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Polarized spectroscopic properties of Ho3+-doped LuLiF4 single crystal for 2 μm and 2.9 μm lasers
Optical Materials 33 (2011) 1610–1615
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Polarized spectroscopic properties of Ho3+-doped LuLiF4 single crystal for 2 lm and 2.9 lm lasers Chengchun Zhao a,b, Yin Hang a,⇑, Lianhan Zhang a, Jigang Yin a,b, Pengchao Hu a,b, En Ma c a
Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China Graduate School of Chinese Academy of Sciences, Beijing 100039, People’s Republic of China c Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China b
a r t i c l e
i n f o
Article history: Received 21 November 2010 Received in revised form 13 April 2011 Accepted 13 April 2011 Available online 7 May 2011 Keywords: Spectral properties Czochralski method Laser materials
a b s t r a c t Polarized spectroscopic properties of a Ho3+-doped LuLiF4 (Ho:LuLF) single crystal grown by the Czochralski method have been investigated as a promising material for 2 lm and 2.9 lm lasers. The Judd–Ofelt (J– O) model has been applied to the analysis of the polarized room temperature absorption spectra to establish the so-called J–O intensity parameters. Based on the calculated parameters, we determined the emission probabilities, branching ratio and radiative lifetime for the Ho3+ transitions from the excited state manifolds to the lower-lying manifolds. Ho:LuLF crystal shows long fluorescence lifetime of 5I7 manifold (16 ms) and broad absorption and emission spectra, which exhibit strong polarization characteristics. Stimulated emission cross-sections spectra of the 5I6 ? 5I7 and 5I7 ? 5I8 transitions were derived and compared with those of the other well-known Ho3+-doped laser crystals. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Solid-state lasers based on Ho-doped single crystals have been extensively investigated because of interest in offering 2 lm and 2.9 lm output. Lasers with the two wavelengths are useful for remote sensing, medicine, coherent lidar and the generation of longer wavelengths via nonlinear optics. In the case of 2 lm lasers, singly Ho-doped crystals have shown more efficient energy extraction than those shown by multiply doped crystals. The main reason is that sensitizer ions introduce a range of undesirable energy transfer processes that increase the threshold and reduce the storage efficiency. In addition, Ho:Tm lasers also suffer from more heating and Ho:Tm energy sharing. On the other hand, the development of high power Tm-based crystalline and fiber lasers operating at 1.9 lm provide effective sources for resonantly pumped singly doped Ho lasers [1,2]. Resonant pumping results in high quantum efficiency and low thermal generation; this, coupled with the high thermal conductivity crystalline hosts, allows generation of high-average power, diffraction-limited output. The host materials for these lasers are usually Y3Al5O12 (YAG), YAlO3 and LiYF4 (YLF) [1–4]. Compared with oxide crystals, fluorides are more attractive to achieve high-energy Q-switched operation, as they possess much longer upper laser level life times. In recent years, fluoride crystal LuLiF4 (LuLF) received more and more attention in the field of
⇑ Corresponding author. Tel.: +86 21 69918480. E-mail address: [email protected] (Y. Hang). 0925-3467/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2011.04.010
mid-infrared lasers. The LuLF crystal, like YLF, has several advantages: strong spectral anisotropy for polarized absorption and emission; negative thermal dependence of refractive index, which partially compensates the positive bulging of the end faces of the laser rod owing to the positive thermal expansion coefficients, leading to weak overall thermal lensing [5]. Smaller host ion size of Lu3+ results in larger crystal fields in LuLF than in YLF, leading to larger crystal field splitting of Ho3+ ion [6]. Larger ground-state 5 I8 splitting results in a low thermal occupation factor for the lower laser level and leads to easier population inversion during laser operation. Some optical properties of Ho:LuLF have been reported. High efficient in-band pumped continuous wave and Q-switched Ho:LuLF 2 lm lasers have been demonstrated recently [6–8]. However, relatively little work has been done systematically concerning the polarized spectroscopic properties of this crystal in sufficient detail. Compared with the study of 2 lm lasers, there are fewer reports on Ho-based solid-state lasers around 2.9 lm (5I6 ? 5I7) due to the lack of pumping source [9,10]. However, efficient Ho-doped silica and fluoride glass fiber lasers operating around 2.9 lm have been demonstrated most recently after the development of highly efficient diode lasers operating in the 1150 nm region and the high power Yb-doped fiber lasers [11–14]. So it is necessary and probable to develop 2.9 lm lasers based on Ho-doped crystals. Ho:LuLF crystal is also such a candidate because its low multi-phonon relaxation resulting in long radiative and fluorescence lifetimes of 5I6 manifold. However, to our knowledge there is no report on the emission properties of Ho:LuLF in this wavelength range.
C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
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In the present work, we reported the room temperature polarized absorption spectra, fluorescence decay lifetime and emission properties at 2 lm and 2.9 lm. The spectral parameters were calculated by using absorption spectra based on J–O theory [15– 17]. From the obtained intensity parameters, we calculated the fluorescence branching ratio and radiative lifetime. Finally, the stimulated emission cross-sections of the 5I6 ? 5I7 and 5I7 ?5I8 transitions were also provided and discussed.
2. Experimental details A single crystal of Ho:LuLF with high optical quality was grown by the Czochralski method in inductively heated graphite crucible under a high purity CF4 atmosphere. The starting materials were prepared from high purity (>99.99%) commercial fluoride powders of LiF, LuF3 and HoF3. The constituent fluorides were weighted and mixed according to the following chemical composition: LiLu0.99Ho0.01F4 because Ho3+ is expected to replace Lu3+ in LuLF crystal. The pulling rate was 0.8 mm/h, and the rotation rate was 7 rpm. Growth orientation was controlled using the a-axis oriented LuLF seed crystal. In order to prevent the crystal from cracking, the crystal was cooled to room temperature slowly after growth. Inductively coupled plasma atomic emission spectrometry (ICPAES) was used to measure the concentrations of Ho and Lu elements in Ho:LuLF crystal. The measured sample was cut from the upper part of as-grown Ho:LuLF crystal, and then was ground to powder in an agate mortar. The Ho3+ concentration in the top of the crystal was measured to be 1.58 1020 cm3. The segregation coefficient of the holmium ion in the LuLF crystal is equal to 1.09. The distribution coefficient is close to unity due to the comparable radius of Ho3+ and Lu3+, and the concentration of Ho distribution along the crystal growth axis is expected to be quite uniform. A sample for spectroscopic measurements was cut from the asgrown bulk crystal with face perpendicular to the [1 0 0] crystallographic direction and mechanically polished to spectral quality with thickness of 1 mm (Fig. 1). The polarized absorption spectra of Ho:LuLF crystal in the 300–2200 nm spectra range were measured using a spectrophotometer (Lambda 900, Perkin-Elmer) with the polarization of the incident light parallel (p) or perpendicular (r) to the [0 0 1] crystallographic axis. The fluorescence spectra and the fluorescence decay curves under excitation of 637 nm were recorded by Edinburgh Instruments FLS920 and FSP920 spectrophotometers, under excitation with an 8 ns pulse of an optical parametric oscillator. All measurements were performed at room temperature.
