- 96-8 Figotin A., Klein A.
- Localized Classical Waves Created by Defects
Jan 12, 96
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Abstract. We study acoustic and electromagnetic waves in a periodic medium (or any other
background medium with a spectral gap) disturbed by a single defect,
i.e., a local disturbance analogous to a well potential in solid state
physics. We show that defects do not change the essential spectrum of the
associated nonnegative operators and can only create isolated eigenvalues
of finite multiplicity in a gap of the periodic medium,with the eigenmodes
decaying exponentially. We give a constructive and simple description of
defects in acoustic and dielectric media, including a simple condition on
the parameters of the medium and of the defect, which ensures the rise of
a localized eigenmode with the corresponding eigenvalue in a specified
subinterval of the given gap of the periodic medium.