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.     

Far-field optical superlens

Far-field optical lens resolution is fundamentally limited by diffraction, which typically is about half of the wavelength. This is due to the evanescent waves carrying small scale information from an object that fades away in the far field. A recently proposed superlens theory offers a new approach by surface excitation at the negative index medium. We introduce a far-field optical superlens (FSL) that is capable of imaging beyond the diffraction limit. The FSL significantly enhances the evanescent waves of an object and converts them into propagating waves that are measured in the far field. We show that a FSL can image a subwavelength object consisting of two 50 nm wide lines separated by 70 nm working at 377 nm wavelength. The optical FSL promises new potential for nanoscale imaging and lithography.     

Comment on the paper: Evanescent waves do contribute to the far field

Abstract

In a series of papers [1], it has been claimed that evanescent waves contribute to the far field of a radiating dipole, i.e. that the amplitude of the sum of the evanescent waves decreases as 1/r with increasing distance, r, from the dipole. In spite of the fact that three recent papers [2] have demonstrated that these claims are incorrect and that they contradict well-established results relating to the farzone behavior of the angular spectrum representation of wavefields [3], the author continues to repeat this claim, most recently in a note with the title ‘Evanescent waves do contribute to the field’. It is the purpose of this note to point out an error in the previous publications [1] which has led to this erroneous conclusion.     

Numerical modelling of MHD waves in the solar chromosphere

Acoustic waves are generated by the convective motions in the solar convection zone. When propagating upwards into the chromosphere they reach the height where the sound speed equals the Alfvén speed and they undergo mode conversion, refraction and reflection. We use numerical simulations to study these processes in realistic configurations where the wavelength of the waves is similar to the length scales of the magnetic field. Even though this regime is outside the validity of previous analytic studies or studies using ray-tracing theory, we show that some of their basic results remain valid: the critical quantity for mode conversion is the angle between the magnetic field and the k-vector: the attack angle. At angles smaller than 30 degrees much of the acoustic, fast mode from the photosphere is transmitted as an acoustic, slow mode propagating along the field lines. At larger angles, most of the energy is refracted/reflected and returns as a fast mode creating an interference pattern between the upward and downward propagating waves. In three-dimensions, this interference between waves at small angles creates patterns with large horizontal phase speeds, especially close to magnetic field concentrations. When damping from shock dissipation and radiation is taken into account, the waves in the low-mid chromosphere have mostly the character of upward propagating acoustic waves and it is only close to the reflecting layer we get similar amplitudes for the upward propagating and refracted/reflected waves. The oscillatory power is suppressed in magnetic field concentrations and enhanced in ring-formed patterns around them. The complex interference patterns caused by mode-conversion, refraction and reflection, even with simple incident waves and in simple magnetic field geometries, make direct inversion of observables exceedingly difficult. In a dynamic chromosphere it is doubtful if the determination of mean quantities is even meaningful.     

Radiation from a current sheet at the interface between a conventional medium and anisotropic negative refractive medium

In this paper we investigate the radiation from a current sheet at the interface between semiinfinite isotropic positive refractive medium and anisotropic negative refractive medium. The distribution of the electric and magnetic fields in two regions and Poynting vectors associated with propagating and evanescent waves are calculated. The reasons for the singularity of the electric or magnetic field are briefly provided if the waves are evanescent in two media.     

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.     

Design of atomic mirror for silicon atoms

Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.     

Design of atomic mirror for silicon atoms

Abstract

Cook and Hill suggested that the gradient of an optical field can be used to reflect atoms. To reflect atoms, the repulsive dipole force is used, which comes from the interaction between the electric dipole moment of atoms and the evanescent field. The evanescent wave is generated when light is totally reflected internally at the interface of different refractive indices. Later, the way to enhance the evanescent wave with a thin dielectric waveguide has been reported. We designed the atomic mirror for silicon atoms, whose structure enhances the evanescent field that is used to repel silicon atoms. We also set up the equations of motion for silicon atoms and derive trajectories of the atoms reflected by the atomic mirror. Optical intensity, incident angle of the light, and effective detuning are described in terms of controlling the trajectory of the atom.     

Travelling and evanescent parts of the optical near field

Abstract

The optical near field of a localized source has been studied by means of the angular spectrum representation of the electromagnetic Green's tensor. This Green's tensor can be expressed in terms of four auxiliary functions, which depend on the field point through the dimensionless radial distance q to the source, or origin of coordinates, and the polar angle ρ with the z axis. Each function separates into a part containing travelling (radiative) waves and a part which is a superposition of evanescent (decaying) waves. We have derived series expansions in q of the four functions, both for the travelling and for the evanescent parts. It is shown that the travelling waves are finite at the origin of coordinates, and that all singular behaviour of the radiation field is governed by the evanescent waves. It is illustrated numerically that the series expansions are applicable up to about five wavelengths from the origin. In order to extend the range to also cover larger values of q, we have derived series expansions of the auxiliary functions which converge rapidly near the x-y plane, and a full asymptotic expansion with the z coordinate as the large variable. Finally, from the properties of the Taylor coefficients we have derived simple new integral representations for the auxiliary functions.     

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.     

Evanescent field in surface plasmon resonance and surface plasmon field-enhanced fluorescence spectroscopies

The highly sensitive nature of surface plasmon resonance (SPR) spectroscopy and surface plasmon field-enhanced fluorescence spectroscopy (SPFS) are governed by the strong surface plasmon resonance-generated evanescent field at the metal/dielectric interface. The greatest evanescent field amplitude at the interface and the maximum attenuation of the reflectance are observed when a nonabsorbing dielectric is employed. An absorbing dielectric decreases the evanescent field enhancement at the interface. The SPR curve of an absorbing dielectric is characterized by a greater reflectance minimum and a broader curve, as compared to those of the nonabsorbing dielectric with the same refractive index. For a weakly absorbing dielectric, such as nanometer-thick surface-confined fluorophores, the absorption is too small to induce a significant change in the SPR curve. However, the presence of a minute amount of the fluorophore can be detected by the highly sensitive SPFS. The angle with the maximum fluorescence intensity of an SPFS curve is always smaller than the resonance angle of the corresponding SPR curve. This discrepancy is due to the differences of evanescent field distributions and their decay characteristics within the metal film and the dielectric medium. The fluorescence intensity in an SPFS curve can be expressed in terms of the evanescent field amplitude. Excellent correlations between the experimentally measured fluorescence intensities and the evanescent field amplitudes are observed.     

Reply: On the evanescent field of dipole

Abstract

Recent controversy over the otherwise tuitional topic of separate contributions of evanescent and propagating waves in dipole radiation in free space has triggered a series of publications. I insisted on the use of changing plane-wave expansion for the decomposition, while other authors persisted on obtaining the field components with fixed plane-wave expansion.     

Anomalous propagation of elastic waves through a boundary between liquid and magnetoacoustic material

We consider a longitudinal acoustic wave incident onto a plane boundary between a liquid and a magnetoacoustic medium representing an antiferromagnetic material with anisotropy of the easy plane type, occurring in the vicinity of an orientational phase transition with respect to magnetic field. The directions of propagation and the amplitudes of reflected and transmitted longitudinal and transverse waves are determined. The possibility of an effective field control for the refraction angle and the wave type transformation is demonstrated. Beginning with a certain critical angle of incidence, the longitudinal and, eventually, the transverse waves in the magnetic medium become inhomogeneous and slide along the interface. If the magnetic material is sufficiently close to the phase transition point, the waves can be reirradiated into the liquid medium.     

Diffraction of evanescent plane waves by a resistive half-plane

Diffraction of evanescent plane waves by a resistive half-plane is examined. The scattering integrals are constructed with the modified theory of physical optics. These integrals are evaluated uniformly by using an unusual method. The scattered fields of evanescent waves are obtained by giving the angle of incidence a complex value. The diffracted waves are plotted numerically for different parameters of the incident field.     

