JOURNAL OF APPLIED PHYSICS
VOLUME 90, NUMBER 8
15 OCTOBER 2001
Spectroscopic properties of CaF2 :U4¿ as a saturable absorber John B. Grubera) Department of Physics, San Jose´ State University, San Jose´, California 95192-0106
Dhiraj K. Sardar Division of Earth and Physical Sciences, University of Texas at San Antonio, San Antonio, Texas 78249-0663
Larry D. Merkle Department of Natural Sciences, University of Houston-Downtown, Houston, Texas 77002-1001
Bahram Zandi Army Research Laboratory/Adelphi Laboratory Center, 2800 Powder Mill Road, Adelphi, Maryland 20783-1107
Richard Jarman Spectragen, Inc., Des Plaines, Illinois 60018-1804
J. Andrew Hutchinson Night Vision and Electronic Sensors Directorate, 10221 Burbeck Road, Suite 430, Ft. Belvoir, Virginia 22060-5806
共Received 16 April 2001; accepted for publication 29 June 2001兲 The spectroscopic properties of crystals of CaF2 :U4⫹ have been examined in light of recent interest expressed for this material as a saturable absorber in the passive Q switching of near infrared solid state lasers. The detailed crystal-field splitting of the energy levels of U4⫹ (5 f 2 ) is analyzed for the ion in different charge-compensated sites. Identification of the site is based on laser excited site-selective spectroscopic studies reported earlier. Experimental Stark levels are compared with calculated levels based on lattice-sum models that include charge compensation in the lattice structure. The final set of atomic parameters for U4⫹ is in good agreement with values reported for the ion in UF4. The predicted non-Kramers’ doublet as the ground-state Stark level for U4⫹ in C3V sites is in agreement with the spectroscopic analysis and with results reported earlier from electron spin-resonance studies of CaF2 :U4⫹. Using pump–probe methods, we have investigated excited state absorption 共ESA兲 at 1.54 m. Consistent with the interpretation of the absorption spectra, we find that the measured ESA is quite small in these crystals. In turn, we use this conclusion to model CaF2 :U4⫹ as a passive Q switch, with good results. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1396833兴
I. INTRODUCTION
the numerous absorption lines and bands were due to transitions between crystal-field split states of divalent, trivalent, and tetravalent uranium ions in the green, red, and yellow crystals, respectively, located in different chargecompensated sites. That the green CaF2 crystal would be the only known sample of U2⫹ occurring in the solid state made the verisimilitude of this particular assignment doubtful. Subsequently, based on chemical analyses and spectroscopic arguments, McLaughlin et al.9 proposed instead that the green CaF2 :U crystals contained mostly U4⫹ ; their conclusions that the red crystals contained a mixture of U3⫹ and U4⫹, and the yellow crystals contained the uranyl complex UO2⫹ 2 in different charge-compensated sites, are substantially consistent with the work of Hargreaves.7,8 To elucidate the details of the spectra, Hargreaves provided Gruber and his colleagues10,11 with samples of green and red CaF2 :U crystals for site-selective spectroscopy measurements. A comparative study between the transmittance and the site-selective laser excitation and fluorescence spectra of both crystals led these investigators to the identification of different charge-compensated sites for U4⫹ in the
Crystals of calcium fluoride (CaF2) and strontium fluoride (SrF2) containing uranium ions have been used to passively Q switch the eyesafe 1.54 m 共Er,Yb兲: glass laser.1–3 A recent study reported appreciable excited state absorption 共ESA兲 at 1.573 m in crystals of CaF2 assuming divalent uranium (U2⫹) as the absorber.4 Details of the complex absorption spectra of these crystals, however, have not been sorted out since the oxidation states of uranium present in the host crystal depend on the methods and materials used to dope and grow the crystal. Charge compensation is required for U3⫹ and U4⫹, and U2⫹ has never been identified or characterized as a stable oxidation state in any compound given its tremendous chemical activity.5 Interpretation of the optical spectra has been problematic ever since Conway6 published an analysis of the absorption spectrum in 1959. Hargreaves7,8 characterized CaF2 :U crystals by their color 共green, red, and yellow兲 and proposed that a兲
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green crystal and different sites for both U4⫹ and U3⫹ in the red crystal. Depending on whether Hargreaves had used UO2 or UF4 as the dopant in growing crystals, Gruber et al.10 found differences in the spectra that were traced to uranium ions in different sites. Two sites of U4⫹ that were identified in the green crystals had C3V symmetry and C2 or C2V symmetry. The C3V symmetry site was also identified from electron spin resonance studies on CaF2 :U4⫹ reported earlier.12,13 The spectroscopic results obtained by Gruber and his colleagues were reported at the 1995 meeting of IEEE/LEOS.11 Recent interest in improving the optical properties of the green crystals for use as a saturable absorber in eye-safe laser transmitters has led to a re-examination of the methods used for growing the crystals. Recently we received several samples of green CaF2 :U4⫹ grown by Spectragen, Inc. We compared the spectra of these crystals with the site-selective spectra analyzed earlier.10,11 The 8 K absorption spectrum obtained from the Spectragen crystals reported in this study in Table I has fewer absorption peaks than Wright et al.11 observed, which suggests that perhaps the U4⫹ ions occupy fewer different charge-compensated sites. This narrower distribution of U sites results, presumably, from a recent modification of the method used in growing the crystals and, as we shall show, results in improved Q switch performance. A closer examination of the details of the 8 K absorption spectrum in comparison to the site-selective spectra, reveals that only spectra involving two sites are observed in the crystals used in the present study. One site has C3V symmetry, and the second site has a lower twofold symmetry. In Table I we report the 8 K absorption spectrum catalogued according to the assignments made to the earlier site-selective spectroscopy measurements obtained from the Hargreaves green crystals.10,11 These assignments form the basis of the crystalfield splitting analyses as well as the pump–probe measurements and modeling studies that we report.
II. EXPERIMENTAL DETAILS
Crystals of CaF2 :U were grown from mixtures of CaF2 共Stella Chemicals兲 and about 1 wt. % UO2 共Cerac兲 by the Bridgeman method using a graphite crucible. To effect complete conversion of the UO2 to the fluoride, between 1 and 10 wt. % PbF2 was added to the mixtures; PbF2 is widely used to getter oxygen during the growth of fluoride crystals. Since the melting point of CaF2 is near 1350 °C, the lead compounds volatilize completely before the melt is formed. Chemical analysis confirms that no lead is incorporated into the crystal. The crucible is positioned inside a graphite heating element that has a linear temperature gradient of about 20 °C/cm. Crystallization was obtained by controlled ramping down of the furnace temperature with the crucible remaining in place. Growth was performed in an inert atmosphere of high-purity argon. The crystals were pale green in color and were cut from boules aligned along the 共111兲 cleavage planes. The crystals used by Burshtein et al.4 were also grown by Spectragen using UF4 as the dopant instead of UO2. In the present study high purity CaF2 and a different furnace were also used.
Gruber et al.
The low-temperature absorption spectra were obtained with an upgraded Cary model 14R spectrophotometer controlled by a desktop computer. The 8 K absorption spectrum reported in Table I covers the wavelength range between 2472 and 537 nm. The spectral bandwidth was set at 0.5 nm and the instrument was internally calibrated to an accuracy of 0.3 nm. The spectra were analyzed and plotted by using the computer software package SIGMA PLOT. The sample was mounted at the cold finger of a CTI model 22 closed-cycle helium cryogenic refrigerator capable of operation between 8 and 300 K. The sample temperature was monitored with a silicon–diode sensor attached to the base of the sample holder and maintained by using a Lake Shore control unit. Figure 1 shows a survey spectrum obtained at 8 and 300 K between 400 and 1800 nm. The room temperature spectrum in Fig. 1 can be compared to the spectrum reported by Burshtein et al.4 between 400 and 2000 nm 共Fig. 1兲. Most of the absorption peaks have similar wavelengths when the different sample spectra are compared at the same temperature. However, the relative intensities of the broad bands that peak at 475, 540, and 650 nm are much weaker, relative to the sharper peaks superimposed on them in our Fig. 1, than in Fig. 1 of Burshtein et al.4 The band observed at 300 K between roughly 700 and 1000 nm 共which contains the spectrum of the 3 H 6 manifold of U4⫹ in Table I of the present study兲, and that peaks near 850 nm in our Fig. 1, is about the same intensity relative to the superimposed sharp-line spectra as the intensity of the similar band in Fig. 1 of Burshtein et al.4 These broad bands, also observed in the Hargreaves crystals, were also found to vary in relative strength depending on whether UO2 or UF4 was used.10,11 Wright et al.11 attribute these broad bands to U4⫹ ions or defect centers in different sites. The crystal-field splitting of the excited electronic configurations of the uranium ion and the coupling of these states with lattice defects leads to changes in spectral intensities and structure depending on the charge-compensated sites.14,15 In Table I, col. 1, the spectroscopic labels, 2S⫹1 L J , are given for U4⫹ (5 f 2 ). We found no spectroscopic evidence for U3⫹ in our crystals. In CaF2 certain multiplet manifolds of U3⫹ absorb where U4⫹ does not.10 These wavelengths include 2261–2216 nm ( 4 I 11/2), 1240–1190 nm ( 4 I 13/2), and certain ‘‘windows’’ between 1040 and 800 nm 共2 H 9/2 , 4 F 5/2 , 4 I 15/2 , 4 F 7/2 , and 4 S 3/2兲. In col. 2 we report the observed absorption spectrum in nm. Figure 2 shows a display of the 8 K absorption spectrum of the 3 H 5 multiplet manifold 共1300–1750 nm兲 and Fig. 3 shows the 8 K absorption spectrum of the 3 F 3 – 3 F 4 manifolds observed between 1040 and 1200 nm. In col. 3 of Table I we give the intensity of the absorption peaks in terms of the absorption coefficient in units of cm⫺1, and in col. 4 the energy of the absorption peak is given in units of vacuum wave numbers. The most intense absorption spectrum is represented by transitions from the ground-state Stark level in 3 H 4 to Stark levels within multiple manifolds 3 F 3 and 4 F 4 共see Fig. 1 and Table I, between 1185 and 1090 nm兲. A strong absorption band is also observed and associated with transitions from the ground state to the 3 H 5 multiplet manifold 共see Fig. 2 and Table I, between 1600 and 1550 nm兲.
