Basically, the iridescent effect comes from light that’s not on the typical reflection path, and where some wavelengths are destroyed or atenuated, for a particular incoming ray, normal vector, and in case of anisometries, a tangent vector.
In your example pictures (a diffraction grating with a bit of tangent noise and quite wide grating distance), the anisometry is vertical to the lettering flow, with multiple orders visible.
Unfortunatly, Cycles doesn’t calculate this on its own.
The fastest way is to give just the impression that some iridescency is going on, just as @DNorman suggested.
There are other options, like different normal maps for each color component (R, G, B), or even stochastic approximations.
I’ve posted about this phenomena some years ago, if you want to look deeper: