On the refractive index for a nonmagnetic two-component medium: Resolution of a controversy

The refractive index of a dielectric medium comprising both passive and inverted components in its permittivity was determined using two methods: (i) in the time-domain, a finite-difference algorithm to compute the frequency-domain reflectance from reflection data for a pulsed plane wave that is normally incident on a dielectric half-space and (ii) in the frequency-domain, the deflection of an obliquely incident Gaussian beam on transmission through a dielectric slab. The dielectric medium was found to be an active medium with a negative real part for its refractive index. Thereby, a recent controversy in the scientific literature was resolved.     

Transformation of a Gaussian light beam reflected in the vicinity of the Brewster angle

Variations in the profile and shift of a Gaussian light beam upon reflection from a plane interface between a transparent dielectric and a medium with a complex refractive index are studied. The beam is assumed to be incident at angles close to the Brewster’s angle, where the effects of transformation of the beam profile are most substantial. Based on numerical analysis, the reflected beam profiles are obtained for different properties of the media, parameters of the incident beam, and positions of the plane of observation.     

Peculiarities of light beam reflection from the boundary of a 1D-photonic crystal

Typical cases of lateral shift and deformation of the profile of two-dimensional light beams reflected from the surface of a one-dimensional photonic crystal are considered. We use harmonic modulation of the spatial dependence of dielectric permeability of a crystal, which permits one to study reflectance profiles analytically. The results of numerical calculations that were performed are presented for the cases when the angular spectrum of the incident beam is split.     

Goos–H?nchen shift at an interface of a composite material: effects of particulate clustering

The Goos–H?nchen (GH) shift of a p-polarized light beam reflected from an interface of a composite material of particulate metals in a dielectric host is studied theoretically using effective medium approaches, with focus on the effects due to the clustering of the metal particles. With application of a fractal-clustering model, it is shown that the composite can have optically metallic behavior even for relatively low volume fraction of metal when clustering takes place, with appreciable negative GH shifts to take place for light of long wavelengths close to grazing incident angles. Furthermore, we confirm that large reflectance is always accompanied with this metal behavior, thus rendering these shifts easily observable.     

Nonlinear reflection of a femtosecond spectral supercontinuum

The spatio-temporal spectrum of optical radiation reflected from a nonlinear dielectric medium with nonresonant dispersion is obtained as a function of the parameters of the spatio-temporal spectrum of a paraxial light beam incident on the boundary of the medium at small angles. Nonlinear reflection of various types of femtosecond spectral supercontinua from the interface between air and fused silica is simulated. It is shown that the time duration and the transverse dimensions of a beam of multiple-frequency radiation generated during the reflection of a superposition of high-intensity fields of two few-cycle pulses with different central wavelengths may be smaller than those of incident ultrashort pulses.     

New mechanism of the schoch effect in nonmagnetic dielectrics

A new type of a linear relation between the components of the magnetic field vector and those of the elastic strain tensor (a dynamic piezomagnetic interaction) is proposed. This relation is irrespective of the crystal symmetry and of the presence of a magnetic structure in the dielectric medium. This leads to anomalies in the reflection of a beam of shear bulk waves incident from the depth of the nonmagnetic dielectric medium on either its mechanically free surface or its slip boundary with a semibounded magnetic medium.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

Reflections of light by the gradient of refractive-index distributions

We report the results of observation of weakly luminous rays produced by the gaussian beam incidence on the surface of inhomogeneous dielectric materials. These rays are experimentally distinguished from the ordinary geometrical optics rays that are reflected at the air-dielectric interface. The results are consistent with the theoretical prediction that the luminous phenomenon is caused by the reflection of the incident ray at every point in the inhomogeneous medium.     

Dual-beam-reflection phenomenon due to leaky modes in a photonic band gap

We show a dual-beam-reflection phenomenon for a Gaussian beam illuminating a hybrid structure of a dielectric waveguide and photonic crystal (WG-PC) inside the photonic band gap by numerical simulations. One reflection beam has a giant negative lateral shift, but the other has a positive lateral shift. The finite-difference time-domain (FDTD) simulations show that this phenomenon has a time delay effect and comes from the leaky surface mode of the hybrid structure. Field profile of the leaky mode demonstrates a strong localized stationary field in the higher dielectric medium. Furthermore, the maximum lateral shift is almost two times of the waist of the incident beam.     

Reflected image of a strongly focused spot

We describe the reflection of a strongly focused beam from an interface between two dielectric media. If the beam is incident from the optically denser medium, the image generated by the reflected light is strongly aberrated. This situation is encountered in high-resolution confocal microscopy and data sampling based on solid immersion lenses and oil immersion objectives. The origin of the observed aberrations lies in the nature of total internal reflection, for which there is a phase shift between incident and reflected waves. This phase shift displaces the apparent reflection point beyond the interface, similarly to the Goos-H?nchen shift.     

Technique to Estimate the Reflectance of a High-Reflectance Dielectric Multilayer Coating Mirror Using Incident Beam Angular Dependence of Its Transmittance

The reflectance of a high-reflectance dielectric multilayer coating mirror tuned to a monochromatic laser wavelength was estimated from its transmittance which was measured with 0.4 ppm accuracy. The transmittance was calculated from its theoretical formula including three parameters (refractive indexes of low and high refractive films (n_L, n_H) and a number of layer units composed of a pair of one low and one high refractive film (N)) which were estimated from the incident beam angular dependence curve of the transmittance. This calculated transmittance agreed with that measured as a ratio of the laser beam power before and after the mirror with 6 ppm difference.     

