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Physics of the Solid State

Deformation Broadening and the Fine Structure of Spectral Lines in Optical Spectra of Dielectric Crystals Containing Rare-Earth Ions

N. M. Abishev, E. I. Baibekov, Malkin Boris Zalmanovich, Marina N. Popova, D. S. Pytalev, С. А. Климин

Published May 1, 2019• 11 citations
Publisher

Abstract

The procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF4 and LaAlO3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ2(3H4) → Γ34(3H5) singlet–doublet transition in the absorption spectrum of Pr3+ ions in the LiLuF4 crystal agrees well with the data of the measurements.

DOI
10.1134/s1063783419050020

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AbstractThe procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF_4 and LaAlO_3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ_2(^3 H _4) → Γ_34(^3 H _5) singlet–doublet transition in the absorption spectrum of Pr^3+ ions in the LiLuF_4 crystal agrees well with the data of the measurements.

Physics of the Solid State•Jan 1, 2019•0 citations

Spectroscopic manifestations of random lattice deformations in rare-earth doped crystals

Marina N. Popova

The inhomogeneous broadening of a zero-phonon line of an optical transition between nondegenerate and degenerate levels of a rare-earth impurity center in a crystal that is caused by random lattice deformations has been considered. Spectra of non-Kramers and Kramers rare-earth ions located at tetragonal and cubic sites have been investigated. Lines of a characteristic shape with a deep dip in the center have been detected.

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Optical Pumping Detection of Anomalous NQR Spectra of Pr3+ in Pr3+:LaF3

Lawrence L. Wald, Erwin Louis Hahn, Matjaž Lukač

The nature of inhomogeneous broadening in rare earth systems plays an important role in the dynamical optical properties of ions in crystals. For this reason much of the work on the nature of the inhomogeneous broadening in rare earth doped systems has concentrated on the investigation of ion-ion interactions such as spectral transfer and up conversion processes.1,3 Variations in homogeneous optical dephasing times across the inhomogeneous optical line have also been reported.4 These studies concentrate on the variations of collective effects of ion- ion interactions at different positions in the inhomogeneous optical line in relatively heavily doped rare earth systems. We report variations in optically detected NQR (ODNQR) linewidths and shifts of Pr3+ hyperfme transitions in the optical ground state as a function of position in the inhomogeneous optical line and for satellite transitions of the 1D2-3H4 transition in lightly doped (0.5 at. %) Pr3+:LaF3.

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Optical Linewidth and Line-Shape Studies of Energy Transfer Mechanisms between Rare-Earth Impurity Ions

William M. Yen, R. L. Greene, W. C. Scott +1 more

We present optical linewidth and line-shape studies of transitions of $4f$ impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of ${\mathrm{Pr}}^{3+}$ in doubly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$ as a function of ${\mathrm{Nd}}^{3+}$ concentration. The 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the ${\mathrm{Pr}}^{3+}$ ion; it follows that in the singly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As ${\mathrm{Nd}}^{3+}$ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition and eventually (at ${\mathrm{Nd}}^{3+}$ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the ${\mathrm{Nd}}^{3+}$ concentration. The width is found to increase linearly with increasing ${\mathrm{Nd}}^{3+}$ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$ systems at the terminating ${(^{3}H_{6})}_{1}$ level of the 5985-\AA{} ${\mathrm{Pr}}^{3+}$ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped La${\mathrm{F}}_{3}$: ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$ system are also presented.

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Abnormal Dielectric Response in an Optical Range Based on Electronic Transition in Rare-Earth-Ion-Doped Crystals

Xiaojian Fu, Yuanda Xu, Ji Zhou

A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd—Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er x Y 1−x ) 3 Al 5 O 12 is calculated numerically in consideration of the transition between 4 I 15/2 and 4 F 9/2 . An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.

