Fig. 1: Principle of integrated THz detection with shifted antennas in a Mach-Zehnder interferometer.
a Cross-section of the lithium niobate waveguide (color map/white) inside the antenna gap (yellow) and surrounded by the SiO2 cladding (grey). The spatial energy density ∣uNIR(r⊥)∣2 of the near-infrared probe mode simulated in a finite element simulation using COMSOL is plotted inside the lithium niobate area (upper plot). The THz field is simulated using CST Microwave Studio and is plotted as a vector field across the whole area (lower plot). b Thin-film lithium niobate-chip for THz detection. The intensity of the probe pulses (red) is divided equally into the two arms of an integrated Mach-Zehnder interferometer, while the THz waveform (blue) is propagating through the substrate of the chip. Two antennas on the arms of the Mach-Zehnder interferometer confine the THz field into the gap, where it overlaps with the probe pulses. After the interaction, the two probe signals are combined into one waveguide. The antennas on the two arms are displaced along the waveguide direction by a distance ΔL. c Interferometer response. The transmission through a Mach-Zehnder interferometer (MZI) is plotted depending on the phase difference of the two interferometer arms (purple line). The geometric path difference of the integrated structure introduces a phase-difference of φMZI, where the slope of the transmission is maximized (black dotted line). Any additional phase difference φ1 − φ2 (green waveform) induced by the interaction with the THz field inside the antenna gaps will result in an intensity modulation ΔI (red waveform). d Differential waveform. Due to the displacement of the two antennas ΔL, the THz field of the probe pulses overlaps with inside the antenna gaps \({E}_{{{{\rm{gap}}}}}(\tau+\frac{\delta {t}_{{{{\rm{shift}}}}}}{2})\) and \({E}_{{{{\rm{gap}}}}}(\tau -\frac{\delta {t}_{{{{\rm{shift}}}}}}{2})\) is shifted by the propagation \(\delta {t}_{{{{\rm{shift}}}}}=\frac{{n}_{{{{\rm{g}}}}}\Delta L}{c}\). The induced phases φ1 and φ2 are proportional to the instantaneous THz field inside the antenna in the moment of interaction (grey dotted line). According to the Mach-Zehnder interferometer response function (c), the temporal shape of the measured waveform ΔI (red solid line in lower plot) is given by the difference of the shifted incoming THz waveforms \({E}_{{{{\rm{gap}}}}}(\tau+\frac{\delta {t}_{{{{\rm{shift}}}}}}{2})-{E}_{{{{\rm{gap}}}}}(\tau -\frac{\delta {t}_{{{{\rm{shift}}}}}}{2})\).
