1. INTRODUCTION

A solar-pumped laser is a device that converts incoherent sunlight into a coherent laser beam. In recent years, solar-pumped lasers have been attracting much attention as novel renewable energy sources in optical communications, energy transfer in space [1], and an energy cycle using magnesium [2]. The development of solar-pumped lasers has a long history. Kiss et al. have achieved continuous wave laser action at $2.36\mathrm{\mu m}$ in the ${\mathrm{Dy}}^{2+}\text{:}{\mathrm{CaF}}_2$ system at liquid neon temperature ($27\mathrm{K}$) using the Sun as the pumping source in 1963 [3]. That was soon after the first laser oscillation using ruby by Maiman in 1960 [4]. Since then, solar-pumped lasers have been attained with ${\mathrm{Nd}}^{3+}\text{:glass}$ [5, 6], ${\mathrm{Nd}}^{3+}\text{:}{\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ garnet (YAG) single crystal [1, 6, 7], and ${\mathrm{Er}}^{3+}$, ${\mathrm{Tm}}^{3+}$, and ${\mathrm{Ho}}^{3+}\text{:}\mathrm{YAG}$ [8]. Recently, a solar-pumped laser with an output of about $80\mathrm{W}$ and an optical-to-optical conversion efficiency of 4.3% was achieved using ${\mathrm{Cr}}^{3+}$, ${\mathrm{Nd}}^{3+}\text{:}\mathrm{YAG}$ transparent ceramic [9].

The reliability, cost performance, and optical-to-optical conversion efficiency of the solar-pumped laser system must be raised considerably, in order to expand the use of solar-pumped lasers worldwide. We believe these issues can be resolved by utilizing ${\mathrm{Nd}}^{3+}$-doped fiber lasers made of glass materials because of the optical confinement provided by the waveguide structure combined with the excellent laser properties of ${\mathrm{Nd}}^{3+}$. It is necessary for fiber lasers to make use of glass material, which can be drawn into an optical fiber easily. ${\mathrm{Nd}}^{3+}$-doped glass laser media has been used in laser fusion and fiber laser applications. However, the possibility of using a low-energy pumping source, such as the Sun, has not been considered, because one of the main targets of these applications is to obtain high-irradiance light sources. It should be elucidated which properties of the host glass dominate the efficiency under sunlight pumping. As the first trial, we have chosen ${\mathrm{SiO}}_2-{\mathrm{B}}_2{\mathrm{O}}_3-{\mathrm{Na}}_2\mathrm{O}-{\mathrm{Al}}_2{\mathrm{O}}_3\mathrm{-CaO-}{\mathrm{ZrO}}_2$ (borosilicate) glass, which has excellent rare-earth solubility and can hold up to $30\mathrm{wt}\mathrm{.}\%{\mathrm{Nd}}_2{\mathrm{O}}_3$ without evidence of Nd clustering [10]. However, the quantum efficiency (QE) of the near-infrared emission of the ${\mathrm{Nd}}^{3+}$-doped borosilicate glass under sunlight excitation was as low as 21% due to the high phonon energy $\sim 1500{\mathrm{cm}}^{-1}$.

${\mathrm{ZrF}}_4\text{-}{\mathrm{BaF}}_2\text{-}{\mathrm{LaF}}_3\text{-}{\mathrm{AlF}}_3\mathrm{-NaF}$ (ZBLAN) glass, found in 1975 [11], has the wide transparent window between about 0.22 and $8\mathrm{\mu m}$ [12], minimum loss as low as $1\mathrm{db}/\mathrm{km}$ [13], low effective phonon energy less than $600{\mathrm{cm}}^{-1}$ [14], and high allowable doping levels up to $10\mathrm{mol}\mathrm{.}\%$ of rare-earth ions [12]. These properties should make ZBLAN glass a promising candidate as a host medium for a solar-pumped laser. In this paper, we present the optical properties of ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass required for the design of a solar-pumped laser. In particular, we focus on the QE of near-infrared emission under sunlight excitation and discuss the dependence of the QE using the Sun and monochromatic light sources on ${\mathrm{Nd}}^{3+}$ concentration.

