optical characterisation of rare-earth doped fluoride and phosphate ...

23to the 4f electrons.If transitions in the 4f levels were allowed by selection rules,the lifetimes would typically be less than a few nanoseconds. Since the transitionsin the 4f levels are only weakly allowed, the lifetimes can range from hundreds ofmicroseconds to milliseconds for metastable levels.The parameters describing the strength of these transitions are the electric dipoleoscillator strength and, to a lesser extent, the magnetic dipole oscillator strength. Itis important to note that higher order interactions are also possible. The selectionrules for electric dipole transitions in their most rigorous form are in Table 1.1 [38].The notation in the table is used to designate energy levels in the form 2S+1 L J , e.g.,4I 15=2 for the ground level in Er 3+ has S = 3=2, L = 6, and J = 15=2. The symbol Jis taken to mean the total angular momentum unless stated otherwise.Table 1.1: Rigorous selection rules for electric dipole transitions.Spin quantum number ¡S = 0Orbital angular momentum ¡L = ¦1Total Angular Momentum ¡J = 0;¦1; J = 0 9 0Absorption measurements over a wide spectral range - from UV to near IR - formthe basis for theoretical calculations. The McCumber theory is a powerful, and yetsimple, tool that equates the absorption cross-section to the emission cross-sectionbased on absorption measurements. Conceptually, the absorption cross-section is thearea of the ion that will absorb a photon passing through it. In a similar vein, theemission cross-section is the area of the ion that will emit a photon. Therefore, thecross-section can be interpreted as a probability of absorbing or emitting a photon.