Direct measurement of the extinction coefficient by differential transmittance

• Published in: Optics express Vol. 31; no. 20; pp. 31734 - 31748
• Main Authors: Larruquert, Juan I., Gutiérrez-Luna, Nuria, Honrado-Benítez, Carlos, López-Reyes, Paloma, Ríos-Fernández, Álvaro, Pérez-García, Manuel, Rodríguez-de Marcos, Luis V.
• Format: Journal Article
• Language: English
• Published: 25-09-2023
• ISSN: 1094-4087; 1094-4087
• DOI: 10.1364/OE.496241

A new procedure to measure the extinction coefficient k of film materials that are relatively transparent is presented. This procedure does not require the use of an optical-constant model or the knowledge of extra physical properties of the material, such as the specific heat capacity. It involves preparing a sample with two areas, at least one of them coated with the film, whereas the other may remain uncoated or may be coated with a different thickness of the same material. The differential transmittance between the two sample areas is shown to be proportional to k of the film material in the following measurement conditions: the incident light is p polarized and it impinges at the film material Brewster angle. The differential transmittance is obtained with a single measurement by making the light beam or the sample to oscillate with respect to one another and by using a lock-in amplifier; for normalization purposes, the transmittance in one of the sample areas is also measured. The proportionality factor between the normalized differential transmittance and k only involves the wavelength, the film thickness, and the Brewster angle. The knowledge of the film Brewster angle requires that the film refractive index ( n ) is measured beforehand; this can be performed with standard procedures, such as ellipsometry, since such techniques are efficient at measuring n of a transparent material, but are inefficient at measuring a small k . The procedure is exemplified with the calculation of k in the far ultraviolet of AlF 3 films deposited by evaporation. The dependence of the uncertainty of k obtained with this procedure is analyzed in terms of the uncertainty of the film n , of wavelength, and of the degree of polarization of the incident beam. The selection of a substrate with similar n to the film material is also discussed. The uncertainties involved with the present procedure were analyzed for a specific example and an uncertainty of 2 × 10 −5 in k calculation is considered feasible.