Evanescent waves in the magnetic field of an electric dipole

The magnetic field of radiation emitted by an electric dipole contains travelling and evanescent waves when represented as an angular spectrum. The evanescent waves decay exponentially away from the xy-plane, and will therefore not contribute to the detectable radiation in the far field, in general. It is well known, however, that in a small region around the z-axis the evanescent waves of the electric field do end up in the far zone. We have studied the corresponding magnetic evanescent waves, and we have found that the evanescent waves of the magnetic field do not contribute to the far zone in the neighbourhood of the z-axis. When considering the neighbourhood of the xy-plane, it appears that both the electric and magnetic evanescent waves end up in the far field, and the travelling and evanescent waves contribute equally to the radiation in the far zone. Close to the dipole the radiation field diverges, and we have shown that this is entirely due to the evanescent waves.     

Linear <Emphasis Type="Italic">s</Emphasis>-polarized surface waves in a medium inhomogeneous in one dimension

Linear s-polarized surface waves can exist at the boundary between an isotropic homogeneous medium and a medium inhomogeneous in one dimension (1D-inhomogeneous medium). This is related to deformation of the spatial envelope of the electric and magnetic components of the surface wave propagating in the 1D-inhomogeneous medium (in particular, in a plane-stratified medium). Such linear s-polarized surface waves can appear only provided that the refractive index of the inhomogeneous medium increases with the distance from the interface.     

Transmission of dipole radiation through interfaces and the phenomenon of anti-critical angles

Radiation emitted by an electric dipole consists of traveling and evanescent plane waves. Usually, only the traveling waves are observable by a measurement in the far field, since the evanescent waves die out over a length of approximately a wavelength from the source. We show that when the radiation is passed through an interface with a medium with an index of refraction larger than the index of refraction of the embedding medium of the dipole, a portion of the evanescent waves are converted into traveling waves, and they become observable in the far field. The same conclusion holds when the waves pass through a layer of finite thickness. Waves that are transmitted under an angle larger than the so-called anti-critical angle theta (1) ac are shown to originate in evanescent dipole waves. In this fashion, part of the evanescent spectrum of the radiation becomes amenable to observation in the far field. We also show that in many situations the power in the far field coming from evanescent waves greatly exceeds the power originating in traveling waves.     

Surface plasmon resonance spectroscopy based on evanescent field treatment

The reflectance in a surface plasmon resonance (SPR) curve can be expressed in terms of the integration of the product between the evanescent electric field and the imaginary part of the dielectric constant of all absorbing media. The evanescent field in the metal film consists of two fields, one originating at the prism/metal interface and the other at the metal/dielectric interface. Near the resonance angle, the evanescent field strength at the metal/dielectric interface is much greater than that at the prism/metal interface. The evanescent field in dielectric medium has a single origin at the metal/dielectric interface. Due to the optical enhancement at the interface, the amplitude of the evanescent electric field in the dielectric medium is much greater than that in the metal film. This field, however, is not being utilized in conventional SPR where changes in the refractive index of the nonabsorbing dielectric media are of interest. In a system with an absorbing dielectric medium, the absorption of the medium is enhanced by the strong evanescent electric field. The evanescent field distributions in the metal film and in the dielectric medium are significantly altered by the absorbing dielectric, which results in shifting of the resonance angle, increasing of the reflectance, and broadening of the SPR curve. Since the absorption contribution from the absorbing dielectric can be separated from that of the metal film via knowledge of evanescent field distribution, an in-depth analysis of the SPR curve of an absorbing medium and its relationship with the material characteristics are possible.     

The asymmetric lossy near-perfect lens

We extend the ideas of the perfect lens recently proposed [J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has a negative dielectric constant, with air on one side and other media such as glass or GaAs on the other side as an ‘asymmetric’ lossy near-perfect lens for p-polarized waves. It is found that retardation has an adverse effect on the imaging due to the positive magnetic permeability of silver, but we conclude that subwavelength image resolution is possible in spite of it.     

