Group Delay in THz Spectroscopy with Ultra-Wideband Log-Spiral Antennae

Abstract

We report on the group delay observed in continuous-wave terahertz spectroscopy based on photomixing with phase-sensitive homodyne detection. We discuss the different contributions of the experimental setup to the phase difference ϕ(ν) between transmitter arm and receiver arm. A simple model based on three contributions yields a quantitative description of the overall behavior of ϕ(ν). Firstly, the optical path-length difference gives rise to a term linear in frequency ν. Secondly, the ultra-wideband log-spiral antennae effectively radiate and receive in a frequencydependent active region, which in the most simple model is an annular area with a circumference equal to the wavelength. The corresponding term changes by roughly 6π between 100 GHz and 1 THz. The third contribution stems from the photomixer impedance. In contrast, the derivative ∂ ϕ/∂ν is dominated by the contribution of periodic modulations of ϕ(ν) caused by standing waves, e.g., in the photomixers' Si lenses. Furthermore, we discuss the Fourier-transformed spectra, which are equivalent to the waveform in a time-domain experiment. In the time domain, the group delay introduced by the log-spiral antennae gives rise to strongly chirped signals, in which low frequencies are delayed. Correcting for the contributions of antennae and photomixers yields sharp peaks or "pulses" and thus facilitates a time-domain-like analysis of our continuous-wave data.

2.75 THz tuning with a triple-DFB laser system at 1550 nm and InGaAs photomixers

“…3 illustrate the overlap between the "mid-frequency" [lasers #2, #3] and "high-frequency" [lasers #1, #3] regimes and illustrate that not only the frequencies, but also the dynamic range levels measured with both combinations are in excellent agreement. The ripples visible in the signal have a period of~4.2 GHz, which implies that they originate from multiple reflections within the Silicon lenses of the packaged photomixer modules [22].…”

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“…However, ideal linear devices do not exist, and all system devices contain nonlinearity which can lead to the phase defocusing of the swept system, resulting in reduced depth resolution. THz broadband devices, especially electronic devices such as frequency multipliers and harmonic mixers in the system, have strong group delay jitter [27][28][29], and their nonlinearity cannot be ignored [30]. These nonlinearities extend the well-focused spectral response of the target to different frequencies, leading to negative effects such as reduced distance resolution, loss of signal-to-noise ratio, elevated side flaps, and main flap asymmetry.…”

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“…Thus, the nonlinearity of VCO is degraded by the increase of sweeping bandwidth. Besides, the nonlinearity of THz broadband devices could not be neglected [25,26,[28][29][30] because of their drastic group delay jitter [31][32][33][34], especially for electron devices like frequency multiplier and harmonic mixer in our system.…”