Spectroscopic Investigation of Yb-doped Silica Glass for Solid-State Optical Refrigeration
Esmaeil Mobini, Mostafa Peysokhan, Behnam Abaie, Markus P. Hehlen, Arash Mafi
SSpectroscopic Investigation of Yb-doped Silica Glass for Solid-State OpticalRefrigeration
Esmaeil Mobini,
1, 2
Mostafa Peysokhan,
1, 2
Behnam Abaie,
1, 2
Markus P. Hehlen,
1, 3 and Arash Mafi
1, 2, ∗ Department of Physics & Astronomy, University of New Mexico, Albuquerque, NM 87131, USA Center for High Technology Materials, University of New Mexico, Albuquerque, NM 87106, USA Engineered Materials (MST-7), Los Alamos National Laboratory, Los Alamos, NM 87545, USA (Dated: October 24, 2018)We have argued that a high-purity Yb-doped silica glass can potentially be cooled via anti-Stokes fluorescence optical refrigeration. This conclusion is reached by showing, using reasonableassumptions for the host material properties, that the non-radiative decay rate of Yb ions can bemade substantially smaller than the radiative decay rate. Therefore, an internal quantum efficiencyof near unity can be obtained. Using spectral measurements of the fluorescence emission from a Yb-doped silica optical fiber at different temperatures, we estimate the minimum achievable temperaturein Yb-doped silica glass for different values of internal quantum efficiency.
I. INTRODUCTION
In solid-state optical refrigeration, anti-Stokes fluores-cence removes thermal energy from the material, result-ing in net cooling. Solid-state optical cooling was firstproposed by Pringsheim in 1929 [1] and was put on asolid thermodynamic foundation by Landau in 1946 [2].Solid-state optical cooling was first experimentally ob-served in 1995 by Epstein’s group at Los Alamos Na-tional Laboratory in Yb-doped ZBLANP glass [3]. Muchattention has since been devoted to solid-state opticalrefrigeration in different materials and geometries due toits interesting basic science properties and potential ap-plications [4]. The quest for solid-state optical cooling innew configurations and materials is on-going [5].In particular, solid-state optical refrigeration of Yb-doped silica glass, which is extensively used in high-powerfiber lasers, is highly desirable. New generations of highpower fiber amplifiers and lasers now operate at few kilo-Watt levels [6]. However, the significant heat-load inhigh-power operation has hindered the efforts to furtherscale up the power in fiber lasers and amplifiers [6–9].Different methods have been developed to manage theheat-load in high-power fiber lasers or amplifiers; in par-ticular, solid-state optical refrigeration via anti-Stokesfluorescence has been suggested as a viable path for heatmitigation [10–12]. So far, there is no report of solid-stateoptical refrigeration in Yb-doped silica; this manuscriptis intended to highlight its possibility.In this context, Radiation-Balanced Lasers (RBL) werefirst introduced by Bowman in 1999 [10]. In radiationbalancing, the heat that originates from the quantumdefect of the laser as well as parasitic absorption can beremoved by anti-Stokes fluorescence under a very subtlebalance condition between different parameters of a laser(or an amplifier) [10, 11, 13]. In other words, the anti-Stokes fluorescence removes the excess heat generated in ∗ mafi@unm.edu the medium. Therefore, heat mitigation by radiation-balancing via anti-Stokes fluorescence is highly desirableand will have great practical implications if it can beachieved in Yb-doped silica glass, which is the material ofchoice for most high-power fiber lasers and amplifiers [6,14, 15].The investigation of solid-state optical refrigerationcan be done either directly or indirectly. In a direct in-vestigation, the material is exposed to a laser in a ther-mally isolated setup, often in a sophisticated vacuum en-vironment [16], and its temperature is measured directlyby a thermal camera or similar methods. In an indi-rect method, the spectroscopic properties of materialsat different temperatures are measured to evaluate thepossibility of