Modeling of the self-Q-switching behavior of lasers based on chromium doped active material

Theoretical investigations of the g factors and the local structures for the orthorhombic Nd3+ centers in the garnets

“…Unlikely, here we take into account the contributions from the second-order perturbation terms, which result from the admixture of the lowest (Γ 5 + Γ 6 ) doublet with the other ten irreducible representations Γ x [i.e., five (Γ 5 + 6 ) and five (Γ 7 + 8 )] due to the orthorhombic splitting of the ground 4 I 9/2 and the first excited 4 I 11/2 states via crystal-field H CF and orbital angular momentumĴ interactions, as pointed out for a 4f 11 ion in axial (tetragonal or trigonal) symmetry in our recent works [16,17]. In the above expressions, the second-order perturbation contribution g (2) x or g (2) y vanishes because none of the ten Γ x has non-zero matrix element with the lowest (Γ 5 + Γ 6 ) doublet, for bothĤ CF and the x or y component ofĴ operators.…”

“…[28]. (2) Based on the calculations, we find that the contributions to g (2) z are about 10-11% those from the first-order perturbation terms. So, in order to explain the g factors for Nd 3+ centers in crystals to a better extent, the second-order perturbation contributions should be taken into account.…”

“…So, in order to explain the g factors for Nd 3+ centers in crystals to a better extent, the second-order perturbation contributions should be taken into account. According to the studies, importance of the contributions due to the second-order perturbation terms is related to the orthorhombic crystal-fields, i.e., both the numerators and the denominators in g (2) z increase with increasing the strength of the crystal-fields. Meanwhile, the contributions due to some irreducible representations Γ x are very small or cancel one another.…”

“…Similar to the perturbation procedures in Refs. [16,17], the perturbation formulas of the g factors for the 4f 3 ion in orthorhombic symmetry can be derived, i.e., g x = g (1) x + g (2) x , g (1) x = 2g J Γγ|Ĵ X |Γγ , g (2) x = 0,…”

“…Garnets doped with Nd 3+ have attracted extensive interests because of their applications in solid-state lasers [1][2][3][4], as well as upconversion luminescence [5][6][7] and magnetooptical and magnetic properties [8,9]. Usually, these properties are closely related to the local structures and properties of the Nd 3+ impurities in the hosts.…”