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Er codoped NaY(WO4)2 crystal
Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
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Optical spectroscopy of Yb/Er codoped NaY(WO4)2 crystal Z.X. Cheng a,*, S.J. Zhang a, F. Song b, H.C. Guo c, J.R. Han a, H.C. Chen a a
The State key Lab of Crystal Materials, Shandong University, Jinan 250100, People's Republic of China b Photonics center, collage of physics, Nankai University, Tianjin, People's Republic of China c Physics department, Peking University, Beijing, People's Republic of China Received 22 February 2001; revised 1 February 2002; accepted 14 February 2002
Abstract Erbium and ytterbium codoped double tungstates NaY(WO4)2 crystals were prepared by using Czochralski (CZ) pulling method. The absorption spectra in the region 290±2000 nm have been recorded at room temperature. The Judd±Ofelt theory was applied to the measured values of absorption line strengths to evaluate the spontaneous emission probabilities and stimulated emission cross sections of Er 31 ions in NaY(WO4)2 crystals. Intensive green and red lights were measured when the sample were pumped by a 974 nm laser diode (LD), especially, the intensities of green upconversion luminescence are very strong. The mechanism of energy transfer from Yb 31 to Er 31 ions was analyzed. Energy transfer and nonradiative relaxation played an important role in the upconversion process. Photoexcited luminescence experiments are also ful®lled to help analyzing the transit processes of the energy levels. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Optical materials; A. Inorganic compounds; B. Crystal growth; D. Luminescence; D. Optical properties
1. Introduction Nowadays, peoples show great interests in compact laser operating in the infrared (,1.5 and 3 mm) for optical communications, medical and eye-safe light detecting and ranging (LIDAR) applications [1±3], and in the visible region (blue±green), for data storage, undersea communications, etc. Diode pumped solid-state lasers could provide compact and ef®cient devices with the advantage of easy coupling with ®ber integrated optical systems. For diode pumped laser emission at mid infrared and visible regions (upconversion based lasers), Er 31 seems to be a natural candidate due to its 1.5 mm ( 4I13/2 ! 4I15/2) and 2.8 mm emissions ( 4I11/2 ! 4I13/2). Its green emission is at ,0.54 mm ( 4S3/ 4 2 ! I15/2) and its absorption bands at ,0.8 and ,0.98 mm. Among several techniques that are currently used to obtain compact visible lasers, the upconversion lasing is one of the most promising techniques since it does not require a nonlinear media for second harmonic generation [4]. The overlapping of 2F5/2 energy level of Yb 31 ions and 4I11/2 energy level of Er 31 ions produce ef®cient resonant transfer between both ions. So it is possible to perform selective * Corresponding author. Fax: 186-531-856-5403. E-mail address: [email protected] (Z.X. Cheng).
excitation of the Yb 31 ions and realize energy transfer between the two ions. Upconversion laser performance of Er 31 has been observed in some crystals and glass ®bers [5±7]. The hosts play important roles in the upconversion luminescence. Er/Yb:NaY(WO4)2 crystal is a new kind of crystal demonstrating good optical performance. NaY(WO4)2 crystal (here denoted as NYW) is classi®ed among the disorder crystalline host for lasing rare-earth ions [8]. The disorder structure presents the broadening of the optical features in the absorption and emission spectrum even at low temperature. This fact has some interesting results on the optical properties of the materials. The addition of proper RE oxides to the starting mixture allows obtaining crystals suitable for spectroscopic experiments. NYW has been demonstrated to be a promising host lattice for lasing ions: laser action has been reported for Nd 31 doped in the matrix [9]. In this letter, we report the absorption spectra of Yb/Er codoped NYW and whose analysis on the basis of the Judd± Ofelt theory. The three phenomenological J±O intensity parameters V t (t 2; 4 and 6) of Er 31 ions in NYW crystals are determined by performing a least square ®t of calculated and observed absorption line intensities. These intensity parameters are then used to determine the spontaneous emission probabilities and branching ratios. We measured
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(02)00187-7
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Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
tions are of 0.5% and 2% substituting for Y 31. The depth of the Pt crucible was 30 mm, and the diameter is 55 mm. Crystal growth began on a k101l oriented seed. The rotation rate is 55±60 rpm and pulling rate 1.5 mm/h. The obtained sample shows pink color, and its size reaches up to B2 £ 4 cm. No macro-defects were observed in the sample. The rare earth concentration in the sample was determined by atomic absorption spectrometry method. The distribution coef®cient is close to unity. That is the rare earth concentration in the crystal is close to that in the formula. The quantities of Er 31 and Yb 31 ions in the sample are 3.27 £ 10 19/ cm 3 and 1.308 £ 10 20/cm 3 respectively.
