A light source includes an LED die with an emitting surface and a collimating optical element. The optical element includes an input surface in optical contact with the LED emitting surface, and an output surface. The optical element has a first portion that comprises the input surface, made of a first optical material, and a second portion that comprises the output surface, made of a second optical material. The first optical material, which may include sapphire, diamond, or silicon carbide, has a higher refractive index, thermal conductivity, or both relative to the second optical material.