Evanescent wave

In electromagnetics, an evanescent field, or evanescent wave, is an oscillating electric and/or magnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated in the vicinity of the source (oscillating charges and currents). Even when there is a propagating electromagnetic wave produced (e.g., by a transmitting antenna), one can still identify as an evanescent field the component of the electric or magnetic field that cannot be attributed to the propagating wave observed at a distance of many wavelengths (such as the far field of a transmitting antenna). A hallmark of an evanescent field is that there is no net energy flow in that region. Since the net flow of electromagnetic energy is given by the average Poynting vector, this means that the Poynting vector in these regions, as averaged over a complete oscillation cycle, is zero. In many cases one cannot simply say that a field is or is not evanescent. For instance, in the above illustration energy is indeed transmitted in the horizontal direction. The field strength drops off exponentially away from the surface, leaving it concentrated in a region very close to the interface, for which reason this is referred to as a surface wave. However, there is no propagation of energy away from (or toward) the surface (in the z direction), so that one could properly describe the field as being 'evanescent in the z direction'. This is one illustration of the inexactness of the term. In most cases where they exist, evanescent fields are simply thought of and referred to as electric or magnetic fields, without the evanescent property (zero average Poynting vector in one or all directions) ever being pointed out. The term is especially applied to differentiate a field or solution from cases where one normally expects a propagating wave. Everyday electronic devices and electrical appliances are surrounded by large fields, which have this property. Their operation involves alternating voltages (producing an electric field between them) and alternating currents (producing a magnetic field around them). The term 'evanescent' is never heard in this ordinary context. Rather, there may be concern with inadvertent production of a propagating electromagnetic wave and thus discussion of reducing radiation losses (since the propagating wave steals power from the circuitry) or interference. On the other hand, 'evanescent field' is used in various contexts where there is a propagating (even if confined) electromagnetic wave involved, to describe accompanying electromagnetic components which do not have that property. Or in some cases where there would normally be an electromagnetic wave (such as light refracted at the interface between glass and air) the term is invoked to describe the field when that wave is suppressed (such as with light in glass incident on an air interface beyond the critical angle). Although all electromagnetic fields are classically governed according to Maxwell's equations, different technologies or problems have certain types of expected solutions, and when the primary solutions involve wave propagation the term 'evanescent' is frequently applied to field components or solutions which do not share that property. For instance, the propagation constant of a hollow metal waveguide is a strong function of frequency (a so-called dispersion relation). Below a certain frequency (the cut-off frequency) the propagation constant becomes an imaginary number. A solution to the wave equation having an imaginary wavenumber does not propagate as a wave but falls off exponentially, so the field excited at that lower frequency is considered evanescent. It can also be simply said that propagation is 'disallowed' for that frequency. The formal solution to the wave equation can describe modes having an identical form, but the change of the propagation constant from real to imaginary as the frequency drops below the cut-off frequency totally changes the physical nature of the result. The solution may be described as a 'cut-off mode' or an 'evanescent mode';:360 while a different author will just state that no such mode exists. Since the evanescent field corresponding to the mode was computed as a solution to the wave equation, it is often discussed as being an 'evanescent wave' even though its properties (such as not carrying energy) are inconsistent with the definition of wave. Although this article concentrates on electromagnetics, the term evanescent is used similarly in fields such as acoustics and quantum mechanics where the wave equation arises from the physics involved. In these cases, solutions to the wave equation resulting in imaginary propagation constants are likewise termed 'evanescent' and have the essential property that no net energy is transmitted even though there is a non-zero field. In optics and acoustics, evanescent waves are formed when waves traveling in a medium undergo total internal reflection at its boundary because they strike it at an angle greater than the so-called critical angle. The physical explanation for the existence of the evanescent wave is that the electric and magnetic fields (or pressure gradients, in the case of acoustical waves) cannot be discontinuous at a boundary, as would be the case if there was no evanescent wave field. In quantum mechanics, the physical explanation is exactly analogous—the Schrödinger wave-function representing particle motion normal to the boundary cannot be discontinuous at the boundary. Electromagnetic evanescent waves have been used to exert optical radiation pressure on small particles to trap them for experimentation, or to cool them to very low temperatures, and to illuminate very small objects such as biological cells or single protein and DNA molecules for microscopy (as in the total internal reflection fluorescence microscope). The evanescent wave from an optical fiber can be used in a gas sensor, and evanescent waves figure in the infrared spectroscopy technique known as attenuated total reflectance.