4.1.1 Ho³⁺-doped FIG

The optical properties of Ho³⁺-doped glasses and crystals have been studied aiming to the operation of UPC lasers 〚48, 49〛. Blue–green UPC luminescence owing to 4f–4f transitions of Ho³⁺ has been observed upon visible and infrared excitation, with efficiencies that are highly dependent on the host matrix 〚50, 51〛, demonstrating the importance of studying UPC processes in new materials.

In this section, we discuss the UPC phenomenon in Ho³⁺-doped FIG excited by a nanosecond laser operating at 640 nm. Green and blue anti-Stokes emissions owing to ET mechanisms were observed and the analysis of the results allowed us to identify the pathways that contribute to the UPC emissions.

The absorption spectrum of sample Ho5 is shown in Fig. 1a. No changes were observed in the lineshape or in the peak positions corresponding to the various transitions, for different Ho³⁺ concentrations. The method of spectral-band intensity analysis 〚52〛 was used to estimate the JO parameters of our samples; the values are presented in Table 2.

The UPC spectrum is shown in Fig. 2 for excitation at 640 nm, in resonance with the transition ⁵I₈→⁵F₅. Fig. 2a shows two bands centered at ∼550 nm and ∼490 nm due to transitions ⁵S₂→⁵I₈ and ⁵F₃→⁵I₈, respectively, while Fig. 2b shows bands centered at ∼395 nm and ∼425 nm corresponding to transitions (³K₇, ⁵G₄)→⁵I₈ and ⁵G₅→⁵I₈, respectively. The intensities of the bands shown in Fig. 2b are two orders of magnitude weaker than those shown in Fig. 2a.

The green luminescence at ∼550 nm presented a rise time between 3.2 and 4.2 μs, and a decay time that changes more than 50% (116 to 48 μs) for the range of Ho³⁺ concentrations investigated here. The blue emission at ∼490 nm presented a rise time that is shorter than the green signal rise time and shows a double exponential decay. The longer decay time component of the blue emission (22 to 18 μs) is dependent on the Ho³⁺ concentration. The results are summarized in Table 3. The dependence of the UPC signal as a function of pump intensity and Ho³⁺ concentration were also investigated. A quadratic dependence was observed in both experiments indicating that two laser photons are absorbed to originate each UPC photon and a pair of Ho³⁺ ions are involved in the UPC process. The emissions at ∼380 nm and ∼440 nm are very weak and it was not possible to analyze their temporal behavior. It is important to note that these emissions have not been observed in other glass hosts 〚53〛, probably because their intensities were strongly reduced, due to nonradiative relaxation.

Fig. 3 shows the energy level diagram of Ho³⁺ and the main pathways responsible for the UPC processes. We expect that the UPC emission is due to ET between two ions at level ⁵F₅, which are directly excited by laser photons at 640 nm. The lifetime of level ⁵F₅ is large enough to allow significant ET between excited ions and two possible channels may populate level ⁵F₃ via ET. One channel is an indirect ET assisted UPC (ETAU) via ⁵F₅ + ⁵F₅→⁵I₇ + (³K₇, ⁵G₄), with subsequent population decay to level ⁵F₃ via multiphonon emission from levels ⁵G₄ and ³K₇. The other channel is related to a direct ETAU via ⁵F₅ + ⁵F₅→⁵I₅ + ⁵F₃. We observed that the intensity of the UPC signal shows a quadratic dependence with Ho³⁺ concentration, which indicates that pair interaction is a relevant process.