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J. Appl. Phys., Vol. 90, No. 8, 15 October 2001
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TABLE I. Absorption spectrum of CaF2 :U4⫹ at 8 K.a 2S⫹1 3
F2
3
H5
3
F3
3
F4
3
H6
L Jb
共nm兲c
␣共cm⫺1兲d
E obs 共cm⫺1兲e
E calc 共cm⫺1兲f
⌫ n calcg
%M J maxh
Sitei
4054 4101 4147 5805 5818 5837 5863 5895 5906 5913 5931 5945 5975 6223 6282 6322 6358 6407 6421 6582
3 1 3 1 3 1 2 1 1 3 1 2 2 1 1 2 3 3 2 2
78关 3 F 2 ,1典 81关 3 F 2 ,0典 81关 3 F 2 ,2典 33关 3 H 5 ,3典 47关 3 H 5 ,5典 41关 3 H 5 ,2典 33关 3 H 5 ,⫺3 典 16关 3 H 5 ,4典 22 关 3 H 5 ,⫺4 典 55关 3 H 5 ,1典 42关 3 H 5 ,5典 47关 3 H 5 ,⫺5 典 29关 3 H 5 , 3 典 44关 3 H 5 ,0典 67关 3 H 5 ,0典 46关 3 H 5 ,⫺3 典 41关 3 H 5 ,2典 68关 3 H 5 ,4典 26关 3 H 5 ,⫺1 典 12关 3 H 5 ,1典
7435
1
22关 3 H 5 ,2典
8428 8448 8496 8467 8500 8512 8571 8561 8573 8590 8624
1 2 3 2 1 2 3 1 2 1 2
88关 3 F 3 ,0典 43关 3 F 3 ,⫺3 典 54关 3 F 3 ,2典 11关 3 F 4 ,⫺3 典 19关 3 F 3 ,0典 38关 3 F 3 ,1典 57关 3 F 3 ,1典 23关 3 F 3 ,2典 10关 3 F 3 ,1典 14关 3 F 4 ,2典 16关 3 F 3 ,2典
C3V C3V C3V C3V C3V C2V C2V C2V C2V C3V C2V C2V C2V C2V C3V C3V C3V C3V C2V C2V vib vib vib C2V vib C3V C3V C3V C2V C2V C2V C3V C2V C2V C2V C2V
8771 8828
2 1
47关 3 F 3 ,⫺3 典 18关 3 F 3 ,1典
C3V C2V
8982 9000 9064 9106 9120 9198 9273 9336 9481 9495 10631 10773 10874 10902 10915 10994 11099 11148 11392
2 1 1 3 2 1 2 3 1 3 1 3 1 1 1 1 2 3 2
23关 3 F 4 ,1典 26关 3 F 4 ,0典 31关 3 F 4 ,0典 29关 3 F 4 ,1典 33关 3 F 4 ,1典 10关 3 H 6 ,0典 21关 3 F 4 ,3典 52关 3 F 4 ,2典 17关 3 F 4 ,⫺3 典 30关 3 F 4 ,4典 27关 3 H 6 ,⫺3 典 51关 3 H 6 ,2典 27关 3 H 6 ,5典 20关 3 H 6 ,⫺2 典 32关 3 H 6 ,6典 23关 3 H 6 ,0典 25关 3 H 6 ,⫺3 典 46关 3 H 6 ,1典 23关 3 H 6 ,3典
C2V C3V C2V C3V C2V C2V C3V C3V C3V C3V C3V C3V C2V C2V C3V C3V C2V C3V C2V
2472 2446 2426 1717.5 1713.5 1711.5 1704 1697 1695 1690.5 1687 1683.5 1673 1606.5 1586.5 1575.5 1570 1566 1556共sh兲i 1526.5 1500共vb兲 1487共sh兲 1446共vb兲 1347 1305共vb兲 1185 1182 1179 1177 1174.5 1173共sh兲 1170 1168共sh兲 1166共sh兲 1163.5 1160.5 1156共sh兲 1145共vb兲 1139 1135.5 1122共vb兲 1114 1108.5 1104.5 1098.5 1097 1085 1079.5 1070.5
0.79 1.3 0.84 2.4 2.04 2.09 4.34 3.16 2.62 2.04 1.96 2.98 2.63 3.39 4.07 4.77 5.07 6.08 3.91 2.89 2.82 2.74 2.43 2.64 1.73 10.7 5.82 6.63 2.61 4.34 2.91 4.79 2.98 2.4 2.28 2.31 2.14 1.86 2.3 2.41 1.86 2.51 3.16 2.51 14.6 16 3.7 3.92 3.71
4044 4090 4121 5821 5834 5841 5867 5891 5898 5914 5926 5938 5976 6223 6301 6345 6368 6384 6421 6547 6665 6723 6920 7422 7661 8437 8458 8479 8494 8512 8523 8545 8559 8574 8592 8615 8648 8731 8777 8804 8910 8974 9019 9051 9101 9113 9214 9257 9335
929.5 920 917.5 916 907.5 903 897 878.5
1.75 1.92 1.9 2 1.79 1.8 1.87 1.41
10756 10867 10896 10914 11016 11071 11145 11380
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J. Appl. Phys., Vol. 90, No. 8, 15 October 2001