Fig. 2. Polarized absorption spectra of Ho:LuLF crystal measured at room temperature.
3. Results and discussion 3.1. Absorption spectra The polarized absorption spectra of Ho3+ (1 at.%)-doped LuLF single crystal at room temperature are shown in Fig. 2. The absorption peaks are corresponding to the transitions from the groundstate 5I8 to the excited states. It is noticeable that the absorption spectra exhibit strong polarization characteristics, which are quite useful for the selection of wavelength and polarization of the pumping source. The absorption cross-section for q polarization was calculated using
rabs q ðkÞ ¼
Fig. 1. A polished plate of Ho:LuLF crystal.
ODq ðkÞ ; N0 L log e
ð1Þ
where OD(k) is the absorption optical density, N0 is the Ho3+ concentration in ions per cubic centimeters, and L is the thickness of the polished sample. The peak absorption cross-section and corresponding full width at half maximum (FWHM) for the main absorption bands are listed in Table 1. The peak absorption at 1940 nm is well adapted for in-band pumping with commercially available high-power Tm-doped silica fiber laser [7,8]. On the other hand, the absorption peaks around 1150 nm is well matched with the emission wavelength of diode lasers emitting at 1150 nm and Ybdoped fiber lasers at 1147 nm [13,14]. The peak absorption crosssections around 1940 nm are 0.39 1020 cm2 and 0.64 1020 cm2 for r and p polarization, respectively, whereas those around 1150 nm are 0.21 1020 cm2 (r) and 0.29 1020 cm2 (p).
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
Table 1 The mean wavelengths, peak absorption cross-sections, and measured and calculated absorption line strengths of the transitions in the Ho:LuLF crystal at room temperature. 5
I8?
5
I7 5 I6 5 F5 5 S2 + 5F4 5 G6 + 5F1 3 G5 3 K7 + 5G4
rabs (1020 cm2)
FWHM
k (nm)
(1020 cm2) Sed;mea q
Sed;cal (1020 cm2) q
r
p
r
p
r
p
r
p
r
p
1969 1161 646 539 457 416 385
1968 1163 641 537 461 417 386
64 61 22 10 8 5 5
137 60 3 5 4 5 4
0.39 0.21 0.46 0.69 1.5 0.33 0.16
0.64 0.29 3.1 2.5 1.5 1.1 0.20
1.930 0.8762 1.291 1.707 5.661 0.5916 0.1982
3.381 1.501 3.012 3.216 5.433 2.245 0.3005
2.045 0.8934 1.207 1.407 5.620 0.6694 0.1447
3.571 1.522 2.980 2.869 5.419 2.356 0.3001
3.2. Judd–Ofelt analysis In this work, the Judd–Ofelt (J–O) theory was used to investigate the room temperature polarized absorption spectra of Ho:LuLF and calculate the J–O intensity parameters, from which spontaneous emission probabilities, fluorescence branching ratios and radiative lifetimes can be obtained. The J–O theory has been extensively used to analyze the spectroscopic properties of the 4f transitions of rare-earth ions doped in crystals and glasses and has proved to be quite accurate for obtaining manifold to manifold branching ratios, especially for Ho3+ doped fluoride crystals [17]. The detailed calculation procedure is similar to that reported in [18]. The refractive indices of LuLF crystal taken in this work are 1.464 and 1.488 for the ordinary and extraordinary refractive indices, respectively [19]. Considering the intermediate coupling and the selection rules for md transitions in the lanthanides, only the 5 I8 ? 5I7 transition in all observed transitions includes a magnetic dipole (md) component. The values can be calculated from the formula proposed by Weber [20]. The line strength of md transition for the 5I8 ? 5I7 was 9.506 1021 cm2. The values of the measured (Sed;mea ) and calculated (Sed;cal ) line strengths of electronic dipole q q (ed) transitions are listed in Table 1. Seven absorption bands were used to obtain the intensity parameters Xt,q (t = 2, 4, 6). The results of J–O intensity parameters and the root-mean-square (RMS) deviation between the experimental and calculated strengths for different polarizations are given in Table 2. A lower RMS confirms a better consistency of our fitting. In accordance with the measured polarized absorption spectra (Fig. 2), the large difference between J–O intensity parameters of the two polarizations indicates the strong anisotropic optical properties of Ho:LuLF. The obtained J– O intensity parameters are applied to determine the probabilities md for spontaneous emission of ed radiation Aed q , md radiation Aq , fluorescence branching ratio bq and radiative lifetime sr of the J manifold sr. The reduced matrix element needed in the calculation of Aed q can be obtained from [21]. All the calculated values of these spectral parameters are listed in Table 3. The J–O intensity parameters for Ho3+ in LuLF crystal calculated in this work are close to those for Ho:YLF that reported in [17] because the two fluoride crystals are isostructural. For the same reason, the radiative lifetimes of 5I7, 5I6, 5I5, and 5I4 are similar to those found in [17]. However, it can be seen that there is some discrepancy between the results in [6] and that in this work. We suppose that it is the errors
Table 2 Judd–Ofelt intensity parameters and corresponding RMS deviations for Ho:LuLF crystal. Intensity parameter
r
p
Xeff
X2 (1020 cm2) X4 (1020 cm2) X6 (1020 cm2) RMS (1020 cm2)
2.89 1.25 1.19 0.17
0.94 4.41 1.94 0.21
2.24 2.31 1.44 0.18
