Lorentz-boosted evanescent waves

Polarization, spin, and helicity are important properties of electromagnetic waves. It is commonly believed that helicity is invariant under the Lorentz transformations. This is indeed so for plane waves and their localized superpositions. However, this is not the case for evanescent waves, which are well-defined only in a half-space, and are characterized by complex wave vectors. Here we describe transformations of evanescent electromagnetic waves and their polarization/spin/helicity properties under the Lorentz boosts along the three spatial directions.     

Helicity and evanescent waves

It is shown that the projection of the angular momentum of a circularly polarized electromagnetic evanescent wave along the mean velocity of energy transport (= helicity) can be reverted by a Lorentz transformation, in spite of the fact that this velocity is c.     

Huygens-Fresnel diffraction and evanescent waves

Based on a modified Huygens-Fresnel principle valid in the near field, we analytically verify the exponential wave decay of evanescent waves. This field decay along the propagation direction can be considered as the result of interference between elementary oscillating dipole sources rather than point sources. Specific examples where the modified Huygens-Fresnel principle is applicable are also examined. In particular, the diffraction through a single nano-slit, as well as, the propagation of an engineered input leading to a subwavelength focus are presented.     

Tunneling of evanescent waves into propagating waves

The tunneling of evanescent waves into propagating waves is related to the convolution of the high spatial frequencies of the source with those of the detectors. Such an approach is demonstrated by treating the evanescent waves which are diffracted from very narrow apertures in a plane screen (with dimensions much smaller than the wavelength) and are converted to propagating waves by tip detectors. The mechanism responsible for the conversion of evanescent waves into propagating waves is explained and a general formula for the conversion of evanescent waves into propagating waves is derived. PACS 42.25.Fx; 42.30.Kq; 42.25.Bs     

Shock waves in nanomechanical resonators

We study the formation of shock waves in a nanomechanical resonator with an embedded two-dimensional electron gas using surface acoustic waves. The mechanical displacement of the nanoresonator is read out via the induced acoustoelectric current. Applying acoustical standing waves, we are able to determine the so-called anomalous acoustocurrent. This current is found only in the regime of shock wave formation.     

Focusing of evanescent vector waves

We study focusing of two and three-dimensional evanescent vector waves, with a particular emphasis on identifying suitable intensity structures for applications in optical data storage. For two-dimensional evanescent waves large transverse spatial wave vectors result in purely circularly polarized evanescent states. We suggest that these may have applications in all-optical data storage through the inverse Faraday effect. On the other hand, for three-dimensional evanescent waves longitudinally polarized modes are observed to give the most tightly focused spot, and this may be utilized to confine light behind a solid immersion lens.     

Anomalous propagation characteristics of evanescent waves

An analysis is done of the crossing of a forbidden region in a thin plate by a backward propagating Lamb wave: the refraction/reflection effects undergone by the coupled modes produced at each boundary of the forbidden region are taken into consideration, as well as the penetration of the backward wave as an evanescent wave. The outcome of the acoustic perturbation is analysed for a few angles of incidence and experiments are performed that confirm the theoretical predictions.     

Transmission enhancement by conversion of evanescent waves into propagating waves

The convolution between spatial modes of two different parts of an optical system can convert evanescent waves into propagating waves. This principle is applied to different optical systems for analyzing various effects in transmission enhancements experiments. We discuss here the differences between the present principle which is related to broadening of resonances and the near-field optical microscopy based on a tunneling effect by a tip detector. The present analysis is applied in particular to two systems: a) transmission enhancement in one slit by coupling the transmitted radiation with transversal Fabry–Pérot electromagnetic (EM) modes, and b) transmission enhancement by coupling between a metallic film with arrays of holes and surface plasmons (SP). The present approach gives more information on transmission enhancement phenomena than that obtained by conventional treatments and can also solve certain disagreements between different theories. The differences between the present process of converting evanescent waves into propagating waves, and that related to the new development of getting a super-resolution by an hyperlens are discussed. PACS 41.20.Jb; 73.20.Mf; 42.79.Dj     

