A New Method for Determining the Optical Constants of Highly Transparent Solids

Abstract

Highly transparent substrates are of interest for a variety of applications, but it is difficult to measure their optical constants precisely, especially the absorption index in the transparent spectral region. In this paper, a combination technique (DOPTM-EM) using both the double optical pathlength transmission method (DOPTM) and the ellipsometry method (EM) is presented to obtain the optical constants of highly transparent substrates, which overcomes the deficiencies of both the two methods. The EM cannot give accurate result of optical constants when the absorption index is very weak. The DOPTM is suitable to retrieve the weak absorption index; however, two sets of solutions exist for the retrieved refractive index and absorption index, and only one is the true value that needs to be identified. In the DOPTM-EM, the optical constants are measured first by using the EM and set as the initial value in the gradient-based inverse method used in the DOPTM, which ensures only the true optical constants are retrieved. The new method simultaneously obtains the refractive index and the absorption index of highly transparent substrate without relying on the Kramers-Kronig relation. The optical constants of three highly transparent substrates (polycrystalline BaF, CaF, and MgF) were experimentally determined within wavelength range from ultraviolet to infrared regions (0.2-14 µm). The presented method will facilitate the measurement of optical constants for highly transparent materials.

A New Simple Analytical Method for a Highly Accurate Determination of the Optical Parameters of a Slab from Transmittance Data

“…Thus, two limitations of the present method may be considered: for highly transparent samples, T 1 and T 2 may be too close to each other to be well separated (hence, thicker samples may be used in a reasonable range to explore). Conversely, for regions with very high absorption, the transmittance is too low to be measured by FT-IR; in this case, our method cannot be used, and alternative methods (e.g., reflectance spectroscopy 32,33 and ellipsometry 16 ) are effective for measuring high k values (>10 À3 ).…”

“…6 Moreover, materials with low-refractive index yield weak reflection; thus, the precise measurement of R appears tricky in this case. 16,17 (iii) Transmittance of several samples of the same material: this (T 1 , T 2 )→(k, n) method has been applied to one-layer structures (solid slabs [18][19][20] or liquids in a simplified model 17 ), as well as to three-layer structures to determine the optical parameters of liquids. [21][22][23][24] In all the cases, the (T 1 , T 2 )→(k, n) inverse problem corresponds to a set of nonlinear equations, which are too complex to be solved mathematically; hence, numerical iterative techniques have been used.…”

“…These methods are inherently confronted with difficulties, such as convergence towards several possible values 16,22 or slow convergence speed. 18,19 To overcome such difficulties, different strategies have been proposed recently, such as faster iterative algorithms 20,22 or a combined transmittance-ellipsometry approach 16,23,24 which also includes a numerical iterative step.…”

LabVIEW-Based Automated Setup for Interferometric Refractive Index Probing

“…Different methods for the measurement of n for transparent materials have been proposed, 1–4 but experimental techniques are still being improved to increase accuracy, speed up measurement processes, and extend the spectral range. 5–8 In the visible range, the most widely used methods for precise materials characterization are the ellipsometry method, 9,10 the method of immersion interferometry, and the method of minimum deflection (method of the prism). 11 Each of these methods has its advantages and disadvantages as well as a corresponding field of application.…”

“…It is required to have at least 10 −3 accuracy of refractive index determination for most optical media to achieve competitive results in new materials characterization. 17–19 To reach this level of precision, one needs to eliminate most of the factors possibly influencing the experimental results. The automation and precise computerized control of the measuring procedure is an important step toward high accuracy and reliability of the experiment.…”