Evanescent and propagating fields of a strongly focused beam

Evanescent- and propagating-field distributions from a strongly-focused-wave beam with subwavelength waist w(a) < lambda as a function of polar angle and distance are investigated. Exact amplitudes and intensities of evanescent E(ev) and propagating E(p) fields, including interference terms, are presented both in near- and far-field regions. It is shown that the amplitude of E(ev) decays as exp(-r/w(a)) in the near-field region and that evanescent waves do not contribute to the far field in the forward direction as they do in the transverse directions theta = pi/2, even though the oscillating evanescent field of the same strength but opposite in sign to the propagating field exists in the transverse plane.     

波浪从离岸防波堤上的反射和传递

该文用Rayleigh展开和阻抗分析研究水波从离岸堤上的反射和传递,所得公式比现有计算公式简单,在正向或小的入射角作用下的反射和传递特征与现有结果吻合很好。在波长大于波栅常数时,结构厚度对绕射的影响显著,呈现出增强传递现象,迅衰波的作用变弱。相反情况,结构厚度的影响可忽略,迅衰波的作用明显。     

Diffraction effects in the propagation of radiation in polarizable layers

The very low transmission of light through holes smaller than the wavelength has been found to be enhanced for subwavelength apertures in metallic surfaces with periodic corrugations. This effect has been attributed to the interaction of light with surface plasmons. Similar effects obtained subsequently for non-metallic surfaces have been attributed to evanescent waves on the surface produced by the diffracted Bloch waves from different points in the array. We present an exact solution of Maxwell's equations in the discrete dipole approximation (DDA) for a periodic array of polarizable point dipoles in a layer. Metallic as well as non metallic layers are described. When the wavelength is smaller than the lattice period there is a Bragg's scattered wave, while for subwavelength conditions an evanescent wave on the surface appears. The transmission/reflection coefficients are found to oscillate as a function of frequency, with resonances occurring in a broad range of frequencies depending on the polarizability, at which the evanescent field is enhanced. A detailed study is presented for nanostructured arrays. We find that this model agrees with features observed in experiments through hole arrays supporting the role played by diffraction during light transmission through such arrays without invoking surface plasmons and providing a base to analyze more complex geometries.     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.     

Surface waves and atomic force microscope probe-particle near-field coupling: discrete dipole approximation with surface interaction

Evanescent waves on a surface form due to the collective motion of charges within the medium. They do not carry any energy away from the surface and decay exponentially as a function of the distance. However, if there is any object within the evanescent field, electromagnetic energy within the medium is tunneled away and either absorbed or scattered. In this case, the absorption is localized, and potentially it can be used for selective diagnosis or nanopatterning applications. On the other hand, scattering of evanescent waves can be employed for characterization of nanoscale structures and particles on the surface. In this paper we present a numerical methodology to study the physics of such absorption and scattering mechanisms. We developed a MATLAB implementation of discrete dipole approximation with surface interaction (DDA-SI) in combination with evanescent wave illumination to investigate the near-field coupling between particles on the surface and a probe. This method can be used to explore the effects of a number of physical, geometrical, and material properties for problems involving nanostructures on or in the proximity of a substrate under arbitrary illumination.     

Traveling and evanescent parts of the electromagnetic Green's tensor

The angular spectrum representation of the electromagnetic Green's tensor has a part that is a superposition of exponentially decaying waves in the +z and -z directions (evanescent part) and a part that is a superposition of traveling waves, both of which are defined by integral representations. We have derived an asymptotic expansion for the z dependence of the evanescent part of the Green's tensor and obtained a closed-form solution in terms of the Lommel functions, which holds in all space. We have shown that the traveling part can be extracted from the Green's tensor by means of a filter operation on the tensor, without regard to the angular spectrum integral representation of this part. We also show that the so-called self-field part of the tensor is properly included in the integral representation, and we were able to identify this part explicitly.