The evanescent waves named as EW1, EW2, EW3 are described in 3 respective experimental setups: 1) total internal reflection; 2) scattering on an inhomogeneous planar target; and 3) propagation along a waveguide. Some interactions are considered between EW2 and the environment. The latter may include a beam of probing particles and/or the screen on which the EW2 are formed. Some new properties of EW are described, such as complex energy eigenvalues in case of a movable screen, and evanescence exchange between the interacting objects. This reveals the connection between evanescent states and the Gamow states of the studied system. The 4-momentum exchange between EW2 and the probe is highly selective and may collapse the superposition of studied EW2- eigenstates to a single EW-eigenstate of the probing particle. Possible imprints of EW2 in the far field are briefly discussed and a simple experiment is suggested for their observation. .
The evanescent waves named as EW1, EW2, EW3 are described in 3 respective experimental setups: 1) total internal reflection; 2) scattering on an inhomogeneous planar target; and 3) propagation along a waveguide. Some interactions are considered between EW2 and the environment. The latter may include a beam of probing particles and/or the screen on which the EW2 are formed. Some new properties of EW are described, such as complex energy eigenvalues in case of a movable screen, and evanescence exchange between the interacting objects. This reveals the connection between evanescent states and the Gamow states of the studied system. The 4-momentum exchange between EW2 and the probe is highly selective and may collapse the superposition of studied EW2- eigenstates to a single EW-eigenstate of the probing particle. Possible imprints of EW2 in the far field are briefly discussed and a simple experiment is suggested for their observation. .
The evanescent states are common in the electro-magnetic environments,it's basic feature is the field strength decrease according to the exponential law from orginal position to far away.The electro-magnetic waves propagate through the reactive medium are common situations,corresponding wave propagation in the guided wave modes,dispersion mediums,and the ionic gases.In 1897,Lord Rayleigh's calculation predicated the evanescent states appear to propagate in rectangular metal waveguides.In order to analyze the phenomenon of waveguide below cut-off(WBCO),it seems that the evanescent states have a imaginary wave vector(a imaginary wave number).And so,we can say it is like a standing wave,the variation of field occurs in every position simultaneously,this means that they do not experience a phase shift in propagate direction.But the behaviour of WBCO was a bit strange,sometimes the phase constant β is negative,then in THz experiments the pulse delay is negative.Although the phase velocity of waveguide to be superluminal is well-known,the theoretical discussion does not explain why the phase velocity and the phase refractive index becomes negative.In quantum mechanics(QM),in barrier the evanescent states also have a imaginary wave parame-ter.This state can be explained by the Schrdinger equation,it is analogy with the Helmholtz equation in classical electro-magnetic theory.In practice,quantum tunnelling is the most popular physical process,it can be observed in many cases: the propagation of the graded index optical fiber,the two glass prisms of Bose experiment,etc.In scientist's opinion,to defy the light-speed limit is possible;for example,photons tunnel across a gap between two prisms yet arrive at same time as reflected photons that travelled a shorter distance,that means an ultra-fast transit between the two prisms:so much faster than the speed of light.As well-known,we are used the virtual particles in microscopic interaction processes since R.Feynman,but now we perhaps demonstrated here an example in the macroscopic range of a meter since G.Nimtz's experiment.
After a brief introduction to the field of atom optics and to atomic mirrors, we present experimental results obtained in our group during the last two years while studying the reflection of rubidium atoms by an evanescent wave. These involve the first measurement of the van der Waals force between an atom in its ground state and a dielectric wall, as well as the demonstration of a reflection grating for atoms at normal incidence. We also consider the influence of quantum reflection and tunnelling phenomena. Further studies using the atomic mirror as a probe of the van der Waals interaction, and of very small surface roughness are briefly discussed.
Any discussion of the nature of light must include a reminder that whenever we make the observation of light (photons), we only observe particle-like properties. This paper provides a reiteration that we don't need wave-like properties to scattered photons to describe phenomena such as diffraction or refraction of light. This paper updates the original ideas of Duane, later revived by Lande, which provided a description of light diffraction without making reference to a wave nature. These are updated using terminology more common to quantum electrodynamics which describes the interaction of particles in terms of the exchange of virtual photons. Diffraction is described in terms of an ensemble of distinct, probability weighted paths for the scattered photons. The scattering associated with each path results from the quantized momentum exchange with the scattering lattice attributed to the exchange or reflection of virtual photons. The probability for virtual particle exchange/reflection is dependent upon the allowed momentum states of the lattice determined by a Fourier analysis of the lattice geometry. Any scattered photon will exhibit an apparent wavelength inversely proportional to its momentum. Simplified, particle-like descriptions are developed for Young's double slit diffraction, Fraunhofer diffraction and Fresnel diffraction. This description directly accounts for the quantization of momentum transferred to the scattering lattice and the specific eigenvalues of the lattice based upon the constraints to virtual photon exchange set by the Uncertainty Principle, Δπi = h/ζi.
When light scatters from an object, it can impart some physical quantity such as momentum or angular momentum. This can act as a measurement on the photon, which collapses on to an eigenstate of the measurement operator. However the corresponding operator is not the same as that describing the total linear or angular momentum in free space. Optical eigenmodes provide a powerful method to describe this interaction by expanding the field as a linear combination of some basis modes and examining the eigenvalues and eigenvectors of the quadratic measure in question. We extend this to the quantum case by writing the quantum operator corresponding to a given measurement such as energy, momentum or angular momentum as a superposition of creation and annihilation operators for each eigenmode. Upon measurement we find that the possible states of a single photon are simply the classical eigenmodes of the measurement. As an application, we examine the force and torque on a general, possibly anisotropic, material. By looking at eigenvalues of the measurement operator we show that the amount of a given quantity transferred in an interaction with matter is not in general the expected amount which a photon carries in free space, even at the single photon level. In particular the difference in linear or angular momentum from before and after is in general not equal to ~k or ~ which are the eigenvalues of these quantities in free space.
Simultaneous observation of the wave and particle natures of a quantum object under one experimental arrangement represents the latest development regarding wave-particle duality. In this work, we propose a simple scheme using linear-optics devices to observe either the particle nature or wave nature or the wave-particle superposition (WPS) of photons by controlling a relevant classical parameter. Our setup consists of two stages, the preparation and measurement stages, with the latter stage containing an additional classical variable whose value will be given only after the first stage in order to avoid any possible communication between the two stages and thus rule out the classical hidden-variable model. We not only develop the theory but also perform the corresponding experiments. The experimental observations perfectly agree with the theoretical predictions. Our findings are the following. The frequency (wavelength) of both single- and two-photon systems is independent of whether the photon(s) is wavelike or in a WPS state, with the common fact being that the frequency (wavelength) of two photons as a whole entity is twice (half) that of a single photon. As for the interference-pattern visibility, it is always lower in the case of WPS than in the case of a wavelike state for a single photon as well as for two photons. Remarkably, with a given value of the control parameter, the interference visibility in the case of WPS is always higher in the single-photon scenario than in the two-photon one. Although here we are dealing with photons, the obtained results apply equally well to matter particles.
Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tunneling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.