If you're comfortable working with triangles (and geometry in general) then you could achieve this without having to use shaders.
If you have, say, a sector (of a circle), this is clearly multiple triangles (since the edge is curved). If they are all have a point in the centre of the circle, you can simply give the light's colour to that point and the same colour with alpha of zero to the other two points. This will create a linear gradient.
If you require more control over the gradient, you can split the sector into multiple "pieces" and create gradients for each part.
Obviously, if they are just triangles instead sectors, there's no need to split.
