Instituto de Óptica “Daza de Valdés”

Direct measurement of the extinction coefficient by differential transmittance

Óptica para el espacio e iones de alta energía (GOLDION)

  • Thin films used as optical coatings have a light extinction coefficient that is barely measurable today.

Madrid / November 22, 2023

A team of researchers from the “Daza de Valdés” Institute of Optics and the “Blas Cabrera” Institute of Physical Chemistry of the CSIC and NASA Goddard Space Center has developed an innovative procedure to precisely measure the extinction coefficient for sheets of very transparent materials. The study, published in the journal Optics Express, describes a pioneering optical method that eliminates the need to assume that the material behaves following a constant optical model and knowledge of additional physical properties of the material.

Traditionally, measuring the extinction coefficient has been a challenge in the design of optical coatings, since the materials are very thin and transparent and have small values of extinction coefficient (k), difficult to detect accurately. However, this new procedure offers a promising solution.
The proposed method is based on the preparation of a sample with two zones, at least one of them covered with a film of the target material. By measuring the differential transmittance between these two areas, the researchers demonstrated that this difference is proportional to the extinction coefficient k of the film material, under specific measurement conditions.
Scheme showing the path that light follows when passing through the different layers of materials
Ray tracing for a beam crossing a sample with two areas: a) an uncoated area and an area coated with a film of thickness x1; b) the two coated areas have thicknesses x1a and x1b, with x1a < x1b; we call x1 = x1b-x1a. The beam is polarized and incident on the film at the Brewster angle θB of the film material; that is why there is no reflected ray between the incident medium and the film material. / Optics Express
The key to the success of this method lies in the polarization and angle of incidence of the light used, as well as the use of a lock-in amplifier to obtain differential transmittance with a single measurement.
The procedure requires knowing the Brewster angle of the film, which is achieved by previously measuring the refractive index of the material. The refractive index of these thin films can be easily measured using ellipsometry.
The team of researchers demonstrated the usefulness of the method by calculating the extinction coefficient in AlF3 films deposited by evaporation in the far ultraviolet spectrum. Furthermore, they analyzed the uncertainty associated with the new procedure in terms of the uncertainty of the refractive index of the film, the wavelength and the degree of polarization of the incident light, concluding that an uncertainty of 2 × 10-5 is achievable in the measurement of the extinction coefficient k.
The results obtained with this new procedure open new possibilities in the design and development of more efficient optical coatings. This innovative study represents a significant advance in the direct measurement of the extinction coefficient in transparent materials, offering a valuable tool for the research and development of cutting-edge optical applications.

IO-CSIC Communication

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