Dieke diagram

Trivalent rare Earth Ions the Dieke Diagram... 

Figure 6.2 The absorption spectium of Nd ions in LiNbOs, taken at room temperature (right-hand side) (registered by the authors). The Dieke diagram levels corresponding to the Nd + ion are shown on the left-hand side.

Figure 6.3 The low-temperature emission spectrum of Eu + ions in LiNbOs. Part of the Dieke diagram for the Eu + ion is included for explanation (reproduced with permission from Munoz et at., 1995).

In general, the Dieke diagram can be nsed as a guide to roughly predict the average... 

The wavenumber of the 285 nm emitted photons is 35 088 cm . Examining the Dieke diagram column corresponding to Tm + ions in Figure 6.1, we observe that that the energy matches the energy difference between the Po excited state and the ground state. Thus, the transition that should operate at about 285 nm is the Po He transition. 

In the Dieke diagram, which is used to interpret the spectra of trivalent rare earth ions (Figure 6.1), we emphasized the emitting levels by marking a semicircle below them. 

From the Dieke diagram of Figure 6.1, the energy-gap values can be determined for each energy level, giving... 

A lithium niobate crystal doped with Pr + ions is excited with light of wavelength 470 nm. Structured emission bands centered around 620 nm, 710 nm, 880 nm, and 1062 nm are observed. Using the Dieke diagram, identify the excited and terminal states responsible for the previous emission bands. 

The fluorescence lifetime of the /2 metastable state of Nd + ions in LaBGeOs (a solid state laser) is 280 /u.s and its quantum efficiency is 0.9. (a) Calculate the radiative and nonradiative rates from this excited state, (b) If the effective phonons responsible for the nonradiative rate have an energy of 1100 cm, use the Dieke diagram to determine the number of emitted effective phonons from the F3/2 excited state, (c) From which three excited states of the Nd + ions in LaBGeOs do you expect the most intense luminescence emissions to be generated ... 

Yttrium aluminum borate, YAlj (603)4 (abbreviated to YAB), is a nonlinear crystal that is very attractive for laser applications when doped with rare earth ions (Jaque et al, 2003). Figure 7.9 shows the low-temperature emission spectrum of Sm + ions in this crystal. The use of the Dieke diagram (see Figure 6.1) allows to assign this spectrum to the " Gs/2 Hg/2 transitions. The polarization character of these emission bands, which can be clearly appreciated in Figure 7.9, is related to the D3 local symmetry of the Y + lattice ions, in which the Sm + ions are incorporated. The purpose of this example is to use group theory in order to determine the Stark energy-level structure responsible for this spectrum. 

Chapter 6 is devoted to discussing the main optical properties of transition metal ions (3d" outer electronic configuration), trivalent rare earth ions (4f 5s 5p outer electronic configuration), and color centers, based on the concepts introduced in Chapter 5. These are the usual centers in solid state lasers and in various phosphors. In addition, these centers are very interesting from a didactic viewpoint. We introduce the Tanabe-Sugano and Dieke diagrams and their application to the interpretation of the main spectral features of transition metal ion and trivalent rare earth ion spectra, respectively. Color centers are also introduced in this chapter, special attention being devoted to the spectra of the simplest F centers in alkali halides. 

Dieke diagram 7 4.1. Calculations of free trivalent RE ions 15... 

Fig. 1. Dieke diagram (energy levels of free RE3+ ions up to 42000 cm 1).

Table 2 contains corrected energies of Pr3"1" obtained by multiplication of the E2 values by the averaged ratio X = l/N flfL] Eu/E2[ = 0.75 (where N is the total number of / manifolds, Eu and Eu are the / th energies obtained by the semiempirical and first principles calculations, respectively). Inclusion of this correction significantly improves the agreement of the first principles results with semiempirical ones as well as with the Dieke diagram (fig. 1). 

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