TABLE 1. 共Continued.兲a 2S⫹1
1
D2
1
G4
3
P0
3
P1
L Jb
共nm兲c
␣共cm⫺1兲d
E obs 共cm⫺1兲e
E calc 共cm⫺1兲f
⌫ n calcg
%M J maxh
Sitei
873.5
1.42
11445
11460 11578 11680 11788
3 2 3 2
46关 3 H 6 ,4典 34关 3 H 6 ,⫺3 典 54关 3 H 6 ,5典 29关 3 H 6 ,3典
C3V C3V C3V C3V
771 727 666 660 659 658 657 655 650.5 645.5 636.5 628 626.5 622 616 607 602 539 537共sh兲
1 0.7 0.42 0.89 0.67 0.58 0.44 0.52 3.09 1.03 0.52 0.53 0.87 0.51 0.54 0.43 0.48 0.46 0.33
12967 13765 15011 15147 15170 15193 15216 15263 15369 15488 15707 15919 15957 16073 16177 16470 16607 18548 18617
15002 15150 15173 15210 15225 15275 15393 15474 15714 15904 15967 16054 16165 16472 16622 18545 18613
3 1 3 1 2 1 1 1 3 3 2 3 1 3 1 3 1
36关 1 D 2 ,1典 56关 1 D 2 ,0典 32关 1 D 2 ,2典 46关 1 D 2 ,2典 36关 1 D 2 ,1典 42关 1 D 4 ,2典 27关 1 D 4 ,⫺3 典 36关 1 G 4 ,0典 37关 3 F 4 ,1典 35关 1 G 4 ,2典 25关 1 G 4 ,3典 20关 1 G 4 ,1典 55关 3 P 0 ,0典 30关 1 G 4 ,2典 37关 3 P 0 ,0典 99关 3 P 1 ,1典 98关 3 P 1 ,0典
C3V C3V C3V C2V C2V C2V C3V C3V C3V C3V C3V C3V C3V C3V C3V C3V C3V
a
No spectroscopic evidence was observed for U3⫹ in this crystal. Spectroscopic label for state, 5 f 2 ( 2S⫹1 L J ). c Wavelength in nanometers; sh, shoulder; vb, very broad including unresolved vibronic structure. d Absorption coefficient cm⫺1; sample thickness 0.325 cm. e Observed energy in vacuum wave number. f Calculated level based on B nm parameters given in Table II. g Predicted symmetry label for site symmetry. h Percent maximum M J contribution to the wave function; C3 v symmetry M J ⫽1, 2, 4, and 5 involve both ⫹ and ⫺ signs since ⌫ 3 is twofold degenerate. i Symmetry of U4⫹ site, C3V and C2V ; vib refers to vibronic structure. j Spectra observed between 1556 and 1305 nm are represented as a broad vibronic band 共see Fig. 2兲. b
The broad bands that appear in Fig. 2 represent transitions from the ground state to the vibronic levels coupled to the electronic 共Stark兲 levels of the 3 H 5 multiplet manifold. The absorption at 1.54 m, makes it possible to passively Q switch the 共Er,Yb兲:glass laser.
The remaining spectrum observed at wavelengths shorter than 900 nm in Fig. 1 is relatively weak. The multiplets 1 D 2 , 1 G 4 , 1 I 6 , and 3 P J are strongly mixed 共see Table I兲 and it is not possible to isolate individual multiplet manifolds. It is also of interest that transitions from the ground state to the
FIG. 1. Survey absorption spectra of CaF2 :U4⫹ between 400 and 1800 nm. The upper spectrum was obtained at 8 K; the lower spectrum, represented by a dashed line, was obtained at 300 K; sample thickness was 0.325 cm.
FIG. 2. Absorption spectrum of the 3 H 5 multiplet manifold between 1300 and 1750 nm; the spectrum was obtained at 8 K; sample thickness was 0.325 cm.
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Gruber et al.
