FDTD Investigation on Electromagnetic Scattering from Two-Layered Rough Surfaces under UPML Absorbing Condition

Electromagnetic scattering from one-dimensional two-layered rough surfaces is investigated by using finite-difference time-domain algorithm （FDTD）. The uniaxial perfectly matched layer （UPML） medium is adopted for truncation of FDTD lattices, in which the finite-difference equations can be used for the total computation domain by properly choosing the uniaxial parameters. The rough surfaces are characterized with Gaussian statistics for the height and the autocorrelation function. The angular distribution of bistatic scattering coefficient from single-layered perfect electric conducting and dielectric rough surface is calculated and it is in good agreement with the numerical result with the conventional method of moments. The influence of the relative permittivity, the incident angle, and the correlative length of two-layered rough surfaces on the bistatic scattering coefficient with different polarizations are presented and discussed in detail.     

Electromagnetic Wave Transmission from Slightly Gaussian Rough Surface of Layered Medium

The electromagnetic wave transmission from the slightly rough surface of three-layered medium is studied, and formulae of the transmission coefficients for different polarizations are derived using the small perturbation method. A Gaussian rough surface is presented for describing rough surface of the layered medium, the influence of permittivity of the layered medium, the mean layer thickness of the intermediate medium, the roughness surface parameters and the incident frequency on the transmission coefficient of HH polarization are obtained and discussed with numerical implementation.     

Time-Domain Scattering Modelling of Two-Dimensional Cylinder Located on a Rough Surface

Numerical modelling on the transient electromagnetic scattering by a two-dimensional （21）） cylinder located on a time-evolving rough surface is presented by using time-domain integral equations. The proposed special choice of a tapered Gauss pulse incident wave removes the truncation error from the rough surface. Additionally, a two-level averaging technique is utilized to overcome the instability from the time marching procedure of solving integral equations. Excellent correspondences between the surface current distributions, as well as the far-zone fields, computed by the proposed method and that obtained by the traditional method of moments associated with the inverse discrete Fourier transformation scheme demonstrate the accuracy of the modelling.     

Height distribution on a rough plane and specularly diffracted light amplitude are Fourier transform pair

In this report we show that the amplitude of specularly diffracted light from a plane rough surface as a function of incident angle cosine is Fourier transform of the height distribution on the surface. Therefore, an even height distribution function, which is the case for many rough surfaces, can be obtained by measuring the specularly diffracted light intensities. Also, it is observed that for polychromatic illumination the spectrum of the specularly diffracted light is modified and the modification depends on roughness, incident angle, and wavelength. It is also shown that, for a fixed incident angle, the height distribution on the rough plane is Fourier transform of the spectral modifying function. Experimental studies on some surfaces of different roughnesses, prepared by grinding sheet-glasses by powders of different grain sizes, show that the corresponding height distributions are Gaussian and the rms heights obtained by the two approaches are quite consistent.     

Rubinowicz transform of the MTPO surface integrals

The surface integral of the modified theory of physical optics is reduced to a line integral by using the Rubinowicz transform for the incident scattered fields by an arbitrary aperture in a black surface. The integral theorem of Kirchhoff is applied to the scattering geometry and the diffracted fields are expressed in terms of a line integral along the contour of the diffracting edge.     

Anomalous reflection and excitation of surface waves in metamaterials

We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general anomalous. In particular, we note that the specular reflection vanishes and that the incident energy is totally reflected in the backward direction, when the conditions for resonant excitation of leaking surface waves are fulfilled.     

Simultaneous slow and fast light in C60 solution

Recently, many researchers have reported their work about sub- and superluminal propagation. And many experiments have demonstrated the group velocity transition between slow and fast light. In this letter, the authors reported simultaneous slow and fast light in a single light beam which could be explained by the photorefractive lens-like effect and the spatial dispersion qualitatively. In our experiment, a focused light beam at 532 nm normally incident upon a thin quartz cell full of C₆₀ solution and spatial diffraction rings were observed behind the cell. Recurring to a pinhole diaphragm, we measured the group velocity of light of different position on the diffraction rings. The experimental results demonstrated that slow and fast could exist in a single beam at the same time. We could acquire slow or fast light just by adjusting the position of the detector and keeping the experimental parameters, such as: modulation frequency and incident intensity, unchanged. Our experiment put forward a new way to control the group velocity in nonlinear optical material.     

