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Abstract
We present spectroscopic properties of the low-maximum-phonon energy host material, barium fluoride (BaF2) doped with Er3+ ions. Following optical excitation at 800 nm, Er3+:BaF2 exhibited broad mid-IR emission bands centered at ∼2.75, ∼3.5, and ∼4.5 µm, corresponding to the 4I11/2 → 4I13/2, 4F9/2 → 4I9/2 and 4I9/2 → 4I11/2 transitions, respectively. Temperature-dependent fluorescence spectra and decay times were recorded for the 4I9/2 level, which was resonantly excited at ∼800 nm. The multi-phonon decay rates of several closely spaced Er3+ transitions were derived using the well-known energy-gap law, and the host-dependent energy-gap law parameters B and α were determined to be 9.15 × 108 s−1 and 5.58 × 10−3 cm, respectively. The obtained parameters were subsequently used to describe the temperature dependence of the ∼4.5 µm mid-IR emission lifetime in a temperature range of 12 - 300 K. The stimulated emission cross-section of the 4I9/2 → 4I11/2 transition of Er3+ ion was derived for the first time among the known fluoride hosts, to the best of our knowledge, and found to be 0.11 × 10−20 cm2 at room temperature and 0.21 × 10−20 cm2 at 77 K.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Lasers that operate at wavelengths in the mid-IR spectral region (3–5 µm) are of great interest for military, remote sensing, and medical applications [1–4]. Progress on the development of mid-IR solid-state lasers beyond 3 µm has been limited by the lack of suitable gain materials. The challenge in achieving efficient mid-IR laser generation is the prevalence of multiphonon quenching of the mid-IR emission in most of the known laser hosts. Trivalent rare-earth (RE) dopants exhibit broadband transitions in mid-IR bands of interest but require hosts with low maximum phonon energies to mitigate the impact of nonradiative decay on upper laser level lifetime [1–6]. Novel laser hosts with low maximum phonon energies include certain fluorides [7,8], chlorides [4,9–11], sulfides [12,13], and chalcogenides [14–16]. Among fluoride materials, fluorites (CaF2, SrF2, and BaF2) are laser hosts of interest due to their low maximum phonon energies as well as high thermal conductivities, and compatibility with RE dopants [17–19].
Trivalent erbium (Er3+) is a laser active ion that can produce distinct near- and mid-IR emission lines and can be directly pumped with commercial laser diodes. Studies of visible and upconversion luminescence as well as Judd-Ofelt modeling of Er3+-doped BaF2 crystals were reported [17,20]. More recently, the enhancement of 3.9-µm emission from Ho3+ through sensitization by added Tm3+ dopant has been reported in BaF2 via ∼800-nm excitation [21]. Many studies on the RE-doped fluorites (CaF2, SrF2, CdF2) have been reported up to the 3-µm spectral region and laser operation at 2.7 µm has been demonstrated [18,19]. Orlovskii et al. reported the multiphonon relaxation rates for the mid-IR spectral range in fluorite-type crystals doped with RE ions [5]. In this work, mid-IR (3-5 µm) emission characteristics are explored for Er3+-doped BaF2 single crystals, which have a reported maximum phonon energy of ∼320 cm−1 [17,22].
2. Experimental details
BaF2 has a cubic crystal structure with a space group symmetry of Fm3 m. The unit cell parameter is a = 0.62 nm and the number of molecules per unit cell is Z = 4 [6] BaF2 has a density of 4.89 g/cm3 [17] and a thermal conductivity of 7 W/mK at room temperature [23]. It can be assumed that RE ions are incorporated into the divalent Ba2+ lattice sites, which require a charge compensation mechanism. It was reported that, for RE doped into fluorites, if there is no charge compensating co-dopants [17–19], the compensation is achieved by an interstitial fluorine ion at the nearest neighbor position of either trigonal C3v or tetragonal C4v symmetry. BaF2 has a wide transparency range from 0.2 to 14 µm. Er3+-doped BaF2 crystals were grown by traditional Bridgman technique. The Er3+ concentrations in the samples were determined using inductively coupled plasma optical emission spectroscopy (ICP-OES) by Galbraith Laboratories, Inc.
