Growth, Thermal and Spectral Properties of Er3+-Doped and Er3+/Yb3+-Codoped Li3Ba2La3(WO4)8 Crystals
Identifieur interne : 000387 ( Pmc/Corpus ); précédent : 000386; suivant : 000388Growth, Thermal and Spectral Properties of Er3+-Doped and Er3+/Yb3+-Codoped Li3Ba2La3(WO4)8 Crystals
Auteurs : Bin Xiao ; Zhoubin Lin ; Lizhen Zhang ; Yisheng Huang ; Guofu WangSource :
- PLoS ONE [ 1932-6203 ] ; 2012.
Abstract
This paper reports the growth and spectral properties of Er3+-doped and Er3+/Yb3+-codoped Li3Ba2La3(WO4)8 crystals. The Er3+: Li3Ba2La3(WO4)8 crystal with dimensions of 56 mm×28 mm×9 mm and Er3+/Yb3+: Li3Ba2La3(WO4)8 crystal with dimensions of 52 mm×24 mm×8 mm were obtained by the top-seeded solution growth (TSSG) method. Thermal expansion coefficients and thermal conductivity of both crystals were measured. The spectroscopic characterizations of both crystals were investigated. The spectroscopic analysis reveals that the Er3+/Yb3+: Li3Ba2La3(WO4)8 crystal has much better optical properties than the Er3+: Li3Ba2La3(WO4)8 crystal, thus it may become a potential candidate for solid-state laser gain medium material.
Url:
DOI: 10.1371/journal.pone.0040631
PubMed: 22808214
PubMed Central: 3396601
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PMC:3396601Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Growth, Thermal and Spectral Properties of Er<sup>3+</sup>-Doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-Codoped Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> Crystals</title><author><name sortKey="Xiao, Bin" sort="Xiao, Bin" uniqKey="Xiao B" first="Bin" last="Xiao">Bin Xiao</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff2"><addr-line>Graduate School of Chinese Academy of Sciences, Beijing, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Lin, Zhoubin" sort="Lin, Zhoubin" uniqKey="Lin Z" first="Zhoubin" last="Lin">Zhoubin Lin</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Zhang, Lizhen" sort="Zhang, Lizhen" uniqKey="Zhang L" first="Lizhen" last="Zhang">Lizhen Zhang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Huang, Yisheng" sort="Huang, Yisheng" uniqKey="Huang Y" first="Yisheng" last="Huang">Yisheng Huang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Wang, Guofu" sort="Wang, Guofu" uniqKey="Wang G" first="Guofu" last="Wang">Guofu Wang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">22808214</idno><idno type="pmc">3396601</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3396601</idno><idno type="RBID">PMC:3396601</idno><idno type="doi">10.1371/journal.pone.0040631</idno><date when="2012">2012</date><idno type="wicri:Area/Pmc/Corpus">000387</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000387</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Growth, Thermal and Spectral Properties of Er<sup>3+</sup>-Doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-Codoped Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> Crystals</title><author><name sortKey="Xiao, Bin" sort="Xiao, Bin" uniqKey="Xiao B" first="Bin" last="Xiao">Bin Xiao</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation><affiliation><nlm:aff id="aff2"><addr-line>Graduate School of Chinese Academy of Sciences, Beijing, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Lin, Zhoubin" sort="Lin, Zhoubin" uniqKey="Lin Z" first="Zhoubin" last="Lin">Zhoubin Lin</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Zhang, Lizhen" sort="Zhang, Lizhen" uniqKey="Zhang L" first="Lizhen" last="Zhang">Lizhen Zhang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Huang, Yisheng" sort="Huang, Yisheng" uniqKey="Huang Y" first="Yisheng" last="Huang">Yisheng Huang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author><author><name sortKey="Wang, Guofu" sort="Wang, Guofu" uniqKey="Wang G" first="Guofu" last="Wang">Guofu Wang</name><affiliation><nlm:aff id="aff1"><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></nlm:aff></affiliation></author></analytic><series><title level="j">PLoS ONE</title><idno type="eISSN">1932-6203</idno><imprint><date when="2012">2012</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>This paper reports the growth and spectral properties of Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-codoped Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystals. The Er<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal with dimensions of 56 mm×28 mm×9 mm and Er<sup>3+</sup>/Yb<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal with dimensions of 52 mm×24 mm×8 mm were obtained by the top-seeded solution growth (TSSG) method. Thermal expansion coefficients and thermal conductivity of both crystals were measured. The spectroscopic characterizations of both crystals were investigated. The spectroscopic analysis reveals that the Er<sup>3+</sup>/Yb<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal has much better optical properties than the Er<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal, thus it may become a potential candidate for solid-state laser gain medium material.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Gallis, S" uniqKey="Gallis S">S Gallis</name></author><author><name sortKey="Huang, M" uniqKey="Huang M">M Huang</name></author><author><name sortKey="Kaloyeros, Ae" uniqKey="Kaloyeros A">AE Kaloyeros</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhao, D" uniqKey="Zhao D">D Zhao</name></author><author><name sortKey="Wang, Gf" uniqKey="Wang G">GF Wang</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chen, G" uniqKey="Chen G">G 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<front><journal-meta><journal-id journal-id-type="nlm-ta">PLoS One</journal-id><journal-id journal-id-type="iso-abbrev">PLoS ONE</journal-id><journal-id journal-id-type="publisher-id">plos</journal-id><journal-id journal-id-type="pmc">plosone</journal-id><journal-title-group><journal-title>PLoS ONE</journal-title></journal-title-group><issn pub-type="epub">1932-6203</issn><publisher><publisher-name>Public Library of Science</publisher-name><publisher-loc>San Francisco, USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">22808214</article-id><article-id pub-id-type="pmc">3396601</article-id><article-id pub-id-type="publisher-id">PONE-D-12-03824</article-id><article-id pub-id-type="doi">10.1371/journal.pone.0040631</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Materials Science</subject><subj-group><subject>Crystallography</subject></subj-group><subj-group><subject>Material by Attribute</subject></subj-group><subj-group><subject>Material by Structure</subject></subj-group><subj-group><subject>Material Properties</subject></subj-group><subj-group><subject>Materials Characterization</subject></subj-group><subj-group><subject>Materials Chemistry</subject></subj-group><subj-group><subject>Materials Physics</subject></subj-group></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics</subject><subj-group><subject>Condensed-Matter Physics</subject><subj-group><subject>Crystallography</subject></subj-group></subj-group><subj-group><subject>Materials Physics</subject></subj-group><subj-group><subject>Solid State Physics</subject></subj-group></subj-group></article-categories><title-group><article-title>Growth, Thermal and Spectral Properties of Er<sup>3+</sup>-Doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-Codoped Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> Crystals</article-title><alt-title alt-title-type="running-head">Growth and Property of Er/Yb Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub></alt-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Xiao</surname><given-names>Bin</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Lin</surname><given-names>Zhoubin</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Zhang</surname><given-names>Lizhen</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Huang</surname><given-names>Yisheng</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Wang</surname><given-names>Guofu</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>Key Laboratory of Optoelectronics Material Chemistry and Physics, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian, China</addr-line></aff><aff id="aff2"><label>2</label><addr-line>Graduate School of Chinese Academy of Sciences, Beijing, China</addr-line></aff><contrib-group><contrib contrib-type="editor"><name><surname>Haverkamp</surname><given-names>Richard G.