2. PROCEDURES

2A. Experimental

Glass compositions prepared in this study were $51{\mathrm{ZrF}}_4-20{\mathrm{BaF}}_3-4.5{\mathrm{LaF}}_3-4.5{\mathrm{AlF}}_3-20\mathrm{NaF}-x{\mathrm{NdF}}_3$ ($x=0.03$, 0.05, 0.1, 0.2, 0.5, 1.0, 3.0, 5.0), in mole percent. The raw materials were mixed thoroughly in an alumina mortar and then melted in an electric furnace at $800°\mathrm{C}$ for $30\min$ with an $N_2$ atmosphere in platinum crucibles. Subsequently, the glass melts were quenched by pouring them onto stainless steel plates preheated to $250°\mathrm{C}$. Each glass was then annealed at $250°\mathrm{C}$ for $4\mathrm{h}$. The glasses were cut to a thickness of around $2.5\mathrm{mm}$ and then polished to optical quality to optical measurements.

The density of the glass was measured by the Archimedes method.

Optical absorption spectra were recorded by a double-beam monochromator (PerkinElmer, Lambda 900) over a range of $175–3300\mathrm{nm}$.

The refractive indices were measured by a prism coupler (Metricon, 2010) at the wavelengths of 632.8, 974, 1320 and $1544\mathrm{nm}$.

Judd–Ofelt (JO) analysis [15, 16] was carried out to calculate the radiative lifetime ${\tau }_r$ and the stimulated emission cross section ${\sigma }_{\text{se}}$ for ${\mathrm{Nd}}^{3+}$ ions. The parameters used in the JO analysis were taken from Refs. [17, 18].

The emission lifetime (${\tau }_f$) of the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ was estimated from the e-folding time of a emission decay curve. Emission from the sample excited by a Ti:sapphire laser (Coherent, 890) was dispersed by a single monochromator with a diffraction grating blazed at $1000\mathrm{nm}$ and detected by a near-infrared photomultiplier tube (Hamamatsu Photonics, H9170-75). The decay curve of the emission was obtained by a digital oscilloscope (Yokogawa, DL-1620).

The procedure of QE measurement using an integrating sphere was the in same manner described elsewhere [19]. A schematic figure of the QE measurement system is shown in Fig. 1. Sunlight was focused onto the tip of an optical fiber bundle by a lens with a focal length of $100\mathrm{mm}$ and a diameter of $50\mathrm{mm}$. They were fixed on an altazimuth mount with an automatic Sun tracking system (Vixen, SKYPOD) on a tripod. Two different photonic multichannel analyzers (PMAs) were used sequentially as spectrometers and detectors for the QE measurements. One is a visible PMA (Hamamatsu, C9220-02) covering the wavelength range of $200–950\mathrm{nm}$ with a resolution of $2\mathrm{nm}$, and the other is a near-infrared PMA (Ohtsuka Denshi, Photal MCPD-5000) covering the wavelength range of $900–1600\mathrm{nm}$ with a resolution of $3.4\mathrm{nm}$. The spectral sensitivities of these PMAs were calibrated with standard light sources by the manufacturers. The QE measurement for one sample was completed within $2\min$. It was confirmed that the spectral intensity and the shape of sunlight was unchanged during a series of the QE measurements. All QE measurements using sunlight were performed between 11 o’clock in the morning and 2 o’clock in the afternoon on bright and clear days.

The QE measurements under monochromatic wavelength excitation was also done using a xenon lamp and a Ti:sapphire laser as excitation sources in the excitation wavelength ranges of $450–700\mathrm{nm}$ and $700–900\mathrm{nm}$, respectively.

