So it sounds like we'd have a layered sequence of dialectric mirrors (themselves many layers each) each reflecting a different wavelength. The first layer lasts until the laser redshifts out of that layer's efficient reflection range, then vaporizes revealing the next layer tuned to the redshifted laser. That layer lasts until the laser redshifts even further, then vaporizes to reveal the next, and so on.

Sacrificial layers may also help with heat management, I suppose.