Crystal field analysis and emission cross sections of ${\mathrm{Ho}}^{3+}$ in the locally disordered single-crystal laser hosts $M^{+}\mathrm{Bi}{\left(X{\mathrm{O}}_4\right)}_2$ ($M^{+}=\mathrm{Li},\mathrm{Na}$; $X=\mathrm{W},\mathrm{Mo}$)

The spectroscopic properties of ${\mathrm{Ho}}^{3+}$ laser channels in locally disordered tetragonal $\mathrm{Na}\mathrm{Bi}{\left(\mathrm{W}{\mathrm{O}}_4\right)}_2$ (NaBiW), $\mathrm{Na}\mathrm{Bi}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ (NaBiMo), and $\mathrm{Li}\mathrm{Bi}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ (LiBiMo) single crystals grown by the Czochralski method have been studied in the $5–300\text{−}\mathrm{K}$ temperature range using several holmium concentrations $\left[\mathrm{Ho}\right]\approx 0.05–0.6\times {10}^{20}{\mathrm{cm}}^{-3}$. Here $5\text{−}\mathrm{K}$ polarized optical absorption and photoluminescence measurements have been used to determine the energy position of 85, 56, and 39 ${\mathrm{Ho}}^{3+}$ Stark levels in NaBiW, NaBiMo, and LiBiMo crystals, respectively. These energy levels were labeled with irreducible representations corresponding to the $S_4$ local symmetry of an average optical center. Single-electron Hamiltonians combining together free-ion and crystal-field interactions have been used in the fit of experimental energy levels and in the simulation of the corresponding $4f^{10}$ ${\mathrm{Ho}}^{3+}$ configuration for NaBiW and NaBiMo crystals. Very satisfactory correlations were obtained between experimental and calculated crystal-field levels, with rms deviations $\sigma =8.8$ and $7.3{\mathrm{cm}}^{-1}$ for NaBiW and NaBiMo, respectively. The radiative properties and emission cross sections of ${\mathrm{Ho}}^{3+}$ laser channels in these hosts were calculated by the Judd-Ofelt theory and compared with experimental results. The emission cross sections of ${\mathrm{Ho}}^{3+}$ in NaBiW are similar to those observed in other crystal laser hosts, and positive gain cross sections can be achieved in extended spectral ranges. These properties make the ${\mathrm{Ho}}^{3+}$-doped double tungstates and double molybdates feasible materials for tunable and short-pulse laser operation.

Figure 1

Comparison of the $5\text{−}\mathrm{K}$ (solid line) and $75\text{−}\mathrm{K}$ (dashed line) selected optical absorption of ${\mathrm{Ho}}^{3+}$ in NaBiW. $\left[\mathrm{Ho}\right]=0.35\times {10}^{20}{\mathrm{cm}}^{-3}$. $\pi$ spectra are arbitrarily displaced in the $y$ axis for clarity.

Figure 2

$5\text{−}\mathrm{K}$ ${}^{2S+1}L_J\to {}^{5}I_8$ unpolarized photoluminescence of ${\mathrm{Ho}}^{3+}$ in NaBiMo (solid line) and in LiBiMo (dashed line).

Figure 3

Polarized $5\text{−}\mathrm{K}$ optical absorption of ${\mathrm{Ho}}^{3+}$ in NaBiW single crystal. $\left[\mathrm{Ho}\right]=0.35\times {10}^{20}{\mathrm{cm}}^{-3}$. The arrows indicate transitions considered as starting in ${}^{5}I_8\left(0\right)$.

Figure 4

$300\text{−}\mathrm{K}$ ground state $({}^{5}I_8\to {}^{2S+1}L_J)$ optical absorption of ${\mathrm{Ho}}^{3+}$ in NaBiW single crystal. ${\left[\mathrm{Ho}\right]}_{\mathrm{crys}}=0.35\times {10}^{20}{\mathrm{cm}}^{-3}$.

Figure 5

$300\text{−}\mathrm{K}$ fluorescence of ${\mathrm{Ho}}^{3+}$ in NaBiW. (a) Unpolarized fluorescence, ${\lambda }_{\mathrm{exc}}=454\mathrm{nm}$ $({}^{5}G_6+{}^{5}F_1)$. (b) Unpolarized fluorescence, ${\lambda }_{\mathrm{exc}}=488\mathrm{nm}$ $\left({}^{5}F_3\right)$. (c) $\pi$-polarized (dashed line) and $\sigma$-polarized (solid line) fluorescences, ${\lambda }_{\mathrm{exc}}=488\mathrm{nm}$ $\left({}^{5}F_3\right)$.

Figure 6

Lifetimes of ${}^{5}S_2$ and ${}^{5}F_5$ levels of ${\mathrm{Ho}}^{3+}$ in NaBiW. $\left[\mathrm{Ho}\right]=0.07\times {10}^{20}{\mathrm{cm}}^{-3}$. (a) Light intensity ${}^{5}S_2\to {}^{5}I_8$ decays (${\lambda }_{\mathrm{exc}}=455\mathrm{nm}$, ${\lambda }_{\mathrm{emi}}=550\mathrm{nm}$) at several temperatures (points) and fits to a single-exponential law (lines). (b) Temperature dependence of the ${}^{5}S_2$ experimental lifetime (points), fit to a multiphonon model [Eq. (3)] (dashed line) and fit taking into account Eq. (4) (solid line). (c) Temperature dependence of the ${}^{5}F_5$ (${\lambda }_{\mathrm{exc}}=650\mathrm{nm}$, ${\lambda }_{\mathrm{emi}}=660\mathrm{nm}$) experimental lifetime (points) and fit to the multiphonon model [Eq. (3)] (line).

Figure 7

Optical absorption line shape of ${}^{5}I_8\to {}^{5}F_5$ ${\mathrm{Ho}}^{3+}$ Stark transition at $5\mathrm{K}$ in ordered monoclinic $\alpha$-KGdW and in disordered tetragonal $M\mathrm{Bi}{\left(X{\mathrm{O}}_4\right)}_2$ crystals.

Figure 8

Gap law representation of the nonradiative probability $W_{\mathrm{nr}}$ for tetragonal NaBiW (solid symbols), NaBiMo (open symbols), and LiBiMo (crossed symbols). ${\mathrm{Ho}}^{3+}:{}^{5}F_5$, ◻; ${}^{5}S_2$, 엯. ${\mathrm{Er}}^{3+}:{}^{4}S_{3∕2}$, ▵; ${}^{4}I_{13∕2}$, $★$.

Figure 9

Emission cross sections at $300\mathrm{K}$ of ${\mathrm{Ho}}^{3+}$ in NaBiW. The ground-state absorption cross section ${\sigma }_{\mathrm{GSA}}$ is indicated with the dashed line. The experimental photoluminescence by points and the calculated emission cross section ${\sigma }_{\mathrm{emi}}$ by the solid lines. Unpolarized ${}^{5}S_2\to {}^{5}I_J$ (a)–(c). Unpolarized ${}^{5}F_5\to {}^{5}I_J$ (d)–(f). Polarized ${}^{5}I_6\to {}^{5}I_8$ (g). Polarized ${}^{5}I_7\to {}^{5}I_8$ (f)–(i).

Figure 10

Gain cross section for the ${}^{5}I_7\to {}^{5}I_8$ transition of ${\mathrm{Ho}}^{3+}$ in NaBiW. (a) $\sigma$ and $\pi$ configurations. (b) Gain cross section in $\pi$ configuration for increasing population inversion ratios $\beta$.