Physical review. B, Condensed matter

Temperature dependence of two-photon absorption linewidths of Eu2+ in CaF2

Luiz A. O. Nunes, Liderio Citrangulo Ioriatti Junior, Jarbas Caiado de Castro, Sérgio Carlos Zílio

Published Apr 15, 1988• 3 citations

Abstract

Two-photon absorption linewidths of $^{8}\mathrm{S}_{7/2}$${\ensuremath{\rightarrow}}^{6}$${\mathrm{P}}_{7/2}$ transitions in ${\mathrm{Eu}}^{2+}$-doped ${\mathrm{CaF}}_{2}$ are studied as a function of the temperature. Linewidths are shown to have a linear dependence on the occupation number of LO phonons (${n}_{\mathrm{LO}}$) of the ${\mathrm{CaF}}_{2}$ lattice. This result is explained by means of the different polarizabilities of the ground and the excited states, which give rise to elastic phonon scattering. By using the polarizability of ${\mathrm{Eu}}^{2+}$ in ${\mathrm{EuF}}_{2}$ we predict a slope for the linewidth \ensuremath{\Gamma}(T) versus ${n}_{\mathrm{LO}(\mathrm{T}}$) curve, which is in fairly good agreement with the experimental data. The linewidth at T close to zero is ascribed to inelastic phonon scattering which causes the 4${f}^{7}$-4${f}^{6}$5d configuration mixing. The theory also predicts a line shift proportional to the occupation number.

DOI: 10.1103/physrevb.37.7058

Related papers

Line shift of two-photon transitions of Eu2+ in CaF2 as a function of temperature

Liderio Citrangulo Ioriatti Junior, Jarbas Caiado de Castro, Luiz A. O. Nunes +1 more

Physical review. B, Condensed matterOct 15, 19881 citation

Two-photon excitation spectroscopy of 4f7→4f7 transitions of Eu2+ ions doped in a KMgF3 crystal

Hyo Jin Seo, Byung Kee Moon, T. Tsuboi

Physical review. B, Condensed matterNov 15, 200022 citations

Two‐Photon Absorption of CaF2:Eu2+

Eberhard G. Bayer, Gerhard Schaack

physica status solidi (b)Jan 1, 197037 citations

Dynamic Processes in the Line Shift and Linewidth of CaF₂ and CsCdBr₃ Doped with Er³⁺

Reynolds, Adrian John

Jan 1, 20120 citations

Static and dynamic contributions to the lowest 4f→5dtwo-photon transition in CaF2 : Ce3+

R C Leavitt

Physical review. B, Condensed matterJun 15, 198723 citations

Optical echo spectroscopy and phase relaxation of Nd3+ ions in CaF2 crystals

Tasoltan T. Basiev, Alexander Ya. Karasik, Vladimir Fedorov +1 more

Journal of Experimental and Theoretical PhysicsJan 1, 199817 citations

Physical review. B, Condensed matter

Temperature dependence of two-photon absorption linewidths of Eu2+ in CaF2

Luiz A. O. Nunes, Liderio Citrangulo Ioriatti Junior, Jarbas Caiado de Castro, Sérgio Carlos Zílio

Published Apr 15, 1988• 3 citations

Publisher

Abstract

Two-photon absorption linewidths of

^{8}\mathrm{S}_{7/2}$${\ensuremath{\rightarrow}}^{6}$${\mathrm{P}}_{7/2}

transitions in

{\mathrm{Eu}}^{2+}

-doped

{\mathrm{CaF}}_{2}

are studied as a function of the temperature. Linewidths are shown to have a linear dependence on the occupation number of LO phonons (

{n}_{\mathrm{LO}}

) of the

{\mathrm{CaF}}_{2}

lattice. This result is explained by means of the different polarizabilities of the ground and the excited states, which give rise to elastic phonon scattering. By using the polarizability of

{\mathrm{Eu}}^{2+}

{\mathrm{EuF}}_{2}

we predict a slope for the linewidth \ensuremath{\Gamma}(T) versus

{n}_{\mathrm{LO}(\mathrm{T}}

) curve, which is in fairly good agreement with the experimental data. The linewidth at T close to zero is ascribed to inelastic phonon scattering which causes the 4

{f}^{7}

-4

{f}^{6}

5d configuration mixing. The theory also predicts a line shift proportional to the occupation number.