Efficient self phase matched third harmonic generation of ultrashort pulses in a material with positive dispersion

An ultrafast transient refractive index grating, produced in barium fluoride, a material with positive dispersion, promotes very efficient third harmonic generation. The significant enhancement of the generation up to a conversion efficiency of about 3% is due to self phase matching, involving the instantaneous grating. At the same time several diffraction orders of the third harmonic signal are observed behind the sample. Received: 17 October 2000 / Published online: 21 February 2001     

Giant positive and negative lateral shifts from the Kretschmann-Raether configuration with a weakly absorbing left-handed slab

The lateral shift of a TE-polarized beam reflected from the Kretschmann-Raether structure with a weakly absorbing left-handed slab is studied theoretically. It is shown that the lateral shift can be very large negative as well as positive near the resonant condition. These large negative and positive shifts can be one order of magnitude much larger than the shift from the corresponding nonabsorbing slab. As the absorption factor increases, the incident angle of producing largest lateral shift increases when the thickness is kept unchanged but the thickness of the slab of producing largest lateral shift decreases when the incident angle is kept unchanged.     

Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial

We present a bi-layer Y-shaped chiral metamaterial (CMM) that can realize a giant optical activity and circular dichroism (CD) effect to the incident linear polarization wave in the terahertz (THz) region. Numerical simulation results exhibit that the pronounced CD effect with a great difference between the transmission coefficients for the circularly polarized waves can be obtained at 5.06 THz, meanwhile the 90°-polarization rotation can be observed at 5.2 THz when a y-polarized wave is incident to this CMM propagating along the −z-axis. The mechanism of the optical activity and giant CD effect is illustrated by simulated surface current distributions. Further, the influences of the structural parameters of the proposed CMM to the optical activity and CD effect have been investigated numerically.     

A Simple Model for Measuring Refractive Index of a Liquid Based upon Fresnel Equations

Due to many experimental data required and a lot of calculations involved, it is very complex and cumbersome to model prism-based liquid-refractive-index-measuring methods. We develop a new method of mathematical modelling for measuring refractive index of a liquid based upon the Fresnel formula and prism internal reflection at an incident angle less than the critical angle. With this method, only two different concentrations measurements for a kind of solution can lead to the determination of computational model. Measurements are performed to examine the validity of the theoretical model. Experimental results indicate the feasibility of the theoretical model with an error of 1%. The method is also capable of measuring even smaller changes in the optical refractive index of the material on a metal surface by the surface plasma resonance sensing techniques.     

Microwave Experimental Observation of Transmitted Enhanced Goos--Hänchen Displacement in Symmetry-Double-Prism Configuration

It is theoretically proven that the transmitted Goos-Hiinchen （GH） displacement in the symmetry-double prism could be resonantly enhanced when the incident angle is less than but near the critical angle, and is modulated by the slab thickness between two prisms and the incident angle. This enhancement effect is directly observed in microwave experiments in which the incident angle is properly chosen. The measured data are in good agreement with the result of the numerical simulation.     

Rotations of eigenvibration direction in anisotropic crystals

The electric field of incident light induces dipoles in anisotropic media, vibrating in two perpendicular directions of the principal axes. Because of the tensor property of the dielectric constant, an induced dipole is subject to a torque, tending to rotate it about the axis parallel to the propagation direction. The directions of eigenvibration of the ordinary (o-ray) and extraordinary (e-ray) waves are no longer perpendicular in this sense. We propose here the relationships to describe the rotation of the induced dipole in the perpendicular electric fields. The rotation angles are found to increase with increasing dielectric constants and electric field strength of the incident light, exhibiting large values near the resonance frequencies in the infrared range at the azimuth angle /4 of the polarized incident light. Piezoelectric and ferroelectric crystals have a large value of the dielectric constant in the infrared frequency range. Rotations of the vibration direction of the o-ray and the e-ray waves are shown in the infrared transmission spectra recorded by incidence of the polarized light and transmission through piezoelectric and ferroelectric crystals (-quartz, LiNbO₃, and LiTaO₃). Interference of the o-ray and the e-ray waves transmitted through the crystals confirms the rotations of the vibration directions, a self-modulation effect of light in piezoelectric and ferroelectric crystals induced by the electric field of the propagating light.     

Boundary reflection from curved liquid surfaces and its application

A boundary light reflection from curved liquid surfaces was discovered. Due to the wetting effect, the liquid surface near the plate which was inserted into the liquid was deformed. When a collimated light beam vertically illumined the curved liquid surface, special reflective patterns of a strip-shape dark region in the center and the visibility interference fringes on both sides was observed for the up-curved liquid surface. The width of the dark region increases with the decreasing width of the incident beam. The relation of the dark region width and the incident beam width was derived theoretically. The slope and the height of curved liquid surface were obtained directly from measuring the dark central region width of the reflection pattern and the incident beam width. Furthermore, the analytic expression of the profile of the curved liquid surface was derived. As a result, it shows that an effective and practical technique for measuring the characterization of curved liquid surface was found.     

