Guided modes in slab waveguides with a left handed material cover or substrate

We study guided modes propagating along a dielectric slab waveguide with a left handed material (LHM) cover or substrate. The dispersion relation is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal dispersion curves. Different from a slab waveguide with a LHM core, we find that guidance properties are strongly dependent on dielectric permittivity ε and magnetic permeability μ of the substrate and cover layers. For oscillating guided modes, fundamental zero order mode is not always absence, sometimes it exists in a restricted range of normalized propagation constant. First order mode behaves as other higher order modes and exists up to infinite high frequency. Higher order modes have no double degeneracy in the case of LHM cover layer. For surface guided modes, the existence and the type of the mode solutions with respect to different parameters are classified systematically and discussed in detail. Unlike a slab waveguide with a LHM core where the dispersion curve of TE₁ surface mode continues with that of oscillating TE₁ mode, the dispersion curve of TE₁ surface mode continues with that of oscillating TE₀ mode. It seems that the two different kinds of modes compensate each other to form one whole mode. Both TE and TM guided modes are discussed.     

An additional kind of nonlinear s-polarized surface plasmon polaritons

We have explored the dispersion relations for s-polarized surface plasmon polaritons guided by a metal film sandwiched between a linear substrate and a cladding with an intensity-dependent refractive index. In contrast to a previous paper we found surface plasmon polaritons for this configuration which exhibit a definite power threshold and a limited range for permitted propagation constants as well.     

Excitation of ultrasonic Lamb waves using a phased array system with two array probes: Phantom and in vitro bone studies

Long bones are good waveguides to support the propagation of ultrasonic guided waves. The low-order guided waves have been consistently observed in quantitative ultrasound bone studies. Selective excitation of these low-order guided modes requires oblique incidence of the ultrasound beam using a transducer-wedge system. It is generally assumed that an angle of incidence, θ_i, generates a specific phase velocity of interest, c_o, via Snell’s law, θ_i = sin⁻¹(v_w/c_o) where v_w is the velocity of the coupling medium. In this study, we investigated the excitation of guided waves within a 6.3-mm thick brass plate and a 6.5-mm thick bovine bone plate using an ultrasound phased array system with two 0.75-mm-pitch array probes. Arranging five elements as a group, the first group of a 16-element probe was used as a transmitter and a 64-element probe was a receiver array. The beam was steered for six angles (0°, 20°, 30°, 40°, 50°, and 60°) with a 1.6-MHz source signal. An adjoint Radon transform algorithm mapped the time-offset matrix into the frequency-phase velocity dispersion panels. The imaged Lamb plate modes were identified by the theoretical dispersion curves. The results show that the 0° excitation generated many modes with no modal discrimination and the oblique beam excited a spectrum of phase velocities spread asymmetrically about c_o. The width of the excitation region decreased as the steering angle increased, rendering modal selectivity at large angles. The phenomena were well predicted by the excitation function of the source influence theory. The low-order modes were better imaged at steering angle ?30° for both plates. The study has also demonstrated the feasibility of using the two-probe phased array system for future in vivo study.     

Multilayer graphene waveguides

We study dispersion properties of TM-polarized electromagnetic waves guided by a multilayer graphene metamaterial. We demonstrate that both dispersion and localization of the guided modes can be efficiently controlled by changing the number of layers in the structure. Remarkably, we find that in the long wavelength limit, the dispersion of the fundamental mode of the N-layer graphene structure coincides with the dispersion of a plasmon mode supported by a single graphene layer, but with N times larger conductivity. We also compare our exact dispersion relations with the results provided by the effective media model.     

Guided and surface modes in chiral nihility fiber

Guided and surface modes in the chiral nihility fiber consisting of a chiral nihility metamaterial core with an achiral cladding have been investigated. The dispersion equations of guided and surface modes in the chiral nihility fiber and their cutoff frequencies are derived. Dispersion curves of guided and surface modes are presented and the effect of chirality parameter on dispersion curves is discussed in detail. Some novel propagation characteristics are found.     

Kramers–Kronig transform for the surface energy loss function

A new pair of Kramers–Kronig (KK) dispersion relationships for the transformation of surface energy loss function Im[−1/(ɛ + 1)] has been proposed. The validity of the new surface KK transform is confirmed, using both a Lorentz oscillator model and the surface energy loss functions determined from the experimental complex dielectric function of SrTiO₃ and tungsten metal. The interband transition strength spectra (J_cv) have been derived either directly from the original complex dielectric function or from the derived dielectric function obtained from the KK transform of the surface energy loss function. The original J_cv trace and post-J_cv trace overlapped together for the three modes, indicating that the new surface Kramers–Kronig dispersion relationship is valid for the surface energy loss function.     

Investigation of the guided modes in anisotropic diffused slab waveguide with embedded metal layer

Abstract

The optical characteristics of the TE and TM guided modes of a multilayer anisotropic two-dimensional waveguide are investigated by using the field component transformation matrix, and also taking into account the substrate intrinsic dispersion. The embedded thin metal layer effects on the propagation constant for both lossless approximated and exact solutions are presented. The lossless approach is accurate enough for the TE waves, but it is not for the TM ones, which exhibit changes of about 10^?6 for the equivalent index. The TM modes also present attenuation constant changes between the lossy and weakly-lossy solutions of the order of 9 dB/cm. Several complex field component mappings are drawn, and the surface plasma waves are also examined.     