Using a rate equations approach to describe the UPC process, it is possible to estimate the ET rates from level ⁵F₅ to level ⁵F₃ considering the following equations:

The fluorescence intensity at ∼490 nm is proportional to n₂(t) and, from the data shown in Table 3, we associate γ₂ to the short-decay time component and therefore it is related to level ⁵F₃ lifetime (estimated ca 5 μs from Table 2). The value of (γ₃)^–1 is dominated by (γ₃₂)^–1 ∼0.6 μs, while the lifetime of ⁵F₅ is ∼47 μs. The Stokes shifted emission at 653 nm (transition ⁵F₅→⁵I₈) was used to evaluate the lifetime of level ⁵F₅ using the less concentrated sample available with low excitation power at 640 nm. The signal decay was fitted with a single exponential curve yielding ∼ 47 μs of decay time. Therefore (γ₃)^–1 is associated to the rise time of the blue luminescence while (2 γ₁ + W₁₂ + W₁₃)^–1 is associated with the decay time. The cross-relaxation rates found are shown in Table 4. The measured rise time (0.4 μs), shorter than the value estimated via multiphonon emission rates from level (³K₇, ⁵G₄), may be due to the fact that the signal centered at ∼490 nm has a contribution from excited pairs decaying coherently (simultaneously) to lower-lying energy levels on a faster timescale than those pairs decaying incoherently. Values for A, B and C were obtained fitting the expression for n₂(t) to the experimental data for the intensity decay.

To understand the behavior of the emission at ∼550 nm, we assume that the population at level ⁵S₂ is loaded via level ⁵F₃, because the rise time of the green fluorescence has the same order of magnitude as the lifetime of state ⁵F₃, which is dominated by the nonradiative relaxation ⁵F₃ → ⁵S₂ (2 × 10⁵ s^–1). We recall that the green fluorescence decay time is dependent on the Ho³⁺ concentration, as indicated in Table 3. The cross-relaxation channel that depopulates level ⁵S₂ (⁵S₂ + ⁵I₈ → ⁵I₄ + ⁵I₇) is efficient only after the cross-relaxation processes that lead to the blue luminescence takes place (see Fig. 3) 〚53〛. Again, the rate equations approach is used to estimate the cross-relaxation rates from level ⁵S₂ through the following equations:

Here, 1 corresponds to level ⁵F₃ and 2 is associated to level ⁵S₂. The parameter ${\gamma }_1^{\text{'}}\left({\gamma }_2^{\text{'}}\right)$ is the decay rate of level ⁵F₃ (⁵S₂) and W_R is the cross-relaxation rate. The ground state population was assumed to be non-depleted and thus the solution of the rate equations system yielded a simple equation that governs the dynamics of the population at level ⁵S₂, given by $n_2^{\text{'}}\left(t\right)=\mathrm{A}{e}^{-{\gamma }_1^{\text{'}}t}-{\mathrm{Be}}^{-\left({\gamma }_2^{\text{'}}+{\mathrm{W}}_{\mathrm{R}}\right)t}$. The parameter ${\left({\gamma }_1^{\text{'}}\right)}^{-1}$ is the lifetime of level ⁵F₃ and ${\left({\gamma }_2^{\text{'}}+{\mathrm{W}}_{\mathrm{R}}\right)}^{-1}$ corresponds to the quenched lifetime of level ⁵S₂. As the values of γ^′₁ and γ^′₂ are known, it is straightforward to find W_R from the data of Tables 2 and 3. The values found for W_R are shown in Table 4.

4.1.2 Tm³⁺-doped FIG

Thulium (Tm³⁺) is one of the most efficient rare-earth ions for obtaining laser emission, frequency upconversion, as well as to be used in optical amplifiers, when doping different hosts 〚44, 54, 55〛. Frequency upconversion in a variety of Tm³⁺ doped materials has also been investigated 〚23, 56–62〛. Of particular interest is the possibility of obtaining strong blue emission from Tm³⁺ doped materials pumped in the red and in the infrared. Upconversion laser emission and amplified spontaneous emission studies have been reported for Tm³⁺ doped optical fibers 〚63, 64〛.

In this section we present spectroscopic properties of FIG samples doped with Tm³⁺. Fig. 1b shows the absorption spectrum of one of the samples. The dynamics of the fluorescence was studied and a model for the UPC process is given. Rates of energy transfer between Tm³⁺ ions are also provided.

