A light source includes an LED that emits excitation light, an optically transparent body, a phosphor material positioned to receive the excitation light and disposed on or in the optically transparent body, the phosphor material emitting visible light when illuminated with the excitation light, and a non-planar flexible multilayer reflector that reflects the excitation light and transmits visible light. The non-planar polymeric multilayer reflector is positioned to reflect LED light onto the phosphor material.