in experiments that lead to the difference between the J–O parameters calculated in the present work and that in [6]. The following experiment factors may lead to a deviation of calculated J–O parameters: (1) the optical quality of the Ho:LuLF single crystal which has effects on the accuracy of the absorption spectra; (2) the determination of the concentration of Ho3+ ions in the sample used to obtain polarize absorption spectra; (3) the orientating, cutting and polishing of the crystal may introduce direction errors to the sample; (4) different spectrophotometers may give polarized absorption spectra with some difference even though the same sample is used due to the stability of the apparatuses. We noticed these factors and made an effort to minimize experiment errors from crystal growth to the polarized absorption spectrum measurement. The fluorescence decay curve for the transition from 5I7 and 5I6 manifolds at room temperature are presented in Figs. 3 and 4. The rise time observed at the beginning of the decay profile in Fig. 3 allows it to be inferred that the 5I7 is populated by relaxation attribution from the upper states higher than 5I7. The relationship in the figure displays single exponential behavior of the decay, and the fluorescence lifetime could be obtained from the fitting line. The effective phonon energy is expected to be a little smaller in LuLF than in YLF (458 cm1) because of the higher mass of the Lu3+ compared with the Y3+ ions [22]. So the effect of multi-phonon relaxation is quite weak for the 5I7 ? 5I8 transition due to the large energy gap (5080 cm1) [23]. The discrepancy between the measured fluorescence lifetime (sf = 16 ms) and the calculated radiative lifetime (sr = 15.2 ms) may be caused by the effect of radiative trapping and excitation trapping [24,25]. The fluorescence lifetime of the 5I7 manifold in the Ho:LuLF crystal is longer than those of the previously reported lifetime of 7.8 ms for Ho:YAG and is comparable to that of 16.1 ms for Ho:YLF [26]. Relatively long upper-state fluorescence lifetime allowing higher energy storage makes Ho:LuLF crystals suitable for medium–high power Qswitched lasers at 2 lm wavelength with high pulse energy. In addition, the measured fluorescence lifetime (sf = 1.8 ms) of the 5 I6 manifold of Ho:LuLF is close to that of Ho:YLF (sf = 1.7 ms) and much longer than those of Ho:YAlO3 (sf = 0.69 ms) and Ho:YAG (sf < 0.03 ms) [27], which indicates that Ho:LuLF can be used in laser operation around 2.9 lm. 3.3. Emission cross-section of the 5I6 ? 5I7 (2 lm) and 5I7 ?5I8 (2.9 lm) transitions For the important transition channel 5I7 ? 5I8 of the Ho3+ laser, the emission cross-section can be calculated by the reciprocity method (RM) [28]. This method derives the emission cross-section from the absorption cross-section and the Stark level schemes of the Ho3+ in crystals: abs rem q ðkÞ ¼ rq ðkÞ
Zl Ezl hc=k exp ; kB T Zu
ð2Þ
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615 Table 3 Spontaneous emission probabilities, branching ratio and radiative lifetime of Ho:LuLF crystal. J?
J0
k (nm)
5
5
1969 1162 2834 900 1659 4002 760 1238 2198 4876 644 958 1447 2266 4233 538 741 1003 1339 1846 3272
I7 ? 5 I6 ? 5
I5 ?
5
I4 ?
5
F5 ?
5
S2 ?
I8 5 I8 5 I7 5 I8 5 I7 5 I6 5 I8 5 I7 5 I6 5 I5 5 I8 5 I7 5 I6 5 I5 5 I4 5 I8 5 I7 5 I6 5 I5 5 I4 5 F5
Aed (s1)
Amd (s1)
A (s1)
r
p
r
p
r
p
r
p
36.11 88.47 9.313 31.05 43.84 2.923 4.697 22.51 17.53 2.565 831.2 204.8 46.97 3.935 0.03035 698.4 482.6 83.53 22.13 23.66 0.2091
66.30 158.5 17.43 59.65 77.31 5.744 8.089 39.74 31.47 4.770 2150 508.9 96.65 7.409 0.08665 1203 831.0 164.4 39.92 44.57 0.6754
19.19
20.14
10.98
11.53
55.29 88.47 20.29 31.05 43.84 7.502 4.697 22.51 17.53 4.645 831.2 204.8 46.97 3.935 0.03035 698.4 482.6 83.53 22.13 23.66 0.2091
86.45 158.5 28.95 59.65 77.31 10.55 8.089 39.74 31.47 6.954 2160 508.9 96.65 7.409 0.08665 1203 831.0 164.35 39.92 44.57 0.6754
100 81.3 18.7 37.7 53.2 9.10 9.51 45.6 35.5 9.41 76.5 18.8 4.32 0.362 0 53.3 36.8 6.37 1.69 1.81 0.0160
100 84.6 15.4 40.4 52.4 7.15 9.38 46.1 36.5 8.06 77.9 18.4 3.49 0.267 0 52.7 36.4 7.20 1.75 1.95 0.0296
4.579
2.080
4.808
2.184
Fig. 3. Room-temperature fluorescence decay curve of Ho:LuLF crystal for the 5I7 manifold.
where Zl and Zu are the partition functions of the lower and upper manifolds, Ezl is the zero-line energy defined as the energy gap between the lowest Stark levels of the 5I7 and 5I8 manifolds, and kB is the Boltzmann constant. For the Ho:LuLF crystal, the energy levels reported in literature were utilized to obtain the values of Zl/ Zu = 0.79 and Ezl = 5154.5 cm1 [6]. Eq. (2) tells us that the profile of the emission cross-section spectrum is determined by the values of rabs q ðkÞ and exp½ðEzl hc=kÞ=kB TÞ, whereas Zl, Zu, and Ezl only influence the magnitude of the emission cross-section. The stimulated emission cross-sections can also be calculated from the polarized IR fluorescence spectra using the Fuchtbauer– Ladenburg (F–L) formula [29]:
rem q ðkÞ ¼
k5 Aq ðJ ! J 0 ÞIq ðkÞ R ; 8pcn2q Iq ðkÞkdk
b (%)
ð3Þ
where Iq(k) is the fluorescence intensity at wavelength k with q polarization. The wavelength dependences of the absorption cross-section and the emission cross-sections calculated by the two methods are shown in Fig. 5 for comparison. The difference
sr (ms)
sf (ms)
15.2 7.41
16 1.8
9.61
16.2
0.606
0.612
Fig. 4. Room-temperature fluorescence decay curve of Ho:LuLF crystal for the 5I6 manifold.