From the absorption spectra of the samples studied we calculated the JO parameters: O₂ = 2.36 × 10^–20 cm², O₄ = 1.59 × 10^–20 cm², and O₆ = 1.21 × 10^–20 cm². Oscillator strengths, branching ratios, radiative lifetimes and multiphonon relaxation rates were determined for all Tm³⁺ levels and the results are presented in Tables 5 and 6.

Fluorescence measurements were performed tuning the dye laser wavelength from 624 to 686 nm. Fig. 4 shows the emission spectrum of the sample Tm10 pumped at 650 nm, in resonance with transition ³H₆→³F₂. The band centered at 12 625 cm^–1 corresponds to transition ³F₄→³H₆. The UPC emissions are associated to transitions ¹D₂→³F₄ (22 220 cm^–1) and ¹D₂→³H₆ (27 550 cm^–1). The emissions from state ¹D₂ present a quadratic dependence with the laser intensity and the excitation spectrum of both UPC emissions show a peak at 658 nm. No UPC emission is observed when the laser is tuned to transition ³H₆→³F₃.

The time evolution of the fluorescence shows a non-exponential decay for the three samples studied indicating the contribution of ion–ion interactions. Signal risetimes in the range from 150 ns to 316 ns, depending on the Tm³⁺ concentration, were measured for transition ³H₄→³H₆ with decay times varying from 560 to 44 μs. The risetime of the UPC transitions follows the laser pulse, while the decay time decrease from 26 to 6 μs as the Tm³⁺ concentration increases. The identified UPC pathway is indicated in Fig. 5, where the excited state absorption ³H₄→¹D₂ is indicated as the dominant process.

Interaction between Tm³⁺ ions, as revealed by the non-exponential decay of transitions ¹D₂→³F₄, ¹D₂→³H₆ and ³H₄→³H₆, was studied using the Inokuti–Hirayama procedure 〚65, 66〛. The results indicate a dominant dipole–dipole interaction between Tm³⁺ ions. The data allowed us to determine the critical radius for different concentrations as shown in Table 7. A comparison of the critical radius with the average distance between ions suggests the presence of Tm³⁺ clusters in the samples. Formation of clusters may contribute to increase the UPC efficiency of the samples but it may be detrimental for operation of lasers. On the other hand, clusters may also favor radiation quenching, which is not of interest in general. Of course, further improvements in the preparation techniques have to be introduced to have control of clustering formation for particular applications.

4.1.3 Pr^3+/Nd³⁺-codoped FIG

UPC processes involving pairs of Pr³⁺ or pairs of Nd³⁺ were reported in the past. For instance, in crystals doped with Pr³⁺, it was identified a process where two Pr³⁺ ions in the excited state ¹D₂ exchange energy in such way that one of the ions decays nonradiatively to the ground state, while the other one is promoted to multiplet (³P_J, ¹I₆). Emission at 480 nm due to transition ³P₀ → ³H₄ and a weak emission at 470 nm due to transition (³P₁, ¹I₆)→³H₄ were observed 〚67–69〛. In glasses this effect was originally reported in 〚70〛 and later in 〚31, 71〛. Processes involving pairs of Nd³⁺ ions that exchange energy were studied in crystals 〚72, 73〛 and, recently, similar processes were observed in FIG 〚34, 74–77〛, where efficient UPC emission was detected. Experiments were also reported involving triads Nd³⁺–Pr³⁺–Pr³⁺ in LaF₃ 〚78〛 and UPC due to triads of Pr³⁺ was observed in LaF₃:Pr³⁺ 〚79, 80〛. More recently, UPC due to Nd³⁺ triads was investigated in crystals 〚81〛 and in fluoroindate glasses 〚35〛.

In this section we discuss evidences of ET processes involving triads and quartets of Nd³⁺/Pr³⁺ ions.

