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Angular deviations: from a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams

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Abstract

Angular deviations and lateral displacements are optical effects widely investigated in the literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic expression for the beam reflected by and (upper) transmitted through a dielectric prism. These analytical approximations lead to a cubic equation which allows to determine the angular deviations of the optical beams. Near the Brewster angles, under specific conditions, we obtain a universal formulation for the cubic equation. Its explicit solution determines the peak position of the reflected and (upper) transmitted beams. The universal solution could be of great utility in future experimental implementations. The analytic results show an excellent agreement with the numerical calculation, and the analytic expressions given for the reflected and (upper) transmitted beams should play an important role in the weak measurements analysis.

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Acknowledgements

One of the authors (S.D.L.) thanks the CNPq (grant 2018/303911) and Fapesp (grant 2019/06382-9) for financial support. The authors are also grateful to A. Alessandrelli, L. Maggio, and L. Solidoro for their scientific comments and suggestions during the preparation of this article and to Profs. G. \(\hbox {Co}^\prime \), L. Girlanda, M. Martino, and M. Mazzeo for their help in consolidating the research BRIT project of international collaboration between the State University of Campinas (Brazil) and the Salento University of Lecce (Italy).

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Authors and Affiliations

  1. Department of Applied Mathematics, State University of Campinas, São Paulo, Brazil

    Stefano De Leo

  2. Department of Mathematics and Physics, University of Salento, Lecce, Italy

    Alessia Stefano

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  1. Stefano De Leo
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  2. Alessia Stefano
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Correspondence to Stefano De Leo.

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De Leo, S., Stefano, A. Angular deviations: from a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams. Eur. Phys. J. Plus 136, 507 (2021). https://doi.org/10.1140/epjp/s13360-021-01509-6

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01509-6

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