between the profiles of the two emission cross-section spectra is caused by the effect of the re-absorption on the measured emission spectra. It can be seen that both absorption and emission spectra around 2 lm are smooth and broad. A number of important spectral parameters of the Ho:LuLF are summarized and compared with those of other well-known Ho3+-doped laser crystals in Table 4. The absorption and emission cross-sections are comparable to those of Ho:YLF and Ho:YAG. A relatively broad absorption band allows for good flexibility in the selection of the pumping source. At the same time, the broad emission bandwidth of Ho:LuLF makes it a promising crystal for generating ultrashort laser pulses in the 2 lm wavelength band. Since the Ho3+ laser via the 5I7 ? 5I8 transition operates in a quasi-three-level scheme, the gain cross-section as a function of wavelength should be calculated to evaluate the possible laser wavelength range: abs rgq ðkÞ ¼ brem q ðkÞ ð1 bÞrq ðkÞ;
ð4Þ
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
Fig. 6. Gain cross-sections of Ho:LuLF crystal versus the wavelength.
Fig. 5. Polarized absorption and stimulated emission cross-sections of Ho:LuLF crystal.
3+
where b represents the ratio of the excited state to total Ho population. Emission cross-section calculated by RM method is used here. The calculated gain cross-sections for p and r polarizations as a function of wavelength with different b values are shown in Fig. 6. The gain cross-section becomes positive from 2027 nm once the population inversion level reaches 30%. When the level is larger than 50%, the wavelength edges move to the left of 1957 nm for the two polarizations. At the inversion level of 70%, gain cross-sections come to 0.77 1020 cm2 (at 2060 nm) and 0.41 1020 cm2 (at 2066 nm) for p and r polarization, respectively. For the transition channel 5I6 ? 5I7 of the Ho:LuLF crystal, the stimulated emission cross-sections, as shown in Fig. 7, were calculated from the IR fluorescence spectrum using the F–L formula. Since the spectrum is unpolarized, the spontaneous emission probability A and the refractive index of the crystal n in the F-L equation are calculated by using A = (2Ar + Ap)/3 and n = (2nr + np)/3. The
transitions from the 5I6 ? 5I7 manifolds in Ho:LuLF extend from 2806 nm to 2966 nm. This region is of great interest for both medical and spectroscopy applications due to the strong water vapor absorptions there. It can be seen that Ho:LuLF exhibits a broad emission band near 2.9 lm with three main peaks located at 2840 nm, 2898 nm and 2944 nm, with emission cross-sections of 1.7 1020 cm2, 1.2 1020 cm2 and 0.59 1020 cm2, respectively, which are larger than those Ho3+ in YLF [30]. The laser wavelength is expected on the long wavelength part of this transition because of the re-absorption from the longer lived 5I7 lower laser level. It should be pointed out that, for the applications requiring laser operation at 2.9 lm, singly doped Ho:LuLF crystal only has the potential for pulsed laser operation due to the longer lifetime of the lower laser level 5I7 when compared with that of 5I6. However, continuous wave operation in this wavelength range is expected if deactivator ions such as praseodymium (Pr3+) were used [11,12]. The experiments on Ho:Pr:LuLF crystals are under process, and results will be published.
Table 4 Comparison of several important parameters between Ho:LuLF, Ho:YLF and Ho:YAG. Host crystal
LuLF
YLF
YAG
Symmetry Ho3+ concentration (at.%) Peak absorption wavelength kabs (nm) FWHM at kabs (nm) Absorption cross-section at kabs (1020 cm2) Peak emission wavelength kem (nm) FWHM at kem (nm) Emission cross-section at kem (1020 cm2) Fluorescence lifetime of 5I7 (ms) References
Tetragonal 1.0 1940 (p), 1940 (r) 33 (p), 36 (r) 0.64 (p), 0.39 (r) 2060 (p), 2066 (r) 43 (p), 47 (r) 1.3 (p), 0.67 (r) 16 This work
Tetragonal 0.5 1940 (p), 1945 (r) – 1.0 (p), 0.58(r) 2050 (p), 2062 (r) – 1.5 (p), 0.83 (r) 16.1 [17] and [26]
Cubic 1.0 1880, 1908 – 0.65, 0.85 2090, 2021 – 1.62, 0.80 7.8 [3] and [26]
C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
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With such good spectroscopic properties, we conclude that Ho:LuLF crystal is a serious contender for 2 lm and 2.9 lm laser systems. Acknowledgements This work was supported by the State Key Program for Basic Research of China (Grant No. 2010CB630703) and the Fund of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (Grant No. 2010KL0012). References
Fig. 7. Stimulated emission cross-sections for the 5I6 ? 5I7 transition of Ho:LuLF crystal.
4. Conclusions An in-depth spectroscopic analysis of the 1 at.% Ho:LuLF single crystal grown by the Czochralski method was performed, including the absorption and emission cross-sections and the fluorescence lifetimes. The accurate concentration of Ho3+ in LuLF crystal was measured by the ICP method and the segregation coefficient was calculated to be 1.09. The peak absorption cross-sections at 1940 nm are 0.39 1020 cm2 and 0.64 1020 cm2 for r and p polarization, respectively, whereas those around 1150 nm are 0.21 1020 cm2 (r) and 0.29 1020 cm2 (p). These two absorption bands match the emitting wavelengths of high-power Tmdoped fiber laser (1937 nm), diode laser based on highly strained InGaAs quantum wells (1150 nm) and Yb-doped fiber laser (1147 nm) J–O theory was applied to the analysis of the room temperature polarized absorption spectra. The effective phenomenological intensity parameters X2,eff, X4,eff and X6,eff were obtained to be 2.24 1020 cm2, 2.31 1020 cm2 and 1.44 1020 cm2, respectively. The stimulated emission cross-sections of the 5I7 ? 5 I8 transition were calculated by using RM and F-L methods, and the polarized gain cross-section curves were provided and discussed. When comparing the spectroscopic parameters of Ho:LuLF crystal with those of other Ho-doped laser crystals, we can see that it possesses long fluorescence lifetimes and broad emission bandwidths. This indicates that Ho:LuLF is a promising candidate material for Q-switched, ultrashort pulse and tunable laser systems operating at 2 lm. Furthermore, the emission cross-sections of the 5I6 ? 5I7 transition were determined using the F–L formula.
