Temperature-Dependent Stimulated Emission Cross-Section in Nd3+:YLF Crystal

materials

Article Temperature-Dependent Stimulated Emission Cross-Section in Nd3+:YLF Crystal

Giorgio Turri 1, Scott Webster 2, Michael Bass 2 and Alessandra Toncelli 3,4,*

1 Mathematics and Science Department, Full Sail University, 3300 University Blvd, Winter Park, FL 32792, USA; [email protected] 2 CREOL, The College of Optics and Photonics, University of Central Florida, 4304 Scorpius St., Orlando, FL 32816, USA; [email protected] (S.W.); [email protected] (M.B.) 3 Physics Department, University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy 4 Italian National Research Council (CNR), Institute of Nanoscience (NANO), 56127 Pisa, Italy * Correspondence: [email protected]

Abstract: Spectroscopic properties of neodymium-doped yttrium lithium fluoride were measured at different temperatures from 35 K to 350 K in specimens with 1 at% Nd3+ concentration. The absorption spectrum was measured at room temperature from 400 to 900 nm. The decay dynamics 4 of the F3/2 multiplet was investigated by measuring the fluorescence lifetime as a function of the sample temperature, and the radiative decay time was derived by extrapolation to 0 K. The 4 4 4 4 stimulated-emission cross-sections of the transitions from the F3/2 to the I9/2, I11/2, and I13/2 levels were obtained from the fluorescence spectrum measured at different temperatures, using the Aull–Jenssen technique. The results show consistency with most results previously published at room temperature, extending them over a broader range of temperatures. A semi-empirical formula for the magnitude of the stimulated-emission cross-section as a function of temperature in the 250 K 4 4 to 350 K temperature range, is presented for the most intense transitions to the I11/2 and I13/2 levels. Keywords: Nd:YLF; stimulated-emission cross-section; thermal effects; solid-state laser; rare-earth Citation: Turri, G.; Webster, S.; Bass, doped crystal; absorption; decay dynamics M.; Toncelli, A. Temperature- Dependent Stimulated Emission Cross-Section in Nd3+:YLF Crystal. Materials 2021, 14, 431. https:// 1. Introduction doi.org/10.3390/ma14020431 3+ Nd-doped Yttrium Lithium Fluoride (Nd :LiYF4) is one of the most commonly used Received: 30 November 2020 solid-state laser elements for its long fluorescence decay time at room temperature, weak Accepted: 6 January 2021 thermal lensing, and natural birefringence [1–4]. 4 4 Published: 16 January 2021 It is usually optically pumped to the F5/2 level, or directly to the F3/2 upper laser level, by 808 nm or 880 nm wavelength light, respectively, though recently laser operations Publisher’s Note: MDPI stays neu- have also been achieved with 908 nm wavelength pump [5]. 4 4 4 tral with regard to jurisdictional clai- The three main decay channels lead to the I13/2, I11/2, and I9/2 levels, with the ms in published maps and institutio- emission of light at ~1.3 µm; ~1.0 µm, and ~0.9 µm wavelengths, respectively. The most nal affiliations. common Nd:YLF lasers, by far, operate at 1047 nm (π-polarization) and 1053 nm (σ- polarization) because of the stronger intensity, but laser operation has also been achieved for the other two final laser levels [4,6–8]. Figure1 depicts the energy levels of interest for laser applications, as well as the transitions that will be investigated in this work. We Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. are reporting the Stark multiplet energies as published by Zhang [9], other authors have This article is an open access article reported slightly different values [10,11]. distributed under the terms and con- Most of the previous investigations of the spectroscopic properties of Nd:YLF have 3+ 4 ditions of the Creative Commons At- focused on the excitation and the decay of the Nd F3/2 level at room temperature. tribution (CC BY) license (https:// Although the decay dynamics of that level are in general considered well understood, there creativecommons.org/licenses/by/ is some inconsistency among the published values of the stimulated emission cross-section, 4.0/). especially when estimated with different techniques [12,13]. There are also disagreements

