The spectroscopic properties of different infrared-emitting neodymium-doped nanoparticles (LaF3:Nd3+, SrF2:Nd3+, NaGdF4: Nd3+, NaYF4: Nd3+, KYF4: Nd3+, GdVO4: Nd3+, and Nd:YAG) have been systematically analyzed. A comparison of the spectral shapes of both emission and absorption spectra is presented, from which the relevant role played by the host matrix is evidenced. The lack of a “universal” optimum system for infrared bioimaging is discussed, as the specific bioimaging application and the experimental setup for infrared imaging determine the neodymium-doped nanoparticle to be preferentially used in each case.

The multiphonon relaxation (MR) rates for a large number of 3- to 5-phonon transitions of ${\mathrm{Er}}^{3+}$ ions in ${\mathrm{LiYF}}_4$ and ${\mathrm{LaF}}_3$ crystals were measured at 77 K. The MR rates of ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$ ions in these crystals have been analyzed with a point-charge (or ionic) nonlinear relaxation mechanism and a covalent nonlinear relaxation mechanism, rather than the traditional linear relaxation mechanism. The functional dependencies of the experimental MR rates on the number of phonons n participating in the radiationless transitions were explained in terms of the two nonlinear coupling mechanisms. The mean values of the parameter of the theory η=${\mathit{u}}^2$/${\mathit{R}}_0^2$, where ${\mathit{R}}_0$ is the equilibrium minimal distance between the rare-earth ion and the ligands and u is the amplitude of the vibrations of the ligands, have been evaluated in these crystals for n=3–4 where the contribution of the exchange interaction is small. On the basis of these calculations it was established that the strength of dynamic electron-phonon coupling is larger in ${\mathrm{LaF}}_3$ than in ${\mathrm{LiYF}}_4$. Also, the influence on the MR rates of the exchange interaction between the 4f electron and the ligands has been analyzed. Its inclusion gives higher theoretical MR probabilities and better agreement with the experimental relaxation rates.

An analytical expression is obtained for the radiative-decay rate of an excited optical center in an ellipsoidal dielectric nanoparticle (with sizes much less than the wavelength) surrounded by a dielectric medium. It is found that the ratio of the decay rate A _nano of an excited optical center in the nanoparticle to the decay rate A _bulk of an excited optical center in the bulk sample is independent of the local-field correction and, therefore, of the adopted local-field model. Moreover, the expression implies that the ratio A _nano/A _bulk for oblate and prolate ellipsoids depends strongly on the orientation of the dipole moment of the transition with respect to the ellipsoid axes. In the case of spherical nanoparticles, a formula relating the decay rate A _nano and the dielectric parameters of the nanocomposite and the volumetric content c of these particles in the nanocomposite is derived. This formula reduces to a known expression for spherical nanoparticles in the limit c ≪ 1, while the ratio A _nano/A _bulk approaches unity as c tends to unity. The analysis shows that the approach used in a number of papers {H. P. Christensen, D. R. Gabbe, and H. P. Jenssen, Phys. Rev. B 25, 1467 (1982); R. S. Meltzer, S. P. Feofilov, B. Tissue, and H. B. Yuan, Phys. Rev. B 60, R14012 (1999); R. I. Zakharchenya, A. A. Kaplyanskii, A. B. Kulinkin, et al., Fiz. Tverd. Tela 45, 2104 (2003) [Phys. Solid State 45, 2209 (2003)]; G. Manoj Kumar, D. Narayana Rao, and G. S. Agarwal, Phys. Rev. Lett. 91, 203903 (2003); Chang-Kui Duan, Michael F. Reid, and Zhongqing Wang, Phys. Lett. A 343, 474 (2005); K. Dolgaleva, R. W. Boyd, and P. W. Milonni, J. Opt. Soc. Am. B 24, 516 (2007)}, for which the formula for A _nano is derived merely by substituting the bulk refractive index by the effective refractive index of the nanocomposite must be revised, because the resulting ratio A _nano/A _bulk turns out to depend on the local-field model. The formulas for the emission and absorption cross sections σ_nano for nanoparticles are derived. It is shown that the ratios σ_nano/σ_bulk and A _nano/A _bulk are not equal in general, which can be used to improve the lasing parameters. The experimentally determined and theoretically evaluated decay times of metastable states of dopant rare-earth ions in crystalline YAG and Y₂O₃ nanoparticles are compared with the corresponding values for bulk crystals of the same structure.