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Polarized spectroscopic properties of Ho3+-doped LuLiF4 single crystal for 2 lm and 2.9 lm lasers Chengchun Zhao a,b, Yin Hang a,⇑, Lianhan Zhang a, Jigang Yin a,b, Pengchao Hu a,b, En Ma c a
Key Laboratory of Materials for High Power Laser, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China Graduate School of Chinese Academy of Sciences, Beijing 100039, People’s Republic of China c Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China b
a r t i c l e
i n f o
Article history: Received 21 November 2010 Received in revised form 13 April 2011 Accepted 13 April 2011 Available online 7 May 2011 Keywords: Spectral properties Czochralski method Laser materials
a b s t r a c t Polarized spectroscopic properties of a Ho3+-doped LuLiF4 (Ho:LuLF) single crystal grown by the Czochralski method have been investigated as a promising material for 2 lm and 2.9 lm lasers. The Judd–Ofelt (J– O) model has been applied to the analysis of the polarized room temperature absorption spectra to establish the so-called J–O intensity parameters. Based on the calculated parameters, we determined the emission probabilities, branching ratio and radiative lifetime for the Ho3+ transitions from the excited state manifolds to the lower-lying manifolds. Ho:LuLF crystal shows long fluorescence lifetime of 5I7 manifold (16 ms) and broad absorption and emission spectra, which exhibit strong polarization characteristics. Stimulated emission cross-sections spectra of the 5I6 ? 5I7 and 5I7 ? 5I8 transitions were derived and compared with those of the other well-known Ho3+-doped laser crystals. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Solid-state lasers based on Ho-doped single crystals have been extensively investigated because of interest in offering 2 lm and 2.9 lm output. Lasers with the two wavelengths are useful for remote sensing, medicine, coherent lidar and the generation of longer wavelengths via nonlinear optics. In the case of 2 lm lasers, singly Ho-doped crystals have shown more efficient energy extraction than those shown by multiply doped crystals. The main reason is that sensitizer ions introduce a range of undesirable energy transfer processes that increase the threshold and reduce the storage efficiency. In addition, Ho:Tm lasers also suffer from more heating and Ho:Tm energy sharing. On the other hand, the development of high power Tm-based crystalline and fiber lasers operating at 1.9 lm provide effective sources for resonantly pumped singly doped Ho lasers [1,2]. Resonant pumping results in high quantum efficiency and low thermal generation; this, coupled with the high thermal conductivity crystalline hosts, allows generation of high-average power, diffraction-limited output. The host materials for these lasers are usually Y3Al5O12 (YAG), YAlO3 and LiYF4 (YLF) [1–4]. Compared with oxide crystals, fluorides are more attractive to achieve high-energy Q-switched operation, as they possess much longer upper laser level life times. In recent years, fluoride crystal LuLiF4 (LuLF) received more and more attention in the field of
⇑ Corresponding author. Tel.: +86 21 69918480. E-mail address: [email protected] (Y. Hang). 0925-3467/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2011.04.010
mid-infrared lasers. The LuLF crystal, like YLF, has several advantages: strong spectral anisotropy for polarized absorption and emission; negative thermal dependence of refractive index, which partially compensates the positive bulging of the end faces of the laser rod owing to the positive thermal expansion coefficients, leading to weak overall thermal lensing [5]. Smaller host ion size of Lu3+ results in larger crystal fields in LuLF than in YLF, leading to larger crystal field splitting of Ho3+ ion [6]. Larger ground-state 5 I8 splitting results in a low thermal occupation factor for the lower laser level and leads to easier population inversion during laser operation. Some optical properties of Ho:LuLF have been reported. High efficient in-band pumped continuous wave and Q-switched Ho:LuLF 2 lm lasers have been demonstrated recently [6–8]. However, relatively little work has been done systematically concerning the polarized spectroscopic properties of this crystal in sufficient detail. Compared with the study of 2 lm lasers, there are fewer reports on Ho-based solid-state lasers around 2.9 lm (5I6 ? 5I7) due to the lack of pumping source [9,10]. However, efficient Ho-doped silica and fluoride glass fiber lasers operating around 2.9 lm have been demonstrated most recently after the development of highly efficient diode lasers operating in the 1150 nm region and the high power Yb-doped fiber lasers [11–14]. So it is necessary and probable to develop 2.9 lm lasers based on Ho-doped crystals. Ho:LuLF crystal is also such a candidate because its low multi-phonon relaxation resulting in long radiative and fluorescence lifetimes of 5I6 manifold. However, to our knowledge there is no report on the emission properties of Ho:LuLF in this wavelength range.
C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
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In the present work, we reported the room temperature polarized absorption spectra, fluorescence decay lifetime and emission properties at 2 lm and 2.9 lm. The spectral parameters were calculated by using absorption spectra based on J–O theory [15– 17]. From the obtained intensity parameters, we calculated the fluorescence branching ratio and radiative lifetime. Finally, the stimulated emission cross-sections of the 5I6 ? 5I7 and 5I7 ?5I8 transitions were also provided and discussed.
2. Experimental details A single crystal of Ho:LuLF with high optical quality was grown by the Czochralski method in inductively heated graphite crucible under a high purity CF4 atmosphere. The starting materials were prepared from high purity (>99.99%) commercial fluoride powders of LiF, LuF3 and HoF3. The constituent fluorides were weighted and mixed according to the following chemical composition: LiLu0.99Ho0.01F4 because Ho3+ is expected to replace Lu3+ in LuLF crystal. The pulling rate was 0.8 mm/h, and the rotation rate was 7 rpm. Growth orientation was controlled using the a-axis oriented LuLF seed crystal. In order to prevent the crystal from cracking, the crystal was cooled to room temperature slowly after growth. Inductively coupled plasma atomic emission spectrometry (ICPAES) was used to measure the concentrations of Ho and Lu elements in Ho:LuLF crystal. The measured sample was cut from the upper part of as-grown Ho:LuLF crystal, and then was ground to powder in an agate mortar. The Ho3+ concentration in the top of the crystal was measured to be 1.58 1020 cm3. The segregation coefficient of the holmium ion in the LuLF crystal is equal to 1.09. The distribution coefficient is close to unity due to the comparable radius of Ho3+ and Lu3+, and the concentration of Ho distribution along the crystal growth axis is expected to be quite uniform. A sample for spectroscopic measurements was cut from the asgrown bulk crystal with face perpendicular to the [1 0 0] crystallographic direction and mechanically polished to spectral quality with thickness of 1 mm (Fig. 1). The polarized absorption spectra of Ho:LuLF crystal in the 300–2200 nm spectra range were measured using a spectrophotometer (Lambda 900, Perkin-Elmer) with the polarization of the incident light parallel (p) or perpendicular (r) to the [0 0 1] crystallographic axis. The fluorescence spectra and the fluorescence decay curves under excitation of 637 nm were recorded by Edinburgh Instruments FLS920 and FSP920 spectrophotometers, under excitation with an 8 ns pulse of an optical parametric oscillator. All measurements were performed at room temperature.