Materials 2021, 14, 431. https://doi.org/10.3390/ma14020431 https://www.mdpi.com/journal/materials Materials 2020, 13, x FOR PEER REVIEW 2 of 12

of that level is in general considered well understood, there is some inconsistency among the Materials 2021, 14, 431 2 of 12 published values of the stimulated emission cross-section, especially when estimated with different techniques [12,13]. Also, there are disagreements about the values of the absorption coefficient, the absorption cross-section, and the general shape of the absorption spectrum in the 800 - 900 nm range, likelyabout caused the values by low of resolution, the absorption inaccurate coefﬁcient, estimates the absorptionof the dopant cross-section, concentration, and or the the general presence of contaminantsshape of the [13-15].– absorption− spectrum in the 800–900 nm range, likely caused by low resolution, inaccurate estimates of the dopant concentration, or the presence of contaminants [13–15].

Energy [cm−1]

−1 4 4 13,408–13,656 cm F7/2 S3/2 ~740 nm −1 4 2 12,535–12,829 cm F5/2 H9/2 ~800 nm −1 4 11,536–11,595 cm F3/2

~870 nm

4 ~1350 nm −1 I13/2 3947–4240 cm −1 4 ~1060 nm 1997–2262 cm I11/2 ~870 nm 4 −1 I9/2 0–527 cm

Figure 1. Partial energy level diagram of Nd:YLF crystal. Fig. 1. Partial energy level diagram of Nd:YLF crystal from [9]. At higher or lower than room temperature, the thermal expansion [16], the thermal lensing [17,18], and the wavelengths shift and width [10,11] have been modeled theoretically or measured experimentally. Still, very few investigations reported the emission spectrumAt higher variation or lower with than the temperatureroom temperature, and only the over thermal a limited expansion temperature [16], the range thermal [15,19 lensing]. [17,18],Knowledge and the of wavelengths the temperature shift dependenceand width [10,11 of the] have absorption, been modeled decay dynamics,theoretically and or emis-measured experimentally.sion of a rare-earth-doped Still, very few crystal investigations or glass, reported carries significantthe emission information spectrum variation for practical with the applications. By controlling its operation temperature, one can tune the emission wave- temperature and only over a limited temperature range [15,19]. Knowledge of the temperature length and intensity, or optimize the pump efficiency, of a solid-state laser [20,21]. Some dependencestudies have of alsothe absorption, shown the possibilitydecay dynamics of obtaining and em temperature-independentission of a rare-earth doped lasers crystal [22 ,23or ].glass, carriesFor laser significant using birefringentinformation for or triaxialpractical crystals applications. as a gain By controlling medium, one its operation can look fortemperature, tem- oneperatures can tune wherethe emission the emission wavelength at different and intensity, polarizations or optimize occurs the pump with efficiency, the same of intensity. a solid-state laserFollowing [20,21]. aSome 1969 studies pioneering have work also byshown Harmer the possibility [14], recently of obtaining Cho et al. temperature-independent [15] obtained simultaneous laser emission with the same intensity, orthogonally-polarized, at 1047 nm and lasers1053 [22,23]. nm by properlyFor lasercooling using birefringent the Nd:YLF or crystal triaxial at cryogeniccrystals as temperature. a gain medium, Optimization one can look of for temperaturesthe simultaneous where laser the performanceemission at wasdifferent accomplished polarizations by finely occurs tuning with the the operating same tem-intensity. Followingperature ofa 1969 the crystal.pioneering Still, work no detailed by Harmer investigation [14], recently of the Cho main et spectroscopical. [15] obtained parameters simultaneous laser(cross-section emission with and the lifetime same intensity, of the observed orthogonally-polarized, transition) has been at 1047 investigated. nm and 1053 nm by properly In this work, we present the emission spectrum and the stimulated emission cross- cooling the Nd:YLF crystal at cryogenic temperature.4 Optimization3+ of the simultaneous laser section of the three main decay channels of the F3/2 state of Nd in LiYF4, at different performancetemperatures was from accomplished ~35 K to ~350 by finely K. Moreover, tuning the we operating present semi-empiricaltemperature of the formulas crystal. that Still, no detailedallow oneinvestigation to estimate of the the stimulated main spectroscopic emission cross-sectionparameters (cross-section as a function and of the lifetime sample of the observedtemperature transition) for a fewhas been selected investigated. wavelengths of possible use for laser purposes. Finally, the absorption and the emission spectra collected in this work at room temperature will be used to discuss some of the partial inconsistencies reported in the literature. The stimulated emission cross-sections were obtained from the measured emission spectra using the Aull–Jenssen technique [24]; a detailed description of this method can be found in the investigations published by these authors for Nd:YAG [20] and Nd:YVO4 [25]. Materials 2021, 14, 431 3 of 12

