Optical Transitions and Excited State Absorption Cross Sections of SrLaGaO4 Doped with Ho3+ Ions

The spectroscopic properties of SrLaGaO4 (SLO) crystal doped with Ho3+ ions were studied in this work. Absorption, emission spectra and decay dynamics of excited states have been measured and discussed using the Judd–Ofelt model. Photoluminescence emissions were attributed to transitions from the excited 3D3, 5S2, 5F5, 5I6 and 5I7 multiplet manifolds. The experimental lifetimes for five excited states have been compared to the theoretical values, calculated using Judd–Ofelt theory, allowing for the determination of the multiphonon relaxation rates (WnR) of the respective states. The experimental data were approximately on a line expressed by WnR = W0 exp(−αΔE) with W0 = 0.5 × 107 s−1 and α = 2.6 × 10−3 cm. To discuss the excited state absorption (ESA) pathways, that originated from several excited levels, we used the Judd–Ofelt formalism allowing determination of the integrated cross section for ESA transitions.


Introduction
The strontium lanthanum gallate SrLaGaO 4 (SLO) and its solid solutions have been extensively investigated since they were considered as a promising substrate for high temperature superconducting (HTSc) films [1]. SLO doped with transition metal (TM) or rare earth (RE) ions was also considered as laser active media [2]. Recently, SLO has been investigated as a host lattice for phosphors, which exhibit unusual and interesting properties when activated by RE or TM ions [3,4]. In particular, when Tb 3+ is introduced into SrLaGaO 4 , long persistent green emission has been reported [3]. The duration of green afterglow was observed even after more than 3.5 h. A novel, far-red emitting SrLaGaO 4 :Mn 4+ phosphor with high brightness and excellent luminescent properties has been synthesized by the simple solid-state reaction and investigated in [5]. In addition, the luminescence spectra of SLO activated by Cr 3+ were reported in [4]. It was shown that Cr 3+ ions occupy more than four different sites in the SLO lattice, which is related to the random distribution of Sr 2+ and La 3+ ions.
The interest in studying RE 3+ doped SLO strongly results both from its structural disorder, and the resulting inhomogeneous broadening of the optical transitions [6], as well as from the ability of this matrix to accept high concentrations of activator [1,2]. Such a broadening helps the generation of ultrashort pulses by mode locking. Thus, due to its good thermal properties and broad gain spectrum, Yb 3+ -doped strontium lanthanum aluminate crystal was reported as a promising material for power-scalable, broadly tunable CW and sub-100 fs mode-locked lasers at~1 µm [7].
Holmium ion activated solids have been the subject of extensive investigations for the development of laser materials, phosphors and color displays [8][9][10]. The use of Ho 3+ as a potential candidate for temperature sensing has been confirmed, and thermal-coupled levels of Ho 3+ ions, 5 F 4 and 5 S 2 , 5 S 2 and 5 F 5 , have been investigated in temperature measurement applications [11].
In particular, much attention has been dedicated to the studies of up-conversion processes in Ho 3+ doped low-energy phonon crystals, optical glasses [12] and glass ceramics [13]. Up-conversion materials have wide applications, such as for bio-imaging, phototherapies, photo-catalysis, solar conversion, temperature sensing, etc. Generally, energy transfer up-conversion (ETU), excited state absorption (ESA), and photon avalanche (PA) are the three main channels for up-conversion fluorescence. The Ho 3+ ion is very suitable for use in up-conversion processes because it has many long-lived intermediate metastable levels, from which ESA can take place resulting in a strong, green anti-Stokes luminescence from 5 S2 level which has been demonstrated in a number of Ho 3+ doped materials after red and infrared excitation [14]. It was also demonstrated that ESA has an important influence on the performance of Ho-doped fiber lasers [15]. Thus, for the modeling of these up-conversion excitation processes the ESA cross sections have to be known.
Although the optical properties of Nd 3+ , Pr 3+ , Eu 3+ , Yb 3+ and Tm 3+ doped SLO crystals have been reported [3,6,7,16], the spectroscopic data on Ho 3+ doped SLO have not, to our knowledge, been presented in detail. In [17] we reported on the nature of strong spectral lines broadening in Ho 3+ doped SrLaGa3O7 and SrLaGaO4 crystals which have been investigated by using the non-resonant fluorescence line narrowing (FLN) technique. Also, upconversion ultraviolet emission from 3 D3 level in these compounds was observed in [18]. The partial energy diagram of Ho 3+ ions in the SLO host, together with the strongest observed emission transitions, is illustrated in Figure 1. Recently, we studied ESA processes that involve the 5 I6 and 5 I7 energy levels of Ho 3+ in singly Ho 3+ -doped ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) glass [12] and also YAlO3 (YAP), Y3Al5O12 (YAG), LiYF4 (YLF) and SrLaGa3O7 (SLG) crystals [14]. In the present investigation, we extend this work by identifying and quantifying a range of pump excited state absorption ESA processes in SLO that may affect the functioning of Ho 3+ -doped SLO green phosphor or laser.

