A General Study for the Complex Refractive Index Extraction Including Noise Effect Using a Machine Learning-Aided Method

This article investigates the extraction of complex refractive indices from the amplitude and phase of the transmitted electric field. In the first step, an incident plane wave has been assumed and the amplitude and phase of the transmitted plane wave is calculated analytically. In this calculation, different values of the complex refractive index have been assumed for the non-magnetic material under test. In fact, the real part and imaginary part of the refractive index are assumed in the range of [1–10] and [0–1], respectively. Furthermore, a general study is made by an assumption of the material thickness to simulation wavelength ratio in the range of [0.01–20]. Due to examining the measurement noise, noisy data are produced for different values of signal-to-noise ratio in the range of [25–40] dB. Due to the difficulties of estimating the refractive index confronted in the theoretical or iterative methods, a Long short-term memory (LSTM) network is proposed and used for the estimation of complex refractive index based on the amplitude and phase of the transmitted electric field. It is shown that the estimation accuracy of about 97% can be achieved in the trained network. Furthermore, the estimation accuracy as a function of thickness-to-wavelength ratio, signal-to-noise ratio, and the values of real and imaginary parts of the refractive index are studied in detail and shown that higher estimation accuracy can be achieved. The simulated results have been confirmed by the measurement for the thickness-to-wavelength ratio below 0.1 and a good agreement has been found. Therefore, the proposed method can replace analytical or repetitive methods as an optimal and more accurate method.