  The Debye source representation for solutions to the time harmonic Maxwell
equations is extended to bounded domains with finitely many smooth boundary
components. A strong uniqueness result is proved for this representation.
Natural complex structures are identified on the vector spaces of time-harmonic
Maxwell fields. It is shown that in terms of Debye source data, these complex
structures are uniformized, that is, represented by a fixed linear map on a
fixed vector space, independent of the frequency. This complex structure
relates time-harmonic Maxwell fields to constant-k Beltrami fields, i.e.
solutions of the equation curl(E) = kE. A family of self-adjoint boundary
conditions are defined for the Beltrami operator. This leads to a proof of the
existence of zero-flux, constant-k, force-free Beltrami fields for any bounded
region in R^3, as well as a constructive method to find them. The family of
self-adjoint boundary value problems defines a new spectral invariant for
bounded domains in R^3.