2B. Analysis of Concentration Quenching Parameters

The decreasing QE as ${\mathrm{Nd}}^{3+}$ concentration increases is found to be accurately described by the decay function

3. RESULTS

3A. Absorption and Emission Cross Sections and Emission Lifetime

The density was $4.352\mathrm{g}/{\mathrm{cm}}^3$ for undoped glass and linearly increased with x to $4.461\mathrm{g}/{\mathrm{cm}}^3$ for $x=5\%$. The refractive indices were 1.500, 1.494, 1.492, and 1.490 for 632.8, 974, 1330, and $1544\mathrm{nm}$, respectively. The JO parameters obtained from the integrated absorption intensities, density, and refractive indices were ${\mathrm{\Omega }}_2=(1.46\pm 0.24)\times {10}^{-20}{\mathrm{cm}}^2$, ${\mathrm{\Omega }}_4=(3.47\pm 0.36)\times {10}^{-20}{\mathrm{cm}}^2$, and ${\mathrm{\Omega }}_6=(3.73\pm 0.18)\times {10}^{-20}{\mathrm{cm}}^2$. The JO parameters of ZBLAN glass were smaller than those of high-index glasses, such as lead bismuth gallate and chalcogenide [26], but were comparable with those of the other fluoride glasses [27].

Figure 2 shows the absorption and stimulated emission cross-section spectra of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass. The absorption cross section was calculated by

The integrated ${\mathrm{Nd}}^{3+}$ absorption in the $400–950\mathrm{nm}$ region has been used a measure of the absorption strengths, which is related to absorption efficiency for broadband exci tation sources [28]. The integration absorptions relative to $1.583\times {10}^{-18}{\mathrm{cm}}^2·\mathrm{nm}$ of ED-2 (or LG670), a high-gain lithium calcium aluminosilicate glass [28], are shown in Table 1. The relative integrated absorption of ZBLAN in the present work was 0.91, which is slightly lower than those of silicate (ED-2) and phosphate (LG750) glasses but larger than those of the other fluoride glasses, such as ${\mathrm{ZrF}}_4-{\mathrm{BaF}}_2-\mathrm{NaF}$ (ZBN) and ${\mathrm{ZrF}}_4-{\mathrm{BaF}}_2-{\mathrm{LaF}}_3$ (ZBL). This means that ${\mathrm{Nd}}^{3+}$-doped ZBLAN can absorb sunlight most effectively among these ${\mathrm{Nd}}^{3+}$-doped fluoride glasses.

The stimulated emission cross section of the ${}^4{F}_{3/2}\to {}^4{I}_{11/2}$ transition was $(2.95\pm 0.18)\times {10}^{-20}{\mathrm{cm}}^2$ at $1050\mathrm{nm}$, which is about twice as large as that of silica glass and almost similar to those of the other fluoride glasses, such as ZBN and ZBL, as shown in Table 1. The stimulated emission cross sections of the ${}^4{F}_{3/2}\to {}^4{I}_{9/2}$ and ${}^4{F}_{3/2}\to {}^4{I}_{13/2}$ for ZBLAN were $(1.00\pm 0.10)\times {10}^{-20}{\mathrm{cm}}^2$ at $867\mathrm{nm}$ and $(0.77\pm 0.04)\times {10}^{-20}{\mathrm{cm}}^2$ at $1318\mathrm{nm}$.

Figure 3 shows the emission lifetime of the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass. The emission lifetime was about $525\mathrm{\mu s}$ at low x and decreased at more than $x\gtrsim 3\mathrm{mol}\mathrm{.}\%$, showing the occurrence of concentration quenching in the high x regime.

The product of the stimulated emission cross section and the radiative lifetime (${\sigma }_{\text{se}}{\tau }_r$) of a laser transition is recognized as a figure of merit of the laser transition, because ${\sigma }_{\text{se}}{\tau }_r$ is proportional to the slope efficiency and inversely proportional to the threshold pump power of a laser. ${\sigma }_{\text{se}}{\tau }_{r}s$ of the ${}^4{F}_{3/2}\to {}^4{I}_{11/2}$ transition of ${\mathrm{Nd}}^{3+}$ for several glasses are tabulated in Table 1. ${\sigma }_{\text{se}}{\tau }_r$ for ZBLAN was $(1.45\pm 0.19)\times {10}^{-23}{\mathrm{cm}}^2·\mathrm{s}$, which is more than twice as large as that for silica glass and comparable to that for LG750. This indicates that ZBLAN glass is one of the most preferable glass materials for ${\mathrm{Nd}}^{3+}$-doped lasers.