DOI: 10.1103/physrevb.37.7058

Related papers

Line shift of two-photon transitions of Eu2+ in CaF2 as a function of temperature

Liderio Citrangulo Ioriatti Junior, Jarbas Caiado de Castro, Luiz A. O. Nunes +1 more

Line shifts of two-photon $^{8}\mathrm{S}_{7/2}$ ${\ensuremath{\rightarrow}}^{6}$ ${\mathrm{P}}_{7/2}$ transitions in ${\mathrm{Eu}}^{2+}$ -doped ${\mathrm{CaF}}_{2}$ are studied as a function of temperature. They show a linear dependence on the occupation number of LO phonons ( ${n}_{\mathrm{LO})}$ of the ${\mathrm{CaF}}_{2}$ lattice. The proportionality constant agrees better than 10% with the theoretical value found previously. The role played by LO and TO phonons in the line shift and broadening mechanisms is discussed.Line shifts of two-photon $^{8}\mathrm{S}_{7/2}$${\ensuremath{\rightarrow}}^{6}$${\mathrm{P}}_{7/2}$ transitions in ${\mathrm{Eu}}^{2+}$-doped ${\mathrm{CaF}}_{2}$ are studied as a function of temperature. They show a linear dependence on the occupation number of LO phonons (${n}_{\mathrm{LO})}$ of the ${\mathrm{CaF}}_{2}$ lattice. The proportionality constant agrees better than 10% with the theoretical value found previously. The role played by LO and TO phonons in the line shift and broadening mechanisms is discussed.

Physical review. B, Condensed matterOct 15, 19881 citation

Two-photon excitation spectroscopy of 4f7→4f7 transitions of Eu2+ ions doped in a KMgF3 crystal

Hyo Jin Seo, Byung Kee Moon, T. Tsuboi

Intraconfiguration ${4f}^{7}\ensuremath{\rightarrow}{4f}^{7}$ transitions of ${\mathrm{Eu}}^{2+}$ in ${\mathrm{KMgF}}_{3}$ have been investigated by two-photon excitation (TPE) spectroscopy at 10 K. Emission bands due to the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ and ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ transitions are obtained by two-photon excitation into the ${}^{6}{I}_{J}$ $(J=7/2,9/2,17/2,11/2,15/2,13/2)$ and ${}^{6}{D}_{J}$ $(J=1/2,7/2,3/2,5/2)$ states. The TPE spectrum of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is observed to be different from that of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission. This is explained by the relative positions of the lowest crystal-field component of the ${}^{6}{I}_{7/2}$ level and the lowest level of the ${4f}^{6}5d$ configuration for cubic-site and non-cubic-site ${\mathrm{Eu}}^{2+}$ ions. The observed TPE spectra are satisfactorily interpreted by a suggestion that the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by only cubic-site ${\mathrm{Eu}}^{2+},$ while the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by both cubic-site ${\mathrm{Eu}}^{2+}$ and non-cubic-site ${\mathrm{Eu}}^{2+}.$ Intraconfiguration ${4f}^{7}\ensuremath{\rightarrow}{4f}^{7}$ transitions of ${\mathrm{Eu}}^{2+}$ in ${\mathrm{KMgF}}_{3}$ have been investigated by two-photon excitation (TPE) spectroscopy at 10 K. Emission bands due to the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ and ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ transitions are obtained by two-photon excitation into the ${}^{6}{I}_{J}$ $(J=7/2,9/2,17/2,11/2,15/2,13/2)$ and ${}^{6}{D}_{J}$ $(J=1/2,7/2,3/2,5/2)$ states. The TPE spectrum of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is observed to be different from that of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission. This is explained by the relative positions of the lowest crystal-field component of the ${}^{6}{I}_{7/2}$ level and the lowest level of the ${4f}^{6}5d$ configuration for cubic-site and non-cubic-site ${\mathrm{Eu}}^{2+}$ ions. The observed TPE spectra are satisfactorily interpreted by a suggestion that the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by only cubic-site ${\mathrm{Eu}}^{2+},$ while the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by both cubic-site ${\mathrm{Eu}}^{2+}$ and non-cubic-site ${\mathrm{Eu}}^{2+}.$

Physical review. B, Condensed matterNov 15, 200022 citations

Two‐Photon Absorption of CaF2:Eu2+

Eberhard G. Bayer, Gerhard Schaack

Abstract The technique of two‐photon‐absorption spectroscopy with polarized laser‐light is applied to localized excitations of 4f‐electrons in crystals. The relevant selection rules are discussed. A method is outlined for the unique determination of the relative magnitude of partial transition‐probabilities with different types of symmetry using linear and circular polarization of the incident light. The anisotropy of the two‐photon absorption has been measured in single crystals of cubic CaF2:Eu2+ at five different wavenumbers. The relative intensities of transitions belonging to the three different types of symmetry active in two‐photon absorption are constant in the range of the e‐band (26,000 to 29,000 cm−1) but differ from these values at 37,700 cm−1 in the range between the e‐ and the t‐band. This result is discussed in the frame of existing interpretations of the 4f65d‐configuration of Eu2+ in CaF2.Abstract The technique of two‐photon‐absorption spectroscopy with polarized laser‐light is applied to localized excitations of 4f‐electrons in crystals. The relevant selection rules are discussed. A method is outlined for the unique determination of the relative magnitude of partial transition‐probabilities with different types of symmetry using linear and circular polarization of the incident light. The anisotropy of the two‐photon absorption has been measured in single crystals of cubic CaF2:Eu2+ at five different wavenumbers. The relative intensities of transitions belonging to the three different types of symmetry active in two‐photon absorption are constant in the range of the e‐band (26,000 to 29,000 cm−1) but differ from these values at 37,700 cm−1 in the range between the e‐ and the t‐band. This result is discussed in the frame of existing interpretations of the 4f65d‐configuration of Eu2+ in CaF2.

physica status solidi (b)Jan 1, 197037 citations

Dynamic Processes in the Line Shift and Linewidth of CaF₂ and CsCdBr₃ Doped with Er³⁺