J. Appl. Phys., Vol. 90, No. 8, 15 October 2001
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TABLE II. Atomic and crystal-field parameters for U4⫹ in CaF2. Parameter
UF4a
4⫹ b U(C 3V )i
4⫹ c U(C 3V ) f
4⫹ d U(C 2V )i
4⫹ e U(C 2V ) f
F2 F4 F6 ␣  ␥ M0 M2 M4 p2 B 20 B 22 B 40 B 42 B 43 B 44 B 60 B 62 B 63 B 64 B 66
44 784 43 107 25 654 34.74 ⫺767.3 913.9 1761 0.775 0.434 0.294 2715 1183 29 ⫺2714 3024
44 871 43 212 24 806 31.31 ⫺585.3 826.9 1789 0.775 0.434 0.294 1653 425
45 122 43 028 23 889 34.69 ⫺585.3 826.9 1789 0.775 0.434 0.294 1653 200
724
870
44 787 43 107 25 654 34.74 ⫺767.3 913.9 1761 0.775 0.434 0.294 2715 1183 29 ⫺2714 3024
44 684 44 128 26 351 37.96 ⫺767.3 913.9 1761 0.775 0.434 0.294 2715 1087 23 ⫺2868 3320
1829
2223
⫺1241
⫺1686
⫺3791 ⫺1433 1267
⫺4178 ⫺1550 1388
⫺118
⫺443
1224
1887
⫺1391 1755
⫺1638 2061
FIG. 3. Absorption spectrum of the 3 F 4 and 3 F 3 multiplet manifolds between 1040 and 1200 nm; the spectrum was obtained at 8 K; sample thickness was 0.325 cm.
3
H 6 manifold between 900 and 700 nm in Fig. 1 are very weak. The possibility for ESA at 1.54 m does not appear too likely in terms of the observed absorption spectra appearing in Table I. This observation is examined more closely in a later section where we describe the pump–probe methods used to investigate excited-state absorption at 1.54 m. In Table I, cols. 5–7, we present the results of the calculations given in Sec. III. Column 8 identifies the absorption peak in terms of the U4⫹ site determined from an analysis of the laser excited site-selective spectra.10,11
III. ENERGY-LEVEL CALCULATIONS
The complete Hamiltonian consists of the isotropic terms in the atomic Hamiltonian, including the spherically symmetric terms in the crystal field, and the crystal-field Hamiltonian. The atomic Hamiltonian is expressed as ˆ a⫽ 具 E 典 ⫹ H
兺k F k ˆf k ⫹ ␣ Lˆ 共 Lˆ ⫹1 兲 ⫹  Gˆ 共 G 2 兲 ⫹ ␥ Gˆ 共 R 7 兲
⫹ s.o.Aˆ s.o.⫹
兺k P k pˆ k ⫹ 兺j M j mˆ j ,
共1兲
where the sums involve k⫽2, 4, 6, and j⫽0, 2, 4. The operators (oˆ ) and their associated parameters are written in conventional form.16 F k and s.o. are the Slater and spin– orbit parameters respectively, for the 5 f 2 electronic configuration. The interconfigurational mixing is given in parameterized form ␣,, and ␥, with operators Lˆ 共total orbital angular ˆ (R 7 ) as the Casimir operators ˆ (G 2 ) and G momentum兲, and G for the groups G 2 and R 7 . Parameters M j represent spin– spin and spin–other-orbit relativistic interactions, and the P k parameters are associated with magnetically correlated corrections to the spin–orbit perturbation. The crystal-field Hamiltonian is written as ˆ CF⫽ H
兺
i,n,m
ˆ nm 共 i 兲 , B nm C
共2兲
⫺3791 ⫺1433 1267 ⫺1391 1755
a
Parameters obtained from Ref. 19. Initial set of parameters obtained from Morrison Ref. 25. c Final set of parameters obtained by varying only F 2 , F 4 , F 6 , ␣, p 2 , and B nm . d Initial set of parameters obtained from Ref. 12. e Final set of parameters obtained by varying only F 2 , F 4 , F 6 , ␣, p 2 , and B nm . b
where i⫽2 for two equivalent 5 f electrons; n⫽0, 2, 4, 6; and m depends on the site symmetry. The operators Cˆ nm (i) are one-electron spherical tensors that transform like the spherical harmonics.17 The B nm are crystal-field parameters that are determined from lattice-sum calculations.18 The total Hamiltonian is diagonalized within the full SLJM J basis set for the 5 f 2 electronic configuration. In our parametric fitting of calculated levels to experimental levels we reduced the number of parameters that are varied by holding fixed M 0 , M 2 , and M 4 , using values reported from the spectroscopic analysis of UF4. 19 Parameter P 2 was allowed to vary with the constraints that P 4 ⫽0.5P 2 , and P 6 ⫽0.01P 2 . We used as a starting set of atomic parameters the values reported for UF4. 