Theory of atomic diffraction from evanescent waves

We review recent theoretical models and experiments dealing with the diffraction of neutral atoms by a reflection grating, formed by a standing evanescent wave. We analyze diffraction mechanisms proposed for normal and grazing incidence, point out their scopes and confront the theory with experiment. Received: 12 June 1999 / Published online: 8 September 1999     

Evidence for quantized displacement in macroscopic nanomechanical oscillators

We report the observation of discrete displacement of nanomechanical oscillators with gigahertz-range resonance frequencies at millikelvin temperatures. The oscillators are nanomachined single-crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. With this novel design, femtometer-level displacement of the frequency-determining element is amplified into collective motion of the entire micron-sized structure. The observed discrete response possibly results from energy quantization at the onset of the quantum regime in these macroscopic nanomechanical oscillators.     

Diffraction of bending waves

This paper is a discussion of the theory of diffraction and scattering of bending waves by mass-impedance loadings of an infinite plane plate. Emphasis is placed on the case of heavy loadings, at which deflexions of the plate are precluded and the scattering is the strongest possible. Examples treated in detail include the diffraction grating, diffraction by a semi-infinite rib, and diffraction by a comb of semi-inifinite ribs.     

From evanescent waves to specified diffraction orders

A grating was designed to convert an evanescent wave into propagating diffraction orders that fulfill a specified optical function.     

Scattering and extinction of evanescent waves by small particles

Received: 14 May 1998/Revised version: 31 July 1998     

Lateral resolution enhancement with standing evanescent waves

A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM). By use of a total-internal-reflection geometry, standing evanescent waves are generated that spatially modulate the excitation of the sample. An enhanced two-dimensional image is formed from a weighted sum of images taken at different phases and directions of the standing wave. The performance of such a system is examined through theoretical calculations of both the point-spread function and the optical transfer function.     

The almost perfect lens and focusing of evanescent waves

We propose a general method for evaluating the field in the focal region of nearly perfect one-dimensional lenses, and study how evanescent waves contribute to the electric field behind subwavelength apertures. The approach presented here may give a better insight into how to shape and focus evanescent waves.     

Amplification of acoustic evanescent waves using metamaterial slabs

We amplified acoustic evanescent waves using metamaterial slabs with a negative effective density. For the amplifying effect of the slab to overcome the dissipation, it is necessary that the imaginary part of the effective density is much smaller than the real part, a condition not satisfied so far. We report the construction of membrane-based two-dimensional negative-density metamaterials which exhibited remarkably small dissipation. Using a slab of this metamaterial we realized a 17-fold net amplitude gain at a remote distance from the evanescent wave source. Potential applications include acoustic superlensing.     

Using the atomic force microscope as a nanomechanical partner to support evanescent field imaging

Quantum Dot (QD)/microsphere structures supporting Whispering Gallery Modes (WGMs) are attached to Atomic Force Microscope (AFM) cantilevers for characterization of the evanescent field around the QD/microsphere and utilization of the evanescent field for sensing at the apical surface of live cells. Following laser excitation, QD emission couples to WGMs that circumnavigate the microsphere via total internal reflection at the internal surfaces of the microsphere. The resulting evanescent field is characterized utilizing the high spatial control of an AFM in approaching a dye monolayer on a test surface. The measured evanescent field extends approximately 50 nm from the microsphere surface, matching theoretical predictions. This system was then used to sense the accumulation of integrin and formation of focal adhesions at the apical surface of cells.     

Analysis of spectral characteristics of scattering of evanescent waves

The spectral scattering characteristics of nanoscale particles exhibited in the field of evanescent waves are analyzed using the method of discrete sources. The effect of various parameters on the behavior of the scattering characteristics is studied. The material of the particles is shown to have the most substantial effect on the scattering cross section.