The room temperature absorption spectra were recorded using a Cary 6000i UV-Vis-NIR spectrophotometer and a Nicolet 6700 Fourier-transform infrared spectrometer. All mid-IR fluorescence spectra were excited by a continuous-wave Spectra-Physics Tsunami Ti:Sapphire laser. Either a Horiba Fluorolog-3 system with an iHR-320 monochromator (λblaze: 2 µm, 300 grooves/mm) or a Princeton Instruments Acton SpectraPro 0.15-m monochromator (λblaze: 4 µm, 150 grooves/mm) was used to collect the mid-IR emissions. The emission signal was recorded by an Infrared Associates liquid-nitrogen-cooled InSb detector in conjunction with a Stanford Research Systems SR830 dual-phase lock-in amplifier. Fluorescence decay measurements were carried out using the output of a pulsed (10-ns pulses, 10 Hz) Nd:YAG pumped Optical Parametric Oscillator system as an excitation source. The decay signal was recorded with a LabVIEW-driven National Instruments (USB-6366 DAQ) data acquisition system. For temperature-dependent emission studies down to 10 K, the sample was mounted on the cold finger of a two-stage closed-cycle CTI Cryodyne cryogenic refrigerator. All the emission spectra presented in this work were corrected for the experimental system response (to include grating, optics, detector, and moisture in the atmosphere).
3. Results and discussion
3.1 Absorption and overview emission spectra
Figure 1 shows the ground state absorption cross section spectrum of Er3+:BaF2 in the 400- to 1700-nm region. The absorption cross section was calculated using an Er3+ concentration of ∼1.55 × 1020 cm−3 for Er3+:BaF2 crystal as measured by Galbraith Laboratories, Inc. The absorption bands of Er3+ ions were centered at ∼1519, 977, 802, 652, 541, 486, and 406 nm corresponding to transitions from the 4I15/2 ground state to the 4I13/2, 4I11/2, 4I9/2, 4F9/2, 2H11/2+4S3/2, 4F7/2, and 2H9/2, respectively. The Er3+ absorption band at ∼800 nm (4I15/2 → 4I9/2), which can be of importance for laser diode pumping, shows a peak absorption cross section of ∼0.145 × 10−20 cm2.
Fig. 1. Room temperature absorption cross-section spectrum of Er3+:BaF2 in the 400 - 1700nm spectral region. Intra-4f absorption bands from the 4I15/2 ground state to higher excited states of Er3+ are indicated.
Judd-Ofelt (J-O) analysis was performed from the absorption data depicted in Fig. 1. The magnetic dipole line strength component of the 4I15/2 → 4I13/2 transition was subtracted from the corresponding experimental line strength value [2]. The J-O analysis yielded the three intensity parameters: Ω2 = 1.98 × 10−20 cm2, Ω4 = 1.18 × 10−20 cm2, and Ω6 = 1.20 × 10−20 cm2. These J-O parameters are in reasonable agreement with previously reported values for Er3+:BaF2 [17,20] as well as those calculated for [i] other fluoride hosts, [ii] oxide hosts, and [iii] chalcogenide glasses, all of which are shown in Table 1 with their respective references.
Table 1. Judd-Ofelt parameters of Er3+ in different hosts.
Figure 2(a) depicts the room temperature mid-IR emission bands of Er3+:BaF2 in the wavelength ranges 2400 - 3100 nm, 3200 - 4000 nm, and 4000 - 5200 nm, which correspond to the 4I11/2 → 4I13/2, 4F9/2 → 4I9/2, and 4I9/2 → 4I11/2 transitions, respectively. Excitation of the upper levels of these transitions was achieved at ∼800 nm (see Fig. 2(b)), which directly populated the 4I9/2 level, and subsequently the 4I11/2 level through radiative and nonradiative transitions. The 4F9/2 level was excited using excitation at 650 nm (Fig. 2(b)). Broad mid-IR emissions centered at ∼4.5, ∼3.5, and ∼2.74 µm, consisting of weakly structured Stark components, were observed with bandwidths of ∼325, 280, and 95 nm at full width at half maximum, respectively. Soulard et al. studied spectroscopic properties of 3.5 µm emission from Er-doped fluoride crystals and reported related laser operating parameters [29]. A schematic diagram of the relevant Er3+ energy levels indicating the excitation transitions and observed emission lines are also illustrated in Fig. 2(b).