3. Optical measurements and results discussion 3.1. Absorption spectra and Judd±Ofelt analysis Fig. 1. Absorption spectra of Er/Yb codoped NaY(WO4)2 crystal at room temperature.
the upconversion luminescence of Er 31/Yb 31 codoped NaY(WO4)2 crystal excited by 974 nm laser diode. The concentration of Er 31 and Yb 31 is about 0.5% and 2% respectively. The thickness of the sample is 3.5 mm and both sides are well polished. 2. Crystal growth Single crystals of NYW are usually grown with CZ pulling method using a MCGS-3 RF single-crystal furnace. The raw materials was prepared according to the following formula: Na 2 CO3 1 1 2 x 2 yY2 O3 1 xEr2 O3 1 yYb2 O3 1 4WO3 ! 2NaY12x2y Erx Yby WO4 2 1 CO2 " In our experiment, the Er 31 and Yb 31 dopants concentra-
The sample was cut along a-face and polished to optical grade. The polarized absorption spectra (p, E k c-axis; s, E ' c-axis) at room temperature in 290±2000 nm of a 2.06 mm a-slice were measured on a Hitachi U-3500 spectrophotometer. The room temperature polarized absorption spectra of Er/Yb codoped NaY(WO4)2 crystal was shown in Fig. 1. The absorption bands of Yb 31 and Er 31 ions appear to be broader than expected for a crystalline material with ordered structure, due to the random distribution of the Na and rare earth ions in the dodecahedra sites of the scheelite structure. As a consequence of the band broadening, there is no point in attempting in an assignment of the Stark components of the individual states exploiting the selection rules for the polarized spectra. The observed absorption wavelength and the related assignments are listed in Table 1. The data from these absorption spectra can be used to predict the radiative lifetime of the excited states, the branching ratios and the radiative transition probabilities of the ¯uorescence transitions, using the Judd±Ofelt (J±O) analysis method. For the polarized absorption spectra, the calculation was the whole consideration of the two polarized
Table 1 The calculated and measured oscillator strength, line strength and three J±O parameters of Er 31 in Er/Yb codoped NaY(WO4)2 crystal (the phenomenological parameters (10 220 cm 2), V 2 18:1; V 4 2:59; V 6 1:21) Energy level
Wavelength (nm)
Measured oscillator strength (10 26)
Calculated oscillator strength (10 26)
Measured line strength (10 220)
Calculated line strength (10 220)
4
365 379 406 442,450 487 520 543 653 800
4.7 60.8 1.03 1.15 3.10 32.3 0.88 3.49 0.68
4.01 59.6 0.99 1.50 2.90 33.5 0.61 3.68 0.71
1.38 18.5 0.33 0.42 1.22 13.5 0.385 1.84 0.44
1.18 18.1 0.32 0.54 1.14 14.1 0.27 1.94 0.46
G9/2 G11/2 2 G9/2 4 F3/2, 4F5/2 4 F7/2 2 H11/2 4 S3/2 4 F9/2 4 I9/2 4
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
spectra, that is the weight of p polarized spectrum is 1/3 and the weight of the s polarized spectra is 2/3. Here we brie¯y introduce the pertinent equations used in the analysis. A more detailed theory and applications can be found in the literature [10±13]. The line strength of the electric±dipole transition between two J states can be measured from the acquired absorption spectra, using the relation [14,15]: Z 3hc 2J 1 1 9n S exp J ! J 0 N021 k l dl 8p3 e2 lmean n2 1 22 J!J' 1 where J and J 0 are the total angular momentum quantum numbers of the initial and ®nal states, respectively, l mean, the mean wavelength of the speci®c adsorption band, n n (l mean), the refractive index at the mean wavelength l mean, c, the velocity of light, e, the electron charge, h, the Planck's constant, and N0 is the Er 31 ions concentration. k l is the absorption coef®cient, which is de®ned as k l ln I0 =I=l: Where l is the thickness of the sample and I0 is the intensity of the input light, I the intensity of output light. The measured line strength can then be used to calculated the J±O intensity parameters V 2, V 4 and V 6 by solving a set of equations for the corresponding transitions between initial u S; LJl and terminal u S 0 ; L 0 J 0 l manifolds expressed by Judd and Ofelt in the form [10,11] X S cal J ! J 0 V t uk S; LJuuU t uu S 0 ; L 0 J 0 lu2 2 t2;4;6