Reynolds, Adrian John

The linewidths and line positions of 4I15/2 to 4I13/2 absorption transitions of trivalent erbium in CsCdBr₃ and CaF₂ were measured as a function of temperature from approximately 10 K to 300 K. By comparing the temperature dependence of these transitions with theoretical models of electron-phonon coupling the primary mechanism involved were determined. For Er3+ doped CaF₂ the Raman scattering processes dominated the line broadening, although the single-phonon direct processes were significant enough to drastically alter the values of the Raman scattering electron-phonon coupling constant. In comparison, the Er³⁺ doped CsCdBr₃ had negligible Raman scattering contributing to the line broadening. This is likely due to the exceedingly low Debye temperature and consequently low number of phonons, reducing the likelihood of two-phonon processes relative to single-phonon processes. The results were then analysed in terms of the bond length with the ligands and compared with other studies showing that as the bond length gets shorter the electron-phonon coupling constant associated with Raman scattering is expected to get smaller. To explain the line shifts in CaF₂:Er³⁺ it is necessary to treat the Debye temperature as a parameter. This indicates that the phonon modes causing the line shifts are different from those causing the line broadening, and in most of the cases are vibronic processes rather than Raman processes. In the case of CsCdBr₃:Er³⁺ there is very little difference between the fits using the fixed Debye temperature and a varied Debye temperature in over half of the cases examined. Given the distribution of phonon modes, it is likely that this small difference arises because combinations of these processes are of similar intensity, meaning that a combination of Raman and optical phonon modes are likely causing the line shift.The linewidths and line positions of 4I15/2 to 4I13/2 absorption transitions of trivalent erbium in CsCdBr₃ and CaF₂ were measured as a function of temperature from approximately 10 K to 300 K. By comparing the temperature dependence of these transitions with theoretical models of electron-phonon coupling the primary mechanism involved were determined. For Er3+ doped CaF₂ the Raman scattering processes dominated the line broadening, although the single-phonon direct processes were significant enough to drastically alter the values of the Raman scattering electron-phonon coupling constant. In comparison, the Er³⁺ doped CsCdBr₃ had negligible Raman scattering contributing to the line broadening. This is likely due to the exceedingly low Debye temperature and consequently low number of phonons, reducing the likelihood of two-phonon processes relative to single-phonon processes. The results were then analysed in terms of the bond length with the ligands and compared with other studies showing that as the bond length gets shorter the electron-phonon coupling constant associated with Raman scattering is expected to get smaller. To explain the line shifts in CaF₂:Er³⁺ it is necessary to treat the Debye temperature as a parameter. This indicates that the phonon modes causing the line shifts are different from those causing the line broadening, and in most of the cases are vibronic processes rather than Raman processes. In the case of CsCdBr₃:Er³⁺ there is very little difference between the fits using the fixed Debye temperature and a varied Debye temperature in over half of the cases examined. Given the distribution of phonon modes, it is likely that this small difference arises because combinations of these processes are of similar intensity, meaning that a combination of Raman and optical phonon modes are likely causing the line shift.

Jan 1, 20120 citations

Static and dynamic contributions to the lowest 4f→5dtwo-photon transition in CaF2 : Ce3+

R C Leavitt

A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in ${\mathrm{CaF}}_{2}$ : ${\mathrm{Ce}}^{3+}$ is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in ${\mathrm{CaF}}_{2}$:${\mathrm{Ce}}^{3+}$ is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.

Physical review. B, Condensed matterJun 15, 198723 citations

Optical echo spectroscopy and phase relaxation of Nd3+ ions in CaF2 crystals

Tasoltan T. Basiev, Alexander Ya. Karasik, Vladimir Fedorov +1 more

Accumulated photon echoes have been used to investigate the mechanisms of optical dephasing in CaF2 crystals activated by Nd3+ ions. Tunable picosecond laser radiation, which permits the selective excitation of various Nd3+ optical centers in the 4 I 9/2→4 G 5/2, 2 G 7/2 transition, is used. The optical phase relaxation times measured at temperatures from 9 to 50 K permit determination of the homogeneous widths of the transitions between the low-lying 4 I 9/2 Stark level and three excited 4 G 5/2, 2 G 7/2 levels, and calculation of the constants of the inter-Stark relaxation transitions in the ground and excited multiplets for the rhombic N and M Nd3+ centers in CaF2 crystals. An analysis of the temperature dependence of the homogeneous linewidth of the transitions between low-lying Stark levels of the ground and excited states shows that the mechanism of optical dephasing in the crystals investigated is described well by direct relaxation processes with resonant inter-Stark absorption of one phonon in the ground and excited states. At T=9 K, the homogeneous linewidth Γh in CaF2 crystals is almost an order of magnitude smaller than Γh in disordered CaF2-YF3 crystals. This difference can be attributed to the significantly greater spectral phonon density of states in disordered crystals.Accumulated photon echoes have been used to investigate the mechanisms of optical dephasing in CaF2 crystals activated by Nd3+ ions. Tunable picosecond laser radiation, which permits the selective excitation of various Nd3+ optical centers in the 4 I 9/2→4 G 5/2, 2 G 7/2 transition, is used. The optical phase relaxation times measured at temperatures from 9 to 50 K permit determination of the homogeneous widths of the transitions between the low-lying 4 I 9/2 Stark level and three excited 4 G 5/2, 2 G 7/2 levels, and calculation of the constants of the inter-Stark relaxation transitions in the ground and excited multiplets for the rhombic N and M Nd3+ centers in CaF2 crystals. An analysis of the temperature dependence of the homogeneous linewidth of the transitions between low-lying Stark levels of the ground and excited states shows that the mechanism of optical dephasing in the crystals investigated is described well by direct relaxation processes with resonant inter-Stark absorption of one phonon in the ground and excited states. At T=9 K, the homogeneous linewidth Γh in CaF2 crystals is almost an order of magnitude smaller than Γh in disordered CaF2-YF3 crystals. This difference can be attributed to the significantly greater spectral phonon density of states in disordered crystals.

