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

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.

Non-destructive evaluation and fast conductivity calculation of various nanowire-based thin films with artificial neural network aided THz time-domain spectroscopy

Terahertz time-domain spectroscopy (THz-TDS) has been utilized extensively to characterize materials in a non-destructive way. However, when materials are characterized with THz-TDS, there are many extensive steps for analyzing the acquired terahertz signals to extract the material information. In this work, we present a significantly effective, steady, and rapid solution to obtain the conductivity of nanowire-based conducting thin films by utilizing the power of artificial intelligence (AI) techniques with THz-TDS to minimize the analyzing steps by training neural networks with time domain waveform as an input data instead of a frequency domain spectrum. For this purpose, Al-doped and undoped ZnO nanowires (NWs) on sapphire substrates and silver nanowires (AgNWs) on polyethylene terephthalate (PET) and polyimide (PI) substrates have been measured for dataset creation via THz-TDS. After training and testing a shallow neural network (SSN) and a deep neural network (DNN) to obtain the optimum model, we calculated conductivity in a conventional way, and the prediction based on our models matched successfully. This study revealed that users could determine a sample's conductivity without fast Fourier transform and conventional conductivity calculation steps within seconds after obtaining its THz-TDS waveform, demonstrating that AI techniques have great potential in terahertz technology.

A General Neural Network Model for Complex Refractive Index Extraction of Low-Loss Materials in the Transmission-Mode THz-TDS

The complex refractive index for low-loss materials is conventionally extracted by either approximate analytical formula or numerical iterative algorithm (such as Nelder-Mead and Newton-Raphson) based on the transmission-mode terahertz time domain spectroscopy (THz-TDS). A novel 4-layer neural network model is proposed to obtain optical parameters of low-loss materials with high accuracy in a wide range of parameters (frequency and thickness). Three materials (TPX, z-cut crystal quartz and 6H SiC) with different dispersions and thicknesses are used to validate the robustness of the general model. Without problems of proper initial values and non-convergence, the neural network method shows even smaller errors than the iterative algorithm. Once trained and tested, the proposed method owns both high accuracy and wide generality, which will find application in the multi-class object detection and high-precision characterization of THz materials.

Analysis of the multilayer organization of a sunflower leaf during dehydration with terahertz time-domain spectroscopy

We apply reverse engineering techniques (RET) to analyze the dehydration process of a sunflower leaf with terahertz time-domain spectroscopy. The multilayer structure of the leaf is extracted with accuracy during the entire process. Time variations of thickness and the complex index are emphasized for all leaf layers (2 cuticules, 2 epiderms, and 2 mesophylls). The global thickness of the sunflower leaf is reduced by up to 40% of its initial value.

Extracting complex refractive indices from THz-TDS data with artificial neural networks

Terahertz time-domain spectroscopy (THz-TDS) benefits from high signal-to-noise ratios (SNR), however extraction of material parameters involves a number of steps which can introduce errors into the final result. We present the use of artificial neural networks (ANN) as the first step to achieve a comprehensive approach for the extraction of the complex refractive index from THz-TDS data. The ANN shows performance superior to approximation methods and has a more straightforward implementation than root finding methods. Deep and convolutional neural networks are demonstrated to accept an entire frequency range at once, providing a tool for fitting where SNR is low, producing a more stable result.