Fig. 2
From: Large-area photonic circuits for terahertz detection and beam profiling
Quasi-phase-matching with antenna arrays. a Simulation of the enhanced THz electric field on the z-y plane of the antenna, at the resonance, computed via CST Microwave Studio. The field is uniformly distributed along the entire gap ensuring coherent build-up of the probe phase modulation. For the sake of clarity, the geometrical parameters of the antenna are overlaid to the electric field map. b Sketch depicting the coherent build-up of the phase modulation imparted to the probe beam by the THz wave and leading to the amplitude modulation operated by the MZI. The latter is realized with an arm length difference leading to a build-in phase imbalance (ϕB) allowing for operation at its quadrature point. A probe beam with an initially null THz-induced phase retardation (Δϕ = 0) enters the MZI and is split into two identical beams. Each probe crosses an array of Nant antennas (shown in number of 3 for simplicity), where it experiences a phase retardation that is proportional to the THz electric field established in the antenna gap. The spatial period of the array (D1) sets the arrival of the probe beam at each antenna at multiples of the time interval Δt1. This leads to a coherent build-up of all phase modulation contributions imparted along the entire array. If the lower array is displaced by a distance D2 (corresponding to a time interval Δt2), the probe beam in the lower arm will cross each antenna when the THz field oscillations exhibit an opposite polarity compared to the top arm. The latter will impart a total phase modulation of a reverse sign, interfering with that of the top arm and leading to the intensity modulation of the probe beam at the output of the MZI. c Transmission curve of the interferometer operating at the quadrature point excited by a bipolar THz wave where the phase modulation ΔϕU/ΔϕD changes the output probe intensity by \(\Delta {I}_{out}^{+}/\Delta {I}_{out}^{-}\). The plot is not to scale, and deviations from the quadrature point are exaggerated to better visualize the operating principle. In our experiment, relative amplitude variations accounts for less than 0.1%, thus ensuring a linear response of the device a function of the driving THz field, see text. d Experimental configuration to demonstrate the phase-matching mechanism. The broadband THz beam used to study the impulse response of the device H(f), is collimated with a diameter of W = 4 cm and then travels for CL = 57 cm in free space before reaching the chip. To test the case of the single-arm illumination, half of the interferometer is covered with a metallic blade. e THz electric field waveforms reconstructed for the case of single arm illumination (red solid line) and f double arm illumination (blue solid line). In both panels the black dash/dotted lines represent the results of the analytical model computed via Eq. (1), using the simulated complex field Eant(f) as described in the main text. g Power spectra obtained by Fourier transform of the waveforms in (e) and (f), for both experimental and simulated cases. The full-width half-maximum linewidth \(\Delta {f}_{FWHM}^{Exp}\) retrieved for the double arm illumination shows an excellent agreement with that calculated analytically. For comparison, we show the spectrum experimentally retrieved with a MZI device hosting a single antenna on only one of its arm (pink dot-dashed line). h zoom-out of plot in (g) showing higher harmonics, namely second (2fPM) and third (3fPM)