Slow light in a dielectric slab waveguide with a negative refractive index photonic crystal substrate

Slow light effect in a dielectric slab waveguide with a negative refractive index photonic crystal substrate is numerically investigated. The guided modes are confined in the core layer by total internal reflection. Dispersion and wave propagating properties are explored in details. The result demonstrates that light speed can approach zero at two adjacent frequencies, which is also verified by finite-difference time-domain (FDTD) simulation. Calculated Q-factors both exceed several thousand. The structure has the potential to be used as high-Q open cavity for dual-wavelength lasers or traveling wave amplifiers.     

Sensitivity of surface plasmon dispersion and damping to alkali adsorption

I have studied the sensitivity to alkali adsorption of the linear coefficients of surface plasmon dispersion and damping, through the use of self-consistent surface potential barriers which have been shown by Lang to give a good account of the work function changes due to such adsorption. The coefficient of dispersion increases strongly with alkali adsorption on an r_S = 2 substrate, while the coefficient of damping changes less.     

The Investigation of Plasmon-Longitudinal Optical Phonon Coupling and Surface Polariton Modes in Donor Doped GaAs-Al0.33Ga0.67As Multi Quantum Wells

Infrared Fourier transform spectroscopy has been used to investigate phonon, plasmon, surface polariton and plasma-longitudinal optical phonon coupling in highly donor doped multi quantum wells (GaAs/Al_0.33Ga_0.67As) and direct band gap n- type Al_XGa_1-XAs thin layer on GaAs substrate. Using different samples with different concentration of free carriers. The dispersion equation of coupling modes have been calculated by using the condition which the dielectric functions of samples are zero for longitudinal coupled modes and experimental papameters which have been obtained from the best fit p-polarized oblique incidence far infrared reflection spectra. In MQW samples, the free carriers confined to the well and carriers are quasi two dimensional. So, plasmon- LO phonon coupling occur in the well (GaAs). In n- type Al_XGa_1-XAs thin layer, the coupled modes consist of three branches of the high, intermediate and low frequency modes. Their frequencies depend on both concentration and alloy composition. To analyses the surface polariton modes we carry out attenuated total reflection (ATR) measurements. In order to support our assignment the magnetic field profiles and surface polariton dispersion curves have been calculated.     

Surface wave propagation at the interface between lossy metamaterials medium and nonlinear media with arbitrary nonlinearity

The dispersion relation in a system that consists of a lossy metamaterials (MTMs) film surrounded by a linear substrate and a nonlinear cladding with an arbitrary nonlinearity is derived. The surface plasmonic (SP) wave at the interfaces between metamaterials (MTMs) and the nonlinear cover is recovered by taking certain limits. Lossy MTMs have simultaneously complex-negative permeability μ and complex-negative permittivity ε. Results are presented by plotting the SP frequency as a function of the nonlinearity at chosen damping factors. Both the real and imaginary parts are studied. Results also display the wave frequency as a function of plasma frequency. For comparison, the imaginary part is set to zero and curves are reproduced.     

Radiative plasmon polaritons in multilayer structures with a two-dimensional electron gas

Two-dimensional plasmon polaritons are analyzed for a typical experimental configuration in which a layer of two-dimensional electrons with a finite mobility lies on the top of a dielectric waveguide formed by the substrate (a wafer of finite thickness). Two-dimensional plasmons couple strongly to the radiative modes of this dielectric waveguide. It is shown that, as a result of the competition between collisional and radiative processes, a family of eight quasi-stationary normal modes arises. Six of them decay carrying energy to infinity. The two remaining plasmon-polariton modes are nonradiative. One of these modes, the TM-type plasmon polariton, in the limiting case where retardation is disregarded corresponds to the conventional longitudinal two-dimensional plasmon. The other mode, the TE-type plasmon polariton, exists only for a finite thickness of the substrate. All of them are characterized by different dispersion relations of the complex frequency ω(q) = Reω + iImω and differ in both polarization (longitudinal and transverse) and symmetry with respect to the direction of decay (symmetric and asymmetric). The latter modes decay slowly, propagating into free space to plus or minus infinity. The conditions under which the Q factors of certain modes are arbitrarily high are found. In this case, Imω(q ₀) = 0, and dissipative losses in the two-dimensional electron gas are compensated by external sources. As a result, the reflection coefficient for a plane wave whose angle of incidence is determined by the vector q ₀ vanishes.     

INFLUENCE OF THE SUBSTRATE ON THE MAGNETOSTATIC MODES OF A FINITE SUPERLATTICE

In a finite layered system, the substrate influences the spectra of the collective excitations. We solve the dispersion relations for magnetostatic modes in a finite Cd_0.30Mn_0.70Te-Cd_0.89Mn_0.11Te multilayer structure as a prototype antiferromagnetic and paramagnetic su-perlattice grown on the top of a nonmagnetic or a paramagnetic substrate. In perpendicular magnetization geometry where the saturation magnetization lies along the growth axis of the layered structure, surface modes appear in the spectra when the substrate is paramagnetic but disappear when the substrate is nonmagnetic. At the same time, the bands of bulk modes in the spectra are independent of change of substrates.     