</given-names></name><role>Editor</role><xref ref-type="aff" rid="edit1"></xref></contrib></contrib-group><aff id="edit1">Massey University, New Zealand</aff><author-notes><corresp id="cor1">* E-mail: <email>wgf@ms.fjirsm.ac.cn</email></corresp><fn fn-type="con"><p>Conceived and designed the experiments: BX GW. Performed the experiments: BX ZL. Analyzed the data: BX GW. Contributed reagents/materials/analysis tools: YH LZ. Wrote the paper: BX GW.</p></fn></author-notes><pub-date pub-type="collection"><year>2012</year></pub-date><pub-date pub-type="epub"><day>13</day><month>7</month><year>2012</year></pub-date><volume>7</volume><issue>7</issue><elocation-id>e40631</elocation-id><history><date date-type="received"><day>2</day><month>2</month><year>2012</year></date><date date-type="accepted"><day>11</day><month>6</month><year>2012</year></date></history><permissions><copyright-statement>Xiao et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</copyright-statement><copyright-year>2012</copyright-year></permissions><abstract><p>This paper reports the growth and spectral properties of Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-codoped Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystals. The Er<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal with dimensions of 56 mm×28 mm×9 mm and Er<sup>3+</sup>/Yb<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal with dimensions of 52 mm×24 mm×8 mm were obtained by the top-seeded solution growth (TSSG) method. Thermal expansion coefficients and thermal conductivity of both crystals were measured. The spectroscopic characterizations of both crystals were investigated. The spectroscopic analysis reveals that the Er<sup>3+</sup>/Yb<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal has much better optical properties than the Er<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> crystal, thus it may become a potential candidate for solid-state laser gain medium material.</p></abstract><counts><page-count count="9"></page-count></counts></article-meta></front><body><sec id="s1"><title>Introduction</title><p>Er<sup>3+</sup> is a well-known active ion for the solid-state laser in near infrared and up-conversion emission <xref ref-type="bibr" rid="pone.0040631-Gallis1">[1]</xref>–<xref ref-type="bibr" rid="pone.0040631-Chen1">[3]</xref>. The <sup>4</sup>I<sub>13/2</sub>→<sup>4</sup>I<sub>15/2</sub> transition has attracted much attention because its eye-safe emission around 1.55 µm has potential use in optical communication, range finding and medical treatment <xref ref-type="bibr" rid="pone.0040631-Burns1">[4]</xref>, <xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>, <xref ref-type="bibr" rid="pone.0040631-Tolstik1">[6]</xref>. The green output emission of Er<sup>3+</sup> ions has already been used in various fields, such as data storage and laser display <xref ref-type="bibr" rid="pone.0040631-Silversmith1">[7]</xref>, <xref ref-type="bibr" rid="pone.0040631-Scheps1">[8]</xref>. Unfortunately, the optical absorption band of the excited energy level (<sup>4</sup>I<sub>11/2</sub>) is weak, which means Er<sup>3+</sup> ions cannot be effectively pumped. This problem is normally solved by adding a certain amount of Yb<sup>3+</sup> sensitizing ions, since Yb<sup>3+</sup> ions have a broad and high absorption band around 980 nm and the energy transfer from Yb<sup>3+</sup> to Er<sup>3+</sup> ions is efficient <xref ref-type="bibr" rid="pone.0040631-Han1">[9]</xref>, <xref ref-type="bibr" rid="pone.0040631-Zhao2">[10]</xref>, <xref ref-type="bibr" rid="pone.0040631-Wei1">[11]</xref>, <xref ref-type="bibr" rid="pone.0040631-Georgobiani1">[12]</xref>. Laser oscillation has been observed in several Er<sup>3+</sup> and Yb<sup>3+</sup> codoped laser hosts, such as YAG, Y<sub>2</sub>SiO<sub>5</sub><xref ref-type="bibr" rid="pone.0040631-Schweizer1">[13]</xref>, YCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub><xref ref-type="bibr" rid="pone.0040631-Burns1">[4]</xref>, GdCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub><xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>, YVO<sub>4</sub><xref ref-type="bibr" rid="pone.0040631-Soklska1">[14]</xref>, YAl<sub>3</sub>(BO<sub>3</sub>)<sub>4</sub><xref ref-type="bibr" rid="pone.0040631-Chen2">[15]</xref>, and NaCe(WO<sub>4</sub>)<sub>2</sub><xref ref-type="bibr" rid="pone.0040631-Huang1">[16]</xref>. Among them, the slope efficiencies of Er<sup>3+</sup>/Yb<sup>3+</sup> codoped YCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub> and GdCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub> crystals are the highest, and exhibit a better thermal property than phosphate glass <xref ref-type="bibr" rid="pone.0040631-Burns1">[4]</xref>, <xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>. However, the full widths at half the maximum (FWHM) of absorption bands around 980 nm of the Er<sup>3+</sup>/Yb<sup>3+</sup> codoped YCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub> (4 nm) and GdCa4O(BO<sub>3</sub>)<sub>3</sub> (3 nm) crystals are narrow <xref ref-type="bibr" rid="pone.0040631-Burns1">[4]</xref>, <xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>, <xref ref-type="bibr" rid="pone.0040631-Jiang1">[17]</xref>, <xref ref-type="bibr" rid="pone.0040631-Wang1">[18]</xref>. The narrow absorption bands need crucially temperature controlling, because the emission wavelength of the pumping diode changes at 0.2–0.3 nm/°K with the operating temperature of the laser device <xref ref-type="bibr" rid="pone.0040631-Mateos1">[19]</xref>, <xref ref-type="bibr" rid="pone.0040631-Mateos2">[20]</xref>. As a consequence, it is necessary to explore novel materials with large absorption bandwidths for solid-state laser application.</p><p>Li<sub>3</sub>Ba<sub>2</sub>Ln<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> (Ln = La-Lu, Y) belongs to the monoclinic system with space group <italic>C</italic>2/<italic>c</italic>, which was firstly discovered by our group <xref ref-type="bibr" rid="pone.0040631-Li1">[21]</xref>. Due to the existence of a statistical distribution of Ln and Li atoms, these crystals have a high structure disorder, which results in the absorption and emission lines broadening homogeneously when rare-earth ions are doped and occupy the positions of Ln<sup>3+</sup> ions <xref ref-type="bibr" rid="pone.0040631-Li2">[22]</xref>. Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(WO<sub>4</sub>)<sub>8</sub> (hereafter denoted as LBLW) is a member of this family. In this work, the thermal expansion coefficients and thermal conductivity of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW single crystals grown by TSSG method were measured. The room-temperature polarized absorption and fluorescence spectra as well as the up-conversion mechanism of both kinds of crystals were reported and analyzed.</p></sec><sec sec-type="materials|methods" id="s2"><title>Materials and Methods</title><sec id="s2a"><title>1. Crystal Growth</title><p>The Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals were grown by the top-seeded solution growth (TSSG) method from a flux of Li<sub>2</sub>WO<sub>4</sub>. The crystal growth was carried out in a vertical tubular furnace. The schematic diagram of crystal growth apparatuses is same as that in Ref. <xref ref-type="bibr" rid="pone.0040631-Li3">[23]</xref>. The furnace temperature was controlled by an AL-708 controller with controlling accuracy of ±0.1 K. The raw materials of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW were synthesized by the solid-state reaction. The chemicals used were WO<sub>3</sub>, Li<sub>2</sub>CO<sub>3</sub>, BaCO<sub>3</sub>, La<sub>2</sub>O<sub>3</sub>, Er<sub>2</sub>O<sub>3</sub> and Y<sub>2</sub>O<sub>3</sub> with the purity of 99.99%. The solutions were composed of 25 mol% of solute (LBLW) and 75 mol% of solvent (Li<sub>2</sub>WO<sub>4</sub>).The crystal growth procedure is similar to that in Ref <xref ref-type="bibr" rid="pone.0040631-Li3">[23]</xref>. When the growth ended, the crystals were drawn out of the solution and cooled down to room temperature at a cooled rate of 15 K/h. <xref ref-type="fig" rid="pone-0040631-g001">Fig. 1</xref> shows the grown Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals with dimensions of 56 mm×28 mm×9 mm and 52 mm×24 mm×8 mm, respectively.