19 In fitting the data we found relatively small changes in these parameters. The starting set and final set of atomic parameters for U4⫹ are given in Table II. The initial set of crystal-field parameters was obtained from a point-charge lattice-sum model adapted to include charge compensating ions in lattice sites so that overall charge neutrality is maintained. The C3V symmetry site was established by placing U4⫹ in a Ca2⫹ site surrounded by a cube of F⫺ ions with two F⫺ ions occupying the centers of cubes whose corners are common with the opposite corner of the cube containing U4⫹. For the lower symmetry site the F⫺ ion occupies the center of the cube that is adjacent to the cube containing U4⫹. We approximated the lower symmetry site as C2V following the approach used by Carnall et al.19 since the spectra of U4⫹ in this site is similar to the spectra of
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J. Appl. Phys., Vol. 90, No. 8, 15 October 2001
U4⫹ in UF4. The formal site locations and the cation and anion distances within the unit cell, as well as the size of the unit cell are known from x-ray crystallographic studies.20–22 The lattice-sum components for both the C3V and C2V sites are given as
A nm ⫽⫺e 2
兺j q j
C nm 共 rˆj兲 rjn⫹1
,
共3兲
where q j represents the effective ionic charges on the ions at r j , and the sum is taken over all ions in the lattice; values of m depend on the symmetry of the site. In the point-charge model, the lattice-sum components are related to the crystalfield parameters B nm through a term n which accounts for shielding and reduction of the 具 r n 典 values that occur when the ion is placed in the lattice.23,24 Values for n for several of the trivalent and tetravalent actinide ions were determined by Morrison,25 and his values for U4⫹ in C3V sites are used as the starting set of B nm given in Table II. For C2V sites we used as a starting set the values reported by Carnall et al.19 for U4⫹ in UF4. In the analyses of the calculated-to-observed levels we chose 39 experimental Stark levels for the C3V site designated in col. 8 in Table I. The final rms deviation between these levels and the calculated levels is 16 cm⫺1. The final set of B nm parameters is given in Table II 共column 4兲. The final calculation predicts a splitting for the ground-state multiplet manifold 3 H 4 , as follows: 0 ( 2 ⌫ 3 ), 103 ( 1 ⌫ 1 ), 437 ( 2 ⌫ 3 ), 672 ( 2 ⌫ 3 ), 765 ( 1 ⌫ 2 ), and 836 ( 1 ⌫ 1 ), all in cm⫺1, with twofold degeneracy for the three 2 ⌫ 3 Stark levels. The predicted ground-state Stark level is a non-Kramers’ doublet whose wave function consists of 51% 3 H 4 , M J ⫾4. For this level we obtain a calculated value of g 储 ⫽3.10, g⬜ ⫽0. This value compares favorably with results obtained from the electron paramagnetic resonance experiments that established a trigonal site symmetry for some of the U4⫹ ions in CaF2. 12,13 Thirty experimental levels were assigned to spectra of U4⫹ in the lower symmetry site. The final set of B nm parameters for this site symmetry, approximated as C2V , is given in Table II with a rms deviation of 14 cm⫺1 between 30 calculated to experimental levels. The final calculation for this symmetry predicts a splitting for the 3 H 4 as follows: 0, 187, 823, 1060, 1481, 1724, 1934, 2327, and 2379, in units of cm⫺1. The splitting of the U4⫹ energy levels in the lower symmetry site is much larger than the splitting in the C3V site. The observed spectrum reported in Table I for both sites shows no evidence of sharp line absorption from 3 H 4 to 3 H 6 between 873.5 and 771 nm, although a weak, very broad band near 850 nm may be due to U4⫹ in another site. From these observations we conclude that ESA should not be a serious consideration for passive Q switching of the 共Er,Yb兲: glass laser. This conclusion is supported by the experiment described Sec. IV in which a crystal similar to those used in the spectroscopic studies was investigated for ESA at 1.54 m.
FIG. 4. Average of five CaF2 :U4⫹ pump–probe experiments at 1.54 m, smoothed using the 25-point Savitzky–Golay algorithm.