Chinese Physics Letters•Feb 1, 2012•3 citations
The procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF4 and LaAlO3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ2(3H4) → Γ34(3H5) singlet–doublet transition in the absorption spectrum of Pr3+ ions in the LiLuF4 crystal agrees well with the data of the measurements.
AbstractThe procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF_4 and LaAlO_3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ_2(^3 H _4) → Γ_34(^3 H _5) singlet–doublet transition in the absorption spectrum of Pr^3+ ions in the LiLuF_4 crystal agrees well with the data of the measurements.
The nature of inhomogeneous broadening in rare earth systems plays an important role in the dynamical optical properties of ions in crystals. For this reason much of the work on the nature of the inhomogeneous broadening in rare earth doped systems has concentrated on the investigation of ion-ion interactions such as spectral transfer and up conversion processes.1,3 Variations in homogeneous optical dephasing times across the inhomogeneous optical line have also been reported.4 These studies concentrate on the variations of collective effects of ion- ion interactions at different positions in the inhomogeneous optical line in relatively heavily doped rare earth systems. We report variations in optically detected NQR (ODNQR) linewidths and shifts of Pr3+ hyperfme transitions in the optical ground state as a function of position in the inhomogeneous optical line and for satellite transitions of the 1D2-3H4 transition in lightly doped (0.5 at. %) Pr3+:LaF3.
We present optical linewidth and line-shape studies of transitions of 4f4f4f impurity ions in doubly doped systems and show that interactions which involve excitation transfer between the impurity systems produce homogeneous broadening and line-shape changes in the optical transitions. In particular, we have studied the behavior of the 5985-\AA{} line of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ as a function of Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition at 4.2\ifmmode^\circ\else\textdegree\fi{}K involves two long-lived electronic states of the Pr3+{\mathrm{Pr}}^{3+}Pr3+ ion; it follows that in the singly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+ the transition shows a Gaussian shape which is characteristic of inhomogeneous strain and imperfection broadening. As Nd3+{\mathrm{Nd}}^{3+}Nd3+ is added to the system, a broader Lorentzian component begins to appear in the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition and eventually (at Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentrations of \ensuremath{\sim}1% or above) completely dominates the width and shape of the transition. The Lorentzian component of the transition line shape was successfully separated using a Fourier-transform technique and the width of this component was studied as a function of the Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration. The width is found to increase linearly with increasing Nd3+{\mathrm{Nd}}^{3+}Nd3+ concentration up to concentrations of 2%; at higher concentrations, the linewidth saturates and approaches an asymptotic value of \ensuremath{\sim}2 ${\mathrm{cm}}^{\ensuremath{-}1}$. We construe this homogeneous component to be evidence of a rapid short-range energy transfer mechanism between the Pr3+{\mathrm{Pr}}^{3+}Pr3+ and Nd3+{\mathrm{Nd}}^{3+}Nd3+ systems at the terminating (3H6)1{(^{3}H_{6})}_{1}(3H6​)1​ level of the 5985-\AA{} Pr3+{\mathrm{Pr}}^{3+}Pr3+ transition. Various mechanisms are investigated as causes of the energy transfer process; it is concluded that the spin-exchange interaction is the most probable cause for the transfer. Results of other spectroscopic measurements on the doubly doped LaF3{\mathrm{F}}_{3}F3​: Pr3+{\mathrm{Pr}}^{3+}Pr3+, Nd3+{\mathrm{Nd}}^{3+}Nd3+ system are also presented.
We experimentally demonstrate cavity-enhanced spectroscopy of a rare-earth-ion-doped crystal (Pr³⁺:Y₂SiO₅). We succeeded in observing very small absorption due to the ions appropriately prepared by optical pumping, which corresponds to the single-pass absorption of 4 × 10-6. We also observed a power law for the inhomogeneous broadening of optical transitions of ions in the crystal. Compared with a theoretical model, the result of the power law indicates that the dominant origin of the inhomogeneous broadening may be some charged defects.
A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd—Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er x Y 1−x ) 3 Al 5 O 12 is calculated numerically in consideration of the transition between 4 I 15/2 and 4 F 9/2 . An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.