Reflection and refraction of plane waves at the interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and refraction of a plane wave incidence obliquely at the interface between piezoelectric and piezomagnetic media. The materials are assumed to be transversely isotropic. Numerical calculations are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, incidence of the coupled quasi-pressure (QP) and quasi-shear vertical (QSV) wave from BaTiO₃ or CoFe₂O₄ media, are discussed. The reflection and transmission coefficients and energy coefficients varying with the incident angle are examined. Calculated results are verified by considering the energy conservation. Results show that the reflected and transmitted wave fields in the sagittal plane consist of six kinds of waves, i.e. the coupled QP and QSV waves, evanescent electroacoustic (EA) and magnetic potential (MP) waves in the piezoelectric medium (BaTiO₃), evanescent magnetoacoustic (MA) and electric potential (EP) waves in the piezomagnetic medium (CoFe₂O₄), among which the EA, MA, MP and EP waves propagate along the interface. The most amount of the incident energy goes with the waves that are the same type as the incident wave, while the energy arising from wave mode conversion occupies a less part of the incident energy. The electric energy in BaTiO₃ is higher than the magnetic energy in CoFe₂O₄; they both attain their maximum values at/before the critical angle. Critical angles have little effect on evanescent waves except when the total reflection takes place. These results would provide useful complementary information for magnetoelectric composite materials.     

Electromagnetic waves in a magnetogyrotropic chiral medium

The propagation of electromagnetic waves in a magnetogyrotropic medium possessing chiral properties has been theoretically studied. Dispersion relations for the eigenmodes in such a medium are obtained and conditions necessary to realize a negative refractive index are established. The transmission of waves through a plane-parallel chiral plate is analyzed. A change in the polarization plane rotation with allowance for a dissipation in this system is determined.     

Power of a simple electric multipole of finite size

A simple electric multipole of finite size in the form of a spherical current sheet with a surface current density in the theta direction varying as sin 2theta is considered. The electromagnetic fields outside the spherical surface are of the same form as that of the corresponding point electric multipole situated at the origin and oriented in the z direction. The power is separated into the radiative and the reactive parts and compared with the separation made on the basis of propagating and evanescent waves. The evanescent waves contribute only to the reactive power, and the propagating waves contribute to both the radiative and the reactive powers. The power flux density is also separated into the real and the reactive parts, and the characteristics of the two parts of the power flux density are discussed.     

Propagation of axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

A new features on S-waves propagation in a nonhomogeneous anisotropic incompressible medium under influence of gravity field and initial stress with and without electromagnetic field and rotation

The present article is concerned with the investigation of the propagation of shear waves in a nonhomogeneous anisotropic incompressible medium under the effect of the electromagnetic field, gravity field, rotation, and initial stress taking into account a comparison between presence and absence of magnetic field, initial stress, and rotation. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, nonhomogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. Some special cases are also deduced from the present investigation. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, anisotropy, and rotation are very pronounced. Also, the absence of initial stress, magnetic field, and rotation tends to increasing of the S-waves velocity compared with presence of them.     

On the Properties of Surface Plasmon Polarization Beam Splitters

Abstract

The transmission and cross-coupling characteristics of a surface-plasmon-based polarization beam splitter with multimode interlay between two polished optical fibre blocks are presented. Through the continuous monitoring of the characteristics as a function of interlay refractive index and wavelength it was found that the device is symmetrical in terms of optical power coupling in the cross direction and asymmetrical in terms of transmission, with respect to input launch direction. The fibre fixed in the metal-coated block has a transverse electric (TE) mode transmission which is independent of the refractive index of interlay. The transmission of the other (uncovered) block shows resonance-type interaction for both TE and transverse magnetic modes owing to evanescent field coupling to the multimode interlay.     

Artificial dielectric medium possessing simultaneously negative permittivity and magnetic permeability

An artificial dielectric medium comprising two sublattices of spherical particles made of a high-dielectric-constant (high-ε) material, which are embedded into a low-ε dielectric matrix, are considered. Particles belonging to different sublattices have different diameters. It is shown that the properties of this composite structure are equivalent to those of an isotropic medium possessing a negative refractive index (n < 0) in the vicinity of frequencies at which the H ₁₁₁ and E ₁₁₁ oscillation modes exhibit simultaneous resonance in particles of different diameters, which leads to the appearance of electric and magnetic dipole moments, respectively. Averaging of these dipole moments over the volumes of cells formed by the corresponding spherical particles determines their contributions to the permittivity and magnetic permeability of the composite medium. At frequencies above the resonance, both contributions become negative and, hence, the medium exhibits simultaneously negative values of the permittivity and magnetic permeability. The proposed composite structure consists only of dielectric components. Spherical particles with ε_d > 200 can be made of a ferroelectric material.     

