Fresnel polarisation of infra-red radiation by elemental bismuth
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Fresnel polarisation of infra-red radiation by elemental bismuth Bruno S.C. Alexandre 1 , Lu´ıs C. Martins 2 , Jaime E. Santos 1,a , Ant´onio J. Pontes 2 , and Nuno M.R. Peres 1,3 1 2 3
Centro de F´ısica, Universidade do Minho, 4710-057 Braga, Portugal Instituto de Pol´ımeros e Comp´ ositos, Universidade do Minho, 4800-058 Guimar˜ aes, Portugal International Iberian Nanotechnology Laboratory, Avenida Mestre Jos´e Veiga s/n, 4715-330 Braga, Portugal Received 18 February 2020 / Received in final form 14 May 2020 Published online 24 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous. We derive the Fresnel coefficients of the system and the Poynting vectors at the interface, in order to compute the reflectance and transmittance of the system. We use a particular parametrisation of the referred Fresnel coefficients so as to make a connection with the ones obtained for refraction by an interface between two lossless media. This analysis allows the discussion of an actual application, namely the Fresnel polarisation of infra-red radiation by elemental bismuth, based on the concept of pseudo Brewster’s angle.
1 Introduction Propagation of electromagnetic (EM) waves is a central problem in electromagnetism and optics. The most elementary scattering problem involving electromagnetic waves is that of refraction by a plane interface separating two dielectric media with distinct electrical and/or magnetic properties [1–3]. One can study more complex problems by considering that one or both media are dissipative [4–11] and/or dispersive [12] and generalize for multiple media transmission [13,14]. Frezza et al. [5] investigate the transmission of a plane wave between two lossy media and show the absence of total-reflection in these systems, whereas Kim et al. [7] considered the transmission of light from a transparent medium onto an absorbing substrate. They specifically derive an analytical solution for the pseudo Brewster’s angle, that is, the angle of incidence of the incoming wave for which one of the polarised components of the reflected wave shows a minimum of intensity (unlike the case of two dielectric media for which such a minimum attains a zero value, in which case one speaks of a true Brewster’s angle). Reflection of EM waves by such an angle is thus a method for obtaining polarised light, the so-called Fresnel polarisation method. Dummer et al. [15] designed and constructed a linear polariser consisting of four germanium plates arranged in a chevron geometry that can be used in a frequency band going from infrared to visible radiation (0.4 µm to 500 µm). They claimed that germanium is the appropriate material for such a device given its high and a
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