</p><fig id="pone-0040631-g001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g001</object-id><label>Figure 1</label><caption><title>LBLW crystals grown from TSSG method: (a) facets marked by Miller indices (hkl); (b) Er<sup>3+</sup>: LBLW crystal; (c) Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal.</title></caption><graphic xlink:href="pone.0040631.g001"></graphic></fig><p>The concentrations of rare earth ions were determined to be 0.41 at.% Er<sup>3+</sup> in Er<sup>3+</sup>: LBLW crystal and 0.48 at.% Er<sup>3+</sup> and 3.18 at.% Yb<sup>3+</sup> in Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Ultima2, Jobin-Yvon).</p><fig id="pone-0040631-g002" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g002</object-id><label>Figure 2</label><caption><title>Thermal expansion properties of Er<sup>3+</sup>: LBLW crystal: (a) thermal expansions measured along the crystallo-physical axes (<italic>a</italic>, <italic>b</italic>, <italic>c*</italic>) and along the anti-clockwise 45° with respect to the <italic>c</italic>-axis (<italic>c’</italic>); (b) Orientation relationship among the crystallo-physical axes (<italic>a</italic>, <italic>b</italic>, <italic>c*</italic>), principal axes (<italic>X</italic><sub>I</sub>, <italic>X</italic><sub>II</sub>, <italic>X</italic><sub>III</sub>) and optical indicatrix axes (<italic>X</italic>, <italic>Y</italic>, <italic>Z</italic>).</title></caption><graphic xlink:href="pone.0040631.g002"></graphic></fig></sec><sec id="s2b"><title>2. Thermal Properties</title><p>The thermal expansion of crystal is an important thermal factor for the crystal growth <xref ref-type="bibr" rid="pone.0040631-Zhang1">[24]</xref>, <xref ref-type="bibr" rid="pone.0040631-Dhanaraj1">[25]</xref>. The thermal expansion coefficients were measured using a thermal expansion dilatometer (NETZSCH DIL 402 PC). The linear thermal expansion coefficient is defined as:<disp-formula><graphic xlink:href="pone.0040631.e001"></graphic><label>(1)</label></disp-formula>where <italic>L</italic><sub>0</sub> is the initial length of the sample at room temperature, and <inline-formula><inline-graphic xlink:href="pone.0040631.e002.jpg" mimetype="image"></inline-graphic></inline-formula> is the change in length when the temperature changes <inline-formula><inline-graphic xlink:href="pone.0040631.e003.jpg" mimetype="image"></inline-graphic></inline-formula>. Since the LBLW crystal with monoclinic is of anisotropy, the thermal expansion coefficient <bold><italic>α<sub>ij</sub></italic></bold> is a second rank tensor with four nonzero components in the orthogonal crystallo-physical axes (<italic>a, b, c*</italic>) <xref ref-type="bibr" rid="pone.0040631-Ge1">[26]</xref>. Thus, in order to obtain thermal expansion ellipsoid, the measurement should be carried out along at least four different directions. Therefore, four rectangular samples were cut from both the Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-codoped LBLW crystals, of which three were along the crystallographic <italic>a</italic>-, <italic>b</italic>- and <italic>c*</italic>-axis and the fourth, namely <italic>c’,</italic> was cut with the anti-clockwise angle (<italic>φ</italic>) 45° with respect to the <italic>c</italic>-axis. During the measurement, the samples were heated at a heating rate of 5 K/min in the range of 300∼1100 K in the air atmosphere.</p><table-wrap id="pone-0040631-t001" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.t001</object-id><label>Table 1</label><caption><title>Comparison of linear thermal expansion values of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW with other crystals (in units 10<sup>−6</sup> K<sup>−1</sup>).</title></caption><alternatives><graphic id="pone-0040631-t001-1" xlink:href="pone.0040631.t001"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1"></td><td colspan="3" align="left" rowspan="1">Crystallo-physical axes</td><td colspan="3" align="left" rowspan="1">Principal axes</td><td colspan="3" align="left" rowspan="1">Optical indicatrix axes</td><td align="left" rowspan="1" colspan="1">Ref</td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><italic>α<sub>a</sub></italic></td><td align="left" rowspan="1" colspan="1"><italic>α<sub>b</sub></italic></td><td align="left" rowspan="1" colspan="1"><italic>α<sub>c*</sub></italic></td><td align="left" rowspan="1" colspan="1"><italic>X</italic><sub>I</sub></td><td align="left" rowspan="1" colspan="1"><italic>X</italic><sub>II</sub></td><td align="left" rowspan="1" colspan="1"><italic>X</italic><sub>III</sub></td><td align="left" rowspan="1" colspan="1"><italic>α</italic><sub>X</sub></td><td align="left" rowspan="1" colspan="1"><italic>α</italic><sub>Y</sub></td><td align="left" rowspan="1" colspan="1"><italic>α</italic><sub>Z</sub></td><td align="left" rowspan="1" colspan="1"></td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1">Er<sup>3+</sup>:LBLW</td><td align="left" rowspan="1" colspan="1">11.30</td><td align="left" rowspan="1" colspan="1">8.07</td><td align="left" rowspan="1" colspan="1">8.82</td><td align="left" rowspan="1" colspan="1">11.33</td><td align="left" rowspan="1" colspan="1">8.07</td><td align="left" rowspan="1" colspan="1">8.79</td><td align="left" rowspan="1" colspan="1">11.17</td><td align="left" rowspan="1" colspan="1">8.07</td><td align="left" rowspan="1" colspan="1">8.94</td><td align="left" rowspan="1" colspan="1">This work</td></tr><tr><td align="left" rowspan="1" colspan="1">Er<sup>3+</sup>/Yb<sup>3+</sup>:LBLW</td><td align="left" rowspan="1" colspan="1">10.25</td><td align="left" rowspan="1" colspan="1">8.01</td><td align="left" rowspan="1" colspan="1">9.15</td><td align="left" rowspan="1" colspan="1">11.32</td><td align="left" rowspan="1" colspan="1">8.01</td><td align="left" rowspan="1" colspan="1">9.08</td><td align="left" rowspan="1" colspan="1">11.18</td><td align="left" rowspan="1" colspan="1">8.01</td><td align="left" rowspan="1" colspan="1">9.22</td><td align="left" rowspan="1" colspan="1">This work</td></tr><tr><td align="left" rowspan="1" colspan="1">KGd(WO<sub>4</sub>)<sub>2</sub></td><td align="left" rowspan="1" colspan="1">13.6</td><td align="left" rowspan="1" colspan="1">2.8</td><td align="left" rowspan="1" colspan="1">20.5</td><td align="left" rowspan="1" colspan="1">10.6</td><td align="left" rowspan="1" colspan="1">2.8</td><td align="left" rowspan="1" colspan="1">23.4</td><td align="left" rowspan="1" colspan="1">14.56</td><td align="left" rowspan="1" colspan="1">2.8</td><td align="left" rowspan="1" colspan="1">19.54</td><td align="left" rowspan="1" colspan="1"><xref ref-type="bibr" rid="pone.0040631-Pujol1">[31]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1">KLu(WO<sub>4</sub>)<sub>2</sub></td><td align="left" rowspan="1" colspan="1">10.6</td><td align="left" rowspan="1" colspan="1">3.35</td><td align="left" rowspan="1" colspan="1">15.1</td><td align="left" rowspan="1" colspan="1">8.89</td><td align="left" rowspan="1" colspan="1">3.35</td><td align="left" rowspan="1" colspan="1">16.72</td><td align="left" rowspan="1" colspan="1">11.19</td><td align="left" rowspan="1" colspan="1">3.35</td><td align="left" rowspan="1" colspan="1">14.55</td><td align="left" rowspan="1" colspan="1"><xref ref-type="bibr" rid="pone.0040631-Silvestre1">[32]</xref></td></tr><tr><td align="left" rowspan="1" colspan="1">Er<sup>3+</sup>: Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(MoO<sub>4</sub>)<sub>8</sub></td><td align="left" rowspan="1" colspan="1">16.9</td><td align="left" rowspan="1" colspan="1">18.5</td><td align="left" rowspan="1" colspan="1">≈19.6</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><xref ref-type="bibr" rid="pone.0040631-Song1">[33]</xref></td></tr></tbody></table></alternatives></table-wrap><fig id="pone-0040631-g003" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g003</object-id><label>Figure 3</label><caption><title>Thermal conductivity properties of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals with each crystal measured along the crystallographic directions directions <italic>a</italic>, <italic>b</italic>, <italic>c</italic> and <italic>c*,</italic> respectively: (a) for Er<sup>3+</sup>: LBLW crystal; (b) for Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal.</title></caption><graphic xlink:href="pone.0040631.g003"></graphic></fig><p>The processes to determine the thermal expansion tensor in both crystals is similar, therefore here, for brevity, we mainly discuss the Er<sup>3+</sup>-doped one. The measured thermal expansion ratios <inline-formula><inline-graphic xlink:href="pone.0040631.e004.jpg" mimetype="image"></inline-graphic></inline-formula> versus <italic>T</italic> are shown in <xref ref-type="fig" rid="pone-0040631-g002">Fig. 2</xref> (a). It can be found that when the temperature is below 450 K, the value of <inline-formula><inline-graphic xlink:href="pone.0040631.e005.jpg" mimetype="image"></inline-graphic></inline-formula> rise nonlinearly with the temperature. This may be due to the error caused by the thermal dilatometer at temperature below 450 K <xref ref-type="bibr" rid="pone.0040631-Fan1">[27]</xref>, <xref ref-type="bibr" rid="pone.0040631-Guo1">[28]</xref>. By linear fitting of the curves above 450 K, the values of the thermal expansion coefficients along <italic>a</italic>, <italic>b</italic>, <italic>c*</italic> and <italic>c’</italic> axes are derived as <italic>α<sub>a</sub></italic> = 11.3×10<sup>−6</sup> K<sup>−1</sup>, <italic>α<sub>b</sub></italic> = 8.07×10<sup>−6</sup> K<sup>−1</sup>, <italic>α<sub>c*</sub></italic> = 8.82×10<sup>−6</sup> K<sup>−1</sup> and <italic>α<sub>c’</sub></italic> = 9.81×10<sup>−6</sup> K<sup>−1</sup>, respectively. The values of the diagonal elements in the crystallo-physical axes are <italic>α</italic><sub>11</sub> = <italic>α<sub>a</sub></italic>, <italic>α</italic><sub>22</sub> = <italic>α<sub>b</sub></italic> and <italic>α</italic><sub>33</sub> = <italic>α<sub>c*</sub></italic>. <italic>α</italic><sub>13</sub> = <italic>α</italic><sub>31</sub> can be deduced from the equation <xref ref-type="bibr" rid="pone.0040631-Ge1">[26]</xref>,<disp-formula><graphic xlink:href="pone.0040631.e006"></graphic><label>(2)</label></disp-formula></p><p>Thus, the thermal expansion tensor for the Er<sup>3+</sup>-doped LBLW crystal in the crystallo-physical axes can be written as<disp-formula><graphic xlink:href="pone.0040631.e007"></graphic><label>(3)</label></disp-formula></p><p>The next step is to find the values of the principal thermal expansion. For a monoclinic crystal, one of the principal axes (<italic>X</italic><sub>II</sub>) of the thermal expansion ellipsoid coincides with the crystallographic <italic>b</italic>-axis. The other two principle axes (<italic>X</italic><sub>I</sub>, <italic>X</italic><sub>III</sub>) which can be calculated from the secular equation <italic>det</italic>(<italic>α<sub>ij</sub></italic>-<italic>λδ<sub>ij</sub></italic>) = 0 <xref ref-type="bibr" rid="pone.0040631-Sdmeyer1">[29]</xref> are in the (0 1 0) plane. For Er<sup>3+</sup>-doped LBLW crystal, the eigenvalues are <italic>α’</italic><sub>11</sub> = 11.33 K<sup>−1</sup> and <italic>α’</italic><sub>33</sub> = 8.80 K<sup>−1</sup>, and the linear thermal expansion tensor in the principal axes is<disp-formula><graphic xlink:href="pone.0040631.e008"></graphic><label>(4)</label></disp-formula>the angle <italic>ρ</italic> between the crystallo-physical <italic>c*</italic>-axis and principal <italic>X</italic><sub>III</sub> axis can be evaluated by<disp-formula><graphic xlink:href="pone.0040631.e009"></graphic><label>(5)</label></disp-formula>the minus value of ρ denotes the clockwise angle from c*-axis to the XIII axis (see <xref ref-type="fig" rid="pone-0040631-g002">Fig. 2</xref> (b)).</p><p>The values of the linear thermal expansion coefficients along the optical indicatrix axes are more important in practice because the laser elements are normally cut along these axes. The orientation of the optical indicatrix axes (<italic>X</italic>, <italic>Y</italic>, <italic>Z</italic>) with respect to the crystallographic axes (<italic>a</italic>, <italic>b</italic>, <italic>c</italic>) is from that of Ref <xref ref-type="bibr" rid="pone.0040631-Pan1">[30]</xref>: (<italic>a</italic>, <italic>X</italic>) = 19° and (<italic>c</italic>, <italic>Z</italic>) = 20° (see <xref ref-type="fig" rid="pone-0040631-g002">Fig. 2</xref> (b)). Using the detailed procedure described in Ref. <xref ref-type="bibr" rid="pone.0040631-Ge1">[26]</xref>, the ellipsoid in the optical indicatrix axis can be determined as<disp-formula><graphic xlink:href="pone.0040631.e010"></graphic><label>(6)</label></disp-formula></p><p>The linear thermal expansion coefficient for the both Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-doped crystals along the directions of crystallo-physical axes (<italic>a</italic>, <italic>b</italic>, <italic>c*</italic>), principal axes (<italic>X</italic><sub>I</sub>, <italic>X</italic><sub>II</sub>, <italic>X</italic><sub>III</sub>) and optical indicatrix axes (<italic>X</italic>, <italic>Y</italic>, <italic>Z</italic>) are included in <xref ref-type="table" rid="pone-0040631-t001">Table 1</xref>. The values of <italic>α<sub>b</sub></italic>/<italic>α<sub>a</sub></italic> and <italic>α<sub>a</sub></italic>/<italic>α<sub>c*</sub></italic> are 0.71 and 0.78, respectively. The thermal expansion exhibits a larger anisotropy than Li<sub>3</sub>Ba<sub>2</sub>La<sub>3</sub>(MoO<sub>4</sub>)<sub>8</sub> crystal <xref ref-type="bibr" rid="pone.0040631-Song1">[33]</xref>, which means the LBLW crystal is easier to crack during the cooling process. Therefore, a slow annealing rate should be applied in the crystal growth procedure.</p><fig id="pone-0040631-g004" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g004</object-id><label>Figure 4</label><caption><title>Polarized absorption spectra of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals at room temperature.</title></caption><graphic xlink:href="pone.0040631.g004"></graphic></fig><p>The thermal conductivity coefficient (<italic>κ</italic>) of both Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-doped crystals were measured by the laser-flash method (Model NETZSCH LFA 457, Germany) in the temperature range 350–700 K. Four samples along <italic>a</italic>, <italic>b</italic>, <italic>c</italic> and <italic>c*</italic> crystallographic directions for each crystal were prepared for thermal conductivity measurements. The dimension of the samples was about 6 mm×6 mm×2 mm. <xref ref-type="fig" rid="pone-0040631-g003">Fig. 3</xref> shows the evolution of <bold><italic>κ</italic></bold> with temperature of both kinds of crystals. The average values of thermal conductivity at 400 K are 0.95 and 0.94 Wm<sup>−1</sup>K<sup>−1</sup> for Er<sup>3+</sup>-doped and Er<sup>3+</sup>/Yb<sup>3+</sup>-codoped LBLW, respectively. Compared with other typical tungstate crystals, such as KGd(WO<sub>4</sub>)<sub>2</sub> (≈3.3 Wm<sup>−1</sup>K<sup>−1</sup>) <xref ref-type="bibr" rid="pone.0040631-Sdmeyer1">[29]</xref>, KY(WO<sub>4</sub>)<sub>2</sub> (≈2.7 Wm<sup>−1</sup>K<sup>−1</sup>) <xref ref-type="bibr" rid="pone.0040631-Aggarwal1">[34]</xref> and KLu(WO<sub>4</sub>)<sub>2</sub> (≈3.3 Wm<sup>−1</sup>K<sup>−1</sup>) <xref ref-type="bibr" rid="pone.0040631-Petrov1">[35]</xref>, the thermal conductivity of the LBLW crystal is very low. The low thermal conductivity may be related to the disordered structure of LBLW crystal which can increase the probability of phonon-phonon scattering. In fact, NdGd(WO<sub>4</sub>)<sub>2</sub> with disordered structure also has very low thermal conductivity (≈1.2 Wm<sup>−1</sup>K<sup>−1</sup>) <xref ref-type="bibr" rid="pone.0040631-Sdmeyer1">[29]</xref>.</p><table-wrap id="pone-0040631-t002" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.t002</object-id><label>Table 2</label><caption><title>Polarized oscillator strength parameters <inline-formula><inline-graphic xlink:href="pone.0040631.e011.jpg" mimetype="image"></inline-graphic></inline-formula>, measured and calculated line strengths for polarized spectra of Er<sup>3+</sup>: LBLW crystal at room temperature.