solid-state optical refrigeration [3, 16–18].In this manuscript, we use the indirect method to arguefor the potential of high-quality Yb-doped silica glass forsolid-state optical refrigeration and radiation-balancingin lasers and amplifiers.In order to characterize the cooling potential of Yb-doped silica glass, we use the cooling efficiency η c definedas [16, 18] η c ( λ p , T ) = η q η abs ( λ p , T ) λ p λ f ( T ) − . (1)In Eq. 1, λ f is the mean fluorescence wavelength and λ p is the pump wavelength. η q is the internal quantumefficiency and η abs is the absorption efficiency; they aredefined as η q = W r W tot , W tot = W r + W nr , (2) η abs ( λ p , T ) = α r ( λ p , T ) α r ( λ p , T ) + α b , (3)where W r , W nr , and W tot are radiative, non-radiative,and total decay rates of the excited state, respectively. α b is the background absorption coefficient, and α r isthe resonant absorption coefficient. Note that α b doesnot contain the attenuation due to scattering as this pro-cess does not lead to heating of the material. We have a r X i v : . [ phy s i c s . op ti c s ] O c t assumed that due to the small cross sectional area ofoptical fibers, the fluorescence escape efficiency to beunity [3, 19]. The mean fluorescence wavelength is de-fined by λ f ( T ) = (cid:82) ∆ λ S ( λ, T ) dλ (cid:82) ∆ S ( λ, T ) dλ , (4)where S ( λ, T ) is the fluorescence power spectral density,which is a function of the glass temperature T , and ∆ isthe spectral domain encompassing the relevant emissionspectral range [16, 18].In order to achieve net solid-state optical refrigera-tion, it is necessary for the cooling efficiency to be pos-itive. Therefore, we must show that η c > λ p and T values. It can be seenfrom Eq. 1 that because λ p and λ f are often very closeto each other in solid-state optical refrigeration schemes,the internal quantum efficiency η q has to be close to unity( η q ≈
1) [3, 16]. There are two main processes thatlower the internal quantum efficiency: the multi-phononnon-radiative relaxation and the concentration quench-ing effect [20–27]. We will argue that the multi-phononnon-radiative relaxation is negligible in Yb-doped silicaglass and the concentration quenching process can beprevented if the Yb ion density is kept lower than thecharacteristic Yb ion quenching concentration.In order to evaluate the absorption efficiency η abs , weneed to know the background absorption ( α b ) and res-onant absorption ( α r ) coefficients. For the backgroundabsorption coefficient in Yb-doped silica glass, we willuse typical values reported in the literature [28–30]. Bycapturing the power spectral density of a Yb-doped sil-ica optical fiber from its side at different temperatures, S ( λ, T ), we can also obtain the resonant absorption coef-ficient ( α r ) as well as the mean fluorescence wavelength( λ f ). Therefore, we will have all the necessary param-eters in Eq. 1; using this information we will estimatethe cooling efficiency and show that solid-state opticalrefrigeration is feasible in Yb-doped silica glass. II. INTERNAL QUANTUM EFFICIENCY
The internal quantum efficiency is the fraction of theradiative decay versus the total decay of an excited statein a medium; therefore, the presence of non-radiativedecay channels characterized by the non-radiative decayrate W nr in Eq. 2 are responsible for decreasing η q belowunity. The non-radiative decay channels in a typical Yb-doped silica glass can be broken down according to thefollowing equation: W nr = W mp + W OH − + W Yb + (cid:88) TM W TM + (cid:88) RE W RE . (5)The partial non-radiative decay channels are as follows: W mp represents the multi-phonon decay of the Yb excited state, W OH − accounts for non-radiative decay of the Ybexcited state via the high-energy vibrational modes ofOH − impurities, W Yb accounts for non-radiative decayin Yb ion clusters, and W TM and W RE represent non-radiative decay due to interactions of the excited statewith various transition-metal and rare-earth ion impuri-ties, respectively.In the