Ideal, constant-loss nanophotonic mode converter using a Lagrangian approach

Coupling light between an optical fiber and a silicon nanophotonic waveguide is a challenge facing the field of silicon photonics to which various mode converters have been proposed. Inverted tapers stand out as a practical solution enabling efficient and broadband mode conversion. Current design approaches often use linearly-shaped tapers and two dimensional approximations; however, these approaches have not been rigorously verified and there is not an overarching design framework to guide the design process. Here, using a Lagrangian formulation, we propose an original, constant-loss framework for designing shape-controlled photonic devices and apply this formalism to derive an ideal constant-loss taper (CLT). We specifically report on the experimental demonstration of a fabrication-tolerant, 15-µm-long CLT coupler, that produces 0.56 dB fiber-chip coupling efficiency, the highest efficiency-per-length ratio ever reported.