Correspondence of the luminescence enhancement of Er$^{3+}$ ions and the local electric field of Ag nanoparticles aggregates in oxide glasses

Using the oxide glasses doped with Er$^{3+}$ ions with different refractive indices containing Ag nanoparticles (NPs) with widely variable average sizes and degree of agglomeration of NPs, a quantitative correspondence has been established between the average enhancement of the intensity of experimental photoluminescence (PL) of Er$^{3+}$ ions and the calculated local electric field (LEF) in the vicinity of silver NPs agglomerates. It is shown that for Ag NPs with sizes $\ge$ 5 nm, the LEF enhancement is the dominant mechanism for enhancement of PL of RE ions. It has been established that the value of the average enhancement of the PL intensity of the RE ions in the studied glass can be obtained by calculation of LEF intensity for a “representative aggregate” consisting of rather small number of plasmonic NPs, with the structural parameters of the aggregate determined by transmission electron microscopy. The possibility of using such an aggregate for quantitative estimation of the PL of RE ions allowed to suggest that the main effect of the PL enhancement was due to those of the RE ions that were located in the areas of high density of NPs, or in the vicinity of particles agglomerates. To characterize an average agglomerate, a representative aggregate of NPs in the studied glass was introduced, which was characterized by its natural wavelength, determined by the average particle size, the minimum distance between them, and the refractive index of the glass. This wavelength is in good agreement with the position of the maximum in the experimental optical absorption spectrum of this glass. Using of the natural wavelength of a representative aggregate as an optical characteristic of the doped glass makes it possible to formulate optimal requirements for glass synthesis and for the choice of the exciting radiation wavelength, providing the most effective enhancement of the intensity of RE ions PL due to an increase in the intensity of LEF of plasmonic NPs.