where the elements k¼iU t i¼l are the reduced matrix elements of unit tensor operator U t of rank t. Since the 4f 3 electron are well shield by other layers in trivalent rare earth ions (Re 31), the reduced matrix elements k¼iU t i¼l are virtually independent of the ligand species surrounding the Re ions [16]. Numerous sets of reduced matrix elements data calculated through various approaches in the literature con®rm this fact [17,18] and thus can be readily applied in intensity analysis. The three phenomenological parameters V 2, V 4 and V 6, on the other hand, exhibit the in¯uence of the host on the radiative transition probabilities, since they contain implicitly the effects of the odd-symmetry crystal®eld terms, intercon®gurational radical integrals and energy denominators. Nine absorption bands lying between 300 and 900 nm regions were selected and numerically integrated. Values of the doubly reduced matrix elements k¼iU t i¼l of the unit tensor operators for these bands were taken from the set of values for Er 31 ions listed by Kaminskii et al. When two or more absorption manifolds overlapped, the matrix element was taken to be the sum of the corresponding squared matrix elements. The best set of V t (t 2; 4 and 6) parameters was determined by a least squared ®tting of the calculated S values given by Eq. (2) to the experimental ones given by Eq. (1). All these values (V 2,4,6, Scal and Sexp) were in Table 1.
2013
In order to estimate the quality of our ®tting, rms deviation were evaluated: rms
q X S cal 2 Sexp 2 q2p i1
!1=2 3
where q is the number of transitions taken in the ®tting, nine in our case, and p is the number of adjustable parameters, three in our case. The value obtained for such deviation (0.29) remarks the consistency of our ®tting. The radiative transition rates and the branching ratios of the electro±dipole transitions inter the excited states and the ground state now can be calculated from V t parameters. The transition rate from initial J manifold u S; LJl to the terminal J 0 manifold u S 0 L 0 J 0 l is given by [19] 0 Aed JJ
64p4 e2 n n2 1 22 ed SJJ 0 9 3h 2J 1 1l3
4
where n n2 1 22 =9 is the local-®eld correction for the Er 31 ion in the initial J manifold. The ¯uorescence branching ratios for transitions originating on a speci®c initial manifold u S; LJl are de®ned by [19] A S; LJ; S 0 ; L 0 J 0 b S; LJ; S 0 ; L 0 J 0 X A S; LJ; S 0 ; L 0 J 0
5
S0L0J 0
where the sum is over all possible terminal manifolds u S 0 ; L 0 J 0 l: The sum represents the total transition probability for radiative decay from the initial manifold. The radiative lifetime of a level is related to the total transition probability as [19] ( )21 X tcrad A S; LJ; S 0 ; L 0 J 0 A21 6 total S0L0J 0
The integrated emission cross section can be obtained from the spontaneous emission probability:
s
l2 AJJ 0 8pn2 c
7
The total 9 spontaneous emission transition rates A and the branching ratio b for the Er 31 ion in the NYW crystal are listed in Table 2, together with the total spontaneous emission probability (Atotal). The radiative lifetime tcrad ; computed as the reciprocal of the total transition probability Atotal, also is given in Table 2. This radiative lifetime calculated from J±O intensity parameters is inversely proportional to a linear combination of V t parameters. 3.2. Fluorescence measurements The upconversion luminescence spectra at room temperature excited by 974 nm laser diode were measured by using Model F111AI ¯ouro-meter. It should be emphasized that