Interference approach applied to dual-grating dielectric resonant grating reflection filters

The resonant mechanisms associated with dual-grating dielectric resonant grating reflection filters are described by use of an interference approach. These structures consist of two modulated regions of equal period separated by a higher-index film region. We show that the spectral linewidth is dependent on the separation between the modulated regions and can range from theoretically zero to approximately four times what would be obtained by use of a single-grating geometry.     

The TEM101 mode laser beam—A powerful tool for optical levitation of various types of spheres

We point out in this paper that a TEM¹₀₁ mode laser beam is convenient to stably levitate either solid or hollow dielectric spheres or metallic ones. Except a sufficient incident flux, there is no stability condition required to levitate solid transparent spheres having a refractive index larger than the one of the surrounding medium. According to the beam and sphere diameters, the equilibrium position will be centered on the beam axis or off-axis. In the case of hollow dielectric or metallic spheres, the lateral stability requires specific conditions on sphere and beam diameters. These conditions are discussed and then experimentally shown by performing optical levitation of these various kinds of spheres either in vertical or in horizontal beams.     

Transverse or off-axis localization of electromagnetic waves in random one- and two-dimensional dielectric systems which are periodic on average

We study the transverse or off-axis localization of electromagnetic waves for several different random dielectric systems which are periodic on average. Unlike previous scalar wave treatments of transverse localization, in the present work we present results based on a full vector treatment of the electromagnetic fields based on Maxwell's equations. In a first system, we consider a random semi-infinite array of slabs with plane waves or finite beams of electromagnetic waves obliquely incident on the slab surfaces. The localization of the fields in a region near the surface of illumination is studied as a function of the oblique angle of incidence. In a second system, an array of semi-infinite slabs with random thickness is considered with an incident finite beam of electromagnetic waves initially directed parallel to the slab surfaces. The spreading of the beam width is computed as it propagates through the array of semi-infinite slabs. In a final system, we consider a semi-infinite array of random dielectric rods (2D system) with obliquely incident plane waves. The localization length of the plane-wave fields is computed as a function of the oblique angle of incidence and as a function of the strength of the disorder of the dielectric medium. All the random media we consider, when averaged over their randomness, are periodic on average. The above systems are studied for both p- and s-polarizations of incident electromagnetic waves, and the difference in the transverse localization of the electromagnetic field for these two polarizations is determined.     

平面电磁波在任意方向运动的介质-介质界面上的反射和透射

研究平面电磁波从一种介质入射到另一种以任意方向运动的介质时,在介质界面上发生的反射和透射现象,从Maxwell方程组、运动界面的边值关系和运动介质的本构关系出发,得到了反射波和透射波电磁场矢量与入射波电磁场矢量的关系的表达式、反射和透射系数,讨论了反射波、透射波与入射波之间的能量关系,电磁波对运动介质作用力的性质,并得出一些新的结论． 关键词：     

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method. Based on the plane-wave angular spectrum expansion and Fresnel approximation, the analytical expressions of the reflected field, internal field as well as transmitted field in each region are obtained. Through numerical simulations, the intensity distributions of the incident beam, reflected beam, internal beam as well as transmitted beam are presented at oblique incidence. Besides, we also compare the intensity distributions of the geometrical-optics beam field, the first order beam mode field and the actual beam field, which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab. Meanwhile, the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated. Finally, the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail. The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.     

Reflectance of an array of charged conducting layers

The theoretical reflectance of a charged conducting layer and an array of layers is studied using a hydrodynamic model. In both cases, the reflectance depends strongly on the polarization of the incident radiation and the angle of incidence. When the wavelength is long compared to the spacing between layers, the layered array behaves like an anisotropic continuum. Refraction suppresses the anisotropy of the medium when the background dielectric constant is large, because the direction of wave propagation is nearly perpendicular to the layers even for large angles of incidence.Research sponsored in part by U.S. Air Force grant no. AFOSR-74-1576. ITP-492.     

Manipulating light flow with one-dimensional photonic crystals of an electromagnetically induced transparency medium

The band structures and equifrequency contours of one-dimensional photonic crystals (PCs), which consist of an electromagnetically induced transparency (EIT) medium and a common dielectric medium, can be dramatically changed by tuning the coupling field intensity (or coupling Rabi frequency, CRF) of the EIT medium. It is found that for a probe light at a fixed frequency, either positive or negative refraction in the EIT PC can be realized with a proper CRF. The behavior of a Gaussian beam (probe light) obliquely incident on such an EIT PC slab is simulated numerically. The probe light beam transmitted from the slab can be shifted transversely in a large range, and negative refraction enhances this effect. The present scenario can be applied in some areas such as quantum optical and photonic device designs.     

Reflection and transmission of Laguerre Gaussian beam from uniaxial anisotropic multilayered media

Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.     

Negative refraction and the spectral filtering of terahertz radiation by a photonic crystal prism

We demonstrate how micromachined photonic crystals can be used to negatively refract terahertz frequency light. The photonic crystals, which are constructed from conventional dielectric materials, manipulate the incident beam via interaction with their photonic bands. Consequently, we show that different components of a broadband beam incident on the structure may be positively or negatively refracted, depending upon its frequency and that the structure can be used as an effective spectral filter of THz radiation.