Cylindrical Talbot effect for ultra-compact multimode interference couplers.

Tapered multimode interference (MMI) couplers have been broadly studied for applications in integrated photonic circuits due to their footprints being smaller than conventional MMIs. The operation of an MMI is fundamentally related to the Talbot effect. In this Letter, the Talbot effect is analyzed in cylindrical coordinates, rather than conventional Cartesian coordinates. A cylindrical geometry is found to result in a significant reduction of Talbot distance and, hence, more compact MMIs. Simulation results are compared to theoretical predictions to confirm the accuracy of the method.