An Elementary Dipole Emitter Located Either on the Boundary of a Layered Structure or Inside It
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An Elementary Dipole Emitter Located Either on the Boundary of a Layered Structure or Inside It A. B. Petrin* Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia *e-mail: [email protected] Received June 4, 2020; revised June 4, 2020; accepted July 3, 2020
Abstract—A rigorous theory of radiation of an elementary dipole that is located either on the boundary of a plane-layered structure or inside it is considered. For a particular case of radiation from a dipole located on a free boundary of one film, a method of analytical simplification of the solution is demonstrated. This method has made it possible to reduce the formulas for emitted fields to one-dimensional integrals, which greatly simplified the analysis of the problem and speeded up numerical calculations. As a specific technical application of the theory, directional patterns of point emitters (molecules, nanostructures) located on the free surface of a metal film in the Kretschmann scheme and having an induced dipole moment along the film surface have been obtained. The influence of the surface wave on the directional properties of emitters has been determined. Keywords: nanofocusing, surface plasmons, optical sensors DOI: 10.1134/S0030400X20110193
INTRODUCTION In recent times, physical phenomena that accompany the excitation of a surface plasmonic wave on the surface of a metal film by the Kretschmann scheme [1] (Fig. 1) have attracted considerable interest. A surface plasmonic wave propagates along the metal surface and is localized near this surface [2, 3]; therefore, even insignificant changes in the refractive index in the near-surface region strongly affect the character of its propagation. This forms the basis for the widespread use of the Kretschmann scheme in various types of highly sensitive sensors that respond to changes in the refractive index of a thin (oligo- or monomolecular) surface layer [4]. It has been shown in [5] that the amplitude of a surface wave on the free boundary of a film in the Kretschmann scheme is more than an order of magnitude higher than the amplitude of the incident wave. Since propagating waves in free space above the film are not excited, this makes it possible, by placing nanoparticles or individual molecules on a free surface, to observe precisely their radiation directed towards the free half-space. This radiation is generated by induced electric dipole moments of nanoparticles, which are induced by the surface wave. It is important that only point objects will emit waves that propagate into free space, and only this radiation can be observed with a microscope; in this case, one can be completely sure that the light observed in the microscope emerges precisely from point sources on the surface. In this regard,
a fundamental question arises about how a metal film (or, in the general case, a multi-film structure) in the Kretschmann scheme affects spatial radiation into free space above the film from a point emitter located on the surface. Theoretical methods for findi
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