Fiber nonlinearity measurement with intensity detection and Kramers-Kronig field reconstruction

Accurate knowledge of the Kerr nonlinear coefficient γ is essential for modeling nonlinear propagation in optical fibers, yet most established experimental techniques rely on coherent receivers or interferometric phase measurements. Here, we demonstrate a low-complexity method for measuring γ using direct detection on a photodiode combined with digital Kramers-Kronig (KK) field reconstruction. A receiver-side pilot laser enforces the minimum-phase condition required for KK processing, enabling recovery of the complex optical field without a coherent receiver. Three-tone excitation produces correlated nonlinear phase shifts that are extracted from the reconstructed field and used to extract γ from the power-dependent differential phase. Experiments on telecom fibers ranging from 3.2 to 25.3 km yield γ values consistent with fiber specifications using only milliwatt-level optical powers.