Fig. 2. Polarized absorption spectra of Ho:LuLF crystal measured at room temperature.
3. Results and discussion 3.1. Absorption spectra The polarized absorption spectra of Ho3+ (1 at.%)-doped LuLF single crystal at room temperature are shown in Fig. 2. The absorption peaks are corresponding to the transitions from the groundstate 5I8 to the excited states. It is noticeable that the absorption spectra exhibit strong polarization characteristics, which are quite useful for the selection of wavelength and polarization of the pumping source. The absorption cross-section for q polarization was calculated using
rabs q ðkÞ ¼
Fig. 1. A polished plate of Ho:LuLF crystal.
ODq ðkÞ ; N0 L log e
ð1Þ
where OD(k) is the absorption optical density, N0 is the Ho3+ concentration in ions per cubic centimeters, and L is the thickness of the polished sample. The peak absorption cross-section and corresponding full width at half maximum (FWHM) for the main absorption bands are listed in Table 1. The peak absorption at 1940 nm is well adapted for in-band pumping with commercially available high-power Tm-doped silica fiber laser [7,8]. On the other hand, the absorption peaks around 1150 nm is well matched with the emission wavelength of diode lasers emitting at 1150 nm and Ybdoped fiber lasers at 1147 nm [13,14]. The peak absorption crosssections around 1940 nm are 0.39 1020 cm2 and 0.64 1020 cm2 for r and p polarization, respectively, whereas those around 1150 nm are 0.21 1020 cm2 (r) and 0.29 1020 cm2 (p).
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
Table 1 The mean wavelengths, peak absorption cross-sections, and measured and calculated absorption line strengths of the transitions in the Ho:LuLF crystal at room temperature. 5
I8?
5
I7 5 I6 5 F5 5 S2 + 5F4 5 G6 + 5F1 3 G5 3 K7 + 5G4
rabs (1020 cm2)
FWHM
k (nm)
(1020 cm2) Sed;mea q
Sed;cal (1020 cm2) q
r
p
r
p
r
p
r
p
r
p
1969 1161 646 539 457 416 385
1968 1163 641 537 461 417 386
64 61 22 10 8 5 5
137 60 3 5 4 5 4
0.39 0.21 0.46 0.69 1.5 0.33 0.16
0.64 0.29 3.1 2.5 1.5 1.1 0.20
1.930 0.8762 1.291 1.707 5.661 0.5916 0.1982
3.381 1.501 3.012 3.216 5.433 2.245 0.3005
2.045 0.8934 1.207 1.407 5.620 0.6694 0.1447
3.571 1.522 2.980 2.869 5.419 2.356 0.3001
3.2. Judd–Ofelt analysis In this work, the Judd–Ofelt (J–O) theory was used to investigate the room temperature polarized absorption spectra of Ho:LuLF and calculate the J–O intensity parameters, from which spontaneous emission probabilities, fluorescence branching ratios and radiative lifetimes can be obtained. The J–O theory has been extensively used to analyze the spectroscopic properties of the 4f transitions of rare-earth ions doped in crystals and glasses and has proved to be quite accurate for obtaining manifold to manifold branching ratios, especially for Ho3+ doped fluoride crystals [17]. The detailed calculation procedure is similar to that reported in [18]. The refractive indices of LuLF crystal taken in this work are 1.464 and 1.488 for the ordinary and extraordinary refractive indices, respectively [19]. Considering the intermediate coupling and the selection rules for md transitions in the lanthanides, only the 5 I8 ? 5I7 transition in all observed transitions includes a magnetic dipole (md) component. The values can be calculated from the formula proposed by Weber [20]. The line strength of md transition for the 5I8 ? 5I7 was 9.506 1021 cm2. The values of the measured (Sed;mea ) and calculated (Sed;cal ) line strengths of electronic dipole q q (ed) transitions are listed in Table 1. Seven absorption bands were used to obtain the intensity parameters Xt,q (t = 2, 4, 6). The results of J–O intensity parameters and the root-mean-square (RMS) deviation between the experimental and calculated strengths for different polarizations are given in Table 2. A lower RMS confirms a better consistency of our fitting. In accordance with the measured polarized absorption spectra (Fig. 2), the large difference between J–O intensity parameters of the two polarizations indicates the strong anisotropic optical properties of Ho:LuLF. The obtained J– O intensity parameters are applied to determine the probabilities md for spontaneous emission of ed radiation Aed q , md radiation Aq , fluorescence branching ratio bq and radiative lifetime sr of the J manifold sr. The reduced matrix element needed in the calculation of Aed q can be obtained from [21]. All the calculated values of these spectral parameters are listed in Table 3. The J–O intensity parameters for Ho3+ in LuLF crystal calculated in this work are close to those for Ho:YLF that reported in [17] because the two fluoride crystals are isostructural. For the same reason, the radiative lifetimes of 5I7, 5I6, 5I5, and 5I4 are similar to those found in [17]. However, it can be seen that there is some discrepancy between the results in [6] and that in this work. We suppose that it is the errors
Table 2 Judd–Ofelt intensity parameters and corresponding RMS deviations for Ho:LuLF crystal. Intensity parameter
r
p
Xeff
X2 (1020 cm2) X4 (1020 cm2) X6 (1020 cm2) RMS (1020 cm2)
2.89 1.25 1.19 0.17
0.94 4.41 1.94 0.21
2.24 2.31 1.44 0.18