</title></caption><alternatives><graphic id="pone-0040631-t002-2" xlink:href="pone.0040631.t002"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e012.jpg" mimetype="image"></inline-graphic></inline-formula>-Manifold</td><td colspan="3" align="left" rowspan="1"><italic>E</italic>||<italic>X</italic></td><td colspan="3" align="left" rowspan="1"><italic>E</italic>||<italic>Y</italic></td><td colspan="3" align="left" rowspan="1"><italic>E</italic>||<italic>Z</italic></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e013.jpg" mimetype="image"></inline-graphic></inline-formula> (nm)</td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e014.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e015.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e016.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e017.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e018.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e019.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e020.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e021.jpg" mimetype="image"></inline-graphic></inline-formula></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td colspan="2" align="left" rowspan="1">(10<sup>−20</sup> cm<sup>2</sup>)</td><td align="left" rowspan="1" colspan="1">(nm)</td><td colspan="2" align="left" rowspan="1">(10<sup>−20</sup> cm<sup>2</sup>)</td><td align="left" rowspan="1" colspan="1">(nm)</td><td colspan="2" align="left" rowspan="1">(10<sup>−20</sup> cm<sup>2</sup>)</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>13/2</sub></td><td align="left" rowspan="1" colspan="1">1525</td><td align="left" rowspan="1" colspan="1">1.172</td><td align="left" rowspan="1" colspan="1">1.21</td><td align="left" rowspan="1" colspan="1">1516</td><td align="left" rowspan="1" colspan="1">2.21</td><td align="left" rowspan="1" colspan="1">2.18</td><td align="left" rowspan="1" colspan="1">1520</td><td align="left" rowspan="1" colspan="1">1.25</td><td align="left" rowspan="1" colspan="1">1.26</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>11/2</sub></td><td align="left" rowspan="1" colspan="1">984</td><td align="left" rowspan="1" colspan="1">6.32</td><td align="left" rowspan="1" colspan="1">6.07</td><td align="left" rowspan="1" colspan="1">983</td><td align="left" rowspan="1" colspan="1">7.64</td><td align="left" rowspan="1" colspan="1">7.82</td><td align="left" rowspan="1" colspan="1">981</td><td align="left" rowspan="1" colspan="1">5.74</td><td align="left" rowspan="1" colspan="1">5.66</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>9/2</sub></td><td align="left" rowspan="1" colspan="1">801</td><td align="left" rowspan="1" colspan="1">2.817</td><td align="left" rowspan="1" colspan="1">2.98</td><td align="left" rowspan="1" colspan="1">804</td><td align="left" rowspan="1" colspan="1">4.53</td><td align="left" rowspan="1" colspan="1">3.42</td><td align="left" rowspan="1" colspan="1">803</td><td align="left" rowspan="1" colspan="1">2.11</td><td align="left" rowspan="1" colspan="1">2.25</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>F<sub>9/2</sub></td><td align="left" rowspan="1" colspan="1">656</td><td align="left" rowspan="1" colspan="1">1.147</td><td align="left" rowspan="1" colspan="1">1.14</td><td align="left" rowspan="1" colspan="1">658</td><td align="left" rowspan="1" colspan="1">1.54</td><td align="left" rowspan="1" colspan="1">1.59</td><td align="left" rowspan="1" colspan="1">655</td><td align="left" rowspan="1" colspan="1">9.73</td><td align="left" rowspan="1" colspan="1">9.63</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>S<sub>3/2</sub></td><td align="left" rowspan="1" colspan="1">545</td><td align="left" rowspan="1" colspan="1">1.481</td><td align="left" rowspan="1" colspan="1">1.13</td><td align="left" rowspan="1" colspan="1">547</td><td align="left" rowspan="1" colspan="1">1.75</td><td align="left" rowspan="1" colspan="1">2.70</td><td align="left" rowspan="1" colspan="1">545</td><td align="left" rowspan="1" colspan="1">1.68</td><td align="left" rowspan="1" colspan="1">1.37</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>F<sub>7/2</sub></td><td align="left" rowspan="1" colspan="1">489</td><td align="left" rowspan="1" colspan="1">5.864</td><td align="left" rowspan="1" colspan="1">5.68</td><td align="left" rowspan="1" colspan="1">490</td><td align="left" rowspan="1" colspan="1">1.06</td><td align="left" rowspan="1" colspan="1">1.05</td><td align="left" rowspan="1" colspan="1">489</td><td align="left" rowspan="1" colspan="1">5.58</td><td align="left" rowspan="1" colspan="1">5.74</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>F<sub>5/2</sub>+<sup>4</sup>F<sub>3/2</sub></td><td align="left" rowspan="1" colspan="1">450</td><td align="left" rowspan="1" colspan="1">2.109</td><td align="left" rowspan="1" colspan="1">1.79</td><td align="left" rowspan="1" colspan="1">449</td><td align="left" rowspan="1" colspan="1">4.55</td><td align="left" rowspan="1" colspan="1">4.29</td><td align="left" rowspan="1" colspan="1">447</td><td align="left" rowspan="1" colspan="1">2.19</td><td align="left" rowspan="1" colspan="1">2.18</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>2</sup>H<sub>9/2</sub></td><td align="left" rowspan="1" colspan="1">407</td><td align="left" rowspan="1" colspan="1">1.873</td><td align="left" rowspan="1" colspan="1">1.47</td><td align="left" rowspan="1" colspan="1">407</td><td align="left" rowspan="1" colspan="1">2.76</td><td align="left" rowspan="1" colspan="1">3.12</td><td align="left" rowspan="1" colspan="1">407</td><td align="left" rowspan="1" colspan="1">2.17</td><td align="left" rowspan="1" colspan="1">1.64</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e022.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="3" align="left" rowspan="1">0.36</td><td colspan="3" align="left" rowspan="1">0.72</td><td colspan="3" align="left" rowspan="1">0.30</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e023.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="3" align="left" rowspan="1">14.31, 1.72, 0.51</td><td colspan="3" align="left" rowspan="1">10.52, 1.85, 1.21</td><td colspan="3" align="left" rowspan="1">11.0, 1.23, 0.63</td></tr><tr><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e024.jpg" mimetype="image"></inline-graphic></inline-formula></td><td colspan="9" align="left" rowspan="1">11.94, 1.60, 0.78</td></tr></tbody></table></alternatives><table-wrap-foot><fn id="nt101"><label></label><p><inline-formula><inline-graphic xlink:href="pone.0040631.e025.jpg" mimetype="image"></inline-graphic></inline-formula> is the mean wavelength.</p></fn><fn id="nt102"><label></label><p><inline-formula><inline-graphic xlink:href="pone.0040631.e026.jpg" mimetype="image"></inline-graphic></inline-formula> is the root mean square deviation.</p></fn></table-wrap-foot></table-wrap><table-wrap id="pone-0040631-t003" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.t003</object-id><label>Table 3</label><caption><title>Spontaneous emission probabilities <inline-formula><inline-graphic xlink:href="pone.0040631.e027.jpg" mimetype="image"></inline-graphic></inline-formula>, fluorescence branching ratios <italic>β</italic> and radiative lifetimes <inline-formula><inline-graphic xlink:href="pone.0040631.e028.jpg" mimetype="image"></inline-graphic></inline-formula> for Er<sup>3+</sup>: LBLW crystal.</title></caption><alternatives><graphic id="pone-0040631-t003-3" xlink:href="pone.0040631.t003"></graphic><table frame="hsides" rules="groups"><colgroup span="1"><col align="left" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col><col align="center" span="1"></col></colgroup><thead><tr><td colspan="2" align="left" rowspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td colspan="2" align="left" rowspan="1"><italic>E</italic>||<italic>X</italic></td><td colspan="2" align="left" rowspan="1"><italic>E</italic>||<italic>Y</italic></td><td colspan="2" align="left" rowspan="1"><italic>E</italic>||<italic>Z</italic></td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td colspan="2" align="left" rowspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e029.