2. Materials and Methods Two Nd:YLF samples were provided by VLOC (New Port Richey, FL, USA) and by ACMaterials (Tarpon Springs, FL, USA). Both were about 1 × 2.5 × 5 mm, with a nominal Nd3+ concentration of 1 at%, and were oriented with the optical c axis along the longest dimension. The absorption spectrum was measured at room temperature using a Cary 500 spectrometer (Agilent, Santa Clara, CA, USA). The resolution of the spectrometer was set to 0.5 nm full width at half maximum (FWHM), and the wavelength was changed at 0.125 nm intervals. The fluorescence emission spectra and lifetime measurements were performed in a pressurized helium cryostat combined with a heater and a temperature controller. In the 3+ 4 fluorescence spectroscopy measurements, the sample was pumped to the Nd F3/2 level by a continuous, 1 W diode laser emitting around 800 nm. The power of the pump laser was monitored during data acquisition, and the collected spectra were corrected for the pump variations, which were less than 1%. The emitted fluorescence, after polarization selection, was measured through a monochromator whose resolution was set to 0.5 nm FWHM. The transmission of the monochromator was calibrated through a tungsten-quartz halogen lamp of known intensity at all wavelengths. 3+ 4 The decay dynamic of the Nd F3/2 state was investigated by pumping the sample to 3+ 4 the Nd F3/2 level with a pulsed optical parametric amplifier, set to generate a 4 ns FWHM pulse with energy around 100 mJ/pulse at ~808 nm and 10 Hz repetition rate. The emitted luminescence, after polarization selection, was collected by a fast germanium-detector (response time ~100 ns) and then processed by a digital oscilloscope.

3. Results 3.1. Absorption and Decay Dynamics The absorption spectra of the two samples are very similar, though the VLOC specimen shows systematically slightly higher absorption at all wavelengths probably due to a slightly different actual doping level in the sample. As the differences are 10% or less, they will be ignored, and in the rest of this work, we will present the average of the measurements of the two samples. A 1% Nd concentration in Nd:YLF corresponds to 1.40 × 1020 ions/cm3 as can be determined by the YLF unit-cell dimensions a = 0.5(2) nm; c = 1.09 nm [12,14,16]. Assuming this value, the absorption cross-sections as depicted in Figure2 were obtained for σ- polarized and π-polarized light at room temperature. The peak absorption occurs around 792 nm for π-polarized light with a cross-section of 1.2 × 10−19 cm2. For σ-polarized light, the strongest absorption in the 790 nm region occurs at 797 nm, with a cross-section of 0.25 × 10−19 cm2, though the absorption peak around 733 nm seems to have an even slightly larger cross-section of 0.28 × 10−19 cm2. When compared with literature, our results are in agreement with Cho et al. [15], Fornasiero et al. [2], and Ryan and Beech [13] but the latter for σ-polarized light only. The π-polarized absorption spectrum by Ryan seems to have a worse resolution than ours, which would explain the difference. It is not clear what might cause the gross disagreement with the absorption spectra as published by Harmer [14], whose absorption coefﬁcients, once rescaled to 1% dopant, are a factor 4 lower for σ-polarized light and a factor 10 lower for π-polarized light than our results. 4 An example of a typical exponential decay from the F3/2 state is shown in Figure3(Left) . Figure3(Right) depicts the fluorescence decay time as recorded at different temperatures, all of which can be accurately reproduced by a single exponential. At the pump intensities used in this investigation, we do not see a significant contribution of the higher-order effects such as excited state absorption or energy transfer upconversion, described by Chuang et al. [26] and Zuegel et al. [27]. The trend of the fluorescence lifetime versus temperature shows a constant, approximately linear, increase from the room temperature value of 476 µs toward lower temperatures; by extending the linear trend, we estimate a radiative lifetime of 530 µs. Materials 2021, 14, 431 4 of 12

The accepted value of fluorescence lifetime for 1 at% doping concentration is ~480 µs at room temperature [1], and the estimates of the radiative lifetime range between 510 µs and 550 µs [13,14]. Therefore, both the room temperature fluorescence lifetime and radiative Materials 2021, 14, x FOR PEER REVIEW 4 of 13 lifetime extrapolated at low temperatures by us are in good agreement with the published values.

Figure 2. Absorption spectrum of 1 at% Nd:YLF at room temperature for π–polarized light (Red) and σ–polarized light MaterialsFigure 2021 2., 14Absorption, x FOR PEER spectrum REVIEW of 1 at% Nd:YLF at room temperature for π–polarized light (Red) and σ–polarized light5 of 13 (Blue).(Blue).

The peak absorption occurs around 792 nm for π-polarized light with a cross-section of 1.2 × 10−19 cm2. For σ-polarized light, the strongest absorption in the 790 nm region occurs at 797 nm, with a cross-section of 0.25 × 10−19 cm2, though the absorption peak around 733 nm seems to have an even slightly larger cross-section of 0.28 × 10−19 cm2. When compared with literature, our results are in agreement with Cho et al. [15], Fornasiero et al. [2], and Ryan and Beech [13] but the latter for σ-polarized light only. The π-polarized absorption spectrum by Ryan seems to have a worse resolution than ours, which would explain the difference. It is not clear what might cause the gross disagreement with the absorption spectra as published by Harmer [14], whose absorption coeffi- cients, once rescaled to 1% dopant, are a factor 4 lower for σ-polarized light and a factor 10 lower for π-polarized light than our results. An example of a typical exponential decay from the 4F3/2 state is shown in Figure 3 Figure 3. (left) Fluorescence decay of 1% Nd:YLF,4 4F3/2 level at the temperature of 30 K (red and FigureLeft. Figure 3. (left )3 Fluorescence Right depicts decay the of fluorescence 1% Nd:YLF, decayF3/2 level time at theas recorded temperature at ofdifferent 30 K (red tempera- and 300 K300 (black). K (black). (right (right) Measured) Measured lifetime lifetime vs. samplevs. sample temperature, temperature, the continuousthe continuous line line is a linearis a linear best best ﬁt. fit.tures, all of which can be accurately reproduced by a single exponential. At the pump 3.2.intensities Stimulated used Emission in this investigation, Cross-Section we do not see a significant contribution of the higher- order effects such as excited state absorption or energy transfer upconversion, described 3.2.1.3.2. Stimulated Decay to Emission the 4I CrossLevel-Section by Chuang et al. [2611/2] and Zuegel et al. [27]. The trend of the fluorescence lifetime versus 3.2.1.Figure Decay4 todepicts the 4I11/2 the Level stimulated emission cross-section of the main transition from the 4temperature4 shows a constant, approximately linear, increase from the room temperature valueF3/2Figureto of the 476 4I depictμ11/2s towardlevels the at lowerstimulated three temperatures; different emission temperatures. crossby extending-section The ofthe spectra the linear main measured trend, transition we in estimate from the two the a investigated4 4 samples agree within 10%, so only their average is presented. Fradia3/2 totive the lifetimeI11/2 level of at530 three μs. differentThe accepted temperatures. value of fluorescence The spectra lifetimemeasured for in 1 theat% two doping in- vestigatedconcentration samples is ~480 agree μs withinat room 10% temperature, so only their [1], averageand the isestimates presented. of the radiative lifetime range between 510 μs and 550 μs [13,14]. Therefore, both the room temperature fluorescence lifetime and radiative lifetime extrapolated at low temperatures by us are in good agreement with the published values.

