How do I make a curved arrow? I have a simple arrow like this:



I want to make it curved about the Z axis like this:



In this image it is a texture applied with transparent background to a plane. But I want to make it a 3D model and apply a special material. 

I tried adding a curve modifier and ended up with this:



What is the best method to use?
As others have stated, I need to add more geometry to deform around the curve: