Competing radiative and nonradiative decay of embedded ions states in dielectric crystals: theory, and application to Co²⁺:AgCl₀₅Br₀₅

Abstract

We present a generally applicable theoretical model describing excited-state decay lifetime analysis of metal ions in a host crystal matrix. In contrast to common practice, we include multi-phonon non-radiative transitions competitively to the radiative one. We have applied our theory to Co ions in a mixed AgClBr crystal, and as opposed to a previous analysis, find excellent agreement between theory and experiment over the entire measured temperature range. The fit predicts a zero absolute temperature radiative lifetime τrad(0) = 5.5 ms, more than three times longer than the measured effective low-temperature one τeff(0) = 1.48 ms. Furthermore, the fit configuration potential dissociation energy has been estimated as D = 2500 cm and the lattice vibrational cutoff frequency as ħωco = 180 cm. We have experimentally verified the latter by optical reflection measurement in the far-IR.

Highly Emissive Biological Bilirubin Molecules: Shedding New Light on the Phototherapy Scheme

“…This indicates that nonradiative decay channels are still active at room temperature for the α crystal, suggesting a residual activity of large-scale motions, 20 , 29 , 30 , 39 − 42 aggregation effects, 21 , 29 , 43 or heat dissipation by crystal phonons. 44 , 45 …”

Radiative and non-radiative transitions of excited Ti3+ cations in sapphire

“…In the particular simple case of the non-radiative transition between two separate states, the non-radiative transition rate τ nr −1 is given by 15,16 where 〈 n ( T )〉 is the thermal average occupation number of ω co energy phonons, ω co being the cutoff vibrational energy in the crystal, (measured 25 as 908 cm −1 ), C nr is Burshtein’s multi-phonon non-radiative coefficient factor, which has been theoretically calculated 15 aswhere is the reduced Planck constant, c is the vacuum speed of light constant, e is the elementary charge value, N c is the number of atoms occupying the primitive unit cell (correspondingly forming the ligand for each embedded ion), n is the ion host matrix refractive index, is the average atomic mass in the unit cell, ω co is the cut-off angular frequency of the matrix vibrations (phonons), E g is the energy gap between two initial and final separated states, D is the characteristic dissociation energy of a Morse-type configuration potential 26 (related to the primitive unit cell vibrating in free-space at ω co angular frequency), υ , defined as υ ≡ E g / ω co represents the number of ω co phonons involved in the non-radiative transition. The 〈 n ( T )〉 quantity in Eq.…”

“…Other process parameters are listed in Table 2.

Figure 6Semi-logarithmic plot of the non-radiative fluorescence decay rate τ nr −1 (T) of Ti 3+ ions in the sapphire matrix as a function of 1000/T. Dotted line is a fit based on our previous basic theory 16 , dashed line is a fit that further assumes a temperature dependence of the configuration potential anharmonicity. Fit parameters per Eq.

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“…That particular theory was found to be quite satisfactory in accounting for reported transitions, involving energy gaps of up to approximately 5,000 cm −1 . In a recent publication, it was successfully applied to analysis of fluorescence lifetime temperature dependence of Co 2+ excited states in an AgCl 0.5 Br 0.5 matrix 16 , involving an energy gap of about 2,800 cm −1 . Obviously, energy gaps of Ti:sapphire, approximately 11,500 cm −1 , are considerably larger.…”

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“…В настоящее время из кристаллов данной системы изготавливают световоды в Научном центре волоконной оптики РАН. За рубежом данной тематикой занимаются много лет в Тель-Авивском университете под руководством А. Катцира [24][25][26]. Немецкие фирмы CeramOptec GmbH [20] и Art Photonics GmbH [21] выпускают волоконно-оптическую продукцию на основе галогенидсеребряных световодов для различных областей науки и техники, в том числе для биотехнологий и лазерной медицины.…”