(a)

(b)

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Figure 3. (left) Fluorescence decay of 1% Nd:YLF, 4F3/2 level at the temperature of 30 K (red and 300 K (black). (right) Measured lifetime vs. sample temperature, the continuous line is a linear best fit.

3.2. Stimulated Emission Cross-Section

3.2.1. Decay to the 4I11/2 Level

Materials 2021, 14, 431 Figure 4 depicts the stimulated emission cross-section of the main transition from the5 of 12 4F3/2 to the 4I11/2 level at three different temperatures. The spectra measured in the two investigated samples agree within 10%, so only their average is presented.

(a)

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(b)

(c)

4 4 4 4 FigureFigure 4. Emission 4. Emission cross cross-section-section of the of F the3/2  Fthe3/2 I→11/2 thetransitionI11/2 transitionfor π–polarized for π –polarized(Red) and σ (Red)–po- and larizedσ–polarized (Blue) light, (Blue) at three light, temperatures at three temperatures:: (a) T = 300 (a )K T; =(b 300) T = K; 150 (b )K T; ( =c) 150 T =K; 35 ( cK). T = 35 K.

At Atroom room temperature, temperature, the the cross cross-section-section of of the the two two most most intense transitions atat 10471047 nm nm( (ππ-polarization)-polarization) and and 1053 1053 nmnm ((σσ-polarization)-polarization) areare consistentconsistent withwith the values measured by by Pollak [1] andand byby FornasieroFornasiero [[22],], whowho bothboth usedused the the same same technique technique as as the the present present authors, authors, and with Ryan and Beech [13] who instead applied the Judd–Ofelt technique. On the contrary, the estimates from Maldonado [12] based on the measurement of the laser gain are ~60% higher; this could be due to the different dopant concentration of their sample, namely 0.6 at% rather than 1 at%, or to a somehow lower accuracy of the chosen method. At temperatures ~150 K, the peak emission has the same intensity for both polarizations, consistent with Cho’s finding of the 138 K to 170 K interval (depending on the pump intensity) as the ideal temperature to achieve laser operations with the same laser output power for the two polarizations [15]. When the temperature is further lowered, the cross-section for π–polarized light drops dramatically, and at ~35 K the σ–polarized emission at 1052.6 nm dominates the spectrum. When the temperature increases, the peak emission constantly shifts toward a longer wavelength at a rate of approximately 4 nm/1000 K and 2 nm/1000 K for π-polarization and σ-polarization, respectively. Lasers are mostly operated at a temperature between 250 K to 350 K; as depicted in the inset of Figure 5, the peak intensity of the stimulated emission cross-section within that interval varies approximately linearly. By a simple best-fit regression, one obtains the semi-empirical formulas:

σEM = 2.6 × 10−19 (cm2) − 3 × 10−22 (cm2/K) × T(K) π–polarization σEM = 1.6 × 10−19 (cm2) − 2 × 10−22 (cm2/K) × T(K) σ–polarization

Materials 2021, 14, 431 6 of 12

and with Ryan and Beech [13] who instead applied the Judd–Ofelt technique. On the contrary, the estimates from Maldonado [12] based on the measurement of the laser gain are ~60% higher; this could be due to the different dopant concentration of their sample, namely 0.6 at% rather than 1 at%, or to a somehow lower accuracy of the chosen method. At temperatures ~150 K, the peak emission has the same intensity for both polarizations, consistent with Cho’s ﬁnding of the 138 K to 170 K interval (depending on the pump intensity) as the ideal temperature to achieve laser operations with the same laser output power for the two polarizations [15]. When the temperature is further lowered, the cross- section for π–polarized light drops dramatically, and at ~35 K the σ–polarized emission at 1052.6 nm dominates the spectrum. When the temperature increases, the peak emission constantly shifts toward a longer wavelength at a rate of approximately 4 nm/1000 K and 2 nm/1000 K for π-polarization and σ-polarization, respectively. Lasers are mostly operated at a temperature between 250 K to 350 K; as depicted in the inset of Figure5 , the peak intensity of the stimulated emission cross-section within that interval varies approximately linearly. By a simple best-ﬁt regression, one obtains the semi-empirical formulas:

−19 2 −22 2 σEM = 2.6 × 10 (cm ) − 3 × 10 (cm /K) × T(K) π-polarization Materials 2021, 14, x FOR PEER REVIEW 7 of 13 −19 2 −22 2 σEM = 1.6 × 10 (cm ) − 2 × 10 (cm /K) × T(K) σ-polarization

FigureFigure 5.5. Stimulated emission cross-sectioncross-section forfor thethe peakpeak emissionemission atat ~1047~1047 nm (π-polarization,-polarization, red)red) andand atat ~1053~1053 nmnm ((σσ-polarization,-polarization, blue)blue) asas a a function function of of the the temperature. temperature. The The full full lines lines in in the the inset inset are aare linear a linear best-ﬁt best in-fit the in 250the K–350250 K– K350 temperature K temperature range. range.

AA temperature increaseincrease ofof 1010 KK resultsresults inin thethe reductionreduction ofof thethe emissionemission byby ~2%,~2%, whichwhich isis similarsimilar toto whatwhat waswas observedobserved inin Nd:YAGNd:YAG [[2020]]and and aboutabout halfhalf ofof Nd:YVONd:YVO44 [[2525].]. ThoughThough difﬁcultdifficult toto estimateestimate fromfrom FigureFigure6 6cc of of [ [2121],], Nd:KGWNd:KGW crystalscrystals seemseem toto havehave aa somehowsomehow lowerlower dependencedependence onon thethe temperature.temperature.

(a)

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Figure 5. Stimulated emission cross-section for the peak emission at ~1047 nm (π-polarization, red) and at ~1053 nm (σ-polarization, blue) as a function of the temperature. The full lines in the inset are a linear best-fit in the 250 K–350 K temperature range.

A temperature increase of 10 K results in the reduction of the emission by ~2%, which Materials 2021, 14, 431 is similar to what was observed in Nd:YAG [20] and about half of Nd:YVO4 [25]. Though7 of 12 difficult to estimate from Figure 6c of [21], Nd:KGW crystals seem to have a somehow lower dependence on the temperature.

Materials 2021, 14, x FOR PEER REVIEW 8 of 13

(a)

(b)

(c)

4 4 4 4 FigureFigure 6. Emission 6. Emission cross- cross-sectionsection of the ofF3/2 the  Fthe3/2 I→13/2 thetransitionI13/2 fortransition π–polarized for π –polarized(Red) and σ (Red)–po- and larizedσ–polarized (Blue) light, (Blue) at three light, temperatures at three temperatures:: (a) T = 300 (a )K T; ( =b 300) T = K; 150 (b )K T; ( =c) 150 T = K;35 (Kc). T = 35 K.

4 3.2.2.3.2.2. Decay Decay to the to the4I13/2 ILevel13/2 Level 4 FigureFigure 6 depicts6 depicts the the stimulated stimulated emission emission cross cross-section-section for for the the decay decay of of the the 4F3/2F 3/2levellevel 4 to theto the4I13/2I 13/2at threeat three different different temperatures. temperatures. When When compared compared with with the themeasurements measurements by by Fornasero et al. at room temperature [2], the spectra from the top panel of Figure 6 have the same overall shape and intensities about 40% higher at all wavelengths. Around room temperature, the strongest emission occurs at 1314 nm for σ–polarized light and at 1314 nm and 1322 nm for π–polarized light. For laser purposes, 1314 nm seems an interesting choice since its emission cross-section is almost the same for both polarizations and remains so at least until liquid nitrogen temperatures. For that wavelength, in the 250 K to 350 K temperature range, the peak emission constantly shifts toward longer wavelength at a rate of approximately 6 nm/1000 K, and the peak emission has a linear trend well reproduced by formulas:

σEM = 7.5 × 10−20 (cm2) − 1.6 × 10−22 (cm2/K) × T(K) π–polarization

σEM = 7.5 × 10−20 (cm2) − 1.4 × 10−22 (cm2/K) × T(K) σ–polarization A temperature increase of 10 K results in the reduction of the emission by ~5%, thus showing a stronger dependence on the temperature than the emission around 1047 nm and 1053 nm associated with the decay to the 4I11/2 level.