Light confinement in 3D silicon doped with germanium (n-SixGe1−x) and silicon-on-insulator (SOI) photonic crystal structures

The numerical investigation of photonic band gaps (PBGs) for three-dimensional (3D) photonic crystals (PCs) of silicon doped with germanium (n-Si_xGe_1−x) and silicon-on-insulator (SOI) structures has been illustrated. The effect of germanium-doping (Ge-doping) concentration on the vertical confinement of the light and the band gap size has been presented. A 3D full vectorial plane wave was developed and employed to investigate design parameters of the 3D PC structure and to calculate dispersion relation for guided modes. Calculations of band structures for the triangular lattices of dielectric cylinders in air for quasi-3D PC structures have been performed.     

含左手材料光纤的表面模特性

在弱导条件下,利用Maxwell方程组,对纤芯是左手材料,包层是右手材料的光纤表面模进行了研究,得到了TE (TM)、 EH和 HE表面模的色散方程,.根据色散方程,画出了相应表面模和含左手材料光纤导模的色散曲线.比较这些色散曲线,发现了含左手材料光纤表面模一些新的特性.     

Formation of copper islands on a native SiO2 surface at elevated temperatures

A combination of in situ X-ray photoelectron spectroscopy analysis and ex situ scanning electron- and atomic force microscopy has been used to study the formation of copper islands upon Cu deposition at elevated temperatures as a basis for the guided growth of copper islands. Two different temperature regions have been found: (I) up to 250 °C only close packed islands are formed due to low diffusion length of copper atoms on the surface. The SiO₂ film acts as a barrier protecting the silicon substrate from diffusion of Cu atoms from oxide surface. (II) The deposition at temperatures above 300 °C leads to the formation of separate islands which are (primarily at higher temperatures) crystalline. At these temperatures, copper atoms diffuse through the SiO₂ layer. However, they are not entirely dissolved in the bulk but a fraction of them forms a Cu rich layer in the vicinity of SiO₂/Si interface. The high copper concentration in this layer lowers the concentration gradient between the surface and the substrate and, consequently, inhibits the diffusion of Cu atoms into the substrate. Hence, the Cu islands remain on the surface even at temperatures as high as 450 °C.     

Guided modes in a rectangular waveguide filled with single-negative materials

Based on classical electromagnetic theory, characteristics of guided modes in a rectangular waveguide filled with a pair of single-negative layers are studied. The results show that only surface waves of TE mode can propagate in this peculiar waveguide, no TM mode in any forms can propagate in it. In addition, TE waveguide modes will be affected by permeability ratio μ₁/μ₂ and dielectric layer thickness ratio P. Finally, from the electric field distribution of TE mode, we find the amplitude and location of the electric field can be adjusted by changing the thickness ratio P.     

‘Guided’ polaritons and plasmons in media with surface inhomogeneities

In media with inhomogeneities such that the dielectric tensor decreases with distance z below the surface there may exist propagating polariton or plasmon modes whose amplitudes oscillate before decreasing exponentially with increasing z. We discuss the properties of these ‘guided’ modes, particularly for conducting media, and show that they can exist even for relatively small carrier concentrations if a suitable concentration gradient is maintained over a distance of tens of microns or less.     

Experimental studies of optical surface excitations

Experimental methods for optical excitation of nonradiative surface waves, such as surface plasmons and surface phonons, are reviewed. Results for surface plasmons in InSb obtained by using samples with line gratings in the surface and by using the technique of attenuated total reflection (ATR) are compared. Best agreement between the theoretical and experimental surface plasmon dispersion curve ω(k) of InSb is found when using excitation by ATR, since the sample surface need not be disturbed in this case. Surface phonons have been excited optically by applying ATR to alkali halide crystals and to the polar semiconductor GaP. While agreement with the theoretical dispersion curve is extremely good for GaP and also for CaF₂, there are systematic deviations to lower frequencies for NaF and other alkali halides. In polar semiconductors the free carrier plasmon couples to the LO-phonon when ω_p ≈ ω_LO. This behaviour has been investigated theoretically and experimentally for the surface modes. For an interesting application of the ATR-technique, one can use the fact that dispersion and linewidth are a direct measure of the complex dielectric function ε(ω) in the frequency range of the optical surface waves.     

New nonlinear magnetostatic surface waves in a ferromagnetic (YIG)

The general propagation characteristics of magnetostatic surface waves guided by a single interface of a semi-infinite nonlinear dielectric cover and a ferromagnetic substrate (YIG) have been derived. The nonlinear dielectric cover has intensity dependent refractive indices. The magnetostatic approximation is considered and retardation is ignored in describing the electromagnetic fields in the structure. The used magnetostatic approximation is leading to new waves and might be called nonlinear magnetostatic surface waves. The propagation of these waves is non-reciprocal in contrast to the linear magnetostaic surface waves, which had been only found in the negative direction of propagation.