Resonance-free Fabry-P\'erot cavity via unrestricted orbital-angular-momentum ladder-up

Introducing elements into an optical cavity that modify the transverse spatial field structure can also impact the cavity spectral response. In particular, an intra-cavity spatial mode-converter is expected to induce modal runaway: unrestricted ladder-up in the modal order, concomitantly thwarting coherent field interference, thereby altogether suppressing the resonant response - a phenomenon that has yet to be observed in an optical cavity. Here we show that a single intra-cavity holographic phase mask placed in a compact free-standing planar Fabry-P\'erot cavity renders the cavity spectral response resonance-free. By acting as a mode-converter on a basis of Laguerre-Gaussian (LG) modes, an incident broadband fundamental Gaussian mode exits the cavity in the form of a superposition of a large number of collinearly propagating broadband LG modes of fixed parity whose spectra coincide with that of the input. Crucially, the resonance-free spectral response is maintained while changing the cavity length by $\sim350\%$, raising the prospect of stable resonant optical sensors whose performance is impervious to length perturbations.