Cross-correlation Imaging for Waveguide Characterization

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.