The typical septum polarizer that has gained popularity in the literature may be unsuitable for high-power applications, due to the sharp corners in the design. In order to address this issue, the fundamentals of the septum operation are fi rst revisited, using a graphical visualization through full-wave analysis. A septum profi led with smooth edges is next presented, with enhanced power-handling capabilities in comparison to the stepped-septum polarizer. In this work, the sigmoid function is introduced to represent the smooth contour of the septum, and to enable diverse confi gurations without any discontinuities. The smooth and stepped profi les are optimized using the Particle Swarm Optimization (PSO) technique. The maximum electric-fi eld intensity around the smooth edges is investigated using a full-wave simulator, HFSS. Our observations show that the maximum electric fi eld is reduced by 40% in comparison to the stepped septum. In Appendix 1, the numerical approach is evaluated by comparing the exact series solution for the half-plane scattering problem with the simulated results in HFSS. In Appendix 2, a septum design with rounded edges is also studied as another possible design to reduce the maximum fi elds.