3B. Quantum Efficiencies

Figure 4 shows (a) the spectral intensities from the integrating sphere with a fluoride glass sample of $x=0.5\mathrm{mol}\mathrm{.}\%$ and without the sample under sunlight irradiation and (b) the difference spectrum. The sharp absorption and emission lines due to ${\mathrm{Nd}}^{3+}$ can be seen in Fig. 4b. Though broad absorption due to the host (including defects and impurities) was found for the absorption spectrum of ${\mathrm{Nd}}^{3+}$-doped borosilicate glass [19], such broad absorption seems negligibly small for ZBLAN glass.

Figure 5 shows the radiative QE (${\eta }_r$) of the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ and the internal quantum efficiencies under $793\mathrm{nm}$ excitation (${\eta }_{793}$) and under sunlight (${\eta }_s$).

${\eta }_r$ was about $106\pm 7\%$ in the low x regime and decreased with x due to the concentration quenching for $x\gtrsim 3\%$. The inconsistency that ${\eta }_r$ exceeds 100% (that is, ${\tau }_f>{\tau }_r$) for the low x regime is most probably due to the intrinsic inaccuracy of $10\%–15\%$ in JO analysis [30] and the low nonradiative transition rate due to the low phonon energy of ZBLAN glass ($\sim 600{\mathrm{cm}}^{-1}$). Similar inconsistencies were found also for several glasses [21, 26, 27]. Thus ${\eta }_r$ is thought to be $\sim 100\%$ for the low x regime.

${\eta }_{793}$ was as high as 88% in the low x regime, which is comparable to $\sim 90\%$ of the QE of Czochralski grown ${\mathrm{Nd}}^{3+}\text{:}\mathrm{YAG}$ crystal for $514.5\mathrm{nm}$ excitation [31] but is lower than 94% [32] obtained by the thermal lens methods for ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass. ${\eta }_{793}$ decreased with increase in x to 25% at $x=5\%$ due to concentration quenching.

${\eta }_s$ reached a maximum of 70% at $x=0.5\%$. This high ${\eta }_s$ shows that ZBLAN glass is very attractive for solar-pumped laser applications. For the higher x, ${\eta }_s$ decreased with increase in x due to concentration quenching as well as ${\eta }_r$ and ${\eta }_{793}$. In contrast, ${\eta }_s$ decreased with the decrease in x in the low x regime, which was not found for ${\eta }_r$ and ${\eta }_{793}$.

4. DISCUSSION

4A. Effects of Nonradiative Transition and Ion–Ion Interactions on Quantum Efficiency

The nonradiative relaxation processes of excited rare-earth ions are usually attributed to multiphonon emission relaxation, concentration quenching through energy migration between rare-earth ions and the energy transfer to hydroxyl ($–\mathrm{OH}$) groups.

The nonradiative relaxation rate via multiphonon emission is given by [33]

The concentration quenching in the high x regime was evaluated by fitting of Eq. (5) to the measured radiative QE. $W_0$ was fixed at 0 during the fitting because the nonradiative transitions due to the multiphonon emission and the energy transfer to $–\mathrm{OH}$ groups were negligible as mentioned above. The best fitting was obtained as $R_{DA}=0.35\pm 0.10\mathrm{nm}$ from a pa rameter set of $A_r=2304\pm 145{\mathrm{s}}^{-1}$, $W_0=0{\mathrm{s}}^{-1}$, $R_{DD}=1.20\pm 0.12\mathrm{nm}$ (Table 2). $R_{DD}>R_{DA}$ validates the applications of Burshtein’s hopping model to ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass. $R_{DD}$ and $R_{DA}$ of ZBLAN glass in the present work were comparable to those of the previously reported ZBLAN glass [25] and phosphate [21] glasses within the experimental errors.