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Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
Table 2 Calculated radiative transition rates and branching ratios of Er 31 in Er/Yb codoped NaY(WO4)2 crystal Transitions
Wavelength (nm)
AJJ 0 (s 21)
b
t 0 (ms)
s (10 218cm 2)
4
1537 974 2750 797 1690 4384 653 1152 1981 3614 542 846 1222 1694 3189 521 487 451 442 405 554 693 823 1066 378 504 618 719 898 1377 364 480
239 423 45.4 398 88 2 424 218 176 22.9 2020 818 69.2 126 1.03 40,000 5900 2340 2050 2930 4990 1460 233 103 13,4000 8800 247 1290 4350 78.7 7670 91,300
1 0.903 9.7 0.815 0.18 0.005 0.891 0.057 0.046 0.006 0.666 0.269 0.029 0.041 <0 0.965 0.713 0.392 0.409 0.251 0.539 0.158 0.025 0.011 0.899 0.059 0.002 0.009 0.029 0.001 0.069 0.819
4190 2140
1.99 1.47 1.26 0.93 0.92 0.16 5.37 1.06 2.54 1.1 2.19 2.15 0.38 1.32 0.038 39.9 5.15 1.75 1.48 1.40 5.64 2.58 0.58 0.43 70.4 8.22 0.35 2.46 12.9 0.55 3.74 77.3
I13/2 ! 4I15/2 I11/2 ! 4I15/2 4 I13/2 ! 4I13/2 4 I9/2 ! 4I15/2 4 I9/2 ! 4I13/2 4 I9/2 ! 4I11/2 4 F9/2 ! 4I15/2 4 F9/2 ! 4I13/2 4 F9/2 ! 4I11/2 4 F9/2 ! 4I9/2 4 S3/2 ! 4I15/2 4 S3/2 ! 4I13/2 4 S3/2 ! 4I11/2 4 S3/2 ! 4I9/2 4 S3/2 ! 4F9/2 2 H11/2 ! 4I15/2 4 F7/2 ! 4I15/2 4 F5/2 ! 4I15/2 4 F3/2 ! 4I15/2 2 H9/2 ! 4I15/2 2 H9/2 ! 4I13/2 2 H9/2 ! 4I11/2 2 H9/2 ! 4I9/2 2 H9/2 ! 4F9/2 4 G11/2 ! 4I15/2 4 G11/2 ! 4I13/2 4 G11/2 ! 4I11/2 4 G11/2 ! 4I9/2 4 G11/2 ! 4F9/2 4 G11/2 ! 2H11/2 4 G9/2 ! 4I15/2 4 G9/2 ! 4I13/2 4
the strong green light can be easily seen with naked eyes when the 974 nm diode laser (even only a few milliwatts) is focus on the sample. The upconversion ¯uorescence near 552 and 530 nm is very intense, which were associated with the relaxation of 4S3/2 ! 4I15/2 and 4H11/2 ! 4I15/2; and the emissions peaked 650 and 796 nm is relatively weak, which were associated with the transition of 4F9/2 ! 4I15/2 and 4I9/2 ! 4I15/2.The intensity of green light is about 50 times more intense than the red light at 655 nm. When the pump light become more intense, 407 nm emission and 450 nm were detected, which correspond to transition of 2 H9/2 and 4F5/2 to the ground state. The crystal also emits ¯uorescence at IR±red band centered at 1537 nm, which associated with 4I13/2 ! 4I15/2 transition (Fig. 2). The dependence of the green and red lights emission intensities on the pumping light intensity was measured and the log±log plot was shown in Fig. 3. The slope for 552, 530 nm green light and 655 red lights are 1.99, 2.05 and 1.91, respectively, which indicated that two-photon processes populates the 2H11/2, 4S13/2 and 4F9/2 levels. Even
2050 260
329
24.1 121 168 199 108
6.7
8.97
as the pump power increases, no three-photon process was observed. But the slope for 407 nm emission was 2.50, which indicates a three-photon process populates 2H9/2 energy levels. The energy transfer from Yb 31 to Er 31 can be described with the help of the energy level diagram sketched in Fig. 4. The process were indicated here: the energy overlap between the 2F5/2(Yb 31) and 4I11/2(Er 31) energy level was the basic fact that allows the ef®cient resonant energy transfer between both ions [20]. Nevertheless, the absorption (associated with the 2F7/2 ! 2F5/2 transition) of Yb 31 transitions is broader than the corresponding Er 31 transitions. In this way it is possible to perform selective excitation of the Yb 31 ions (in the wavelength range 900±950 nm) and realize energy transfer from Yb 31 ions to Er 31 ions after excitation of the Yb 31 ions. After the selective excitation of the 2F5/2(Yb 31) level, it may relax radiatively to 2F7/2 ground state, producing luminescence in the range 920±1100 nm, or transfer energy to Er 31 ions and excited it to 4I11/2 level from ground state,
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
2015
Fig. 2. Fluorescence spectrum of Er/Yb codoped NaY(WO4)2 crystal upon excitation at 974 nm (LD).
