  Optical cavities are a cornerstone of photonics. They are indispensable in
lasers, optical filters, optical combs and clocks, in quantum physics, and have
enabled the detection of gravitational waves. Cavities transmit light only at
discrete resonant frequencies, which are well-separated in micro-structures.
Despite attempts at the construction of `white-light cavities', the benefits
accrued upon optically interacting with a cavity -- such as resonant field
buildup -- have remained confined to narrow linewidths. Here, we demonstrate
achromatic optical transmission through a planar Fabry-Perot micro-cavity via
angularly multiplexed phase-matching that exploits a bio-inspired grating
configuration. By correlating each wavelength with an appropriate angle of
incidence, a continuous spectrum resonates and the micro-cavity is rendered
transparent. The locus of a single-order 0.7-nm-wide resonance is de-slanted in
spectral-angular space to become a 60-nm-wide achromatic resonance spanning
multiple cavity free-spectral-ranges. This approach severs the link between the
resonance bandwidth and the cavity-photon lifetime, thereby promising resonant
enhancement of linear and nonlinear optical effects over broad bandwidths in
ultrathin devices.