4B. Effects of Absorptions by Other Than ${\mathrm{Nd}}^{3+}$ on Quantum Efficiency under Sunlight Excitation

The internal QE (${\eta }_{\text{int}}$) of photoluminescence is given by

The absorption efficiency (${\eta }_{\text{abs}}$) is given by

The relaxation efficiency (${\eta }_{\text{rel}}$) is the efficiency that the excited ${\mathrm{Nd}}^{3+}$ relaxes to the initial state of emission (${}^4{F}_{3/2}$) and is given by

The escaping efficiency (${\eta }_{\text{esc}}$) is the efficiency that the photons emitted by excited ${\mathrm{Nd}}^{3+}$ escape out of the sample. ${\eta }_{\text{esc}}$ decreases by reabsorption by ${\mathrm{Nd}}^{3+}$ ions and glass host and thus a function of emission wavelength.

We can discuss ${\eta }_{793}$ and ${\eta }_s$ using Eq. (9), because they are internal QEs for different excitation wavelengths. ${\eta }_{\text{abs}}$, ${\eta }_{\text{rel}}$, and ${\eta }_{\text{esc}}$ do not exceed 100% by definition. Thus ${\eta }_{793}$ and ${\eta }_s$ are always lower than ${\eta }_r$. ${\eta }_{\text{rel}}$ can be assumed to 100% for near-infrared emission from ${\mathrm{Nd}}^{3+}$ as mentioned above. Both ${\eta }_r$ and ${\eta }_{\text{ext}}$ terms in Eq. (9) are common to ${\eta }_{793}$ and ${\eta }_s$. Thus, the difference between ${\eta }_{793}$ and ${\eta }_s$ arises from the dependence of the remaining ${\eta }_{\text{abs}}$ term on wavelength. It is thought that ${\eta }_{\text{abs}}$ is nearly 100% at the wavelengths of the absorption peak of ${\mathrm{Nd}}^{3+}$ and is considerably lower at other wavelengths. Consequently, ${\eta }_s$ is always lower than ${\eta }_{793}$ for the same host and for the same ${\mathrm{Nd}}^{3+}$ concentration (x).

The dependences of ${\eta }_{793}$ and ${\eta }_s$ on the ${\mathrm{Nd}}^{3+}$ concentration can be understood from the dependence of ${\eta }_{\text{abs}}$ on the ${\mathrm{Nd}}^{3+}$ concentration and concentration quenching. As the ${\mathrm{Nd}}^{3+}$ concentration increases, $N_{Nd}$ in Eq. (10) increases although $N_{\text{host}}$ is constant. Thus, ${\eta }_{\text{abs}}$ increases with increasing of the ${\mathrm{Nd}}^{3+}$ concentration. On the other hand, ${\eta }_r$ decreases with increasing of the ${\mathrm{Nd}}^{3+}$ concentration by concentration quenching. Because $N_{Nd}\gg N_{\text{host}}$ for $793\mathrm{nm}$ excitation, the ${\eta }_{\text{abs}}$ term in ${\eta }_{793}$ would be almost 100% even for lower ${\mathrm{Nd}}^{3+}$ concentrations, and ${\eta }_{793}$ decreases monotonically with increasing in the ${\mathrm{Nd}}^{3+}$ concentration. In contrast, as a consequence that ${\eta }_s$ is determined by the product of ${\eta }_r$ and ${\eta }_{\text{abs}}$, ${\eta }_s$ gives a maximum at a specific ${\mathrm{Nd}}^{3+}$ concentration ($x=0.5\%$ in this case).

There is other evidence that the absorption of host affects QE. Figure 6 shows the excitation wavelength dependence of QEs of near-infrared emission from ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass of $x=0.5\%$. The curve in Fig. 6 is the absorption spectrum of the glass. Apparently, the positive correlation with the QE and the absorption coefficient can be seen. That is, the QE at an absorption peak wavelength of ${\mathrm{Nd}}^{3+}$ is higher than that at around the peak. Thus, in principle, the QE obtained using a broadband excitation source, such as sunlight, becomes lower than that obtained using a monochromatic light source at the absorption peak wavelength of ${\mathrm{Nd}}^{3+}$.