Fig. 3. log±log plot of upconversion luminescence (the slope for 552, 530 nm green light and 655 red lights are 1.99, 2.05 and 1.91, respectively).
Fig. 4. Schematic energy level diagram of Er/Yb codoped NaY(WO4)2 crystal.
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Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
Fig. 5. Emission spectra of Yb/Er codoped NaY(WO4)2 crystal.
according to the energy cross-transfer mechanism: 2
F5=2 Yb31 1 4 I15=2 Er31 ! 2 F7=2 Yb31 1 4 I11=2 Er31
shown as process a From the 4I11/2 erbium level the energy can be transferred back to the Yb 31 or relax within the Er 31 ions. This relaxation produces luminescence at around 1000 nm (associated with the 4I11/2 ! 4I15/2 transition), and at around 1500 nm (associated with the 4I13/2 ! 4I15/2 transition) after population of the metastable erbium level ( 4I13/2) via a nonradiative connection. The emission of 1.5 mm can be easily measured. The 1.0 mm is very weak and easily is hidden by the broader Yb 31 emission within similar wavelength range. Er 31 ions at 4I13/2 can absorb another photon from Yb 31 and be excited to 4F9/2 (shown as process b), then red light near 650 nm produced through 4 F9/2 ! 4I15/2 transition. Er 31 at 4I11/2 also can absorb energy from adjacent Yb 31 again and be excited to 2H11/2 according to the energy crosstransfer mechanism: 2
F5=2 Yb31 1 4 I11=2 Er31 ! 2 F7=2 Yb31 1 2 H11=2 Er31
shown as process c 4 H11/2 ! 4I15/2(Er 31) transitions generates 530 nm green light. Parts of erbium ions excited to the 4H11/2 also relaxed nonradiatively to the 4S3/2 level and then relaxed to ground state from where green emission at around 552 nm is observed. In NYW crystal, 4S3/2 level has relative long energy level lifetime and 4S3/2 ! 4I15/2 transition has relative larger integral emission cross section, which are suitable for the accumulating of population of 4S3/2 level. The above analysis showed that red light and green light all are two-photon process. Er 31 at 4F9/2 also can absorb energy from adjacent Yb 31 again and be excited to 4H9/2 according to the energy cross-
transfer mechanism: 2
F5=2 Yb31 1 4 F9=2 Er31 ! 2 F7=2 Yb31 1 2 H9=2 Er31
shown as process d Er 31 ions at 2H9/2 level relax to the ground state and emit 407 nm light. Some ions will nonradiatively decay to the 4 F3/2 and then transit to ground state with 450 nm luminescence. For the 407 nm emission, it is a three-photon process. In order to understand the mechanism of the luminescence, we measured the photoexcited luminescence spectra. When emission wavelength was ®xed at 530 nm, and the excitation wavelength is tuned from 250 to 500 nm, the signal at 363, 406, 450, and 488 nm are observed (Fig. 5). The signal at 363 nm is the most intense. As indicate that the ions at 4G11/2, 4H9/2, 4F5/2, 4F7/2 levels can nonradiatively decay to the 2H11/2 levels. Also the below cross-relaxation process is indicated: 4
I9=2 Er31 1 4 G11=2 Er31 ! 22 H11=2 Er31