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Fornasero et al. at room temperature [2], the spectra from the top panel of Figure6 have the same overall shape and intensities about 40% higher at all wavelengths. Around room temperature, the strongest emission occurs at 1314 nm for σ–polarized light and at 1314 nm and 1322 nm for π–polarized light. For laser purposes, 1314 nm seems an interesting choice since its emission cross-section is almost the same for both polarizations and remains so at least until liquid nitrogen temperatures. For that wavelength, in the 250 K to 350 K temperature range, the peak emission constantly shifts toward longer wavelength at a rate of approximately 6 nm/1000 K, and the peak emission has a linear trend well reproduced by formulas:

−20 2 −22 2 σEM = 7.5 × 10 (cm ) − 1.6 × 10 (cm /K) × T(K) π-polarization

−20 2 −22 2 σEM = 7.5 × 10 (cm ) − 1.4 × 10 (cm /K) × T(K) σ-polarization A temperature increase of 10 K results in the reduction of the emission by ~5%, thus showing a stronger dependence on the temperature than the emission around 1047 nm and 4 1053 nm associated with the decay to the I11/2 level. When the temperature approaches 35 K, the σ–polarized emission at 1317 nm and the π–polarized emission at 1325 nm rapidly increase, dominating the emission spectrum (bottom panel of Figure6).

4 3.2.3. Decay to the I9/2 Level 4 The investigation of the decay to the I9/2 levels is somehow more challenging. First, 4 3+ since the I9/2 is also the Nd ground state, reabsorption is expected. To estimate the amount of reabsorption at room temperature, we applied the reciprocity method [28] to extract the stimulated-emission cross-section from the absorption cross-section. In Figure7 the emission cross-section as obtained by reciprocity and by the Aull–Jenssen technique are compared, together with the measured absorption spectrum. For π-polarization, reabsorption only affects the peak at 863 nm, whereas for σ-polarization, the Aull–Jenssen technique seems to overestimate some of the emission peaks. A second issue, speciﬁc to our investigation, was the low transmission of the monochromator for wavelengths shorter than 900 nm, resulting in noisy spectra, especially for tem- 4 4 peratures below 70 K. For this reason, we will limit our investigation of the F3/2 → I9/2 transition to temperatures of 100 K or higher. It should be noticed that the contribution of the peaks in the 850–900 nm region to the total area of the emission spectrum is minor. Thus, any possible inaccuracy caused by reabsorption of excessive noise when the Aull–Jenssen technique is applied has negligible effects on the estimate of the emission cross-section of 4 4 4 4 the F3/2 → I11/2 and F3/2 → I13/2 transitions. 4 4 Figure8 depicts the stimulated emission cross-section for the F3/2 to I9/2 transition at room temperature and 100 K. The spectrum at room temperature is in reasonable agreement with what Ryan et al. [13] obtained through the Judd–Ofelt technique, except for the peak around 863 nm for π–polarization, and the intensity of the peaks at 903 nm and 908 nm are about 70% of the values reported by Zhang [29]. Materials 2021, 14, x FOR PEER REVIEW 9 of 13

When the temperature approaches 35 K, the σ–polarized emission at 1317 nm and the π–polarized emission at 1325 nm rapidly increase, dominating the emission spectrum (bottom panel of Figure 6).

3.2.3. Decay to the 4I9/2 Level

The investigation of the decay to the 4I9/2 levels is somehow more challenging. First, since the 4I9/2 is also the Nd3+ ground state, reabsorption is expected. To estimate the amount of reabsorption at room temperature, we applied the reciprocity method [28] to extract the stimulated-emission cross-section from the absorption cross-section. In Figure 7 the emission cross-section as obtained by reciprocity and by the Aull–Jenssen technique are compared, together with the measured absorption spectrum. For π-polarization, reab- Materials 2021, 14, 431 sorption only affects the peak at 863 nm, whereas for σ-polarization, the Aull–Jenssen9 of 12 technique seems to overestimate some of the emission peaks.