5. SUMMARY

Optical properties required for the design of a solar-pumped laser were evaluated for ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass. The QE of the near-infrared emission from the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass was directly measured by an integrating sphere method using sunlight as an excitation source was as high as 70%. The stimulated emission cross section of the ${}^4{F}_{3/2}\to {}^4{I}_{11/2}$ emission was ${\sigma }_{\text{se}}=2.96\times {10}^{-20}{\mathrm{cm}}^2$, and the radiative lifetime obtained by JO analysis was ${\tau }_r=496\mathrm{\mu s}$. Thus, their product is ${\sigma }_{\text{se}}{\tau }_r\sim 1.45\times {10}^{-23}{\mathrm{cm}}^2·\mathrm{s}$, which is the largest among those of ${\mathrm{Nd}}^{3+}$ doped in glass media. The integrated absorption strength in the $450–900\mathrm{nm}$ region of ${\mathrm{Nd}}^{3+}$-doped ZBLAN was the largest among ${\mathrm{Nd}}^{3+}$-doped fluoride glasses. These optical properties show that ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass is one of the most promising gain media for solar-pumped lasers. It was revealed that the QE decreased more remarkable for sunlight excitation than for monochromatic excitations at the wavelength of a ${\mathrm{Nd}}^{3+}$ absorption peak. The reduction in QE under sunlight is mainly due to optical loss by the host glass (including defects and impurities) in the case of ${\mathrm{Nd}}^{3+}$- doped ZBLAN glass. This fact would be a clue to design more efficient glass host for solar-pumped lasers.

ACKNOWLEDGMENTS

This work was supported by the Japan Society for the Promotion of Science as a part of the Grant-in-Aid for Scientific Research for Young Scientists (B) (20760039) and by the Ministry of Education, Culture, Sports, Science, and Tech nology as part of the Private University High-Tech Research Center Program (2011–2015).

Table 1. Stimulated Emission Cross Section (${\sigma }_{\text{se}}$), Radiative Lifetime (${\tau }_r$), and ${\sigma }_{\text{se}}{\tau }_r$ of ${\mathrm{Nd}}^{3+}$ and the ${}^4{F}_{3/2}\to {}^4{I}_{11/2}$ Radiative Transition and the Relative Integration Absorption of ${\mathrm{Nd}}^{3+}$ in the 400–950 nm Region

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Table 2. Spectroscopic Parameters for ${\mathrm{Nd}}^{3+}$ Doped in Glasses

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Fig. 1 Measurement system of the QE using an integrating sphere.

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Fig. 2 Absorption and stimulated emission cross- section spectra of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass. The term symbols show the final states of the transitions. The initial states are the ${}^4{I}_{2/9}$ for absorption and the ${}^4{F}_{3/2}$ for emission.

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Fig. 3 Emission lifetime of the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass. The dotted curve is a guide for the eye.

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Fig. 4 (a) Spectral intensities from an integrating sphere with ${\mathrm{Nd}}^{3+}$-doped ZBLAN glass sample of $x=0.5$ (solid curve) and without the sample (dotted curve) under sunlight irradiation. (b) Difference spectrum. The dashed–dotted line shows the baseline.

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Fig. 5 Quantum efficiencies of near-infrared emission from the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass as functions of ${\mathrm{NdF}}_3$ concentration x. The dotted curves are guides for the eye.

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Fig. 6 Excitation wavelength dependence of quantum efficiencies of near-infrared emission from the ${}^4{F}_{3/2}$ state of ${\mathrm{Nd}}^{3+}$ doped in ZBLAN glass of $x=0.5$. The curve shows the absorption spectra of the glass.