基于表面阻抗边界条件的等离子体薄涂层电磁散射的时域有限差分分析

基于表面阻抗边界条件时域有限差分(FDTD)方法研究了一维斜入射情况下非磁化等离子体薄涂层涂敷金属材料的电磁散射特性, 该方法忽略对薄层背景材料进行网格剖分, 大大减少了计算量. 首先推导了理想导体涂敷等离子体薄涂层的表面阻抗频域表达式, 然后代入边界条件并变换到时域, 再用分段线性递推卷积方法将时域表达式离散得到FDTD迭代式. 编程计算了垂直及斜入射情形下的平行极化和垂直极化反射系数, 通过验证算例与解析解对比, 结果表明该方法的准确性和有效性. 最后利用该方法分析了不同入射角对反射系数的影响.     

Two resonances effect for light transmission assisted with surface plasmon through perforated metal film

When light is incident on a nonplanar metal surface, an oscillating dipole is excited at the entrance openings. We show that the enhanced transmission assisted with surface plasmon (SP) through a perforated metal film results from two different SP resonances effects: (i) zero-order Fabry-Perot resonance effect where each air hole can be considered as a section of metallic waveguide, forming a low-quality-factor resonator, and many dipoles are arranged inside the nanoholes region; and (ii) structure-factor-induced charges self-tunnelling effect due to the well-recognized surface structure periodicity, where the positive or negative charges can respectively tunnel into the right surface through the metal walls. Furthermore, when light transmits through the double-layer perforated metal films, the different transport behaviors are also clearly shown, which convinces the existence of dual SP resonances effect.     

Numerical Investigation of Surface Plasmons Associated Subwavelength Optical Single-Pass Effect

Surface plasmons （SPs） associated optical single-pass effect has been investigated in novel subwavelength metallic structures, including single slit and grating structures. With influence of SPs, these metallic structures can enhance transmission in incident direction and suppress it in the opposite direction, exhibiting a single-pass effect. The finite difference time domain method is employed to study the influences of structure parameters on far-field transmission, near-field electric field distribution and extinction ratio of the single-pass transmission effect. A maximal extinction ratio of 47.83dB is achieved in the grating structure.     

Positively and negatively large Goos–Hänchen lateral displacements from a symmetric gyrotropic slab

A detailed study on the lateral displacements of a transverse magnetic (TM) wave transmitted and reflected from a symmetric gyrotropic slab is presented. We give the analytic formulas for the transmission coefficient and the reflection coefficient, as well as the corresponding lateral displacements. It is found that due to the external magnetic field the displacement of a transmitted beam is different from that of reflected one, even for a lossless symmetric configuration. Furthermore, within the chosen frequency band, when the incident angle is near the Brewster angle, the shift of a reflected wave can be large with nonzero reflectance, and can be positive or negative depending on the direction of the applied magnetic field and the incident wave.     

Unique properties of microwave in interlayer exchange-coupled trilayer ferromagnetic films associated with negative imaginary part of permeability

Based upon Landau-Lifshitz equation and Maxwell's equations, we theoretically investigated properties of normally incident microwave propagation in interlayer exchange-coupled trilayer ferromagnetic film. It is found that, near resonance frequency of optic mode, imaginary part of permeability of one ferromagnetic layer is smaller than zero unusually, i.e., the ferromagnetic layer may be taken as an active medium. Thus a number of unique electromagnetic properties are presented, such as, the ferromagnetic layer becomes a left-handed material near low side of the resonance frequency of optic mode, and both phase velocity and time-averaged Poynting flow of the usually defined forward wave are negative simultaneously near high side of the resonance frequency. This work provides a feasible active medium to demonstrate the unique microwave properties.     

Self-modulation of infrared waves in rutile

Electromagnetic waves carry angular and linear momentums and exert torques on anisotropic dielectrics, arising from the fact of the tensor property of the dielectric constant, that is, the direction of electric displacement is not parallel to the electric field vector of the incident light. The torque per unit volume exerted on a wave plate is given by P×E$\mathit{P}\times \mathit{E}$, where P is the polarization and E is the electric field, which induces the rotations of eigenvibration direction in the crystals. The rotation angles increase with the intensity of the incident light and the dielectric constant of the crystals. Because of the large dielectric constants, self-modulation of the incident light in the infrared frequency region was clearly demonstrated in the infrared transmission spectra of ferroelectric and piezoelectric crystals. Rutile (TiO₂) is a non-ferroelectric and non-piezoelectric crystal, but it also has the large dielectric constants. Rotations of the vibration direction of the ordinary (o-ray) and the extraordinary (e-ray) waves were shown in the infrared transmission spectra recorded by incidence of the plane-polarized light and transmission through a rutile plate. Interference of the o-ray and the e-ray waves transmitted through the crystals confirms the rotations of eigenvibration direction, a self-modulation effect of light in the crystal of large dielectric constants and large birefringence in the infrared range.