Materials and Experiment
A SrLaGaO4:Ho 3+ crystal with activator concentrations of 0.3 at % was grown using the Czochralski technique at ITME Laboratory in Warsaw. The samples used were monocrystalline of good optical quality which, after orientation, were cut into 10 × 5 × 2 mm 3 plates and polished carefully in order to meet the requirements for spectroscopic measurements. Polarized absorption spectra were measured in the 200-2900 nm range of wavelength at room temperature on a Cary-50 UV-Vis-NIR spectrophotometer (Varian, Inc., Palo Alto, CA, USA) equipped with Glan-Taylor polarizers. Recently, we studied ESA processes that involve the 5 I 6 and 5 I 7 energy levels of Ho 3+ in singly Ho 3+ -doped ZrF 4 -BaF 2 -LaF 3 -AlF 3 -NaF (ZBLAN) glass [12] and also YAlO 3 (YAP), Y 3 Al 5 O 12 (YAG), LiYF 4 (YLF) and SrLaGa 3 O 7 (SLG) crystals [14]. In the present investigation, we extend this work by identifying and quantifying a range of pump excited state absorption ESA processes in SLO that may affect the functioning of Ho 3+ -doped SLO green phosphor or laser.

Materials and Experiment
A SrLaGaO 4 :Ho 3+ crystal with activator concentrations of 0.3 at % was grown using the Czochralski technique at ITME Laboratory in Warsaw. The samples used were monocrystalline of good optical quality which, after orientation, were cut into 10 × 5 × 2 mm 3 plates and polished carefully in order to meet the requirements for spectroscopic measurements. Polarized absorption spectra were measured in the 200-2900 nm range of wavelength at room temperature on a Cary-50 UV-Vis-NIR spectrophotometer (Varian, Inc., Palo Alto, CA, USA) equipped with Glan-Taylor polarizers.
Luminescence from the sample was excited using both pulsed and CW laser sources. For the pulsed measurements an optical parametric oscillator Surelite OPO (Continuum, Santa Clara, CA, USA) with YAG:Nd laser (Surelite II, Continuum Santa Clara, CA, USA) as a pumping source was used. CW excitation was performed with tunable Ti-sapphire laser (Coherent 899 Ring Laser, (Santa Clara, CA, USA)) pumped by argon laser (Coherent Innova 300, (Santa Clara, CA, USA). Optical signal from the sample was analyzed using DK480 monochromator (CVI Laser Corporation, Albuquerque, NM, USA) and detected by cooled photomultiplier tubes (EMI C1034-02 GaAs (EMI Electronics Ltd., London, England) or Hamamatsu 7102 (Hamamatsu Photonics K.K., Hamamatsu, Japan)) and PbS detector for visible and infrared range, respectively. Stanford SR 400 photon-counting system (Stanford Research Systems Sunnyvale, CA, USA) controlled by PC was used to perform data acquisition. Measurements of luminescence decays were recorded using Stanford  [19,20]. The crystal structure is built from CO 6 (GaO 6 ) layers formed in the ab plane. The Sr 2+ and La 3+ cations are distributed randomly between the layers, taking positions in nine coordinated sites with distorted C4v symmetry. The C cations have a coordination of six and are in a slightly distorted octahedral environment, while Sr and La ions are surrounded by nine oxygens. The elementary cell of SrLaGaO 4 is shown in Figure 2 with the crystal built along the c-axis.