Fig. 2. (a) Room temperature normalized IR emission spectra of 4I9/2 → 4I11/2, 4I11/2 → 4I13/2, and 4F9/2 → 4I9/2 transitions in Er3+:BaF2. (b) The partial energy level diagram of Er3+ ions indicating the pump wavelength and corresponding emission transitions.
The fluorescence lifetimes of the first four excited states of Er3+:BaF2 were determined to be ∼ 16 ms (4I13/2), 9.4 ms (4I11/2), 0.047 ms (4I9/2), and 0.396 ms (4F9/2) at room temperature. These are longer lifetimes than those observed in other Er-doped fluorides [26,29–31], which simply reflects the lower maximum phonon energy of BaF2 and leads to reduced nonradiative relaxation (Table 2). It is worth to mention that the pinhole method [32] was employed for relevant upper manifolds of mid-IR transitions (4I9/2 and 4F9/2) in order to investigate possible influence of reabsorption in these lifetime values. Lengthening of the lifetimes due to reabsorption was found to be negligible.
Table 2. Comparison of measured (experimental) lifetime values of the first four excited states for several Er3+-doped fluorides.
3.2 Temperature dependence emission and decay time studies
Figure 3 displays the mid-infrared emission spectra of the 4I9/2 → 4I11/2 transition for selected temperatures of 12 K, 77 K, 180 K, and 295 K. The spectra were measured by exciting the highest peak absorption at each temperature. They showed narrower and sharper features at low temperatures. The changes in the shape of the emission spectra at higher temperatures are due to the onset of new transitions from thermally populated higher energy Stark levels of the 4I9/2 manifold. The inset of Fig. 3 shows that the overall Er3+ fluorescence intensity decreased by almost 60% as the temperature increased from 12 K to room temperature. According to the “rule of thumb” following the well-known energy-gap law, nonradiative decay through multiphonon relaxation (MPR) process is dominant if less than five phonons are required to bridge the energy gap [2]. In Er3+:BaF2 (ħω ∼ 320 cm−1), ∼7 phonons are needed to bridge the energy gap between 4I9/2 and 4I11/2, which is about 2200 cm−1. Therefore, the probability of MPR processes should be low, however, as will be shown later, that is not quite the case in Er3+:BaF2 crystal.
Fig. 3. Mid-infrared spectra of the 4500 nm emission (4I9/2 → 4I11/2) at 12 K, 77 K, 180 K, and 295 K. The inset shows the integrated Er3+ emission intensities as a function of temperature.
The 4.5 µm emission properties of Er:BaF2 were further explored by measuring the temperature-dependent emission lifetimes of the 4I9/2 level for Er3+:BaF2 over a temperature range from 12 K to 300 K. Under ∼800 nm (4I15/2 → 4I9/2) excitation, the emission lifetimes monitored at ∼1760nm (4I9/2 → 4I13/2) were determined to be ∼0.047 and ∼0.13 ms at 300 K and 77 K, respectively (Fig. 4). Judd–Ofelt analysis [17] yielded a radiative lifetime of 10.45 ms for the 4I9/2 state, which suggests a quantum efficiency of less than 1% at room temperature.
Fig. 4. Decay transients of Er3+:BaF2 monitored at ∼1760nm (4I9/2 → 4I13/2) for 77 K and room temperature
We are going to try to interpret our 4I9/2 fluorescence dynamics data as though they are driven solely by a MPR process. The exponential energy-gap law, which describes the rate of nonradiative decay (Wnr) of a selected energy level through multiphonon relaxation processes, can be expressed as [2]:
The experimental and radiative lifetimes of the selected excited states as well as the corresponding energy gaps (ΔE) to the next lower states are described in Table 3. The Wnr rates for the selected excited states were then calculated using the following relation:
where, τrad is the radiative lifetime as predicted by Judd–Ofelt theory [17]. The acquired Wnr rates and corresponding energy gaps are shown in Fig. 5(a). There is a ∼10% error in measured nonradiative decay rates, attributed to inaccuracy in interpretation of the lifetime data. Fitting the measured nonradiative decay rates to the energy-gap law using Eq. (1) yielded B = 9.15 × 108 s−1 and α = 5.58 × 10−3 cm [33].Fig. 5. Multiphonon decay rate (Wnr) as a function of energy gap (ΔE) for several Er3+ transitions in BaF2. The solid line represents the best fit of the data points to the energy-gap law. (b) Modeling of the nonradiative decay rate of the 4I9/2 level using the energy-gap parameters obtained in Fig. 5(a).
