch theory, we study the band structure of one-dimensional phononic crystal. We summarize the properties of the mode based on the coupling of total evanescent waves and explain its physical mechanism. There are three transmission modes in phononic crystal. Based on the coupling of total evanescent waves, the number of perfect transmission peaks is just equal to the number of structure period, and the thickness of period can be much less than the wave length.     

Quantum transport in honeycomb lattice ribbons with armchair and zigzag edges coupled to semi-infinite linear chain leads

We study quantum transport in honeycomb lattice ribbons with either armchair or zigzag edges. The ribbons are coupled to semi-infinite linear chains serving as the input and output leads and we use a tight-binding Hamiltonian with nearest-neighbor hops. The input and output leads are coupled to the ribbons through bar contacts. In narrow ribbons we find transmission gaps for both types of edges. The appearance of this gap is due to the enhanced quantum interference coming from the multiple channels in bar contacts. The center of the gap is at the middle of the band in ribbons with armchair edges. This particle-hole symmetry is because bar contacts do not mix the two sublattices of the underlying bipartite honeycomb lattice when the ribbon has armchair edges. In ribbons with zigzag edges the gap center is displaced to the right of the band center. This breakdown of particle-hole symmetry is the result of bar contacts now mixing the two sublattices. We also find transmission oscillations and resonances within the transmitting region of the band for both types of edges. Extending the length of a ribbon does not affect the width of the transmission gap, as long as the ribbon’s length is longer than a critical value when the gap can form. Increasing the width of the ribbon, however, changes the width of the gap. In ribbons with zigzag edges the gap width systematically shrinks as the width of the ribbon is increased. In ribbons with armchair edges the gap is not well-defined because of the appearance of transmission resonances. We also find only evanescent waves within the gap and both evanescent and propagating waves in the transmitting regions.     

Effective permittivity and permeability of one-dimensional dielectric photonic crystal within a band gap

We take a finite dielectric photonic crystal as a homogeneous slab and have extracted the effective parameters. Our systematic study shows that the effective permittivity or permeability of dielectric photonic crystal is negative within a band gap region. This means that the band gap might act as ε-negative materials （ENMs） with ε 〈 0 and μ 〉 0, or μ-negative materials （MNMs） with ε 〉 0 and μ 〈 0. Moreover the effective parameters sensitively rely on size, surface termination, symmetry, etc. The effective parameters can be used to design full transmission tunnelling modes and amplify evanescent wave. Several cases are studied and the results show that dielectric photonic band gap can indeed mimic a single negative material （ENM or MNM） under some restrictions.     

Position Dependent Spontaneous Emission Spectra of a Λ-Type Atomic System Embedded in a Defective Photonic Crystal

We investigate the position dependent spontaneous emission spectra of a Λ-type three-level atom with one transition coupled to the free vacuum reservoir and the other one coupled to a double-band photonic band gap reservoir with a defect mode in the band gap.It is shown that,for the atom at the defect location,we have a two-peak spectrum with a wide dark line due to the strong coupling between the atom and the defect mode.While,when the atom is far from the defect location(or in the absence of the defect mode),the spectrum has three peaks with two dark lines due to the coupling between the atom and the photonic band gap reservoir with the largest density of states near the band edges.On the other hand,we have a four-peak spectrum for the atom at the space in between.Moreover,the average spontaneous emission spectra of the atoms uniformly embedded in high dielectric or low dielectric regions are described.It is shown that the atoms embedded in high(low) dielectric regions far from the defect location,effectively couple to the modes of the lower(upper) photonic band.However,the atoms embedded in high dielectric or low dielectric regions at the defect location,are coupled mainly to the defect modes.While,the atoms uniformly embedded in high(low) dielectric regions with a normal distance from the defect location,are coupled to both of defect and lower(upper) photonic band modes.     

Electromagnetic surface waves of multilayer stacks: coupling between guided modes and Bloch modes

The study of the dependence of surface mode dispersion on the termination of multilayer stacks reveals interesting features. For stratified media with high-refractive-index contrasts, surface modes can shift across several bandgaps if the thickness of the final layer is changed. The distance to the photonic band edge influences the decay length of the mode inside the multilayer stack. In the middle of the bandgap, the electromagnetic energy is concentrated in the final layer of the crystal, while near bandgap edges the decay length extends over several periods. Additional evidence suggests that surface modes behave like guided modes that can couple with the extended Bloch modes and give rise to evanescent field profiles oscillating along several periods.     