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Luminescence from the sample was excited using both pulsed and CW laser sources. For the pulsed measurements an optical parametric oscillator Surelite OPO (Continuum, Santa Clara, CA, USA) with YAG:Nd laser (Surelite II, Continuum Santa Clara, CA, USA)) as a pumping source was used. CW excitation was performed with tunable Ti-sapphire laser (Coherent 899 Ring Laser, (Santa Clara, CA, USA)) pumped by argon laser (Coherent Innova 300, (Santa Clara, CA, USA). Optical signal from the sample was analyzed using DK480 monochromator (CVI Laser Corporation, Albuquerque, NM, USA) and detected by cooled photomultiplier tubes (EMI C1034-02 GaAs (EMI Electronics Ltd., London, England) or Hamamatsu 7102 (Hamamatsu Photonics K.K., Hamamatsu, Japan)) and PbS detector for visible and infrared range, respectively. Stanford SR 400 photon-counting system (Stanford Research Systems Sunnyvale, CA, USA) controlled by PC was used to perform data acquisition. Measurements of luminescence decays were recorded using Stanford SR 430 multichannel analyzer (Stanford Research Systems Sunnyvale, California, USA). Low temperatures of the samples were obtained with a Displex Model CSW-202 cryostat (Apd Cryogenics Inc., Allentown, PA, USA).
SrLaGaO4 belongs to a large family of compounds of general chemical formula ABCO4 where A = Ca, Sr, Ba; B = Y, La-Gd; C = Al, Ga. SLO crystallizes in a perovskitelike, tetragonal structure, space group I4/mmm with unit cell parameters of a = b = 0.38437(3) nm and c = 1.26880 (15) nm, the volume of the unit-cell V = 178.27(1) Å 3 and the number of structural units Z = 2 [19,20]. The crystal structure is built from CO6 (GaO6) layers formed in the ab plane. The Sr 2+ and La 3+ cations are distributed randomly between the layers, taking positions in nine coordinated sites with distorted C4v symmetry. The C cations have a coordination of six and are in a slightly distorted octahedral environment, while Sr and La ions are surrounded by nine oxygens. The elementary cell of SrLaGaO4 is shown in Figure 2 with the crystal built along the c-axis. Since the radius of the Ho 3+ ion (0.172 Å) is comparable to those of the La 3+ (0.126 Å) and Sr 2+ (0.131 Å), it can be assumed that both La 3+ and Sr 2+ sites can be occupied by Ho 3+ in SrLaGaO4. It has been shown that the random distribution of the A and B cations over different lattice positions leads to a disordered structure of these crystals resulting in the strong inhomogeneous broadening of the spectral lines.

Absorption Spectra and Optical Transition Intensity Analysis
The structure makes SrLaGaO4 uniaxially anisotropic where the strength of the absorption lines is dependent on the direction of the incident light. Bearing in mind that the optical axis is parallel to the crystallographic c-axis, two orthogonal light polarizations, π (E || c) and σ (E ⊥ c), should be taken into account. Thus, in our spectroscopic study, we have measured the absorption characteristics for two principal light polarizations for acut 0.3 at% Ho 3+ doped SrLaGaO4 crystal. The measured spectra in the 300-2200 nm range are presented in Figure 3. Since the radius of the Ho 3+ ion (0.172 Å) is comparable to those of the La 3+ (0.126 Å) and Sr 2+ (0.131 Å), it can be assumed that both La 3+ and Sr 2+ sites can be occupied by Ho 3+ in SrLaGaO 4 . It has been shown that the random distribution of the A and B cations over different lattice positions leads to a disordered structure of these crystals resulting in the strong inhomogeneous broadening of the spectral lines.