IV. SATURABLE ABSORPTION AT 1.54 m
A crystal of CaF2 :U4⫹ was pumped by a KTA OPO with an unstable resonator design, that in turn was pumped by a Continuum Surelite II Nd:YAG laser. The sample had a thickness of 2.05 mm and absorbed about 6.2% of the light at 1.54 m. At that wavelength the pulse of energy was about 25 mJ at the sample plane. The beam was carefully focused to give an average fluence of 0.22 J/cm2 over the sample volume probed by a free-running passively cooled Kigre 共Er,Yb兲: glass laser. The probe was fired once each 30-s, emitting about 460 mJ over 700 s. The incident and transmitted probe pulses were monitored using Electro-optics Technology, Inc. InGaAs detectors and a Tektronix DSA 602 A digital oscilloscope. The resulting transient change in probe transmission upon pumping is shown in Fig. 4. The changes were averaged over about 300 pulses to reduce the variations due to relaxation oscillations in the probe. Relaxation oscillations obscure the recovery of the bleached absorption, but prompt bleaching clearly increases the ratio of transmitted to incident probe by about 0.0068. Corrected for system response, this corresponds to 0.116⫾0.007 times the unpumped ground state absorption. This result is compared with the expected bleaching if excited state absorption is absent. Considering that the pump pulse is much shorter than the predicted upper state lifetime,3 the fraction of U4⫹ left unexcited after the pump is exp关⫺GS F p /h v p 兴 , where GS is the ground-state absorption 共GSA兲 cross section of 7.0⫻10⫺20 cm2 reported by several groups;1,2,26,27 F p is the average pump fluence, and h v p is the pump photon energy. Assuming 10% uncertainty in measurements and 10% uncertainty in the cross section, we obtain a predicted fraction of ions excited to be 0.114 ⫾0.015. The comparison with the observed fractional absorption change is consistent with excited state absorption. We can place a value on the excited state absorption cross section as unlikely to be larger than 8.5⫻10⫺21 cm2. This value is used in the modeling studies we report in Sec. V. Burshtein et al.4 have recently reported ESA measurements at 1573 nm, giving a cross section of 9.15
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⫻10⫺20 cm2 共GSA兲 and 3.6⫻10⫺20 cm2 共ESA兲. Based on their ground state absorption spectra they estimate the GSA cross section at 1533 nm to be 8.0⫻10⫺20 cm2. We have analyzed our pump–probe data using that value of GS , and find that the observed bleaching is then consistent with an ESA cross section of (7.2⫾8.8)⫻10⫺21 cm2. This certain value is within the uncertainty of our first estimate, supporting our conclusion that ESA is small at a wavelength near 1540 nm in our crystals. Our results are consistent with those reported by Stultz et al.,2 who used the Frantz–Nodvik equation to infer a GSA cross section of about 7⫻10⫺20 cm2 at 1533 nm on the assumption of no ESA. When we assume that value for GS , our data indicate negligible ESA, confirming their assumption. For pump fluences well below saturation, nonzero ESA would, to a first approximation, cause a bleaching experiment to exhibit an effective absorbtion cross section of ( GS⫺ GS). Thus, our estimated ESA cross section assuming GS⫽8.0⫻10⫺20 cm2 is also quite consistent with the Stultz et al.2 result.
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sion that ESA is quite small in the crystals chosen for the present study. VI. CONCLUSION
The spectroscopy of green CaF2 :U4⫹ and our interpretation of these data show why this form of material is favorable for passive Q switching at wavelengths near 1.5 m. These crystals are dominated by tetravalent uranium, rather than the trivalent ion that is not useful for this application. Our spectra further indicate that the dopant ions are concentrated into fewer types of sites in the recent samples grown by Spectragen. This appears to be advantageous for passive Q switching at wavelengths near 1.54 m. To further develop crystal-growth technology that improves performance of the absorber by controlling the number and types of defects and compensators, we have initiated exploratory studies on the green crystals using x-ray spectroscopy and x-ray diffraction at the Advanced Photon Source. ACKNOWLEDGMENTS
V. MODELING CaF2 :U4¿ AS A PASSIVE Q SWITCH AT 1.54 m