The absorption spectrum of the sample Pr2Nd2 in the visible range is shown in Fig. 1c. The broad features can be identified with transitions originating from the Pr³⁺ ground state (³H₄) and from the Nd³⁺ ground state (⁴I_9/2). The spectrum obtained for the sample Pr2Nd1 is similar, with no changes in the wavelengths of maximum absorption. All transitions are inhomogeneously broadened and the bands intensities are dependent on the ions concentrations. The spectrum of the sample without Nd³⁺, but with 0.2% of Pr³⁺, was previously reported 〚31〛.

The emission spectrum for excitation at 588 nm is shown in Fig. 6 for the sample with Pr2Nd1. The four bands located from 350 to 460 nm are due to Nd³⁺ transitions, and the peaks at 470 and 480 nm are due to Pr³⁺ ions. The states involved in the transitions are indicated in Fig. 6.

To characterize the UPC pathways, the intensity of each fluorescence band was measured as a function of the laser intensity. The signals present a quadratic dependence with the laser intensity, which indicates that two laser photons are required to generate each UPC photon emitted. Time-resolved fluorescence measurements were also performed varying the wavelength of the pump dye laser between 577 and 588 nm.

With basis on the signal behavior as a function of the laser intensity, we first investigate the possibility that the fluorescence emission at ∼470 nm and ∼480 nm could be produced via the process reported in 〚67–69〛. However, although ET between two Pr³⁺ ions may be involved in the process that enables emission at 480 and 470 nm, the presence of Nd³⁺ plays an important role in the process. This was verified comparing the UPC efficiency of the Nd³⁺/Pr³⁺-codoped samples with the efficiency of a sample with 0.2% of Pr³⁺ only. An enhancement of the UPC intensity at 480 nm and at 470 nm, by two orders of magnitude with respect to a sample without Nd³⁺, was observed in the codoped samples. This is understood considering that: (i) the presence of Nd³⁺ increases the number of possible excitation pathways; (ii) the oscillator strength of the ⁴I_9/2→(²G_7/2 + ⁴G_5/2) transition in Nd³⁺ is, approximately, five times larger than for transition ³H₄→¹D₂ in Pr³⁺, and (iii) because of the large ET efficiency between Nd³⁺ and Pr³⁺ ions 〚78, 81, 82〛. Thus, the emission at 480 nm and 470 nm may be due to processes that involve pairs (Pr–Pr), triads (Nd–Pr–Pr) or quartets (Nd–Pr–Pr–Nd). The last two process are more probable because of the enhancement factor of ∼100 observed in the samples containing both Nd³⁺ and Pr³⁺. We expect that the absorption of laser photons occur mainly through Nd³⁺ ions, which resonantly transfer their energy to the Pr³⁺ ions in their neighborhood. ET from Nd³⁺ at (²G_7/2+⁴G_5/2) states to Pr³⁺ is a resonant process where the acceptors make transition ³H₄→¹D₂, while the donor Nd³⁺ ion decays to the ground state. Following this step, two Pr³⁺ acceptors in state ¹D₂ exchange energy and one of them is promoted to the multiplet (³P_J, ¹I₆). The other ion decays to the ground state. Finally emission corresponding to ³P₀→³H₄ at 480 nm is observed. Fig. 7 illustrates the UPC process in the quartet case with the relevant states written, in a first approximation, as a direct product of the ions states. The triad and dyad cases can be represented in an analogous way. The rate equations for the density of populations, n_i (i = 1, 2, 3), in the quartets levels can be written as:

The system of equations (11)–(13) has the following solution for t > τ, where τ is the laser-pulse duration.

