Robust Bayesian parameter estimation for spectral encoded single-shot THz spectroscopy

Spectral encoding in terahertz time-domain spectroscopy (THz-TDS) maps the time history of a THz electric field onto intensity modulations of a chirped probe pulse. However, the inherent bandwidth-chirp tradeoff introduces spectral null frequencies and phase nonlinearities that limit the recoverable bandwidth and complicate the interpretation of the reconstructed spectrum. Reliable parameter estimation therefore, requires models that account for the detection process in extracting refractive properties from THz signals. In this work, we develop and validate a dispersion-detection forward model that incorporates descriptions of the detection process, the dispersive properties of a dielectric medium, and the properties of chirped probe pulses that are used to encode THz signals. Parameter estimation is performed using a Bayesian framework that yields the posterior probability density function for each inferred parameter. The framework is validated by measuring the refractive properties of an inductively coupled argon plasma that operates at 27.12 MHz with an input power of 150 W. The chord-averaged electron density (n~_e) and effective electron-neutral collision frequency (ν~_en) are treated as the target plasma parameters, while plasma length (L) and chirped probe pulse width (T_c) are treated as nuisance parameters. Compared with direct fitting approaches that neglect spectral encoding effects, the framework reduces peak residuals approximately 64 % and yields physical values of n~_e and ν~_en in the ranges of [1.55, 2.39] × 10¹⁹~m^-3 and [2.00, 2.46] × 10¹¹~rad/s. The framework is then applied to quantify the refractive index changes during nonlinear bistability in inductively plasma sources.