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1. H. Arashi and Y. Kaneda, “Solar-pumped laser and its second harmonic generation,” Sol. Energ. 50, 447–451 (1993). [CrossRef]  

2. T. Yabe, S. Uchida, K. Ikuta, K. Yoshida, C. Baasandash, M. S. Mohamed, Y. Sakurai, Y. Ogata, M. Tuji, Y. Mori, Y. Satoh, T. Ohkubo, M. Murahara, A. Ikesue, M. Nakatsuka, T. Saiki, S. Motokoshi, and C. Yamanaka, “Demonstrated fossil-fuel-free energy cycle using magnesium and laser,” Appl. Phys. Lett. 89, 261107 (2006). [CrossRef]  

3. Z. I. Kiss, H. R. Lewis, and R. C. Duncan, “Sun pumped continuous optical maser,” Appl. Phys. Lett. 2, 93–94 (1963). [CrossRef]  

4. T. H. Maiman, “Stimulated optical radiation in ruby,” Nature 187, 493–494 (1960). [CrossRef]  

5. G. R. Simpson, “Continuous Sun-pumped room temperature glass laser operation,” Appl. Opt. 3, 783–784 (1964). [CrossRef]  

6. C. G. Young, “A Sun-pumped cw one-watt laser,” Appl. Opt. 5, 993–997 (1966). [CrossRef]   [PubMed]  

7. H. Arashi, Y. Oka, N. Sasahara, A. Kaimai, and M. Ishigame, “A solar-pumped cw $18\mathrm{W}$ Nd:YAG laser,” Jpn. J. Appl. Phys. 23, 1051–1053 (1984). [CrossRef]  

8. R. M. J. Benmair, J. Kagan, Y. Kalisky, Y. Noter, M. Oron, Y. Shimony, and A. Yogev, “Solar-pumped Er, Tm, Ho:YAG laser,” Opt. Lett. 15, 36–38 (1990). [CrossRef]   [PubMed]  

9. T. Ohkubo, T. Yabe, K. Yoshida, S. Uchida, T. Funatsu, B. Bagheri, T. Oishi, K. Daito, M. Ishioka, Y. Nakayama, N. Yasunaga, K. Kido, Y. Sato, C. Baasandash, K. Kato, T. Yanagitani, and Y. Okamoto, “Solar-pumped $80\mathrm{W}$ laser irradiated by a Fresnel lens,” Opt. Lett. 34, 175–177 (2009). [CrossRef]   [PubMed]  

10. I. Bardez, D. Caurant, J. L. Dussossoy, P. Loiseau, C. Gervais, F. Ribot, D. R. Neuville, N. Baffier, and C. Fillett, “Development and characterization of rare earth-rich glassy matrices envisaged for the immobilization of concentrated nuclear waste solutions,” Nucl. Sci. Eng. 153, 272–284 (2006).

11. M. Poulain, M. Poulain, J. Lucas, and P. Brun, “Verres fluores au tetrafluorure de zirconium proprietes optiques d’un verre dope au ${\mathrm{Nd}}^{3+}$,” Mat. Res. Bull. 10, 243–246 (1975). [CrossRef]  

12. X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. Opt. Electron. 2010, 501956 (2010). [CrossRef]  

13. T. Kanamori and S. Sakaguchi, “Preparation of elevated NA fluoride optical fibers,” Jpn. J. Appl. Phys. 25, L468–L470 (1986). [CrossRef]  

14. F. Gan, “Optical properties of fluoride glasses: a review,” J. Non-Cryst. Solids 184, 9–20 (1995). [CrossRef]  

15. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127, 750–761 (1962). [CrossRef]  

16. G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37, 511–520 (1962). [CrossRef]  

17. A. A. Kaminskii, Crystalline Lasers: Physical Processes and Operating Schemes (CRC Press, 1996).

18. K. Rajnak, “Configuration-interaction on the “free-ion” energy levels of ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Er}}^{3+}$,” J. Chem. Phys. 43, 847–855 (1965). [CrossRef]  

19. T. Suzuki, H. Nasu, M. Hughes, S. Mizuno, K. Hasegawa, H. Ito, and Y. Ohishi, “Quantum efficiency measurements on Nd-doped glasses for solar pumped lasers,” J. Non-Cryst. Solids 356, 2344–2349 (2010). [CrossRef]  

20. T. Förster, “Experimentelle und Theoretische Untersuchung des Zwischenmolekularen Ubergangs von Elektronenanregungsenergie,” Z. Naturforsch. B 4a, 321–327 (1949).