following, we will discuss the various non-radiative decay channels in Eq. 5 and show that they canbe made sufficiently small to allow for a near-unity in-ternal quantum efficiency value ( η q ≈ W mp = W e − α h ( E g − E p ) , (6)where E p is the maximum phonon energy of the host ma-terial, and E g is the energy gap of the dopant ion (Yb). W and α h are phenomenological parameters, whose val-ues strongly depend on the host-material [20, 22, 24, 31].Figure 1 shows the multi-phonon non-radiative decayrates of silica and ZBLAN glasses versus the energy gapsof the doped ions at T = 300 K, using the parametersshown in Table I. TABLE I. Parameters related to Eq. 6 and Fig. 1 for silicaand ZBLAN glasses [20, 22, 31].Host W (s − ) α h (cm) E p (cm − )silica 7 . × . × − . × ZBLAN 1 . × . × − . × The vertical solid line in Fig. 1 marks the energygap of a Yb ion. It is evident that for Yb-dopedsilica glass, the non-radiative decay rate is around W silicamp ≈ − s − , which is much smaller than the Yb-doped ZBLAN glass multi-phonon decay rate W ZBLANmp ≈ − s − . This comparison suggests that with respect toYb multi-phonon relaxation, silica glass is a more suitablechoice for solid-state optical refrigeration than ZBLANglass.Considering the advances in materials synthesis of fiberpreforms, the term W OH − in Eq. 5 can be made verysmall (see e.g. dry fiber technology [32]); therefore, itcan be neglected [23]. It has also been shown by Auzelet al. [25] that the total effect of the last three terms inEq. 5, W Yb + Σ W TM + Σ W RE , can be described by aphenomenological equation based on a limited diffusionprocess, modeled as a non-radiative dipole-dipole inter-action between the ions and impurities [25, 26]. Thisconcentration quenching process can be prevented if theYb ion density is lower than the critical quenching con-centration of the Yb-doped silica glass, which exists be- FIG. 1. Multi-phonon non-radiative decay rate ( W mp ) of Yb-doped ZBLAN and silica glasses versus energy gap ( E g ) cal-culated from Eq. 6 and the parameters listed in Table I. cause there are impurities. Therefore, the critical quench-ing concentration is generally a sample specific quantity.That is, it would be higher for lower impurity concen-trations. For a Yb ion density smaller than the criticalquenching concentration, the internal quantum efficiencycan approach η q ≈ η q = 0.95 is reported in [33]for Yb-doped silica, which is consistent with our claimthat W nr can be made quite small in Yb-doped silica. III. ABSORPTION EFFICIENCY AND MEANFLUORESCENCE WAVELENGTH
In order to calculate the cooling efficiency, we stillneed to obtain the resonant absorption coefficient and themean fluorescence wavelength, both of which can be ob-tained from a spectroscopic investigation. The resonantabsorption coefficient is used in conjunction with Eq. 3to determine the absorption efficiency. The setup imple-mented in our experiment consists of a single-mode Yb-doped silica fiber (DF-1100, from Newport Corporation)that is pumped by a Ti:Sapphire laser at λ = 900 nm.The fiber is mounted on a plate whose temperature ischanged from nearly 180 K up to 360 K. The fluores-cence of the Yb-doped silica fiber is captured by a mul-timode fiber from the side of the Yb-doped silica fiberand is sent to an Optical Spectrum Analyzer. Figure. 2shows the measured fluorescence spectra (power spec-tral density S ( λ, T )), normalized to their peak values at λ peak ≈
976 nm, at different temperatures.By inserting the measured fluorescence spectra intoEq. 4 and considering ∆ ∈ { , } , the de-pendence of the mean fluorescence wavelength on tem-perature is obtained. The mean fluorescence wavelengthfollows approximately the following function: λ f ( T ) ≈
999 (nm) + b × T − , b = 2735 ± / K . (7)This behavior at temperatures above 245 K to 360 K isnearly linear, which is similar to that reported in otherhost materials, such as ZBLAN [17, 20]. FIG. 2. Measured peak normalized emission spectra of DF-1100 Yb-doped silica fiber at different temperatures.
