The right object:

A primitive cone, with very little height, can do a few tricks by the nature of it's mapping.

The mapping coordinates generated by a cone are like tapered cylindrical coordinates. If you have a cone with a height value of say 0.01, and then have a smaller value for Radius1 setting than Radius2, the cone sides become a disc, with virtually flat, circular mapping coordinates.

So..

The procedure:

1. Create a Cone like the one described above, turn on "Generate Mapping Coordinates"

Iris:
2. Assign a Multi-Material for the pupil/iris

Shockwave: 2. Add a Volume Select modifier and, in SubObject mode, from a top view of the cone, 2D-scale the Gizmo so it is inside both Radius 1 and Radius 2. 3. Switch to Face and Crossing 4. Add a DeleteMesh modifier, Animate the radii for the shockwave.

Mapping:
The iris:

A Cone has it's materials pre-defined as ID1=Top, ID2=bottom, ID3=sides. A Multi-Material with ID1 as black and ID3 as the colored iris map will give you near perfect iris mapping that will distort 'properly' when you change the pupil diameter (Radius 1 of the Cone object).
Assign a Bitmap to the iris material. It would look something like this...

The Shockwave:

(TBD) For a shockwave effect you will want to animate both the Inner and Outer radii of the Cylinder outward, and animate a Noise map, or similar effect, along the V coordinate to achieve radial motion. The most effective way to do this is to move the Noise "upward" so that it moves outward a bit slower than the overall motion of the shockwave...