shown as process e When the emission wavelength was ®xed at 552 nm, and the excitation wavelength is turned from 250 to 530 nm, the signal at 363, 406, 450, 488 and 533 nm are observed. The signal at 363 and 533 nm are the most intense. As indicate that 4S3/2 level was populated mainly through nonradiative decaying of 2H11/2 level and the crossrelaxation of 4G11/2 level also produce population of 4S3/2. The 530 nm emission at 363 nm excitation was more intense than emissions at 450 and 407 nm excitations, also for the 552 nm emission. Otherwise the 552 nm emission at 363 nm excitation and 488 nm excitation show the almost the same intensity. As is impossible if only nonradiative relaxation exist. When the emission was located at 650 nm, no excitation signal was found in 250±630 nm. As indicated 650 nm emission was mainly from the transit of lower levels to 2 F9/2 level, not from the cross-relaxation of higher energy
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017 2
levels to F9/2 level. When the sample was excitated by 363, 406, and 450 nm, no red light was detected, which indicated no three-photon process exist for 650 nm emission. 4. Conclusions Er/Yb codoped NaY(WO4)2 crystals with good optical quality can be grown by using CZ pulling method. The optical parameters of Er 31 ions in the codoped NaY(WO4)2 crystals were obtained as V 2 18:1 £ 10220 cm2 ; V 4 2:59 £ 10 2 20 cm2 and V 6 1:21 £ 10220 cm2 : Upconversion luminescences of 552 nm green light, 530 nm red light and 407 nm violet light were obtained when the sample was pumped by 974 nm LD. The red light and green light emissions all were two-photon processes and the 407 nm emission is three-photon process. Acknowledgements The author would like to thank Prof. Zhaohe Yang for transmittance measurements. References [1] S. Tacheo, P. Laporta, S. Longhi, O. Svelto, C. Svelto, Appl. Phys. B 63 (1996) 425. [2] N.P. Bames, W.J. Rodriguez, B.M. Walsh, J. Opt. Soc. Am. B 13 (1996) 2872.
2017
[3] A.G. Antipenko, N.V. Aetem'ev, A.A. Betim, V.R. Kamenskii, W.P. Novikov, V.G. Plotnichenko, I.V. Skipachev, G.E. Snopatim, Quant. Elect. 25 (1995) 498. [4] D.W. Nam, R.G. Waarts, Laser Focus World, August 49 (1994). [5] A.J. Silversmith, W. Leth, R.M. Macfarlane, J. Opt. Soc. Am. A3 (1996) 128. [6] Z. Cheng, S. Zhang, H. Chen, J. Cryst. Growth 222 (2001) 797. [7] K. Hirao, S. Todoroki, N. Sogan, J. Non-Cryst. Solids 40 (1992) 143. [8] A.A. Kaminskii, H.J. Eichler, K. Ueda, N.V. Klassen, B.S. Redkin, et al., Appl. Opt. 38 (1999) 4533. [9] Z. Cheng, S. Zhang, H. Chen, Jpn. J. Appl. Phys. (2001) 40. [10] B.R. Judd, Phys. Rev. 127 (1962) 750. [11] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. [12] J.L. Adm, M. Matecki, H. L'hegoualch, B. Jacuquier, Eur. J. Solid State Inorg. Chem. 31 (1994) 337. [13] A.A. Kaminskii, Crystalline Laser: Physical Processes and Operating Schemes, CRC Press, Boca Raton, FL, 1996. [14] R. Reis®eld, C.K. Jorgenson, Lasers and Excited States of Rare Earth, Springer, Berlin, 1977. [15] L.J.F. Broer, C.J. Gorter, J. Hoogschagen, Physica 11 (1945) 231. [16] G. Gashurov, O.J. Sovers, J. Chem. Phys. 50 (1969) 429. [17] W.T. Carnall, P.R. Fields, K. Rajnak, J. Chem. Phys. 49 (1968) 4424. [18] A.A. Kaminskii, G. Boulon, M. Buoncristiani, B. Dibartolo, A. Kornienko, V. Mironov, Phys. Stat. Sol. A 141 (1994) 471. [19] W.F. Krupke, IEEE J. Quant. Electron. Q E-10 (1974) 450. [20] E. Cantelar, F. Cusso, Appl. Phys. B 69 (1999) 29.
