  Confined geometries, such as optical waveguides, support a discrete set of
eigen-modes. In multimoded structures, depending on the boundary conditions,
superposition states can propagate. Characterization of these states is a
fundamental problem important in waveguide design and testing, especially for
optical applications. In this work, I have developed a novel interferometric
method that provides complete characterization of optical waveguide modes and
their superposition states. The basic idea of the method is to study the
interference of the beam radiated from an optical waveguide with an external
reference beam, and detect different waveguide modes in the time-domain by
changing the relative optical paths of the two beams. In particular, this
method, called cross-correlation or C$^2$-imaging, provides the relative
amplitudes of the modes and their group delays. For every mode, one can
determine the dispersion, intensity and phase distributions, and also local
polarization properties. As a part of this work, I have developed the
mathematical formalism of C$^2$-imaging and built an experimental setup
implementing the idea. I have carried out an extensive program of experiments,
confirming the ability of the method to completely characterize waveguide
properties.
