Polarization-resolved transmission matrices of specialty optical fibers.

Transmission matrix measurements of multimode fibers are now routinely performed in numerous laboratories, enabling control of the electric field at the distal end of the fiber and paving the way for the potential application to ultrathin medical endoscopes with high resolution. The same concepts are applicable to other areas, such as space division multiplexing, targeted power delivery, fiber laser performance, and the general study of the mode coupling properties of the fiber. However, the process of building an experimental setup and developing the supporting code to measure the fiber's transmission matrix remains challenging and time consuming, with full details on experimental design, data collection, and supporting algorithms spread over multiple papers or lacking in detail. Here, we outline a complete and self-contained description of the specific experiment we use to measure fully polarization-resolved transmission matrices, which enable full control of the electric field, in contrast to the more common scalar setups. Our exact implementation of the full polarization experiment is new and is easy to align while providing flexibility to switch between full-polarization and scalar measurements if desired. We utilize a spatial light modulator to measure the transmission matrix using linear phase gratings to generate the basis functions and measure the distal electric field using phase-shifting interferometry with an independent reference beam derived from the same laser. We introduce a new method to measure and account for the phase and amplitude drift during the measurement using a Levenberg-Marquardt nonlinear fitting algorithm. Finally, we describe creating distal images through the multimode fiber using phase-to-amplitude shaping techniques to construct the correct input electric field through a superposition of the basis functions with the phase-only spatial light modulator. We show that results are insensitive to the choice of phase-to-amplitude shaping technique as quantified by measuring the contrast of a razor blade at the distal end of the fiber, indicating that the simplest but most power efficient method may be the best choice for many applications. We also discuss some of the possible variations on the setup and techniques presented here and highlight the details that we have found key in achieving high fidelity distal control. Throughout the paper, we discuss applications of our setup and measurement process to a variety of specialty fibers, including fibers with harsh environment coatings, coreless fibers, rectangular core fibers, pedestal fibers, and a pump-signal combiner based on a tapered fiber bundle. This demonstrates the usefulness of these techniques across a variety of application areas and shows the flexibility of our setup in studying various fiber types.