For several years we have reported results from our modeling of various saturable absorbers for the 共Er,Yb兲: glass laser that operates at 1.54 m.3,22 The model makes use of coupled rate equations for a quasithree-level gain medium and a four-level absorber medium that includes ESA. The model was expanded recently to include energy transfer between Yb and Er, upconversion, and ESA in the gain medium. Numerical integration techniques are used to develop solutions. Since we have reported the rate equations earlier,3,28 we will summarize our approach instead. The equations are solved using various ordinary differential equation 共ODE兲 solvers compatible with MATLAB programs. Where possible, we have compared our results to the results obtained using the analytical methods developed by Xiao and Bass.29 The good agreement with their approach provides us with confidence in applying numerical methods to the modeling process. The experimental cross sections and lifetimes and the laser cavity parameters are taken from the open literature and from the operating 共Er,Yb兲:glass laser system currently in operation at the US Army NV and ES Directorate at Ft. Belvoir, VA. The survey spectrum given in Fig. 1 and the levels reported in Table I are useful in identifying the states of U4⫹ (5 f 2 ) involved in the modeling. The chosen states are: 共1兲 the ground state 3 H 4 ; 共2兲 the vibrationally coupled excited levels in the 3 H 5 multiplet manifold; 共3兲 the lowestenergy Stark level of the 3 H 5 multiplet manifold; and 共4兲 the vibronic and electronic levels of 3 H 6 that are candidates for ESA. By using the excited-state cross section of 8.5 ⫻10⫺21 cm2 obtained from our pump–probe measurements, together with other spectroscopic parameters,3 we have obtained calculated Q-switched energy pulses and pulse widths in excellent agreement with experimental values. Details concerning the modeling will be given at the forthcoming CLEO meeting.30 Our modeling results support the conclu-
Part of this work was supported by BMDO under Contract No. DASG 60-00-M-0115 managed by the U.S. Army Space and Missile Defense Command. J.B.G. wishes to acknowledge M.D. Seltzer and A.O. Wright as colleagues in the analysis of the earlier work on the site-selective spectroscopy of CaF2 :U4⫹ that helped to establish the assignments given to U4⫹ in the present study. 1
J. Jiang, R. Wu, D. I. Rhonehouse, M. J. Myers, J. D. Myers, and S. J. Hamlin, Proc. SPIE 1379, 1 共1995兲. 2 R. D. Stultz, M. B. Carmargo, M. Birnbaum, and M. Kokta, OSA/ASSL 42, 460 共1995兲. 3 J. B. Gruber, B. Zandi, and J. A. Hutchinson, Proceedings International Conference on Lasers, December 7–10, 1998, Tuscon, AZ, ’98 Technical Digest, 1998, Vol. 28, p. 36. 4 Z. Burshtein, Y. Shimony, R. Feldman, V. Krupkin, A. Glushko, and E. Galun, Opt. Mater. 15, 285 共2001兲. 5 G. T. Seaborg and J. J. Katz, Chemistry of the Actinides 共Metheun, London, 1984兲. 6 J. G. Conway, J. Chem. Phys. 31, 1002 共1959兲. 7 W. A. Hargreaves, Phys. Rev. B 2, 2273 共1970兲; 44, 5293 共1991兲. 8 W. A. Hargreaves, Phys. Rev. 156, 331 共1967兲. 9 R. McLaughlin, U. Abed, J. G. Conway, N. Edelstein, and E. H. Huffman, J. Chem. Phys. 53, 2031 共1970兲. 10 J. B. Gruber, M. Seltzer, and A. O. Wright 共unpublished, 1995兲. 11 A. O. Wright, M. Seltzer, J. B. Gruber, and J. A. Hutchinson, Proceedings of IEEE/LEOS 1995, 8th Annual Meeting, San Francisco, CA, Oct 30– Nov 2, 1995, pp. 54 –58. 12 R. S. Title, P. P. Sorokin, M. J. Stevenson, G. D. Pettit, J. E. Scarfield, and J. R. Lankard, Phys. Rev. 128, 62 共1962兲. 13 S. D. McLaughlan, Phys. Rev. 150, 118 共1966兲. 14 M. L. Meilman, A. I. Kolomiitsev, A. M. Kevorkov, and Kh. S. Bagdasarov, Opt. Spektrosk. 57, 145 共1984兲; V. Kaufman and L. J. Radziemski Jr., J. Opt. Soc. Am. 66, 599 共1976兲; J. B. Gruber, ‘‘The Ionized States of Uranium,’’ Technical Report, Battelle Memorial Institute, TR-1697-98, August 28, 1998 共unpublished兲. 15 B. R. Judd, Operator Techniques in Atomic Spectroscopy 共McGraw-Hill, New York, 1963兲. 16 C. A. Morrison, Angular Momentum Theory Applied to Interactions in Solids 共Springer, New York, 1988兲. 17 M. E. Rose, Elementary Theory of Angular Momentum 共Wiley, New York, 1957兲. 18 J. B. Gruber, B. Zandi, and M. F. Reid, Phys. Rev. B 60, 15 643 共1999兲. 19 W. T. Carnall, G. K. Lui, C. W. Williams, and M. F. Reid, J. Chem. Phys. 95, 7194 共1991兲.
Downloaded 19 Jun 2003 to 129.115.60.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp
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R. W. G. Wyckoff, Crystal Structures 共Interscience, New York, 1964兲, Vol. 2. 21 S. Fraga, K. M. Saxena, and J. Karwowski, Physical Science Data, Handbook of Atomic Data, 共Elsevier, New York, 1976兲, Vol. 5. 22 P. C. Schmidt, A. Weiss, and T. P. Das, Phys. Rev. B 19, 5525 共1979兲. 23 C. A. Morrison, Crystal Fields for Transition-Metal Ions in Laser Host Materials 共Springer, New York, 1992兲. 24 C. A. Morrison and R. P. Leavitt, J. Chem. Phys. 71, 2366 共1979兲. 25 C. A. Morrison, J. B. Gruber, and B. Zandi 共unpublished, 1995兲. 20
Gruber et al.
J. Appl. Phys., Vol. 90, No. 8, 15 October 2001 26
R. D. Stultz, M. B. Camargo, and M. Birnbaum, J. Appl. Phys. 78, 2959 共1995兲. 27 R. Stultz, M. Camargo, S. Montgomery, M. Birnbaum, and K. Spariosu, Appl. Phys. Lett. 64, 948 共1994兲. 28 J. B. Gruber, A. Kennedy, B. Zandi, and J. A. Hutchinson, Proc. SPIE 3928, 142 共2000兲. 29 G. Xiao and M. Bass, IEEE J. Quantum Electron. 33, 41 共1997兲. 30 B. Zandi, L. D. Merkle, J. B. Gruber, and J. A. Hutchinson, 2001 Conference on Lasers and Electro-Optics, Baltimore, MD, May 9, 2001, p. 174.
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