The advent of high-field terahertz (THz) sources opened the field of nonlinear THz physics and unlocked access to fundamental low energy excitations for ultrafast control of quantum materials and other correlated systems. Recent concepts employing angular momentum of THz light, e.g. for driving chiral excitations, rely on the undistorted measurement of THz fields and on the precise knowledge about sophisticated THz helicity states. Both of these requirements pose experimental challenges when employing intense single-cycle pulses, because THz attenuators commonly do not completely conserve polarization states and the few broadband THz polarization optics suffer from significant transmission losses. Here, we resolve both challenges by employing z-cut α-quartz as a versatile and costefficient electro-optic THz detector. Quartz’s moderate electro-optic coefficient in conjunction with the threefold 𝜒(2) symmetry enables direct retrieval of the vectorial THz field trajectory. The retrieved amplitude- and phase-resolved time domain information can be easily mapped into a circular basis or on a Poincaré sphere in frequency domain. By this approach, we provide a convenient procedure to measure and map sophisticated THz polarization states relevant for interpreting THz ellipsometry data and for THz pulse shaping towards coherent control of chiral low-energy excitations in future.
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