  Cavity electrodynamics offers a unique avenue for tailoring ground-state
material properties, excited-state engineering, and versatile control of
quantum matter. Merging these concepts with high-field physics in the terahertz
(THz) spectral range opens the door to explore low-energy, field-driven cavity
electrodynamics, emerging from fundamental resonances or order parameters.
Despite this demand, leveraging the full potential of field-driven material
control in cavities is hindered by the lack of direct access to the
intra-cavity fields. Here, we demonstrate a new concept of active cavities,
consisting of electro-optic Fabry-Perot resonators, which measure their
intra-cavity electric fields on sub-cycle timescales. We thereby demonstrate
quantitative retrieval of the cavity modes in amplitude and phase, over a broad
THz frequency range. To enable simultaneous intra-cavity sampling alongside
excited-state material control, we design a tunable multi-layer cavity,
enabling deterministic design of hybrid cavities for polaritonic systems. Our
theoretical models reveal the origin of the avoided crossings embedded in the
intricate mode dispersion, and will enable fully-switchable polaritonic effects
within arbitrary materials hosted by the hybrid cavity. Electro-optic cavities
(EOCs) will therefore serve as integrated probes of light-matter interactions
across all coupling regimes, laying the foundation for field-resolved
intra-cavity quantum electrodynamics.