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Optical spectroscopy of Yb/Er codoped NaY(WO4)2 crystal Z.X. Cheng a,*, S.J. Zhang a, F. Song b, H.C. Guo c, J.R. Han a, H.C. Chen a a
The State key Lab of Crystal Materials, Shandong University, Jinan 250100, People's Republic of China b Photonics center, collage of physics, Nankai University, Tianjin, People's Republic of China c Physics department, Peking University, Beijing, People's Republic of China Received 22 February 2001; revised 1 February 2002; accepted 14 February 2002
Abstract Erbium and ytterbium codoped double tungstates NaY(WO4)2 crystals were prepared by using Czochralski (CZ) pulling method. The absorption spectra in the region 290±2000 nm have been recorded at room temperature. The Judd±Ofelt theory was applied to the measured values of absorption line strengths to evaluate the spontaneous emission probabilities and stimulated emission cross sections of Er 31 ions in NaY(WO4)2 crystals. Intensive green and red lights were measured when the sample were pumped by a 974 nm laser diode (LD), especially, the intensities of green upconversion luminescence are very strong. The mechanism of energy transfer from Yb 31 to Er 31 ions was analyzed. Energy transfer and nonradiative relaxation played an important role in the upconversion process. Photoexcited luminescence experiments are also ful®lled to help analyzing the transit processes of the energy levels. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Optical materials; A. Inorganic compounds; B. Crystal growth; D. Luminescence; D. Optical properties
1. Introduction Nowadays, peoples show great interests in compact laser operating in the infrared (,1.5 and 3 mm) for optical communications, medical and eye-safe light detecting and ranging (LIDAR) applications [1±3], and in the visible region (blue±green), for data storage, undersea communications, etc. Diode pumped solid-state lasers could provide compact and ef®cient devices with the advantage of easy coupling with ®ber integrated optical systems. For diode pumped laser emission at mid infrared and visible regions (upconversion based lasers), Er 31 seems to be a natural candidate due to its 1.5 mm ( 4I13/2 ! 4I15/2) and 2.8 mm emissions ( 4I11/2 ! 4I13/2). Its green emission is at ,0.54 mm ( 4S3/ 4 2 ! I15/2) and its absorption bands at ,0.8 and ,0.98 mm. Among several techniques that are currently used to obtain compact visible lasers, the upconversion lasing is one of the most promising techniques since it does not require a nonlinear media for second harmonic generation [4]. The overlapping of 2F5/2 energy level of Yb 31 ions and 4I11/2 energy level of Er 31 ions produce ef®cient resonant transfer between both ions. So it is possible to perform selective * Corresponding author. Fax: 186-531-856-5403. E-mail address: [email protected] (Z.X. Cheng).
excitation of the Yb 31 ions and realize energy transfer between the two ions. Upconversion laser performance of Er 31 has been observed in some crystals and glass ®bers [5±7]. The hosts play important roles in the upconversion luminescence. Er/Yb:NaY(WO4)2 crystal is a new kind of crystal demonstrating good optical performance. NaY(WO4)2 crystal (here denoted as NYW) is classi®ed among the disorder crystalline host for lasing rare-earth ions [8]. The disorder structure presents the broadening of the optical features in the absorption and emission spectrum even at low temperature. This fact has some interesting results on the optical properties of the materials. The addition of proper RE oxides to the starting mixture allows obtaining crystals suitable for spectroscopic experiments. NYW has been demonstrated to be a promising host lattice for lasing ions: laser action has been reported for Nd 31 doped in the matrix [9]. In this letter, we report the absorption spectra of Yb/Er codoped NYW and whose analysis on the basis of the Judd± Ofelt theory. The three phenomenological J±O intensity parameters V t (t 2; 4 and 6) of Er 31 ions in NYW crystals are determined by performing a least square ®t of calculated and observed absorption line intensities. These intensity parameters are then used to determine the spontaneous emission probabilities and branching ratios. We measured
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(02)00187-7
2012
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
tions are of 0.5% and 2% substituting for Y 31. The depth of the Pt crucible was 30 mm, and the diameter is 55 mm. Crystal growth began on a k101l oriented seed. The rotation rate is 55±60 rpm and pulling rate 1.5 mm/h. The obtained sample shows pink color, and its size reaches up to B2 £ 4 cm. No macro-defects were observed in the sample. The rare earth concentration in the sample was determined by atomic absorption spectrometry method. The distribution coef®cient is close to unity. That is the rare earth concentration in the crystal is close to that in the formula. The quantities of Er 31 and Yb 31 ions in the sample are 3.27 £ 10 19/ cm 3 and 1.308 £ 10 20/cm 3 respectively.
