#### Evanescent Wave due to Total Internal Reflection

Note that if
, the horizontal component
of the wavenumber in medium 2 becomes *imaginary*. In this case,
the wave in medium 2 is said to be *evanescent*, and the wave in
medium 1 undergoes *total internal reflection* (no power travels
from medium 1 to medium 2). The evanescent-wave amplitude decays
exponentially to the right and oscillates ``in place'' (like a
standing wave). ``Tunneling'' is possible given a
medium 3 beyond medium 2 in which wave propagation resumes.

To show explicitly the exponential decay and in-place oscillation in an evanescent wave, express the imaginary wavenumber as . Then we have

Thus, an imaginary wavenumber corresponds to an exponentially decaying
evanescent wave. Note that the time dependence (cosine term) applies
to *all points* to the right of the boundary. Since evanescent
waves do not really ``propagate,'' it is perhaps better to speak of an
``evanescent acoustic field'' or ``evanescent standing wave''
instead of ``evanescent waves''.

For more on the physics of evanescent waves and tunneling, see [295].

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Reflectance and Transmittance of a Yielding String Termination

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Reflection and Refraction