Absorption Spectra and Optical Transition Intensity Analysis
The structure makes SrLaGaO 4 uniaxially anisotropic where the strength of the absorption lines is dependent on the direction of the incident light. Bearing in mind that the optical axis is parallel to the crystallographic c-axis, two orthogonal light polarizations, π (E || c) and σ (E ⊥ c), should be taken into account. Thus, in our spectroscopic study, we have measured the absorption characteristics for two principal light polarizations for a-cut 0.3 at% Ho 3+ doped SrLaGaO 4 crystal. The measured spectra in the 300-2200 nm range are presented in Figure 3. Once the polarized absorption spectra had been measured, integrated absorbances Γ were calculated according to Equation (1) [21]: where L is the distance the light has traveled inside the sample, απ(λ) and ασ(λ) are the absorption coefficients for π and σ polarizations and λ is wavelength. Integrated absorbances determined in this way were used to obtain the experimental line strengths needed to perform the Judd-Ofelt [22,23] intensity analysis. Because the drawbacks and precision of the Judd-Ofelt theory have been analyzed in detail elsewhere [24], only the essential results have been included in this article. The main point of this approach is that the oscillator strength fcalc of the electric dipole transition between multiplets of lanthanide ion (J → J') is described as: where h is Planck's constant, J is the angular momentum of the initial level, , U (t) are the doubly reduced matrix elements and Ωt are empirically determined parameters. The value of oscillator strength can be also obtained from experimentally measured absorption or emission spectra. For the absorption line, the experimental oscillator strength fexp, can be defined as where e and m are the electron charge and mass respectively, Γ is the integrated absorbance obtained from Equation (1) and c represents the light velocity.
From the least-square fit of calculated (fcalc) and measured (fexp) oscillator strengths the three Ωt intensity parameters were obtained. The reduced matrix elements needed for this calculation were taken from [25]. The values of calculated and measured oscillator strengths together with the average wavelengths for all measured absorption lines are presented in Table 1   Once the polarized absorption spectra had been measured, integrated absorbances Γ were calculated according to Equation (1) [21]: where L is the distance the light has traveled inside the sample, α π (λ) and α σ (λ) are the absorption coefficients for π and σ polarizations and λ is wavelength. Integrated absorbances determined in this way were used to obtain the experimental line strengths needed to perform the Judd-Ofelt [22,23] intensity analysis. Because the drawbacks and precision of the Judd-Ofelt theory have been analyzed in detail elsewhere [24], only the essential results have been included in this article. The main point of this approach is that the oscillator strength f calc of the electric dipole transition between multiplets of lanthanide ion (J → J') is described as: where h is Planck's constant, J is the angular momentum of the initial level, χ = 1 3 (χ π + 2χ σ ) is an average local field correction factor, where for electric dipole transition χ π,σ = (n 2 π,σ +2) 2 9n π,σ , U (t) are the doubly reduced matrix elements and Ω t are empirically determined parameters. The value of oscillator strength can be also obtained from experimentally measured absorption or emission spectra. For the absorption line, the experimental oscillator strength f exp , can be defined as where e and m are the electron charge and mass respectively, Γ is the integrated absorbance obtained from Equation (1) and c represents the light velocity. From the least-square fit of calculated (f calc ) and measured (f exp ) oscillator strengths the three Ω t intensity parameters were obtained. The reduced matrix elements needed for this calculation were taken from [25]. The values of calculated and measured oscillator strengths together with the average wavelengths for all measured absorption lines are presented in Table 1. The Judd-Ofelt intensity parameters were evaluated to be Ω 2 = 1.25 × 10 −20 cm −1 , Ω 4 = 0.42 × 10 −20 cm −1 , Ω 6 = 1.80 × 10 −20 cm −1 with RMS deviation between the calculated and measured oscillator strength values of 5.3 × 10 −6 . The obtained measure of the quality of the fit is closed to values found by applying the Judd-Ofeld approach to other materials doped with holmium ions [26].  From the calculated set of Ω t intensity parameters the electric dipole transition probabilities A JJ' for emissions between J and J' manifolds of Ho 3+ were calculated using the equation: Evaluated probabilities A JJ' of the radiative transitions from the excited states, the branching ratios β calc and resulting radiative lifetimes are presented in Table 3. The values of radiative lifetimes of the 3 D 3 , 5 F 3 , 5 S 2 , 5 F 5 , 5 I 4 , 5 I 5 , 5 I 6 and 5 I 7 were calculated to be: 477 µs, 217 µs, 211 µs, 372 µs, 5.34 ms, 3.37 ms, 2.83 ms and 8.02 ms, respectively.  The emission characteristic of the crystal was measured at room temperature in the 250 nm-2.5 µm spectral range after CW excitation. All experimentally observed emission lines corresponding to transitions from the 3 D 3 , 5 F 3 , 5 S 2 , 5 F 5 , 5 I 6 and 5 I 7 excited states of SrLaGaO 4 :Ho 3+ are presented in Figure 4. The emission spectrum is dominated by 5 S 2 → 5 I 8 transition, resulting in the strongest luminescence line at about 550 nm. The emission characteristic of the crystal was measured at room temperature in the 250 nm-2.5 μm spectral range after CW excitation. All experimentally observed emission lines corresponding to transitions from the 3 D3, 5 F3, 5 S2, 5 F5, 5 I6 and 5 I7 excited states of SrLaGaO4:Ho 3+ are presented in Figure 4. The emission spectrum is dominated by 5 S2 → 5 I8 transition, resulting in the strongest luminescence line at about 550 nm.