In order to calculate the the resonant absorption co-efficient α r , we first calculate the emission cross section σ e , and then use the McCumber relation to obtain theabsorption cross section σ a and then the resonant ab-sorption coefficient α r [34–36]. The emission cross sec-tion is obtained from the measured fluorescence powerspectral density S ( λ, T ) via the F¨uchtbauer-Ladenburgequation [36, 37]: σ e ( λ, T ) = λ π n c τ r ( T ) × S ( λ, T ) (cid:82) ∆ λ S ( λ, T ) dλ , (8)where n is the refractive index of the fiber core, c is thespeed of light in vacuum, and τ r = W − r is the radiativelifetime.In order to apply Eq. 8, the radiative lifetime at eachtemperature needs to be measured. In high-quality sam-ples for which the non-radiative decay rates are negli-gible compared to the radiative decay rates, the fluo-rescence lifetimes are comparable to the radiative life-times ( τ f ≈ τ r ); therefore, we measured the fluorescencelifetimes at different temperatures from the side of thefiber [38]. Using this assumption, the emission cross sec-tions at different temperatures were calculated and areshown in Fig. 3. The absorption cross sections can bereadily obtained using the McCumber relation: σ a ( λ, T ) = σ e ( λ, T ) × Z ( λ, T ) , (9) Z ( λ, T ) = exp (cid:20) hck b T ( 1 λ − λ ) (cid:21) , where k b is the Boltzmann constant, h is the Planck con-stant and λ = 976 nm is the wavelength correspondingto the zero-line phonon energy [14, 18, 35]. The resonantabsorption coefficient can be calculated from σ a ( λ, T ) inEq. 9 (and Fig. 3) using α r ( λ, T ) = σ a ( λ, T ) × N. (10)Here, we will assume a typical Yb ion density of N =5 × m − . We now have all the necessary ingredients FIG. 3. Emission cross section versus wavelength for DF-1000Yb-doped silica fiber at different temperatures. The spectrawere calculated from Eq. 8 using the emission spectra shownin Fig. 2 and the measured radiative lifetimes from Ref. [38]. to calculate the cooling efficiency η c in Eq. 1. We onlyneed to provide a value for the background absorptioncoefficient in Eq. 3 to determine the absorption efficiency η abs . Here, we assume a background absorption coef-ficient of α b = 10 dB/km ≈ . × − /m, which is atypical value for commercial grade Yb-doped silica fibers.Using this information, we present a contour plot of thecooling efficiency η c in Fig. 4 as a function of the pumpwavelength and temperature, assuming that η q = 1. Notethat we only know the values of α r ( λ, T ) at discrete val-ues of temperature T for which our measurements wereperformed in Fig. 2; the density plot in Fig. 4 is an in-terpolation of the measured values. It is seen in Fig. 4that with a decrease in the temperature, the cooling ef-ficiency decreases; this behavior is due to the red-shiftof the mean fluorescence wavelength and the decrease inthe resonant absorption coefficient with decreasing tem-perature [16, 20].In practice, it is impossible to achieve an internal quan-tum efficiency of unity; therefore, in Fig. 5 we investigatethe effect of a non-ideal internal quantum efficiency onthe cooling efficiency, for λ p = 1030 nm, as a function ofthe temperature. The discrete points in Fig. 5 signify thevalues of η c obtained for the assumed η q at the particularmeasured temperatures reported in Fig. 2. The appar-ent difference between the cooling efficiency obtained for η q = 1 versus η q = 0.98 highlights the importance of hav-ing a high-quality glass for radiative cooling. While thediscrete points in Fig. 5 reveal the main expected behav-ior of η c versus the temperature, it is helpful to estimatethe minimum achievable temperature for solid-state op-tical refrigeration in Yb-doped silica glass, subject to theassumptions made about η q , N , and α b . In order to doso, we next present an analytical fitting to the discretepoints in Fig. 5 that can be used to estimate the minimumachievable temperature. The analytical fitting, which isdescribed in the next paragraph, is used in conjunction FIG. 4. Cooling efficiency versus temperature and pumpwavelength with η q = 1 and α b = 10 dB/km for DF-1100 Yb-doped silica fiber calculated from Eq. 1. The dashed lineconnects the experimental measurements of the mean fluores-cence wavelength versus the