Fig. 8 shows the fluorescence temporal profile for the sample Pr2Nd1 where the solid line represents a fitting of the n₃(t) function, as given in equation (15). The numerical fitting gives a reasonable set of parameters, where it is possible to identify the ³P₀ lifetime, (γ₃^–1) ∼ 14 μs, and the ¹D₂ lifetime, (W₂₃ + γ₂)^–1 ∼ 106 μs. Unfortunately, it was not possible to obtain a value for the ET rate from Nd³⁺ to Pr³⁺, because the nonradiative transition rate between levels 1 and 2 is very large due to the small energy gap of ∼650 cm^–1 between the two levels. Also it is impossible to determine unambiguously the main UPC mechanism (due to triads or quartets) via the temporal fluorescence analysis, because the estimated differences in the time evolution for triads or quartets is less than 1 ns, which is below the resolution of our data acquisition system. Moreover, it is not possible to infer, on the basis of the statistical distribution of ions, which contribution is more important, because, although the number of quartets would be smaller than the number of triads for a homogeneous distribution of RE ions, the probability of quartets excitation is at least five times larger than for the triads. Clustering of RE ions is another possibility that makes the analysis more difficult. All these points will be investigated in further work.

4.2.1 Nd³⁺ doped FIG

The study of multiphonon (MP) assisted processes in RE-doped materials has been a subject of large interest. In the past, luminescence and UPC mediated by phonons have been analyzed by Auzel et al. 〚83–86〛. They demonstrated that it is possible to induce luminescence in solids doped with RE ions, even when the difference between the excitation frequency and the electronic-transition frequency is larger than the maximum phonon frequency of the host material. This was observed both for transitions involving creation or annihilation of phonons. Furthermore, contrary to what was generally thought, Auzel et al. 〚83–86〛 showed that MP-assisted processes should be described in terms of an ‘effective phonon mode’ – EPM (or ‘promoting mode’), with a frequency smaller than the phonon cut-off frequency of the host material. Recently, it was demonstrated that besides the scientific interest, studies of phonon-assisted processes are useful to photonic applications such as phase conjugation 〚87〛, lasers 〚88〛, avalanche UPC 〚89〛 and laser cooling of solids 〚90〛.

In this section, we show that UPC processes assisted by MP absorption can be highly efficient if optical transitions and thermal coupling between electronic levels are conveniently exploited. Our studies were mainly concentrated in the investigation of MP assisted UPC process from 866 nm to 750 nm. A forty-fold enhancement of the UPC emission intensity was observed when the temperature of the sample was varied from 298 to 498 K.

The absorption spectrum of a Nd-doped sample is shown in Fig. 1d.

The upconverted fluorescence spectrum was observed with several emission bands located from 350 to 750 nm. They are mainly due to UPC processes involving ET between two and three Nd³⁺ ions. These processes were studied previously in Ref. 〚34, 35, 75–77〛. However, the line centered at 750 nm presents a linear dependence with the laser power and it was assigned as a transition from level ⁴F_7/2 to the ground state. It originates through a process where one laser photon is absorbed to level ⁴F_3/2, followed by successive absorption of phonons to ⁴F_7/2 via the thermally coupled excited state ⁴F_5/2, as indicated in Fig. 9.

We monitored the integrated fluorescence emission at 750 nm as a function of the sample temperature, while the laser intensity was kept constant at 160 mW. The data obtained are presented in Fig. 10, which shows a signal increase when the temperature is varied from 298 to 498 K. The solid line in the figure represents theoretical results which are obtained considering the subset of energy levels corresponding to ⁴I_9/2 (level 0); ⁴F_3/2 (level 1); ⁴F_5/2 (level 2), ⁴F_7/2 (level 3) and ²P_1/2, ²D_5/2 (level 4) and following the approach described below. A rate equation system written for the population densities n_i (i = 1, 2, 3) assumes the form:

The steady-state population of ⁴F_7/2 level can be found solving equations (16)–(18) and is given by:

The signal intensity shown in Fig. 9 is proportional to n₃(T). Thus, in order to compare equation (19) with the data of Fig. 10, the following procedure was used. To determine n₃(T), a reference temperature (T₀ = 300 K) was chosen and $W_i^{\mathrm{NR}}\left(T\right)$ was determined through the following expression obtained from 〚91, 92〛:

The comparison of equation (19) to the experimental results shown in Fig. 10 was made and the best agreement is observed when EPM are assumed to participate in all MP processes, as proposed in 〚83–86〛. The parameters obtained from the fitting were q = 1, q₁₂ = q₂₃ = 3 and ω = 310 cm^–1. Also shown in Fig. 10 is a curve (dashed line) obtained from equation (19) for ω = 507 cm^–1 which is the energy of the most energetic phonons in the FIG matrix 〚7〛. The mismatch of the dashed line with the experimental points obviates that the most energetic phonons do not dominate the MP absorption processes. In fact, several phonon modes contribute in a way that is determined by the phonon distribution density of states (PDDS) and the description in terms of EPM represents a kind of statistical average, which takes into account the characteristics of the PDDS. The value of ω = 310 cm^–1 obtained from equation (19) corresponds to the EPM frequency of the glassy matrix. A comparison of this result with the results of 〚83〛 for ZBLAN glass (phonon cut-off frequency: ∼580 cm^–1, EPM frequency: 325 cm^–1) indicates a similar energy dependence of the PDDS in both materials.

The results presented above, together with the previous ones reported in 〚91, 92〛, provide indication that the exploitation of MP processes may increase the efficiency of RE-doped systems for particular applications. On the basis of the results above as well as those of 〚91, 92〛, we believe that further exploitation of MP processes may improve the performance of RE-doped upconverters. Of course, in all cases, one must work in temperatures far below the onset of crystallization of the sample.

4.2.2 Yb^3+/Tb³⁺-codoped FIG

In this section, we report the observation of multiphonon-assisted cooperative energy transfer (MACET) between rare-earth ions in FIG. Bright UPC fluorescence from Tb³⁺ ions is observed due to MACET from Yb³⁺ ions excited using an infrared diode laser. This is a new effect reported here for the first time.

The absorption spectrum of a Yb³⁺/Tb³⁺ sample is shown in Fig. 1e.

Fig. 11 shows a typical UPC fluorescence spectrum for excitation at 1064 nm, whose frequency is ∼820 cm^–1, i.e. below the ²F_7/2 → ²F_5/2 resonance of Yb³⁺ ions. The UPC emissions observed are due to Tb³⁺ ions and the corresponding transitions are indicated in the figure. The intensity dependence of the lines at ∼414 nm and ∼545 nm were determined as a function of the laser intensity and showed cubic and quadratic behavior respectively, indicating that three and two laser photons are involved in the UPC processes. The emissions at 545 nm are explained considering that initially Yb³⁺ ions are excited to the ²F_5/2 state by the pump laser with the simultaneous absorption of phonons. Then, cooperative energy transfer between a pair of excited Yb³⁺ ions and a neighbor Tb³⁺ ion in the ground state occurs. Therefore, the Tb³⁺ ion is promoted to state ⁵D₄ and afterwards green fluorescence is emitted.

The blue emission at ∼414 nm also originates from the same MACET process, but after excitation to ⁵D₄, a laser photon is absorbed promoting the Tb³⁺ ion to state ⁵D₁, or a neighbor level, which decays later to ⁵D₃ and ⁵G₆. Finally, radiative emissions from ⁵D₃ and ⁵D₆ to lower Tb³⁺ energy levels take place. The UPC pathways are illustrated in Fig. 12, which exhibits a simplified level scheme of the interacting atoms.

The solid lines indicate the laser excitation and the dotted lines represent the multiphonon absorption process. The dashed lines represent the cooperative energy transfer process. We observed that the blue and green UPC intensity was increased by a factor of ∼55 when the temperature was varied from 300 to 530 K. A detailed study of this UPC process will be published elsewhere.