Table 3. The measured (experimental) and radiative lifetimes as well as the Wnr rates of the selected excited states for Er3+:BaF2.
The obtained B and α parameters were then used to describe the temperature dependence of the measured Wnr rates of the 4I9/2 level (Fig. 5(b)). The observed difference between the experimental and modeled nonradiative rates versus temperature clearly suggests the existence of other nonradiative decay channels besides pure multiphonon relaxation. It could be attributed to a variety of alternative nonradiative decay processes such as: (i) energy transfer to some uncontrollable impurities in the crystal, (ii) energy transfer between Er3+ ions in different incorporation sites (e.g. isolated and clustered ions [34–36]) or (iii) involvement of nonlinear MPR (according to the theory developed by Yu. V. Orlovskii et al. [5]). It is worth mentioning that fluorites (Ca, Sr, BaF2) have a stronger optical phonon interaction than other host materials with similar maximum phonon energies [34,37]. This stronger coupling factor increases the probability of nonradiative decay making it more likely that a higher order phonon process can efficiently bridge the energy gap.
An alternative explanation can involve multi-center activation nature of Er3+ dopants in BaF2. Some evidence for multiple structurally-nonequivalent Er3+ centers was observed during our determining the precise positions of the discrete Stark energy levels using temperature-dependent absorption measurements. Figure 6 shows spectra, for several temperatures, depicting absorption into the 4S3/2 manifold. Being a low site symmetry, splitting into
Fig. 6. Low temperature absorption spectra of ground state level 4I15/2 to 4S3/2. The cold absorption lines are indicated in the figure as short black solid lines.
(2J+1)/2 = 2 Stark levels is expected for the 4S3/2 manifold. Hence, the lowest temperature spectrum should show only have two “cold lines” – i.e. transitions from the lowest Stark level of the ground state. However, analysis of the spectral behavior with increasing temperature showed at least 5 peaks exhibiting “cold line” tendencies, insinuating the presence of multiple incorporation sites. Studies have indicated that RE ions such as Er3+ can occupy a wide variety of sites in CaF2, SrF2, and BaF2 with, also, significant clustering present even at dopant concentration values of less than 0.1% [18,26,34].
3.3 Stimulated emission cross-section
The stimulated emission cross section σemiss is an important parameter because it can predict the potential laser performance of a material based solely on spectroscopic measurements. The emission cross section of the 4I9/2 → 4I11/2 mid-IR transition (∼4.5 µm) was calculated using the Füchtbauer–Ladenburg equation [38]:
Fig. 7. Emission cross-section spectrum for the 4I9/2 → 4I11/2 transition in Er3+:BaF2 at room temperature.
4. Conclusions
Results of a detailed spectroscopic investigation of Er3+-doped BaF2 crystals, grown by the Bridgman technique, were presented. The absorption spectrum of Er3+:BaF2 displayed the characteristic Er3+ transitions in the visible and IR spectral region. Optical excitation into the 4I15/2 → 4I9/2 absorption band at ∼800 nm resulted in observation of mid-IR Er3+ fluorescence bands, corresponding to the 4I11/2 → 4I13/2 (∼2.74 µm), and 4I9/2 → 4I11/2 (∼4.5 µm) transitions, respectively. The room temperature fluorescence lifetimes of the first four excited states of Er3+:BaF2 were determined to be ∼ 16 ms (4I13/2), 9.4 ms (4I11/2), 0.047 ms (4I9/2), and 0.396 ms (4F9/2). An analysis of the temperature dependence of the ∼4.5 µm emission lifetime revealed that the 4I9/2 decay could not be explained by a multiphonon relaxation process alone. A few alternative nonradiative decay processes that may also play a role include energy transfer to other impurities or Er3+ cluster sites as discussed in the body of the paper. The mid-IR emission cross section of the 4I9/2 → 4I11/2 transition at ∼4.5 µm was derived for the first time among all known fluoride hosts. It was determined to be ∼0.11 × 10−20 cm2 at room temperature, and ∼0.21 × 10−20 cm2 at 77 K.
Disclosures
The authors declare no conflict of interest.
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