Correlated inhomogeneous absorption profiles across distinct optical transitions in a rare-earth doped crystal

Abstract

In rare-earth ion-doped crystals, inhomogeneous absorption profiles reflect the distribution of local environments experienced by individual ions. While each optical transition probes this distribution differently, their fine spectral structures may retain correlations arising from shared local perturbations. In this paper, we present a low-temperature, high-resolution spectroscopic study in Er$^{3+}$:YSO of the transition $^{4}I_{15/2}$ - $^{4}I_{11/2}$ at 980 nm and compare it to the well-known transition $^{4}I_{15/2}$ - $^{4}I_{13/2}$ at 1.5 $μ$m. Using spectral hole burning on one transition while monitoring the other, we uncover for the first time spectral correlations between two optical transitions, providing new insight into the microscopic origin of inhomogeneous distributions in rare-earth-doped crystals.

Figures (12)

• Figure 1: (a) Simplified state diagram of Er$^{3+}$:YSO and the corresponding transitions $Z_1 \leftrightarrow Y_1$ and $Z_1 \leftrightarrow X_1$. (b) Crystals dimensions along the dielectric axes $D_1$, $D_2$ and the crystalline b-axis. (c) Experimental setup: the left side is fibered and the right side is free space.
• Figure 2: (a) Absorption profiles of the $Z_1 \leftrightarrow X_1$ transition for the two sites of Er$^{3+}$:YSO (resonant at 980 nm and 982 nm), measured for 10 ppm and 75 ppm doping concentration. The polarisation is along the $D_2$ axis. The site assignation is explained in Section \ref{['sec:siteassign']}. (b) Absorption line area of $Z_1 \leftrightarrow X_1$ in 75 ppm-Er$^{3+}$:YSO versus polarization angle $\theta$ in the ($D_1,D_2$) plane, for site 1 (red triangles) and site 2 (blue squares). Black lines correspond to adjustments to equation (1).
• Figure 3: Spectral hole burning transmission spectra of site 1 in 75 ppm-Er$^{3+}$:YSO under a $\sim$ 10 mT magnetic field along $D_1$. The upper panel shows the $Z_1 \leftrightarrow Y_1$ transition, and the lower panel shows the $Z_1 \leftrightarrow X_1$ transition.
• Figure 4: (a) Left panel: Zeeman splitting spectra for site 1 in 10 ppm-Er$^{3+}$:YSO with magnetic field along $D_1$. The $Z_1 \leftrightarrow Y_1$ (top) and $Z_1 \leftrightarrow X_1$ (bottom) transitions are measured for $|\mathbf{B}|=$ 79 mT with $\mathbf{B} // D_1$ (black dot in shaded area, right panel). Right panel: magnetic field measured from the $\Delta_{Z_1}-\Delta_{Y_1}$ splitting versus magnet–crystal distance $x$, with a $\propto 1⁄x^2$ fit. (b) Zeeman splitting $\Delta_{Z_1}$ (black circles) and $\Delta_{X_1}$ (red triangles) versus magnetic field for $\mathbf{B} // D_1$ and $\mathbf{B} // D_2$. Dashed line separates data obtained with SHB (Fig. \ref{['fig:fig3']}) and inhomogeneous profile measurements (Fig. \ref{['fig:fig4']}(a)). The solid lines correspond to linear fits adjusted with respect to $|\mathbf{B}|$.
• Figure 5: (a) Hole area versus waiting time in 75 ppm-Er$^{3+}$:YSO for site 1 ($Z_1 \leftrightarrow Y_1$, $Z_1 \leftrightarrow X_1$), zero magnetic field. The solid lines are exponential fits to the data, and include a small background. (b) Two-pulse photon echo amplitude in 10 ppm-Er$^{3+}$:YSO, plotted as a function of the delay $t_{12}$, for $Z_1 \leftrightarrow Y_1$ (black circles) and $Z_1 \leftrightarrow X_1$ (red triangles). The solid lines are the adjusted Mims function $E(t)$.