Vector diffraction problem of focusing a category 1 aberrated wavefront through a multilayered lossless medium

Abstract

In optical storage and other imaging applications, a laser beam is focused through a transparent lossless medium of different refractive index. Applications include optical and magneto-optical recording. It is highly likely that, in the near future, conventional magnetic recording will transition to optically/thermally assisted magnetic recording technology. In all these applications, it is necessary to ascertain the quality of the image formed by the focusing apparatus on an imaging surface when in the neighbourhood of the focus, the focused beam of light passes through a stratified lossless medium. This paper examines the vector diffraction problem of focusing radiation through a multilayered medium. The solution is accomplished by first deriving a general solution of the focusing problem in any homogenous medium. This solution is then used to obtain the solution in the multilayered medium by applying continuity of the electric and magnetic fields at the interfaces. The technique used here allows one to calculate the field quantities in the entire image space. Furthermore, the focusing lens may have Seidel aberrations of the fourth order. The salient feature of this method is that the vector diffraction problem is solved only once - for the zeroth layer, immediately next to the exit pupil. In the remaining layers, the results are obtained by solving linear algebraic equations. The solution of the algebraic equations is obtained in closed form.     

Electromagnetic diffraction of light focused through a stratified medium

We consider the focusing of light by a high-aperture lens into a stratified medium. The solution is based on our previously obtained results [J. Opt. Soc. Am. A 12, 325 (1995)], where we represented the illumination incident upon a plane interface between media with mismatched refractive indices as a sum of plane waves. The present solution is obtained in terms of plane waves, and it satisfies Maxwell's equations. The diffraction integrals are obtained in a form that is readily computable. We present numerical examples for some practical cases.     

Magnetic wave propagation in a periodic medium

The propagation of magnetic waves in an infinite medium with a periodic dielectric constant is studied as a simplified example to evaluate the applications of periodic structures. Specifically, the use of those structures for filtering and distributed feedback is investigated, and a new scheme for the generation of magnetic waves using drifting charges and a distributed feedback configuration similar to DFB lasers is studied in some detail.     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Solitons of the envelope of electromagnetic-spin waves in longitudinal magnetized infinite multiferroic medium

An unbounded longitudinal magnetized multiferroic medium possessing both electric and magnetic wave nonlinearities has been investigated. A nonlinear dispersion law has been established for the first time, and the solitons of the envelope of electromagnetic-spin waves propagating in this medium have been investigated. Studies have been carried out in both microwave and THz frequency ranges. It is shown that pulses can be nonlinearly compressed by a factor of more than 11.     

Torsional oscillations of an anisotropic semi-infinite space by an impulsive twist in the presence of a magnetic field

We study magneto-elastic torsional oscillations of an orthotropic, homogeneous semi-infinite space by an impulsive twist applied over some circular region of the free boundary. Taking displacement currents into account, expressions for the elastic displacement, induced magnetic and electric fields in the half space and free space are calculated. The magnetic field acting is supposed to be uniform and normal to the free surface z = 0 and is directed into the medium. It is shown that torsional oscillations develop into shear waves at a large distance from the region of the applied twist in the radial direction. Further it turns out that, when compared with the case of zero displacement current the present case is found to decrease the phase velocity. Expressions for the real phase velocity, attenuation constant, phase angle and the skin depth of each of the two modes, which are predominantly elastic and magnetic in character, are calculated. Results are compared with those available in the literature for some special cases of shear waves in an infinite medium and electro-magnetic waves in conductors.     

Modelling nanofiber Mach–Zehnder interferometers for refractive index sensors

In a single-mode silica nanofibre a large amount of the energy of the guided light is in the form of evanescent waves, making it possible to develop a novel sensing element with high sensitivity. Based on theoretical modelling, a highly-sensitive sensor employing a nanofibre-assembled Mach–Zehnder structure is suggested and investigated here. The sensor is used to measure the refractive indices of isopropyl alcohol (IPA) solutions of different concentrations. A phase shift of the guided mode, originating from the change of refractive index of the ambient medium, is obtained. In addition, the important parameters, including sensitivity and detection limit, are also estimated. The results show that Mach–Zehnder interferometric sensor based on nanofibres exhibits the capability of measuring an index variation of ～10^?6. Our simulations are helpful for studying and developing new miniaturised high-performance sensors with high sensitivity.     

Radiative transfer in a turbid medium with a varying refractive index: comment

In the literature one can encounter at least two different radiative transfer equations for media with spatially varying refractive indices. These are the results of Ferwerda [J. Opt. A Pure Appl. Opt. 1, L1 (1999)] and Tualle and Tinet [Opt. Commun. 228, 33 (2003)]. Accordingly, two different diffusion approximations are derived from these two radiative transfer equations. I reconsider the derivation of the radiative transfer equation in a medium with an inhomogeneous refractive index and confirm the result of Tualle and Tinet. In the diffusion approximation, a simple analytical solution has been found for the steady-state illumination of a non-absorbing turbid medium with a varying refractive index.