Decoding the complex transfer matrix of photonic lanterns

Photonic devices that sort and separate light into spatial modes enable transformative advances in quantum-inspired sub-diffraction imaging, high-fidelity wavefront sensing, free-space optical communication, and quantum information processing. Among these, photonic lanterns offer a compelling solution - efficiently coupling light from a multimode fiber (MMF) into multiple single-mode fibers (SMFs) across a broad wavelength range, facilitating downstream detection and processing. However, effective deployment of photonic lanterns for mode sorting requires knowledge of the full complex transfer matrix—capturing amplitude and phase relationships between MMF modes and SMF outputs. Prior intensity-only approaches fail to recover this essential information. Here we present the first experimental measurement of the complete multimode-to-single-mode complex transfer matrix of a photonic lantern. Using 787 known multimode input fields and a dispersive spectrograph, we reconstruct wavelength-resolved transfer matrices for a 19-port lantern across the 720–880 nm range. We validate the matrices by predicting output intensities for unseen input fields, achieving high fidelity across all wavelengths. This technique enables full-field utilization of photonic lanterns -- including amplitude, phase, polarization, and spectral content -- transforming them from intensity couplers into fully calibrated optical interfaces. Precisely modeling the behavior of arbitrary input fields significantly expands the scope of photonic lantern applications to include information-rich imaging and high-capacity communications.