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e030.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e031.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e032.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e033.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e034.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e035.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e036.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e037.jpg" mimetype="image"></inline-graphic></inline-formula></td><td align="left" rowspan="1" colspan="1"><inline-formula><inline-graphic xlink:href="pone.0040631.e038.jpg" mimetype="image"></inline-graphic></inline-formula></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">(nm)</td><td align="left" rowspan="1" colspan="1">(S<sup>−1</sup>)</td><td align="left" rowspan="1" colspan="1">(S<sup>−1</sup>)</td><td align="left" rowspan="1" colspan="1">(%)</td><td align="left" rowspan="1" colspan="1">(S<sup>−1</sup>)</td><td align="left" rowspan="1" colspan="1">(%)</td><td align="left" rowspan="1" colspan="1">(S<sup>−1</sup>)</td><td align="left" rowspan="1" colspan="1">(%)</td><td align="left" rowspan="1" colspan="1">(ms)</td></tr></thead><tbody><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>13/2</sub>→</td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>15/2</sub></td><td align="left" rowspan="1" colspan="1">1543</td><td align="left" rowspan="1" colspan="1">77.53</td><td align="left" rowspan="1" colspan="1">136.04</td><td align="left" rowspan="1" colspan="1">100.00</td><td align="left" rowspan="1" colspan="1">245.41</td><td align="left" rowspan="1" colspan="1">100.00</td><td align="left" rowspan="1" colspan="1">141.58</td><td align="left" rowspan="1" colspan="1">100.00</td><td align="left" rowspan="1" colspan="1">3.44</td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>11/2</sub>→</td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>13/2</sub></td><td align="left" rowspan="1" colspan="1">2746</td><td align="left" rowspan="1" colspan="1">17.31</td><td align="left" rowspan="1" colspan="1">30.70</td><td align="left" rowspan="1" colspan="1">13.66</td><td align="left" rowspan="1" colspan="1">46.70</td><td align="left" rowspan="1" colspan="1">14.06</td><td align="left" rowspan="1" colspan="1">29.49</td><td align="left" rowspan="1" colspan="1">14.19</td><td align="left" rowspan="1" colspan="1">1.80</td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>15/2</sub></td><td align="left" rowspan="1" colspan="1">988</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">303.54</td><td align="left" rowspan="1" colspan="1">86.34</td><td align="left" rowspan="1" colspan="1">391.43</td><td align="left" rowspan="1" colspan="1">85.94</td><td align="left" rowspan="1" colspan="1">283.13</td><td align="left" rowspan="1" colspan="1">85.81</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"><sup>4</sup>S<sub>3/2</sub>→</td><td align="left" rowspan="1" colspan="1"><sup>4</sup>F<sub>9/2</sub></td><td align="left" rowspan="1" colspan="1">3125</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">0.66</td><td align="left" rowspan="1" colspan="1">0.04</td><td align="left" rowspan="1" colspan="1">1.56</td><td align="left" rowspan="1" colspan="1">0.04</td><td align="left" rowspan="1" colspan="1">0.79</td><td align="left" rowspan="1" colspan="1">0.04</td><td align="left" rowspan="1" colspan="1">0.39</td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>9/2</sub></td><td align="left" rowspan="1" colspan="1">1666</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">82.29</td><td align="left" rowspan="1" colspan="1">5.28</td><td align="left" rowspan="1" colspan="1">144.34</td><td align="left" rowspan="1" colspan="1">3.93</td><td align="left" rowspan="1" colspan="1">80.54</td><td align="left" rowspan="1" colspan="1">4.31</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>11/2</sub></td><td align="left" rowspan="1" colspan="1">1215</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">36.16</td><td align="left" rowspan="1" colspan="1">2.32</td><td align="left" rowspan="1" colspan="1">79.35</td><td align="left" rowspan="1" colspan="1">2.16</td><td align="left" rowspan="1" colspan="1">41.27</td><td align="left" rowspan="1" colspan="1">2.21</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>13/2</sub></td><td align="left" rowspan="1" colspan="1">842</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">428.09</td><td align="left" rowspan="1" colspan="1">27.49</td><td align="left" rowspan="1" colspan="1">1024.96</td><td align="left" rowspan="1" colspan="1">27.94</td><td align="left" rowspan="1" colspan="1">520.20</td><td align="left" rowspan="1" colspan="1">27.82</td><td align="left" rowspan="1" colspan="1"></td></tr><tr><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1"><sup>4</sup>I<sub>15/2</sub></td><td align="left" rowspan="1" colspan="1">545</td><td align="left" rowspan="1" colspan="1"></td><td align="left" rowspan="1" colspan="1">1010.05</td><td align="left" rowspan="1" colspan="1">64.86</td><td align="left" rowspan="1" colspan="1">2418.35</td><td align="left" rowspan="1" colspan="1">65.92</td><td align="left" rowspan="1" colspan="1">1227.38</td><td align="left" rowspan="1" colspan="1">65.63</td><td align="left" rowspan="1" colspan="1"></td></tr></tbody></table></alternatives></table-wrap></sec><sec id="s2c"><title>3. Spectral Properties</title><p>Two cubic samples with dimensions of 7.4 mm×3.8 mm×5.8 mm and 7.2 mm×2.4 mm×4.7 mm were cut from the Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals, respectively. Each face of samples was perpendicular to one of the optical indicatrix axes. All the surfaces of these cuboids were polished for spectral experiments. The polarized absorption spectra from 300 nm to 1700 nm were measured using a Perkin-Elmer UV-VIS-NIR spectrometer (Lambda 900). The polarized fluorescence spectra were recorded by a spectrophotometer (FLS920, Edinburgh) equipped with a xenon lamp as the excitation source. Two photomultiplier tubes (PMT) (Hamamatsu R955 and R5509) were used as the detectors in the VIS and NIR regions, respectively. Furthermore, the up-conversion spectroscopic experiments were carried out by a monochromator (Triax550, Jobin-Yvon) excited at 976 nm with a diode laser, and the power range of the diode emission was from 40 to 1400 mW. The signals were detected with a PMT (R943-02, Hamamasu). All measurements were performed at room temperature.</p><fig id="pone-0040631-g005" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g005</object-id><label>Figure 5</label><caption><title>Polarized stimulated emission cross-section versus wavelength for <sup>4</sup>I<sub>13/2</sub>→<sup>4</sup>I<sub>15/2</sub> transition of Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal calculated by F-L formula.</title></caption><graphic xlink:href="pone.0040631.g005"></graphic></fig><fig id="pone-0040631-g006" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g006</object-id><label>Figure 6</label><caption><title>Polarized gain cross sections of Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal versus wavelength.