21. J. A. Caird, A. J. Ramponi, and P. R. Staver, “Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses,” J. Opt. Soc. Am. B 8, 1391–1403 (1991). [CrossRef]  

22. A. I. Burshtein, “Concentration self-quenching,” Sov. Phys. JETP 57, 1165–1171 (1983).

23. M. Inokuti and F. Hirayama, “Influence of energy transfer by the exchange mechanism on donor luminescence,” J. Chem. Phys. 43, 1978–1989 (1965). [CrossRef]  

24. D. L. Dexter, “A theory of sensitized luminescence in solids,” J. Chem. Phys. 21, 836–850 (1953). [CrossRef]  

25. C. Jacinto, S. L. Oliveira, L. A. O. Nunes, J. D. Myers, M. J. Myers, and T. Catunda, “Normalized-lifetime thermal-lens method for the determination of luminescence quantum efficiency and thermo-optical coefficients: application to ${\mathrm{Nd}}^{3+}$-doped glasses,” Phys. Rev. B 73, 125107 (2006). [CrossRef]  

26. H. Takebe, K. Yoshino, T. Murata, K. Morinaga, J. Hector, W. S. Brocklesby, D. W. Hewak, J. Wang, and D. N. Payne, “Spectroscopic properties of ${\mathrm{Nd}}^{3+}$ and ${\mathrm{Pr}}^{3+}$ in gallate glasses with low phonon energies,” Appl. Opt. 36, 5839–5843 (1997). [CrossRef]   [PubMed]  

27. A. Tesar, J. Campbell, M. Weber, C. Weinzapfel, Y. Lin, H. Meissner, and H. Toratani, “Optical properties and laser parameters of ${\mathrm{Nd}}^{3+}$-doped fluoride glasses,” Opt. Mater. 1, 217–234 (1992). [CrossRef]  

28. S. E. Stokowski, R. A. Saroyan, and M. J. Weber, “Nd-doped laser glass spectroscopic and physical properties,” Technical Report M-095 (Lawrence Livermore National Laboratory, 1981).

29. K. Arai, H. Namikawa, K. Kumata, T. Honda, Y. Ishii, and T. Hanada, “Aluminum or phosphorus co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass,” J. Appl. Phys. 59, 3430–3436 (1986). [CrossRef]  

30. W. J. Miniscalco, “Optical and electronic properties of rare earth ions in glasses,” in Rare Earth Doped Fiber Lasers and Amplifiers, 2nd ed., M. J. F. Digonnet, ed. (Stanford Univ. Press, 2001), pp. 17–112.

31. D. P. Devor, L. G. Deshazer, and R. C. Pastor, “Nd:YAG quantum efficiency and related radiative properties,” IEEE J. Quantum Electron. 25, 1863–1873 (1989). [CrossRef]  

32. A. A. Andrade, T. Catunda, R. Lebullenger, A. C. Hernandes, and M. L. Baesso, “Thermal lens measurements of fluorescence quantum efficiency in ${\mathrm{Nd}}^{3+}$-doped floride glasses,” J. Non-Cryst. Solids 284, 255–260 (2001). [CrossRef]  

33. C. B. Layne, W. H. Lowdermilk, and M. J. Weber, “Multiphonon relaxation of rare-earth ions in oxide glasses,” Phys. Rev. B 16, 10–20 (1977). [CrossRef]  

34. R. Reisfeld and C. K. Jørgensen, “Excited-state phenomena in vitreous materials,” in Handbook on the Physics and Chemistry of Rare Earths, Vol. 9, A. Gschneider and L. Eyring, eds. (Elsevier, 1987), Chap. 58, pp. 1–90. [CrossRef]  

35. S. M. Lima, A. A. Andrade, R. Lebullenger, A. C. Hernandes, T. Catunda, and M. L. Baesso, “Multiwavelength thermal lens determination of fluorescence quantum efficiency of solids: application to ${\mathrm{Nd}}^{3+}$-doped fluoride glass,” Appl. Phys. Lett. 78, 3220–3222 (2001). [CrossRef]