
Publication # 200 


D. A. B. Miller, "Communicating with waves between
volumes  evaluating orthogonal spatial channels and limits on coupling strengths,"
Appl. Opt. 39, 1681 – 1699 (2000) We derive a
rigorous method for finding the bestconnected orthogonal communication channels, modes,
or degrees of freedom, for scalar waves between two volumes of arbitrary shape and
position, explicitly without assuming planar surfaces or paraxial approximations. The
communication channels are the solutions of two eigenvalue problems, and are identical to
the cavity modes of a double phaseconjugate resonator. We also derive a sum rule for the
connection strengths, the sum being a simple volume integral. We use these results to
analyze rectangular prism volumes, small volumes, thin volumes in different relative
orientations, and arbitrary nearfield volumes, all situations where previous planar
approaches fail for one or more reasons. We reproduce previous planar results explicitly,
extending these to finite depth. Depth is shown not to increase the number of
communications modes unless the volumes are close compared to their depth. We discuss how
to estimate the connection strengths in some cases without a full solution of the
eigenvalue problem, so estimates of the number of usable communications modes can be made
from the sum rule. In general, the approach gives a rigorous basis for handling problems
related to volume sources and receivers. It may be applicable especially in nearfield
problems, and in situations where volume is an intrinsic part of the problem.
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