</title></caption><graphic xlink:href="pone.0040631.g006"></graphic></fig><p>The absorption spectra of the Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals at room temperature are shown in <xref ref-type="fig" rid="pone-0040631-g004">Fig. 4</xref>. These sharp absorption lines are attributed to the Er<sup>3+</sup> ions except the broad absorption band at 900–1050 nm, which is the overlap of the <sup>4</sup>I<sub>15/2</sub>→ <sup>4</sup>I<sub>11/2</sub> transition of Er<sup>3+</sup> ions and the <sup>2</sup>F<sub>7/2</sub>→ <sup>2</sup>F<sub>5/2</sub> transition of Yb<sup>3+</sup> ions. In comparison with Er<sup>3+</sup>: LBLW crystal, such broad and strong absorption band around 900–1050 nm was mainly attributed to the <sup>2</sup>F<sub>7/2</sub>→<sup>2</sup>F<sub>5/2</sub> transition of Yb<sup>3+</sup> ions. The absorption coefficients for Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal are 1.76 cm<sup>−1</sup> at 980 nm, 2.54 cm<sup>−1</sup> at 974 nm and 1.80 cm<sup>−1</sup> at 978 nm for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z</italic> respectively. They are roughly ten times as large as those of the Er<sup>3+</sup>: LBLW crystal (0.15 cm<sup>−1</sup>, 0.14 cm<sup>−1</sup> and 0.22 cm<sup>−1</sup> for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z,</italic> respectively). Therefore, the crystal co-doped with Yb<sup>3+</sup> ions can significantly increase the absorption of the pump energy if pumped at around 980 nm. It should be also noted that the FWHMs of Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal around 980 nm are 35 nm, 38 nm and 34 nm for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z</italic>, respectively, and these values are larger than those of Er<sup>3+</sup>/Yb<sup>3+</sup>: YCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub> and Er<sup>3+</sup>/Yb<sup>3+</sup>: GdCa<sub>4</sub>O(BO<sub>3</sub>)<sub>3</sub> crystals <xref ref-type="bibr" rid="pone.0040631-Burns1">[4]</xref>, <xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>. The broad absorption bands which can relax the requirement of accurate temperature control of diode laser make Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal suitable for diode laser pumping.</p><fig id="pone-0040631-g007" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g007</object-id><label>Figure 7</label><caption><title>Up-conversion fluorescence spectrum of Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals excited 976 nm radiation at room temperature.</title></caption><graphic xlink:href="pone.0040631.g007"></graphic></fig><fig id="pone-0040631-g008" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g008</object-id><label>Figure 8</label><caption><title>Transition mechanisms and simplified energy levels of Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal.</title></caption><graphic xlink:href="pone.0040631.g008"></graphic></fig><p>The Judd-Ofelt theory <xref ref-type="bibr" rid="pone.0040631-Judd1">[36]</xref>, <xref ref-type="bibr" rid="pone.0040631-Ofelt1">[37]</xref> has been widely used to analyze the spectroscopic properties of the rare earth ions except Yb<sup>3+</sup> ion in crystals. The oscillator strength parameters Ω<sub>t</sub> (t = 2, 4, 6) can be fitted from the room-temperature absorption spectra, then the spontaneous emission probabilities, radiative lifetime and fluorescence branching ratios can be obtained. The detailed calculation procedure is similar to that reported in Ref <xref ref-type="bibr" rid="pone.0040631-Buse1">[38]</xref>. The reduced matrix elements values of unit tensor operators used in the calculation could be found in Ref <xref ref-type="bibr" rid="pone.0040631-Weber1">[39]</xref>, <xref ref-type="bibr" rid="pone.0040631-Carnall1">[40]</xref>. Except for the two high absorption bands which centered at 524 nm and 379 nm, namely <sup>4</sup>I<sub>15/2</sub>→<sup>2</sup>H<sub>11/2</sub> and <sup>4</sup>I<sub>15/2</sub>→<sup>4</sup>G<sub>11/2</sub>, respectively (see <xref ref-type="fig" rid="pone-0040631-g004">Fig. 4</xref>), all the other ones were chose to fit the oscillator strength parameters for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z</italic> polarizations. Because those two transitions belong to hypersensitive transition <xref ref-type="bibr" rid="pone.0040631-Mason1">[41]</xref>, <xref ref-type="bibr" rid="pone.0040631-Nieboer1">[42]</xref>, they are sensitive to the variation of local structure around Er<sup>3+</sup> ions. Here, only the spectrum of the Er<sup>3+</sup>: LBLW crystal was calculated for brevity. <xref ref-type="table" rid="pone-0040631-t002">Table 2</xref> lists the values of the measured (<italic>S<sup>mea</sup></italic>) and calculated (<italic>S<sup>cal</sup></italic>) line strengths, the intensity parameters Ω<italic><sup>X,Y,Z</sup></italic> for each polarization as well as the effective intensity parameters which are defined as Ω<italic><sup>eff</sup></italic> = (Ω<italic><sup>X</sup></italic>+Ω<italic><sup>X</sup></italic>+Ω<italic><sup>X</sup></italic>)/3. After obtaining the oscillator strength parameters Ω<italic><sup>X,Y,Z</sup></italic> for each polarization, the spontaneous emission probabilities of the electric- and magnetic-dipole transitions (named <inline-formula><inline-graphic xlink:href="pone.0040631.e039.jpg" mimetype="image"></inline-graphic></inline-formula> and <inline-formula><inline-graphic xlink:href="pone.0040631.e040.jpg" mimetype="image"></inline-graphic></inline-formula> respectively), fluorescence branching ratio <italic>β</italic> and radiative lifetime <italic>τ<sub>r</sub></italic> of some typical transitions could be gained. The values of these spectroscopic parameters are all outlined in <xref ref-type="table" rid="pone-0040631-t003">Table 3</xref>.</p><p>The Er<sup>3+</sup>: LBLW crystal could not be efficiently excited by Xenon lamp because of the weak absorption at 976 nm. Moreover, considering the small phonon energy of the (WO<sub>4</sub>)<sup>2−</sup> groups (roughly 900 cm<sup>−1</sup>) <xref ref-type="bibr" rid="pone.0040631-Macalik1">[43]</xref>, the multiphonon relaxation from the <sup>4</sup>I<sub>11/2</sub> to <sup>4</sup>I<sub>13/2</sub> multiplets of Er<sup>3+</sup> ions was slow. Therefore, the emission band surrounding 1550 nm (<sup>4</sup>I<sub>13/2</sub>→<sup>4</sup>I<sub>15/2</sub>) for Er<sup>3+</sup>: LBLW crystal is too weak to be distinguished. Thus, the fluorescence spectra of the Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal were only recorded (see <xref ref-type="fig" rid="pone-0040631-g005">Fig. 5</xref>). The stimulated-emission cross-sections were calculated by the Füchtbauer-Ladenburg (F-L) formula <xref ref-type="bibr" rid="pone.0040631-Aull1">[44]</xref>, <xref ref-type="bibr" rid="pone.0040631-Sato1">[45]</xref>,<disp-formula><graphic xlink:href="pone.0040631.e041"></graphic><label>(7)</label></disp-formula>where <italic>A<sup>q</sup></italic> is the spontaneous emission probability for <italic>q</italic> polarization, <italic>I<sup>q</sup></italic>(<italic>λ</italic>) is the fluorescence intensity as a function of wavelength. The peak emission cross-sections are about 0.81×10<sup>−20</sup>, 1.23×10<sup>−20</sup> and 0.84×10<sup>−20</sup> cm<sup>2</sup> for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z</italic> respectively, which are comparable to other co-doped crystals, such as 1.89×10<sup>−20</sup> cm<sup>2</sup> for Er<sup>3+</sup>/Yb<sup>3+</sup>: KY(WO<sub>4</sub>)<sub>2</sub><xref ref-type="bibr" rid="pone.0040631-Mateos3">[46]</xref>, 0.71×10<sup>−20</sup> cm<sup>2</sup> for Er<sup>3+</sup>/Yb<sup>3+</sup>: LaPO<sub>4</sub><xref ref-type="bibr" rid="pone.0040631-Lisiecki1">[47]</xref> and 0.95×10<sup>−20</sup> cm<sup>2</sup> for Ce<sup>3+</sup>/Er<sup>3+</sup> NaLa(MoO<sub>4</sub>)<sub>2</sub><xref ref-type="bibr" rid="pone.0040631-Sani1">[48]</xref>.</p><p>The Er<sup>3+</sup> laser via the <sup>4</sup>I<sub>13/2</sub>→<sup>4</sup>I<sub>15/2</sub> transition operates in a quasi-three scheme, therefore the re-absorption losses should be considered. The useful laser wavelength could be evaluated by the so-called effective gain cross section <xref ref-type="bibr" rid="pone.0040631-Ohta1">[49]</xref>.<disp-formula><graphic xlink:href="pone.0040631.e042"></graphic><label>(8)</label></disp-formula>here, <inline-formula><inline-graphic xlink:href="pone.0040631.e043.jpg" mimetype="image"></inline-graphic></inline-formula> is the emission cross-section, <inline-formula><inline-graphic xlink:href="pone.0040631.e044.jpg" mimetype="image"></inline-graphic></inline-formula> is the absorption cross-section and <italic>β</italic> is the population inversion of Er<sup>3+</sup> ions. Results of the wavelength dependences around 1550 nm for several <italic>β</italic> values (<italic>β</italic> = 0.4, 0.5, 0.6, 0.7) are shown in <xref ref-type="fig" rid="pone-0040631-g006">Fig. 6</xref>. It can be noted that the wavelengths under the low population inversion, for all polarizations, are all located approximately 1590 nm. Additionally, a laser oscillating at shorter wavelength can also be realized by increasing the values of <italic>β</italic>.