lights

Software:
Blender 2.82

Adding a texture to an area light can make it produce softer and more detailed highlights and an overall more organic lighting effect.

Note:
Since an Area light in Blender isn’t rendered as an actual mesh object with UV coordinates, it’s texture coordinates are parametric (see below).

Adding a texture to an Area Light:

1. In the Area Light properties click the Use Nodes button (see image A) to initiate its node graph and allow texturing it.
2. In the Shader Editor view (with the light selected), drop your texture to the light’s node graph and connect it to the light’s Emission node’s Color input. (see image B)
3. Create a new Input > Geometry node, and connect it’s Parametric output to the Image Texture’s Vector input. (see image B)

A. Without a texture the Area light produces a hard flat highlight:

B. With the vignette texture, the Area light now has a more subtle organic effect:
* The Emission node’s Strength was increased in this case to compensate for the lower light output with the texture.

Related posts:

1. Cycles Area Light pleasent surprise
2. Cycles Area Light shader visibility