temperature. with Eq. 1 to plot the colored lines for each value of η q in Fig. 5 and is in reasonable agreement with the exper-imentally measured discrete data. From the discussions FIG. 5. Cooling efficiency for different values of quantumefficiency versus temperature with α b = 10 dB/km for DF-1100 Yb-doped silica fiber calculated from Eq. 1 for differentinternal quantum efficiencies, η q . The colored lines are plottedusing Eq. 1 and the fitting presented in Eq. 14. above and Eqs. 8, 9, and 10, we note that α r ( λ p , T ) (atthe pump wavelength) can be expressed as: α r ( λ p , T ) ∝ c λ p τ r ( T ) × S ( λ p , T ) (cid:82) ∆ λ S ( λ, T ) dλ × Z ( λ p , T ) . (11)In Ref. [38], we performed fluorescence lifetime measure-ments in Yb-silica. Here, we present a fitting of τ r ( T ) toan analytical form that is based on a two-level excitedstate: τ r ( T ) = 1 + exp( − δE/k b T ) τ − + τ − exp( − δE/k b T ) . (12) τ = 798 ± µ s, and τ = 576 ± µ s are the lifetimesof the first and second energy levels of the excited state,respectively, and δE = 506 ±
56 cm − is the energy dif-ference between these two levels [36, 39]. We also presentthe following approximation: λ p S ( λ p , T ) (cid:82) ∆ λ S ( λ, T ) dλ ≈ . (cid:18) dT (cid:19) , d = 205 . ± . . (13)Using Eqs. 12 and 13, we can approximate α r ( λ p , T )[Eq. 11] with the following mathematical form: α r ( λ p , T ) ≈ α r, c τ r ( T ) × (cid:16) . d/T ) (cid:17) × Z ( λ p , T ) . (14)Fitting the analytical in Eq. 14 to the discrete pointsin Fig. 5, we find the dimensionless coefficient α r, =(0 . ± . × . The fitted lines in Fig. 5 show thatthe minimum achievable temperature can reach down to T min = 138 K for η q = 1, T min = 175 K for η q = 0 . T min = 290 K for η q = 0 .
98. Figure 5 also showsthat the maximum cooling efficiency for Yb-silica glass isaround η max c ≈
2% at room temperature for λ p = 1030 nm.Setting the background absorption to zero ( α b = 0) in-creases this value to η max c ≈ N must beincreased to enhance the resonant absorption coefficient.We note that these requirements are not necessarily com-patible with each other; e.g. increasing N can potentiallydecrease η q due to quenching. Therefore, a compromisedetermined by careful measurements must be obtained. IV. DISCUSSION AND CONCLUSION
It must be noted that by taking N = 5 × m − in this manuscript, we have implicitly assumed that thesilica glass host is co-doped with some modifiers likeAl O , in order to shift the quenching concentration to higher values to reduce clustering and ensure an ade-quate cooling efficiency [40, 41]. For pure silica, ap-plying the model developed by Auzel et al. [25] to theexperimental data from Ref. [23], it can be shown that N = 0 . × m − can guarantee a near unity internalquantum efficiency [40, 41]. Using N = 0 . × m − in pure silica, we have calculated the minimum achiev-able temperature to be T min = 216 K for η q = 1, and T min = 262 K for η q = 0 .
99. For η q = 0 . T min ishigher than the room temperature. As expected, a de-crease in ion density results in a lower cooling efficiency.In conclusion, we have argued that a high-purity Yb-doped silica glass can potentially be cooled via anti-Stokes fluorescence optical refrigeration. We show that,in principle, the non-radiative decay rate W nr can bemade substantially smaller than the radiative decay rate W r . Therefore, an internal quantum efficiency of nearunity can be obtained, making Yb-doped silica glass suit-able for solid-state optical refrigeration. Our assessmentis based on reasonable assumptions for material proper-ties, e.g. we have assumed a typical background absorp-tion coefficient of α b = 10 dB/km and an internal quan-tum efficiency of larger than η q = 0.98. We have madespectral measurements of the fluorescence from a Yb-doped silica optical fiber at different temperatures. Us-ing these measurements, we have reported the temper-ature dependence of the mean fluorescence wavelength,and have estimated the minimum achievable temperaturein Yb-doped silica glass. Our analysis highlights the po-tential for Yb-doped silica glass to be used as the gainmedium for radiation-balanced high-power fiber lasersand amplifiers. ACKNOWLEDGMENT
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