in experiments that lead to the difference between the J–O parameters calculated in the present work and that in [6]. The following experiment factors may lead to a deviation of calculated J–O parameters: (1) the optical quality of the Ho:LuLF single crystal which has effects on the accuracy of the absorption spectra; (2) the determination of the concentration of Ho3+ ions in the sample used to obtain polarize absorption spectra; (3) the orientating, cutting and polishing of the crystal may introduce direction errors to the sample; (4) different spectrophotometers may give polarized absorption spectra with some difference even though the same sample is used due to the stability of the apparatuses. We noticed these factors and made an effort to minimize experiment errors from crystal growth to the polarized absorption spectrum measurement. The fluorescence decay curve for the transition from 5I7 and 5I6 manifolds at room temperature are presented in Figs. 3 and 4. The rise time observed at the beginning of the decay profile in Fig. 3 allows it to be inferred that the 5I7 is populated by relaxation attribution from the upper states higher than 5I7. The relationship in the figure displays single exponential behavior of the decay, and the fluorescence lifetime could be obtained from the fitting line. The effective phonon energy is expected to be a little smaller in LuLF than in YLF (458 cm1) because of the higher mass of the Lu3+ compared with the Y3+ ions [22]. So the effect of multi-phonon relaxation is quite weak for the 5I7 ? 5I8 transition due to the large energy gap (5080 cm1) [23]. The discrepancy between the measured fluorescence lifetime (sf = 16 ms) and the calculated radiative lifetime (sr = 15.2 ms) may be caused by the effect of radiative trapping and excitation trapping [24,25]. The fluorescence lifetime of the 5I7 manifold in the Ho:LuLF crystal is longer than those of the previously reported lifetime of 7.8 ms for Ho:YAG and is comparable to that of 16.1 ms for Ho:YLF [26]. Relatively long upper-state fluorescence lifetime allowing higher energy storage makes Ho:LuLF crystals suitable for medium–high power Qswitched lasers at 2 lm wavelength with high pulse energy. In addition, the measured fluorescence lifetime (sf = 1.8 ms) of the 5 I6 manifold of Ho:LuLF is close to that of Ho:YLF (sf = 1.7 ms) and much longer than those of Ho:YAlO3 (sf = 0.69 ms) and Ho:YAG (sf < 0.03 ms) [27], which indicates that Ho:LuLF can be used in laser operation around 2.9 lm. 3.3. Emission cross-section of the 5I6 ? 5I7 (2 lm) and 5I7 ?5I8 (2.9 lm) transitions For the important transition channel 5I7 ? 5I8 of the Ho3+ laser, the emission cross-section can be calculated by the reciprocity method (RM) [28]. This method derives the emission cross-section from the absorption cross-section and the Stark level schemes of the Ho3+ in crystals: abs rem q ðkÞ ¼ rq ðkÞ
Zl Ezl hc=k exp ; kB T Zu
ð2Þ
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615 Table 3 Spontaneous emission probabilities, branching ratio and radiative lifetime of Ho:LuLF crystal. J?
J0
k (nm)
5
5
1969 1162 2834 900 1659 4002 760 1238 2198 4876 644 958 1447 2266 4233 538 741 1003 1339 1846 3272
I7 ? 5 I6 ? 5
I5 ?
5
I4 ?
5
F5 ?
5
S2 ?
I8 5 I8 5 I7 5 I8 5 I7 5 I6 5 I8 5 I7 5 I6 5 I5 5 I8 5 I7 5 I6 5 I5 5 I4 5 I8 5 I7 5 I6 5 I5 5 I4 5 F5
Aed (s1)
Amd (s1)
A (s1)
r
p
r
p
r
p
r
p
36.11 88.47 9.313 31.05 43.84 2.923 4.697 22.51 17.53 2.565 831.2 204.8 46.97 3.935 0.03035 698.4 482.6 83.53 22.13 23.66 0.2091
66.30 158.5 17.43 59.65 77.31 5.744 8.089 39.74 31.47 4.770 2150 508.9 96.65 7.409 0.08665 1203 831.0 164.4 39.92 44.57 0.6754
19.19
20.14
10.98
11.53
55.29 88.47 20.29 31.05 43.84 7.502 4.697 22.51 17.53 4.645 831.2 204.8 46.97 3.935 0.03035 698.4 482.6 83.53 22.13 23.66 0.2091
86.45 158.5 28.95 59.65 77.31 10.55 8.089 39.74 31.47 6.954 2160 508.9 96.65 7.409 0.08665 1203 831.0 164.35 39.92 44.57 0.6754
100 81.3 18.7 37.7 53.2 9.10 9.51 45.6 35.5 9.41 76.5 18.8 4.32 0.362 0 53.3 36.8 6.37 1.69 1.81 0.0160
100 84.6 15.4 40.4 52.4 7.15 9.38 46.1 36.5 8.06 77.9 18.4 3.49 0.267 0 52.7 36.4 7.20 1.75 1.95 0.0296
4.579
2.080
4.808
2.184
Fig. 3. Room-temperature fluorescence decay curve of Ho:LuLF crystal for the 5I7 manifold.
where Zl and Zu are the partition functions of the lower and upper manifolds, Ezl is the zero-line energy defined as the energy gap between the lowest Stark levels of the 5I7 and 5I8 manifolds, and kB is the Boltzmann constant. For the Ho:LuLF crystal, the energy levels reported in literature were utilized to obtain the values of Zl/ Zu = 0.79 and Ezl = 5154.5 cm1 [6]. Eq. (2) tells us that the profile of the emission cross-section spectrum is determined by the values of rabs q ðkÞ and exp½ðEzl hc=kÞ=kB TÞ, whereas Zl, Zu, and Ezl only influence the magnitude of the emission cross-section. The stimulated emission cross-sections can also be calculated from the polarized IR fluorescence spectra using the Fuchtbauer– Ladenburg (F–L) formula [29]:
rem q ðkÞ ¼
k5 Aq ðJ ! J 0 ÞIq ðkÞ R ; 8pcn2q Iq ðkÞkdk
b (%)
ð3Þ
where Iq(k) is the fluorescence intensity at wavelength k with q polarization. The wavelength dependences of the absorption cross-section and the emission cross-sections calculated by the two methods are shown in Fig. 5 for comparison. The difference
sr (ms)
sf (ms)
15.2 7.41
16 1.8
9.61
16.2
0.606
0.612
Fig. 4. Room-temperature fluorescence decay curve of Ho:LuLF crystal for the 5I6 manifold.