Luminescence Dynamics
Fluorescence decay curves were registered after wavelength selective pulsed excitation. Figure 5 shows decay profiles of the 3 D3, 5 S2, 5 F5, 5 I6 and 5 I7 emissions in 0.3% Ho 3+ doped SrLaGaO4 measured at 300 K. The fluorescence lifetimes of 3 D3, 5 S2, 5 F5, 5 I6 and 5 I7 manifolds were determined with estimated relative errors of 1% to be of 35 μs, 98 μs, 6 μs, 1 ms and 4 ms, respectively. Due to the large energy gap to the next lying lower level of about 4000 cm −1 the 5 I6 and 5 I7 decays could be considered as being predominantly radiative which was confirmed by its temperature independence.

Luminescence Dynamics
Fluorescence decay curves were registered after wavelength selective pulsed excitation. Figure 5 shows decay profiles of the 3 D 3 , 5 S 2 , 5 F 5 , 5 I 6 and 5 I 7 emissions in 0.3% Ho 3+ doped SrLaGaO 4 measured at 300 K. The fluorescence lifetimes of 3 D 3 , 5 S 2 , 5 F 5 , 5 I 6 and 5 I 7 manifolds were determined with estimated relative errors of 1% to be of 35 µs, 98 µs, 6 µs, 1 ms and 4 ms, respectively. Due to the large energy gap to the next lying lower level of about 4000 cm −1 the 5 I 6 and 5 I 7 decays could be considered as being predominantly radiative which was confirmed by its temperature independence.

Luminescence Dynamics
Fluorescence decay curves were registered after wavelength selective pulsed excitation. Figure 5 shows decay profiles of the 3 D3, 5 S2, 5 F5, 5 I6 and 5 I7 emissions in 0.3% Ho 3+ doped SrLaGaO4 measured at 300 K. The fluorescence lifetimes of 3 D3, 5 S2, 5 F5, 5 I6 and 5 I7 manifolds were determined with estimated relative errors of 1% to be of 35 μs, 98 μs, 6 μs, 1 ms and 4 ms, respectively. Due to the large energy gap to the next lying lower level of about 4000 cm −1 the 5 I6 and 5 I7 decays could be considered as being predominantly radiative which was confirmed by its temperature independence. Knowing values of radiative and measured lifetimes, the rates of multiphonon relaxations can be simply calculated using the equation: Calculated radiative lifetimes, measured at low temperature lifetimes, the energy gaps to the next lower level and the multiphonon transition rate for excited states of Ho 3+ in SrLaGaO 4 are shown in Table 4. Dependence of the multiphonon transition probability W nr on the energy gap to the next lower level ∆E can be described as an exponential function [30]: The W nr (∆E) dependence, together with the data for low phonon ZBLAN glass [31], is shown in Figure 6. The values of W 0 and α in Equation (6) were calculated as 0.5 × 10 7 s −1 and 2.6 × 10 −3 cm, respectively.

