https://doi.org/10.1140/epjp/s13360-023-04011-3
Regular Article
Effect of interface interaction on the field localization at the boundary between the constant-index and graded-index media
Belgorod V. G. Shukhov State Technological University, Kostukova St., 46, 308012, Belgorod, Russia
Received:
16
March
2023
Accepted:
19
April
2023
Published online:
8
May
2023
Localized states in the constant-index and graded-index media separated by thin defect layer (interface) are considered. Exact solutions to Schrödinger equation with the delta-function potential and a spatially-dependent term are found in the case of linear, parabolic, and exponential profiles. The influence of the intensity of local interaction the excitations with the interface in short-range approximation on the field localization is studied. The exact dependencies of localization energy on the interface interaction intensity are obtained. Localized states are characterized by the small penetration depth of the field inside the graded-index layer and completely contained inside it. The field distribution turns to zero at the distance of about the thickness of the graded-index layer or more. Localized states exist at both attracting and repulsive types of interface. It is shown that localization depth increases with an increase in the interface interaction intensity. The limitation on the value of the interface interaction intensity, up to which a localized state can form, is found.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