TM-like and TE-like Modes Coupling in a Two-Dimensional Photonic Crystal Slab Composed of Truncated Cone Silicon Rods

We numerically investigate the coupling of TE-like modes and TM-like modes in a two-dimensional （2D） photonic crystal （PC） slab composed of truncated cone silicon rods. In such structures, the classification of TE-like modes and TM-like modes is generally impossible and the coupling occurs due to vertical structural asymmetries. The frequency and wavevector dependences of the mode coupling are discussed by investigating the photonic band structures, and the coupling efficiency is studied by examining the transmittance. The results show that the efficiency of mode conversion is strengthened by the vertical asymmetry and weakened by the clear sinall gap. These structures could be used as polarization conversion devices in integrated optics.     

Temperature and pressure scaling of the alpha relaxation process in fragile glass formers: A dynamic light scattering study

We have experimentally observed the eigenmode splitting due to coupling of the evanescent defect modes in three-dimensional photonic crystals. The splitting was well explained with a theory based on the classical wave analog of the tight-binding (TB) formalism in solid state physics. The experimental results were used to extract the TB parameters. A new type of waveguiding in a photonic crystal was demonstrated experimentally. A complete transmission was achieved throughout the entire waveguiding band. We have also obtained the dispersion relation for the waveguiding band of the coupled periodic defects from the transmission-phase measurements and from the TB calculations.     

Spin hall edge spin polarization in a ballistic 2D electron system

Universal properties of the spin Hall effect in ballistic 2D electron systems are addressed. The net spin polarization across the edge of the conductor is second order, approximately lambda2, in spin-orbit coupling constant independent of the form of the boundary potential, with the contributions of normal and evanescent modes each being approximately radical lambda but of opposite signs. This general result is confirmed by the analytical solution for a hard-wall boundary, which also yields the detailed distribution of the local spin polarization. The latter shows fast (Friedel) oscillations with the spin-orbit coupling entering via the period of slow beatings only. Long-wavelength contributions of evanescent and normal modes exactly cancel each other in the spectral distribution of the local spin density.     

Finite size effects on the helical edge states on the Lieb lattice

For a two-dimensional Lieb lattice,that is,a line-centered square lattice,the inclusion of the intrinsic spin–orbit(ISO)coupling opens a topologically nontrivial gap,and gives rise to the quantum spin Hall(QSH) effect characterized by two pairs of gapless helical edge states within the bulk gap.Generally,due to the finite size effect in QSH systems,the edge states on the two sides of a strip of finite width can couple together to open a gap in the spectrum.In this paper,we investigate the finite size effect of helical edge states on the Lieb lattice with ISO coupling under three different kinds of boundary conditions,i.e.,the straight,bearded and asymmetry edges.The spectrum and wave function of edge modes are derived analytically for a tight-binding model on the Lieb lattice.For a strip Lieb lattice with two straight edges,the ISO coupling induces the Dirac-like bulk states to localize at the edges to become the helical edge states with the same Dirac-like spectrum.Moreover,it is found that in the case with two straight edges the gapless Dirac-like spectrum remains unchanged with decreasing the width of the strip Lieb lattice,and no gap is opened in the edge band.It is concluded that the finite size effect of QSH states is absent in the case with the straight edges.However,in the other two cases with the bearded and asymmetry edges,the energy gap induced by the finite size effect is still opened with decreasing the width of the strip.It is also proposed that the edge band dispersion can be controlled by applying an on-site potential energy on the outermost atoms.     

Transmission enhancement by conversion of evanescent waves into propagating waves

The convolution between spatial modes of two different parts of an optical system can convert evanescent waves into propagating waves. This principle is applied to different optical systems for analyzing various effects in transmission enhancements experiments. We discuss here the differences between the present principle which is related to broadening of resonances and the near-field optical microscopy based on a tunneling effect by a tip detector. The present analysis is applied in particular to two systems: a) transmission enhancement in one slit by coupling the transmitted radiation with transversal Fabry–Pérot electromagnetic (EM) modes, and b) transmission enhancement by coupling between a metallic film with arrays of holes and surface plasmons (SP). The present approach gives more information on transmission enhancement phenomena than that obtained by conventional treatments and can also solve certain disagreements between different theories. The differences between the present process of converting evanescent waves into propagating waves, and that related to the new development of getting a super-resolution by an hyperlens are discussed. PACS 41.20.Jb; 73.20.Mf; 42.79.Dj     