I7
8015 4000 4225 125 Dependence of the multiphonon transition probability Wnr on the energy gap to the next lower level ΔE can be described as an exponential function [30]: The Wnr(ΔE) dependence, together with the data for low phonon ZBLAN glass [31], is shown in Figure 6. The values of W0 and α in Equation (6) were calculated as 0.5 × 10 7 s −1 and 2.6 × 10 −3 cm, respectively.
. Figure 6. The multiphonon relaxation rate Wnr as a function of energy gap ΔE for the excited states of Ho 3+ ion in SrLaGaO4-red line. Open circles denote experimental points. For comparison the data for ZBLAN glass are also presented-blue solid line.
As can be observed from Figure 6 the nonradiative decay rates in SLO are about one order of magnitude higher than in ZBLAN. The difference in results from higher in the case of SLO of the the phonon frequency distribution function, which is approximately hωmax = 707 cm −1 [32], than in ZBLAN matrix, which is 580 cm −1 [3]. As can be observed from Figure 6 the nonradiative decay rates in SLO are about one order of magnitude higher than in ZBLAN. The difference in results from higher in the case of SLO of the the phonon frequency distribution function, which is approximately hω max = 707 cm −1 [32], than in ZBLAN matrix, which is 580 cm −1 [3].

Excited State Absorption Transitions
The high number of long-lived multiplets present in Ho 3+ acting as good population reservoirs leads to the possibility of ESA transitions into higher lying energy levels. The intermediate levels for ESA are therefore 5 I J states (J = 5, 6, 7). Using the Judd-Ofelt formalism it is possible to estimate the ESA integrated cross sections by means of the following expression: where λ is the mean wavelength corresponding to the ESA transition. With this method, the ESA transition cross sections in the spectral range between 400 and 5000 nm in Ho 3+ -doped SLO were calculated and are presented in Figure 7, together with the GSA cross sections.