Journal of Experimental and Theoretical PhysicsJan 1, 199817 citations

Two-photon absorption linewidths of

^{8}\mathrm{S}_{7/2}$${\ensuremath{\rightarrow}}^{6}$${\mathrm{P}}_{7/2}

transitions in

{\mathrm{Eu}}^{2+}

-doped

{\mathrm{CaF}}_{2}

are studied as a function of the temperature. Linewidths are shown to have a linear dependence on the occupation number of LO phonons (

{n}_{\mathrm{LO}}

) of the

{\mathrm{CaF}}_{2}

lattice. This result is explained by means of the different polarizabilities of the ground and the excited states, which give rise to elastic phonon scattering. By using the polarizability of

{\mathrm{Eu}}^{2+}

{\mathrm{EuF}}_{2}

we predict a slope for the linewidth \ensuremath{\Gamma}(T) versus

{n}_{\mathrm{LO}(\mathrm{T}}

) curve, which is in fairly good agreement with the experimental data. The linewidth at T close to zero is ascribed to inelastic phonon scattering which causes the 4

{f}^{7}

-4

{f}^{6}

5d configuration mixing. The theory also predicts a line shift proportional to the occupation number.

Line shifts of two-photon

^{8}\mathrm{S}_{7/2}

${\ensuremath{\rightarrow}}^{6}$

{\mathrm{P}}_{7/2}

transitions in

{\mathrm{Eu}}^{2+}

-doped

{\mathrm{CaF}}_{2}

are studied as a function of temperature. They show a linear dependence on the occupation number of LO phonons (

{n}_{\mathrm{LO})}

of the

{\mathrm{CaF}}_{2}

lattice. The proportionality constant agrees better than 10% with the theoretical value found previously. The role played by LO and TO phonons in the line shift and broadening mechanisms is discussed.

Intraconfiguration ${4f}^{7}\ensuremath{\rightarrow}{4f}^{7}$ transitions of

{\mathrm{Eu}}^{2+}

{\mathrm{KMgF}}_{3}

have been investigated by two-photon excitation (TPE) spectroscopy at 10 K. Emission bands due to the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ and ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ transitions are obtained by two-photon excitation into the

{}^{6}{I}_{J}

(J=7/2,9/2,17/2,11/2,15/2,13/2)

and

{}^{6}{D}_{J}

(J=1/2,7/2,3/2,5/2)

states. The TPE spectrum of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is observed to be different from that of the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission. This is explained by the relative positions of the lowest crystal-field component of the

{}^{6}{I}_{7/2}

level and the lowest level of the

{4f}^{6}5d

configuration for cubic-site and non-cubic-site

{\mathrm{Eu}}^{2+}

ions. The observed TPE spectra are satisfactorily interpreted by a suggestion that the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{I}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by only cubic-site

{\mathrm{Eu}}^{2+},

while the ${}^{6}{\stackrel{\ensuremath{\rightarrow}}{{P}_{7/2}}}^{8}{S}_{7/2}$ emission is produced by both cubic-site

{\mathrm{Eu}}^{2+}

and non-cubic-site

{\mathrm{Eu}}^{2+}.

A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in

{\mathrm{CaF}}_{2}

{\mathrm{Ce}}^{3+}

is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.