evanescent wave: one construct, many systems

In optics an evanescent wave is the non-propagating field that persists just beyond a surface where light undergoes total internal reflection: no energy flows across the boundary on average, yet the field does not stop abruptly but decays exponentially into the rarer medium over a fraction of a wavelength. The effect follows from the wave theory of total internal reflection developed in the Fresnel era and is treated in Born and Wolf's Principles of optics. The referent is a bound, exponentially decaying field with an imaginary wavevector component, exploited in frustrated total internal reflection, near-field microscopy, and fibre sensing, and it is the same mathematical construct that appears as a tunnelling wavefunction and as a below-cutoff waveguide mode.[1]

Unit

The decay length over which the field amplitude falls by a factor e past the interface

Recovery means

Not applicable

Measured by

Probed by the decay length and by coupling a second surface into the field, as in frustrated total internal reflection

In quantum mechanics the same construct is the exponentially decaying tail of a particle's wavefunction inside a region where its energy is below the potential barrier, a region classically forbidden yet where the amplitude is non-zero, so a particle has a finite chance of tunnelling through. Gamow's 1928 Zur Quantentheorie des Atomkernes used exactly this decaying wavefunction inside the nuclear barrier to explain alpha-decay rates, and Griffiths and Schroeter's Introduction to quantum mechanics gives the textbook account. It is the identical exponentially decaying, non-propagating field as the optical evanescent wave, measured here by the barrier's transmission probability.[2][3]

Unit

The decay length of the wavefunction inside the barrier, setting the tunnelling probability

Recovery means

Not applicable

Measured by

Inferred from tunnelling rates and barrier transmission, as in alpha-decay lifetimes or tunnel-junction currents

In microwave engineering the same construct is the evanescent mode of a waveguide driven below its cutoff frequency: the mode cannot propagate, so instead of travelling it decays exponentially along the guide, storing rather than carrying energy. Pozar's Microwave engineering develops these below-cutoff fields and their use in evanescent-mode filters and attenuators. The referent is a non-propagating, exponentially decaying electromagnetic field in a bounded structure, the same mathematical object as the optical evanescent wave and the quantum tunnelling tail, here measured by the attenuation per unit length below cutoff.[4]

Unit

The attenuation length of a non-propagating mode below cutoff

Recovery means

Not applicable

Measured by

Characterised by the attenuation constant of the below-cutoff mode and the coupling between separated guides