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

Reynolds, Adrian John

Published Jan 1, 2012• 0 citations

Abstract

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.

DOI: 10.26021/8541

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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.

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.

Abstract Characterization of the atomic level processes that determine optical transitions in emerging materials is critical to the development of new platforms for classical and quantum networking. Such understanding often emerges from studies of the temperature dependence of the transitions. We report measurements of the temperature dependent Er 3+ photoluminescence in single crystal Er 2 O 3 thin films epitaxially grown on Si(111) focused on transitions that involve the closely spaced Stark-split levels. Radiative intensities are compared to a model that includes relevant Stark-split states, single phonon-assisted excitations, and the well-established level population redistribution due to thermalization. This approach, applied to the individual Stark-split states and employing Er 2 O 3 specific single-phonon-assisted excitations, gives good agreement with experiment. This model allows us to demonstrate the difference in the electron-phonon coupling of the 4 S 3/2 and 2 H 11/2 states of Er 3+ in E 2 O 3 and suggests that the temperature dependence of Er 3+ emission intensity may vary significantly with small shifts in the wavelength (~0.1 nm) of the excitation source.

Phonon-ion interactions have recently been shown to satisfactorily explain the temperature dependence of widths and positions of the

R

lines of some

3d

ions in crystals. These interactions give rise to phonon relaxation processes and are investigated here as the mechanisms responsible for the widths and positions of sharp optical transitions in (

4f

) ions, in particular La

{\mathrm{F}}_{3}

:

{\mathrm{Pr}}^{3+}

. The widths of transitions originating or terminating in the metastable

^{3}P_{0}

state and involving the

^{3}H_{4}

,

^{3}H_{6}

,

^{3}F_{2}

, and

^{3}F_{4}

states of

{\mathrm{Pr}}^{3+}

in La

{\mathrm{F}}_{3}

have been investigated as a function of temperature and are found to be both qualitatively and quantitatively explainable in terms of lifetime broadening of the interacting states via nonradiative processes. Temperature-dependent shifts have also been measured for the above four groups of transitions and are shown to be in qualitative agreement with theoretical predictions. Additional features of the La

{\mathrm{F}}_{3}

:

{\mathrm{Pr}}^{3+}

spectrum, including several unreported weak transitions and vibrational sidebands, are also reported.

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.

We have performed optical photon echo measurements on amorphous toluene doped with zinc-octaethylporphine over a wide temperature interval (0.35–100 K). This broad temperature range, reaching from subkelvins up to the Debye temperature of toluene (100.7 K), enabled a clear separation between the low and high temperature contributions of line broadening processes to the total optical dephasing. The high temperature part of the measured dephasing times was analyzed using recent data from light scattering experiments which determined the spectrum of low-frequency modes of the toluene matrix. The analysis shows that two line-broadening mechanisms contribute mainly to total dephasing: the tunneling transitions of two-level systems, which lead to a power-law temperature dependence of the linewidth at low temperatures (T<3–4 K), and the interaction of the chromophore with low-frequency phonon modes of the glassy matrix, which gives rise to an exponential behavior at high temperatures. It was shown that the contribution of acoustic phonons to optical dephasing in the studied system is negligible over the whole temperature region of the measurements.