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Light scattering [1] has been extensively studied in multilayer optics, and it is today possible to predict and measure total losses lower than a few ppm in the whole continuous spectral range (400nm -1700nm) [2]. Such accuracy is crucial for applications in high precision optics, including space applications, mirrors for gyro-lasers and detection of gravitational waves. Despite this relevant state of the art, numerous efforts are still devoted to control and reduce large-angle scattering in complex interferential filters. The same balance is observed for mirrors for which total losses should not exceed a few ppm.
Within this context it must be stressed that one effect was not considered until now in the energy balance of an optical multilayer. This missing term is the trapped scattering [1], that is, the amount of light which remains embedded within the stack and cannot merge in free space. This paper is focused on the theory of trapped scattering [1,3,4]. One key question concerns the amount of trapped light in multilayers, and mainly, whether this trapped light is greater or lower than the radiative light which merges outside the stack.
It should also be stressed that the trapped scattering intervenes in the absorption. The guided modes are attenuated along propagation and this process creates an additional “modal” absorption. The result is that the modal absorption may dominate the classical absorption, and this information is crucial to avoid any useless optimization of the thin film deposition parameters.
Complex filters are analyzed in detail in this paper and allow a better understanding to address the challenge of the “ppm barrier”. To our knowledge, it is the first time that trapped scattering is quantified within multilayer optics, and we expect this work will be useful for the community.
References
[1] C. Amra, M. Lequime, and M. Zerrad, Electromagnetic Optics of Thin-Film Coatings. Cambridge University Press, 2021.
[2] M. Lequime, S Liukaityte, M. Zerrad, C. Amra, “Ultra-wide-range measurements of thin-film filter optical density over the visible and near-infrared spectrum,” Opt. Express 23, 26863-26878 (2015).
[3] C. Amra and S. Maure, ‘Electromagnetic power provided by sources within multilayer optics: free-space and modal patterns’, J. Opt. Soc. Am. A, Nov. 1997.
[4] C. Amra and S. Maure, ‘Mutual coherence and conical pattern of sources optimally excited within multilayer optics’, J. Opt. Soc. Am. A, Nov. 1997.
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