between the profiles of the two emission cross-section spectra is caused by the effect of the re-absorption on the measured emission spectra. It can be seen that both absorption and emission spectra around 2 lm are smooth and broad. A number of important spectral parameters of the Ho:LuLF are summarized and compared with those of other well-known Ho3+-doped laser crystals in Table 4. The absorption and emission cross-sections are comparable to those of Ho:YLF and Ho:YAG. A relatively broad absorption band allows for good flexibility in the selection of the pumping source. At the same time, the broad emission bandwidth of Ho:LuLF makes it a promising crystal for generating ultrashort laser pulses in the 2 lm wavelength band. Since the Ho3+ laser via the 5I7 ? 5I8 transition operates in a quasi-three-level scheme, the gain cross-section as a function of wavelength should be calculated to evaluate the possible laser wavelength range: abs rgq ðkÞ ¼ brem q ðkÞ ð1 bÞrq ðkÞ;
ð4Þ
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C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
Fig. 6. Gain cross-sections of Ho:LuLF crystal versus the wavelength.
Fig. 5. Polarized absorption and stimulated emission cross-sections of Ho:LuLF crystal.
3+
where b represents the ratio of the excited state to total Ho population. Emission cross-section calculated by RM method is used here. The calculated gain cross-sections for p and r polarizations as a function of wavelength with different b values are shown in Fig. 6. The gain cross-section becomes positive from 2027 nm once the population inversion level reaches 30%. When the level is larger than 50%, the wavelength edges move to the left of 1957 nm for the two polarizations. At the inversion level of 70%, gain cross-sections come to 0.77 1020 cm2 (at 2060 nm) and 0.41 1020 cm2 (at 2066 nm) for p and r polarization, respectively. For the transition channel 5I6 ? 5I7 of the Ho:LuLF crystal, the stimulated emission cross-sections, as shown in Fig. 7, were calculated from the IR fluorescence spectrum using the F–L formula. Since the spectrum is unpolarized, the spontaneous emission probability A and the refractive index of the crystal n in the F-L equation are calculated by using A = (2Ar + Ap)/3 and n = (2nr + np)/3. The
transitions from the 5I6 ? 5I7 manifolds in Ho:LuLF extend from 2806 nm to 2966 nm. This region is of great interest for both medical and spectroscopy applications due to the strong water vapor absorptions there. It can be seen that Ho:LuLF exhibits a broad emission band near 2.9 lm with three main peaks located at 2840 nm, 2898 nm and 2944 nm, with emission cross-sections of 1.7 1020 cm2, 1.2 1020 cm2 and 0.59 1020 cm2, respectively, which are larger than those Ho3+ in YLF [30]. The laser wavelength is expected on the long wavelength part of this transition because of the re-absorption from the longer lived 5I7 lower laser level. It should be pointed out that, for the applications requiring laser operation at 2.9 lm, singly doped Ho:LuLF crystal only has the potential for pulsed laser operation due to the longer lifetime of the lower laser level 5I7 when compared with that of 5I6. However, continuous wave operation in this wavelength range is expected if deactivator ions such as praseodymium (Pr3+) were used [11,12]. The experiments on Ho:Pr:LuLF crystals are under process, and results will be published.
Table 4 Comparison of several important parameters between Ho:LuLF, Ho:YLF and Ho:YAG. Host crystal
LuLF
YLF
YAG
Symmetry Ho3+ concentration (at.%) Peak absorption wavelength kabs (nm) FWHM at kabs (nm) Absorption cross-section at kabs (1020 cm2) Peak emission wavelength kem (nm) FWHM at kem (nm) Emission cross-section at kem (1020 cm2) Fluorescence lifetime of 5I7 (ms) References
Tetragonal 1.0 1940 (p), 1940 (r) 33 (p), 36 (r) 0.64 (p), 0.39 (r) 2060 (p), 2066 (r) 43 (p), 47 (r) 1.3 (p), 0.67 (r) 16 This work
Tetragonal 0.5 1940 (p), 1945 (r) – 1.0 (p), 0.58(r) 2050 (p), 2062 (r) – 1.5 (p), 0.83 (r) 16.1 [17] and [26]
Cubic 1.0 1880, 1908 – 0.65, 0.85 2090, 2021 – 1.62, 0.80 7.8 [3] and [26]
C. Zhao et al. / Optical Materials 33 (2011) 1610–1615
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With such good spectroscopic properties, we conclude that Ho:LuLF crystal is a serious contender for 2 lm and 2.9 lm laser systems. Acknowledgements This work was supported by the State Key Program for Basic Research of China (Grant No. 2010CB630703) and the Fund of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (Grant No. 2010KL0012). References
Fig. 7. Stimulated emission cross-sections for the 5I6 ? 5I7 transition of Ho:LuLF crystal.
4. Conclusions An in-depth spectroscopic analysis of the 1 at.% Ho:LuLF single crystal grown by the Czochralski method was performed, including the absorption and emission cross-sections and the fluorescence lifetimes. The accurate concentration of Ho3+ in LuLF crystal was measured by the ICP method and the segregation coefficient was calculated to be 1.09. The peak absorption cross-sections at 1940 nm are 0.39 1020 cm2 and 0.64 1020 cm2 for r and p polarization, respectively, whereas those around 1150 nm are 0.21 1020 cm2 (r) and 0.29 1020 cm2 (p). These two absorption bands match the emitting wavelengths of high-power Tmdoped fiber laser (1937 nm), diode laser based on highly strained InGaAs quantum wells (1150 nm) and Yb-doped fiber laser (1147 nm) J–O theory was applied to the analysis of the room temperature polarized absorption spectra. The effective phenomenological intensity parameters X2,eff, X4,eff and X6,eff were obtained to be 2.24 1020 cm2, 2.31 1020 cm2 and 1.44 1020 cm2, respectively. The stimulated emission cross-sections of the 5I7 ? 5 I8 transition were calculated by using RM and F-L methods, and the polarized gain cross-section curves were provided and discussed. When comparing the spectroscopic parameters of Ho:LuLF crystal with those of other Ho-doped laser crystals, we can see that it possesses long fluorescence lifetimes and broad emission bandwidths. This indicates that Ho:LuLF is a promising candidate material for Q-switched, ultrashort pulse and tunable laser systems operating at 2 lm. Furthermore, the emission cross-sections of the 5I6 ? 5I7 transition were determined using the F–L formula.
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