</p><p><xref ref-type="fig" rid="pone-0040631-g007">Fig. 7</xref> shows the up-conversion fluorescence spectra for Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystals in the range from 500 to 700 nm excited at 976 nm radiation of diode laser. Note that the fluorescence intensity of Er<sup>3+</sup>/Yb<sup>3+</sup> co-doped LBLW crystal is much larger than that of Er<sup>3+</sup>-doped LBLW. This means there existed fast and efficient Yb<sup>3+</sup>→Er<sup>3+</sup> energy transfer in Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal. <xref ref-type="fig" rid="pone-0040631-g008">Fig. 8</xref> displays the up-conversion mechanisms and simplified energy levels of Er<sup>3+</sup> and Yb<sup>3+</sup> ions in Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal. Two different mechanisms, namely Er<sup>3+</sup> excited state absorption (ESA) and a two-step Yb-Er energy transfer (ET), may exist in the up-conversion process <xref ref-type="bibr" rid="pone.0040631-Denker1">[5]</xref>, <xref ref-type="bibr" rid="pone.0040631-Mateos2">[20]</xref>, <xref ref-type="bibr" rid="pone.0040631-Nii1">[50]</xref>.</p><p>For the Er<sup>3+</sup>/Yb<sup>3+</sup> crystal, the green emissions of 530 and 553 nm (<sup>2</sup>H<sub>11/2</sub>→<sup>4</sup>I<sub>15/2</sub> and <sup>4</sup>S<sub>3/2</sub>→<sup>4</sup>I<sub>15/2</sub>, respectively) can be explained by the following steps: Firstly, the Er<sup>3+</sup> ions were excited from ground state to the excited state <sup>4</sup>I<sub>11/2</sub> by means of ground state absorption (GSA) and by ET process from <sup>2</sup>F<sub>5/2</sub> level of Yb<sup>3+</sup> to Er<sup>3+</sup>. The ET process is dominant because of the large absorption across-section around 980 nm of Yb<sup>3+</sup> ions. Secondly, some Er<sup>3+</sup> ions at the <sup>4</sup>I<sub>11/2</sub> level were promoted up to the higher <sup>4</sup>F<sub>7/2</sub> level by ET process from <sup>2</sup>F<sub>5/2</sub> level of Yb<sup>3+</sup> or by ESA of Er<sup>3+</sup> ions, then the ions at the <sup>4</sup>F<sub>7/2</sub> level relaxed non-radiatively to the lower levels <sup>2</sup>H<sub>11/2</sub> and <sup>4</sup>S<sub>3/2</sub> owning to the small energy gap between them. When the Er<sup>3+</sup> ions at the <sup>2</sup>H<sub>11/2</sub> and <sup>4</sup>S<sub>3/2</sub> levels transited to the ground state, they produced 530 and 553 nm green emissions, respectively. The green emissions of the Er<sup>3+</sup>: LBLW crystal also experienced the above processes except the lack of ET process. Because the lifetime of the <sup>4</sup>S<sub>3/2</sub> level is much longer than that of the <sup>2</sup>H<sub>11/2</sub> level <xref ref-type="bibr" rid="pone.0040631-Song2">[51]</xref>, more ions would non-radiatively decay to the <sup>4</sup>S<sub>3/2</sub> level. As a consequence, the intensity of 553 nm is stronger than 530 nm.</p><fig id="pone-0040631-g009" position="float"><object-id pub-id-type="doi">10.1371/journal.pone.0040631.g009</object-id><label>Figure 9</label><caption><title>The ln-ln plots of integrated emission intensities versus the excitation power for Er<sup>3+</sup>/Yb<sup>3+</sup> crystal.</title></caption><graphic xlink:href="pone.0040631.g009"></graphic></fig><p>For the red emission of 661 nm (<sup>4</sup>F<sub>9/2</sub>→<sup>4</sup>I<sub>15/2</sub>), population on the <sup>4</sup>F<sub>9/2</sub> might be accumulated by two ways: ESA and ET process. Both ways excited Er<sup>3+</sup> ions from <sup>4</sup>I<sub>13/2</sub> to <sup>4</sup>F<sub>9/2</sub>. Besides, the ions at the <sup>4</sup>S<sub>3/2</sub> level also relaxed rapidly to the <sup>4</sup>F<sub>9/2</sub> level. The red emission intensity is also significantly weaker than that of Er<sup>3+</sup>/Yb<sup>3+</sup> crystal because of lacking of ET process in the Er<sup>3+</sup>: LBLW crystal.</p><p>The dependence of integrated up-conversion fluorescence intensity on the excitation power at 976 nm for Er<sup>3+</sup>/Yb<sup>3+</sup> crystal is shown in <xref ref-type="fig" rid="pone-0040631-g009">Fig. 9</xref>. According to the relation <inline-formula><inline-graphic xlink:href="pone.0040631.e045.jpg" mimetype="image"></inline-graphic></inline-formula><xref ref-type="bibr" rid="pone.0040631-Jaque1">[52]</xref>, where <italic>n</italic> is the number of photon involved in the up-conversion process and <italic>I</italic> is the excitation power. The slopes (for green and red light are all near 2) indicate that two photon processed populated the <sup>2</sup>H<sub>11/2</sub>, <sup>4</sup>S<sub>3/2</sub> and <sup>4</sup>F<sub>9/2</sub> levels. However, due to the competition between the linear decay and the depletion of the intermediate excited states, the values of <italic>n</italic> may be lower than 2 (see <xref ref-type="fig" rid="pone-0040631-g009">Fig. 9</xref>) <xref ref-type="bibr" rid="pone.0040631-Pollnau1">[53]</xref>.</p></sec></sec><sec id="s3"><title>Results and Discussion</title><p>The Er<sup>3+</sup>: LBLW and Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW have been successfully grown by the TSSG method from the flux of Li<sub>2</sub>WO<sub>4</sub>. The thermal expansion coefficients in the optical indicatrix axes were <italic>α<sub>X</sub></italic> = 11.17×10<sup>−6</sup> K<sup>−1</sup>, <italic>α<sub>Y</sub></italic> = 8.07×10<sup>−6</sup> K<sup>−1</sup> and <italic>α<sub>Z</sub></italic> = 8.94×10<sup>−6</sup> K<sup>−1</sup> for the Er<sup>3+</sup>: LBLW crystal, and <italic>α<sub>X</sub></italic> = 11.18×10<sup>−6</sup> K<sup>−1</sup>, <italic>α<sub>Y</sub></italic> = 8.01×10<sup>−6</sup> K<sup>−1</sup> and <italic>α<sub>Z</sub></italic> = 9.22×10<sup>−6</sup> K<sup>−1</sup> for the Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal. The anisotropy of thermal expansion indicates that the LBLW crystals are easier to crack; thus, slow cooling rate should be adopted after the crystals were withdrawn from the melt. The Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal has broad absorption bands near 980 nm (35 nm, 38 nm and 34 nm for <italic>E||X</italic>, <italic>E||Y</italic> and <italic>E||Z</italic>, respectively), which make it very suitable for diode pumping. The effective J-O intensity parameters of the Er<sup>3+</sup>: LBLW were calculated to be <inline-formula><inline-graphic xlink:href="pone.0040631.e046.jpg" mimetype="image"></inline-graphic></inline-formula> = 11.94×10<sup>−20</sup> cm<sup>2</sup>, <inline-formula><inline-graphic xlink:href="pone.0040631.e047.jpg" mimetype="image"></inline-graphic></inline-formula> = 1.60×10<sup>−20</sup> cm<sup>2</sup>, <inline-formula><inline-graphic xlink:href="pone.0040631.e048.jpg" mimetype="image"></inline-graphic></inline-formula> = 0.78×10<sup>−20</sup> cm<sup>2</sup>, respectively. Considering the re-absorption losses of the quasi-three scheme, the effective emission cross-section around 1550 nm was also calculated. Under the 976 nm excitation, the up-conversion emissions of three visible optical bands, corresponding to the <sup>2</sup>H<sub>11/2</sub>→<sup>4</sup>I<sub>15/2</sub>, <sup>4</sup>S<sub>3/2</sub>→<sup>4</sup>I<sub>15/2</sub> and <sup>4</sup>F<sub>9/2</sub>→<sup>4</sup>I<sub>15/2</sub>, respectively, for Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal were observed. The investigation of up-conversion spectra denotes that the energy transfer between Yb<sup>3+</sup> and Er<sup>3+</sup> is efficient. The spectroscopic analysis reveals that the Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal has much better optical properties than the Er<sup>3+</sup>: LBLW crystal. Therefore, the Er<sup>3+</sup>/Yb<sup>3+</sup>: LBLW crystal may become a potential candidate for solid-state laser gain medium material.</p></sec></body><back><fn-group><fn fn-type="conflict"><p><bold>Competing Interests: </bold>The authors have declared that no competing interests exist.</p></fn><fn fn-type="financial-disclosure"><p><bold>Funding: </bold>This work is supported by the National Natural Science Foundation of China (No. 61108054) and the National Natural Science Foundation of Fujian Province (No. 2011J01376), respectively. 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