Our hybrid EOC design extends these concepts by providing continuous tunability and the potential for adding active samples for investigations of intra-cavity light-matter interactions. In the ‘empty’ hybrid cavity investigated here, we observe a rich mode structure, spurring development of both a field-based model to quantify these cavity modes and their properties, as well as a complementary coupled-oscillator description to gain further understanding of the delicate interplay between the various sub-cavities, which thereafter constitute the hybrid EOC modes. Our detailed analysis of these theoretical vantage points will be highly valuable when considering the addition of an active material, after which the hybrid cavity optical response will become even more intricate. Integration of active materials into hybrid EOCs will yield novel access to light-matter interactions—namely access to energy exchange on sub-Rabi-cycle timescales, and furthermore local probing and even control over tunable light-matter superposition—the latter two unavailable when viewed by conventional cavity transmission techniques. Potential ‘active materials’ for these in-situ investigations of tunable light-matter interactions include conventional polar semiconductors⁴⁰—oftentimes displaying very large oscillator strengths—atomically-thin monolayers or heterostructures ofion-metal dichalcogenides⁴¹, hybrid organic-inorganic 3D^21,42 and 2D lead-halide perovskites^43,44, and novel, magnetically-ordered systems⁴⁵.

Implementation of EO sampling inside of THz cavities will also significantly advance further areas of contemporary research. As a prominent example, field-resolved probing inside a defined electromagnetic cavity will provide novel opportunities for measurements of electromagnetic vacuum field fluctuations^46,47. Most notably, a high-quality factor EOC constitutes an advantageous testing ground for measurement of quantum vacuum fluctuations, by efficiently excluding sources of external radiation. Moreover, EOCs are not limited to either macroscopic environments or the THz spectral region. Although EO sampling is routinely employed up to the mid-IR spectral region⁹, it has recently been extended even into the visible range⁴⁸, allowing for future broadband measurements of intra-cavity electric fields. Similar sampling techniques have been used to sample electric fields inside of metallic antenna-based cavities^49,50, demonstrating that although on-chip photonic implementations lack the dynamic tunability, the general technique is readily implemented in other near-field contexts, including even tip-based nano-photonic applications⁵¹. Furthermore, EOCs utilizing quartz are uniquely suited candidates for chiral THz cavity phenomena⁵², due to quartz’s capability for straightforward and rapid measurement of vectorial electric field trajectories³⁴.

In conclusion, we have established versatile and compact designs for a new class of active THz cavities, which allow for in-situ retrieval of intra-cavity electric fields. By developing a cavity-correction function formalism for these EOCs, we have demonstrated a rigorous and reliable method to extract absolute fields in a quantitative, and phase-resolved manner. Utilizing straightforward fabrication techniques, we tune the cavities’ quality factors and resonance frequencies. Furthermore, we have introduced a hybrid EOC, offering continuously-tunable cavity modes across the entire THz-frequency range, within a single device. This fundamental advancement lays the groundwork for accommodating additional active materials for in-situ measurement of and control over light-matter coupling. We understand the rich hybrid mode structure, including apparent signatures of strong coupling, via cavity-field and coupled-oscillator formalisms, which will be key to deciphering signatures of light-matter coupling in more complicated devices. Therefore, this work opens new dimensions of THz cavity physics, particularly in the realms of cavity-controlled ground-and excited state material properties. This includes possibilities such as cavity-enhanced THz emission, selectively-driven Floquet states⁵³, and cavity-controlled nonlinear THz driving^15,54, thus paving the way for comprehensive investigations of THz cavity quantum electrodynamics.