Perfect extinction in subwavelength dual metallic transmitting gratings

We investigate the strong electromagnetic coupling that settles in dual metallic grating structures. This coupling is evidenced to lead to a perfect optical extinction in the transmission spectrum. The behavior of this perfect extinction that strongly depends on the longitudinal space and the lateral displacement between the two gratings can be explained by a simple model that describes the interference between a propagating mode and a couple of evanescent modes. The results show that the electromagnetic transmission of the structure can be tuned by controlling the position of this perfect transmission extinction and thus pave the way to new types of infrared tunable filters.     

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.     

Photonic bands, gap maps, and intrinsic losses in three-component 2D photonic crystal slabs

We obtain the photonic bands and intrinsic losses for the triangular lattice three-component two- dimensional （2D） photonic crystal （PhC） slabs by expanding the electromagnetic field on the basis of waveguide modes of an effective homogeneous waveguide. The introduction of the third component into the 2D PhC slabs influences the photonic band structure and the intrinsic losses of the system. We examine the dependences of the band gap width and gap edge position on the interlayer dielectric constant and interlayer thickness. It is found that the gap edges shift to lower frequencies and the intrinsic losses of each band decrease with the increasing interlayer thickness or dielectric constant. During the design of the real PhC system, the effect of unintentional native oxide surface layer on the optical properties of 2D PhC slabs has to be taken into consideration. At the same time, intentional oxidization of macroporous PhC structure can be utilized to optimize the design.     

Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler

An ultrashort polarization beam splitter (PBS) based on an asymmetrical directional coupler is proposed by utilizing the evanescent coupling between a strip-nanowire and a nanoslot waveguide. In order to be convenient for integration with other components, mode converters between the nanoslot waveguide and the strip-nanowire are introduced and merged into S-bends to achieve an ultracompact PBS. As an example a 6.9 μm long PBS based on a silicon-on-insulator platform is designed, and the length of the coupling region is as small as 1.3 μm. Numerical simulations show that the present PBS has a very broad band (>160 nm) for an extinction ratio of >10 dB.     

金刚石晶格上的对角无序与非对角无序非晶量子点

报道金刚石晶格上对角无序与非对角无序非晶量子点的理论研究，用简单的紧束缚哈密顿量描述模型的电子结构，用ｒｅｃｕｒｓｉｏｎ方法求解哈密顿方程，用边界条件对本征值的影响判断局域化，研究发现，带边为扩展态时，带宽的变化趋势与晶态量子点类似；带边为局域态时，尺寸超过某一临界长度后，带宽不变，但带边态密度随尺寸增大而增大。还研究了非晶量子点的介电函数虚部ε₂（?ω）。与扩展态对应的ε₂（?ω），对尺寸变化较敏感。与局域态对应的ε₂（?ω），当尺寸大于 关键词：     

Evanescently coupled resonance in surface plasmon enhanced transmission

The optical transmission through subwavelength holes in metal films can be enhanced by several orders of magnitude by enabling interaction of the incident light with independent surface plasmon (SP) modes on either side of the film. Here, we show that this transmission is boosted by an additional factor of 10 when the energies of the SP modes on both sides are matched. These results, confirmed by a three-dimensional theoretical analysis, give a totally new understanding of the phenomenon of SP enhanced transmission. It is found that the holes behave like subwavelength cavities for the evanescent waves coupling the SPs on either side of the film. In this unusual device, the reflection at either end of the cavity is provided by the SP modes which act as frequency dependent mirrors.     

Evanescent modes are not necessarily Einstein causal

Previously, experiments with microwave signals have shown that evanescent modes can travel faster than light. Several theoretical investigations have proven that in the case of signals with unlimitedly high frequency components, such superluminal velocities do not violate Einstein causality, thus group, signal, and energy velocities are c where c is the vacuum velocity of light. In this letter I shall show that frequency band limitation is a fundamental property of signals and that such signals containing only evanescent modes can violate Einstein causality. Received: 12 December 1998 / Accepted: 14 December 1998