High-precision THz-TDS via self-referenced transmission echo method

Deep neural network ensembles for THz-TDS refractive index extraction exhibiting resilience to experimental and analytical errors

Terahertz time-domain spectroscopy (THz-TDS) achieves excellent signal-to-noise ratios by measuring the amplitude of the electric field in the time-domain, resulting in the full, complex, frequency-domain information of materials' optical parameters, such as the refractive index. However the data extraction process is non-trivial and standardization of practices are still yet to be cemented in the field leading to significant variation in sample measurements. One such contribution is low frequency noise offsetting the phase reconstruction of the Fourier transformed signal. Additionally, experimental errors such as fluctuations in the power of the laser driving the spectrometer (laser drift) can heavily contribute to erroneous measurements if not accounted for. We show that ensembles of deep neural networks trained with synthetic data extract the frequency-dependent complex refractive index, whereby required fitting steps are automated and show resilience to phase unwrapping variations and laser drift. We show that training with synthetic data allows for flexibility in the functionality of networks yet the produced ensemble supersedes current extraction techniques.

Artificial neural networks for material parameter extraction in terahertz time-domain spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) is a proven technique whereby the complex refractive indices of materials can be obtained without requiring the use of the Kramers-Kronig relations, as phase and amplitude information can be extracted from the measurement. However, manual pre-processing of the data is still required and the material parameters require iterative fitting, resulting in complexity, loss of accuracy and inconsistencies between measurements. Alternatively approximations can be used to enable analytical extraction but with a considerable sacrifice of accuracy. We investigate the use of machine learning techniques for interpreting spectroscopic THz-TDS data by training with large data sets of simulated light-matter interactions, resulting in a computationally efficient artificial neural network for material parameter extraction. The trained model improves on the accuracy of analytical methods that need approximations while being easier to implement and faster to run than iterative root-finding methods. We envisage neural networks can alleviate many of the common hurdles involved in analyzing THz-TDS data such as phase unwrapping, time domain windowing, slow computation times, and extraction accuracy at the low frequency range.

THz-TDS parameter extraction: empirical correction terms for the analytical transfer function solution

Terahertz time-domain spectroscopy (TDS) is capable of determining both real and imaginary refractive indices of a wide range of material samples; however, converting the TDS data into complex refractive indices typically involves iterative algorithms that are computationally slow, involve complex analysis steps, and can sometimes lead to non-convergence issues. To avoid using iterative algorithms, it is possible to solve the transfer function analytically by assuming the material loss is low; however, this leads to errors in the refractive index values. Here we demonstrate how the errors created by solving the transfer function analytically are largely predictable, and present a set of empirically derived equations to diminish the error associated with this analytical solution by an impressive two to three orders of magnitude. We propose these empirical correction terms are well suited for use in industrial applications such as process monitoring where analysis speed and accuracy are of the utmost importance.

Reference-free THz-TDS conductivity analysis of thin conducting films

We present a reference-free method to determine electrical parameters of thin conducting films by steady state transmission-mode terahertz time-domain spectroscopy (THz-TDS). We demonstrate that the frequency-dependent AC conductivity of graphene can be acquired by comparing the directly transmitted THz pulse with a transient internal reflection within the substrate which avoids the need for a standard reference scan. The DC sheet conductivity, scattering time, carrier density, mobility, and Fermi velocity of graphene are retrieved subsequently by fitting the AC conductivity with the Drude model. This reference-free method was investigated with two complementary THz setups: one commercial fibre-coupled THz spectrometer with fast scanning rate (0.2-1.5 THz) and one air-plasma based ultra-broadband THz spectrometer for greatly extended frequency range (2-10 THz). Certain propagation correction terms for more accurate retrieval of electrical parameters are discussed.