Excited State Absorption Transitions
The high number of long-lived multiplets present in Ho 3+ acting as good population reservoirs leads to the possibility of ESA transitions into higher lying energy levels. The intermediate levels for ESA are therefore 5 IJ states (J = 5, 6, 7). Using the Judd-Ofelt formalism it is possible to estimate the ESA integrated cross sections by means of the following expression: where λ is the mean wavelength corresponding to the ESA transition. With this method, the ESA transition cross sections in the spectral range between 400 and 5000 nm in Ho 3+ -doped SLO were calculated and are presented in Figure 7, together with the GSA cross sections.   Figure 7 also illustrates that several infrared excitation wavelengths could lead to population of the 5 S 2 state from which green anti-Stokes emission results. These processes for excitation in the 720-750, 870-920 and 960-1000 nm spectral ranges are interpreted in Figure 8 and are confirmed by the excitation spectrum of up-converted 5 S 2 green emission presented in Figure 9. Similar spectra were also reported for other Ho 3+ activated systems [14].  Figure 7 also illustrates that several infrared excitation wavelengths could lead to population of the 5 S2 state from which green anti-Stokes emission results. These processes for excitation in the 720-750, 870-920 and 960-1000 nm spectral ranges are interpreted in Figure 8 and are confirmed by the excitation spectrum of up-converted 5 S2 green emission presented in Figure 9. Similar spectra were also reported for other Ho 3+ activated systems [14].   On the other hand, the energy level diagram in Figure 8 illustrates that in the upconversion excitation of 5 S2 emission several near-resonant transitions, with participation of low energy phonons, are involved. It can also be observed that energies of GSA and ESA transitions are in close proximity, so it is difficult to indicate one responsible process. We have focused our attention on the 750 nm excitation band, as it was reported to be responsible for the efficient photon avalanche process that occurs in Ho 3+ activated solids [33].
As results from Figure 8, after 750 nm excitation, the first step is the weak quasiresonant GSA 5 I8 → 5 I4 absorption, followed by non-radiative de-excitation to the 5 I6 and 5 I7 metastable levels which act as intermediate levels. The next steps are: a strong resonant ESA 5 I7 → 5 S2, 5 F4 and non-resonant ESA 5 I6 → 5 G6, 5 F1 transitions followed by non-radiative de-excitation to the 5 S2, 5 F4 levels from which an intense green emission is obtained.
Calculated GSA and ESA absorption cross section values for transitions involved in the 750 nm excitation process for SrLaGaO4 and several other Ho 3+ activated materials are summarized in  On the other hand, the energy level diagram in Figure 8 illustrates that in the upconversion excitation of 5 S 2 emission several near-resonant transitions, with participation of low energy phonons, are involved. It can also be observed that energies of GSA and ESA transitions are in close proximity, so it is difficult to indicate one responsible process. We have focused our attention on the 750 nm excitation band, as it was reported to be responsible for the efficient photon avalanche process that occurs in Ho 3+ activated solids [33].
As results from Figure 8, after 750 nm excitation, the first step is the weak quasiresonant GSA 5 I 8 → 5 I 4 absorption, followed by non-radiative de-excitation to the 5 I 6 and 5 I 7 metastable levels which act as intermediate levels. The next steps are: a strong resonant ESA 5 I 7 → 5 S 2 , 5 F 4 and non-resonant ESA 5 I 6 → 5 G 6 , 5 F 1 transitions followed by non-radiative de-excitation to the 5 S 2 , 5 F 4 levels from which an intense green emission is obtained.
Calculated GSA and ESA absorption cross section values for transitions involved in the 750 nm excitation process for SrLaGaO 4 and several other Ho 3+ activated materials are summarized in Table 5. The cross-sections of the non-resonant transitions from 5 I 7 and 5 I 6 to the multi-phonon side bands were calculated in the framework of formalism developed by Auzel [34] who showed that the probability for Stokes excitation with respect to an energy gap ∆E to the electronic level is given by: where α S is related to the multi-phonon nonradiative decay parameter α NR by where N = E/hω is the average order of the multi-phonon process, S 0 is the Huang-Rhys electron-phonon coupling parameter at 0 K and hω is the highest phonon frequency of the host. The values of the integrated cross sections calculated according to Equation (7)  Considering the 750 nm excitation conversion to 5 S 2 green emission following values of squared matrix elements, |U λ | 2 should be considered. In Figure 10 the S ed values' dependence on Ω t is presented. The values of the integrated cross sections calculated according to Equation (7)  . Considering the 750 nm excitation conversion to 5 S2 green emission following values of squared matrix elements, ⏐Uλ⏐ 2 should be considered. In Figure 10 the Sed values' dependence on Ωt is presented. It thus results that in the considered 750 nm excitation, the ESA ( 5 I7 → 5 S2 + 5 F4) is the most important process and that for its cross-section to be large, materials with a high value of the Ω6 parameter should be chosen. Thus, according to the Judd-Ofelt parameters presented in Table 2, the highest ( 5 I7 → 5 S2 + 5 F4) ESA cross-sections could be expected for Ho 3+ :LiYF4 crystal. This is confirmed by the data reported by Kuck et al. [35]. From Table  6 and Figure 10 it can also be seen that the 5 I8 → 5 I4 GSA is only Ω6 dependent. It thus results that in the considered 750 nm excitation, the ESA ( 5 I 7 → 5 S 2 + 5 F 4 ) is the most important process and that for its cross-section to be large, materials with a high value of the Ω 6 parameter should be chosen. Thus, according to the Judd-Ofelt parameters presented in Table 2, the highest ( 5 I 7 → 5 S 2 + 5 F 4 ) ESA cross-sections could be expected for Ho 3+ :LiYF 4 crystal. This is confirmed by the data reported by Kuck et al. [35]. From Table 6 and Figure 10 it can also be seen that the 5 I 8 → 5 I 4 GSA is only Ω 6 dependent. The ratio between the GSA and ESA cross sections (β = GSA/ESA) is an important parameter for establishing the photon avalanche process. It was proposed in [36] that a β value lower than 10 −4 is necessary to expect avalanche up-conversion. Above this limit, the up-conversion emission does not exhibit any pump threshold. Evaluated here β = GSA/ESA is about 4 × 10 −3 and is beyond the limit for photon avalanche up-conversion to occur.

Conclusions
The spectroscopy and the fluorescence dynamics of SrLaGaO 4 crystal doped with Ho 3+ ions have been studied in detail and analyzed. Based on polarized absorption spectra, the Judd-Ofelt intensity parameters were determined and radiative transition probabilities for several Ho 3+ excited states were calculated. This, together with the measured fluorescence lifetimes, allowed evaluation of the multiphonon relaxation parameters for SLO matrix.
Several ESA mechanisms which generate the green emission from the 5 S 2 level in SLO under 750, 900 and 980 nm band excitations have been proposed. The Judd-Ofelt analysis, which is usually performed for transitions from the ground-state manifold, was used to determine the integrated cross-sections of the ESA transitions and to predict the possibility of photon avalanche up-conversion occuring under 750 nm pumping.