Rapid complex mode decomposition of vector beams by common path interferometry.

We have used common path interferometry for rapid determination of the electric field and complex modal content of vector beams, which have spatially-varying polarization. We combine a reference beam with a signal beam prior to a polarization beam splitter for stable interferograms that preserve intermodal phase shifts even in noisy environments. Interferometric decomposition into optical modes (IDIOM) provides a direct, sensitive measure of the complete electric field, enabling rapid modal decomposition and is ideally suited to single-frequency laser sources. We apply the technique to beams exiting optical fibers that support up to 10 modes. We also use the technique to characterize the fibers by determining a scattering matrix that transforms an input superposition of modes into an output superposition. Furthermore, because interferograms are linear in the field, this technique is very sensitive and can accurately reconstruct beams with signal-to-noise << 1.