(a)

(b)

FigureFigure 7. 7.TheThe absorption absorption spectrum spectrum (black) (black) and and the theemission emission spectra spectra as obtained as obtained by Aull by Aull–Jenssen–Jenssen (red)(red) and and by by reciprocity reciprocity (blue) (blue) techniques, techniques, at at 300 300 K K:: (a ()a π) -πpolarization-polarization;; (b (b) σ) σ-polarization-polarization..

A second issue, specific to our investigation, was the low transmission of the monochromator for wavelengths shorter than 900 nm, resulting in noisy spectra, especially for

Materials 2021, 14, x FOR PEER REVIEW 11 of 13 Materials 2021, 14, 431 10 of 12

(a)

(b)

4 4 4 4 FigureFigure 8. Emission 8. Emission cros cross-sections-section of the of F the3/2 F the3/2 →I9/2 thetransitionI9/2 transition for π–polarized for π–polarized (Red) and σ (Red)–po- and larizedσ–polarized (Blue) light, (Blue) at light, two temperatures at two temperatures:: (a) T = 300 (a) TK =; (b 300) TK; = 100 (b) TK. = 100 K.

4. 4.Conclusions Conclusions InIn this this work, work, we we investigated investigated the the absorption absorption cross cross-section-section at atroom room temperature temperature and and thethe emission emission lifetime lifetime and and cross cross-section-section at atdifferent different temperatures temperatures in in the the 35 35 K Kto to 350 350 K Krange range of of1 at% 1 at% Nd:YLF Nd:YLF crystals crystals.. The The results results are are consistent consistent with with most most previously previously published published works works andand extend extend them them over over a broader a broader temperature temperature and/or and/or wavelength wavelength range. range. In particular In particular,, we derivedwe derived two sets two of sets semi of-empirical semi-empirical formulas formulas that allow that one allow to predict one to predictthe stimulated the stimulated emis- 4 → 4 sionemission cross-section cross-section of the peak of the emission peak emission at 1047 nm at 1047and 1053 nm andnm 1053(4F3/2  nm 4I (11/2F 3/2transition)I11/2 4 → 4 andtransition) at 1314 nm and (4F at3/2 1314  4I nm13/2 transition) ( F3/2 Iin13/2 thetransition) 250–350 K in temperature the 250–350 range K temperature. We also con- range. We also conﬁrmed Cho’s results that at around 150 K, the peak emission of the 4F → firmed Cho’s results that at around 150 K, the peak emission of the 4F3/2  4I11/2 transition3/2 4 hasI 11/2the sametransition cross has-section the same for the cross-section π– and the for σ– thepolarization,π– and the andσ–polarization, showed that and a similar showed that a similar situation occurs for the peak emission of the 4F → 4I transition, but situation occurs for the peak emission of the 4F3/2  4I13/2 transition3/2, but in13/2 that case over a broadin that range case of over temperatures a broad range and with of temperatures the two emissions and with at the the same two emissionswavelength, at though the same withwavelength, a less strength though. with a less strength.

Author Contributions: Conceptualization, A.T. and G.T.; methodology, A.T. and G.T.; investigation, Author Contributions: Conceptualization, A.T. and G.T.; methodology, A.T. and G.T.; investiga- M.B., A.T. and G.T.; resources, M.B., S.W. and G.T.; data curation, A.T. and G.T.; writing—original tion, M.B., A.T. and G.T.; resources, M.B., S.W. and G.T.; data curation, A.T. and G.T.; writing— draft preparation, G.T.; writing—review and editing, M.B., S.W. and A.T.; supervision, M.B.; project

Materials 2021, 14, 431 11 of 12

administration, A.T. and G.T.; funding acquisition, A.T. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the University of Pisa grant number PRA_2018_34 (“ANISE”). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available because the authors do not wish to publish supplementary materials. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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