3. Optical measurements and results discussion 3.1. Absorption spectra and Judd±Ofelt analysis Fig. 1. Absorption spectra of Er/Yb codoped NaY(WO4)2 crystal at room temperature.
the upconversion luminescence of Er 31/Yb 31 codoped NaY(WO4)2 crystal excited by 974 nm laser diode. The concentration of Er 31 and Yb 31 is about 0.5% and 2% respectively. The thickness of the sample is 3.5 mm and both sides are well polished. 2. Crystal growth Single crystals of NYW are usually grown with CZ pulling method using a MCGS-3 RF single-crystal furnace. The raw materials was prepared according to the following formula: Na 2 CO3 1 1 2 x 2 yY2 O3 1 xEr2 O3 1 yYb2 O3 1 4WO3 ! 2NaY12x2y Erx Yby WO4 2 1 CO2 " In our experiment, the Er 31 and Yb 31 dopants concentra-
The sample was cut along a-face and polished to optical grade. The polarized absorption spectra (p, E k c-axis; s, E ' c-axis) at room temperature in 290±2000 nm of a 2.06 mm a-slice were measured on a Hitachi U-3500 spectrophotometer. The room temperature polarized absorption spectra of Er/Yb codoped NaY(WO4)2 crystal was shown in Fig. 1. The absorption bands of Yb 31 and Er 31 ions appear to be broader than expected for a crystalline material with ordered structure, due to the random distribution of the Na and rare earth ions in the dodecahedra sites of the scheelite structure. As a consequence of the band broadening, there is no point in attempting in an assignment of the Stark components of the individual states exploiting the selection rules for the polarized spectra. The observed absorption wavelength and the related assignments are listed in Table 1. The data from these absorption spectra can be used to predict the radiative lifetime of the excited states, the branching ratios and the radiative transition probabilities of the ¯uorescence transitions, using the Judd±Ofelt (J±O) analysis method. For the polarized absorption spectra, the calculation was the whole consideration of the two polarized
Table 1 The calculated and measured oscillator strength, line strength and three J±O parameters of Er 31 in Er/Yb codoped NaY(WO4)2 crystal (the phenomenological parameters (10 220 cm 2), V 2 18:1; V 4 2:59; V 6 1:21) Energy level
Wavelength (nm)
Measured oscillator strength (10 26)
Calculated oscillator strength (10 26)
Measured line strength (10 220)
Calculated line strength (10 220)
4
365 379 406 442,450 487 520 543 653 800
4.7 60.8 1.03 1.15 3.10 32.3 0.88 3.49 0.68
4.01 59.6 0.99 1.50 2.90 33.5 0.61 3.68 0.71
1.38 18.5 0.33 0.42 1.22 13.5 0.385 1.84 0.44
1.18 18.1 0.32 0.54 1.14 14.1 0.27 1.94 0.46
G9/2 G11/2 2 G9/2 4 F3/2, 4F5/2 4 F7/2 2 H11/2 4 S3/2 4 F9/2 4 I9/2 4
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spectra, that is the weight of p polarized spectrum is 1/3 and the weight of the s polarized spectra is 2/3. Here we brie¯y introduce the pertinent equations used in the analysis. A more detailed theory and applications can be found in the literature [10±13]. The line strength of the electric±dipole transition between two J states can be measured from the acquired absorption spectra, using the relation [14,15]: Z 3hc 2J 1 1 9n S exp J ! J 0 N021 k l dl 8p3 e2 lmean n2 1 22 J!J' 1 where J and J 0 are the total angular momentum quantum numbers of the initial and ®nal states, respectively, l mean, the mean wavelength of the speci®c adsorption band, n n (l mean), the refractive index at the mean wavelength l mean, c, the velocity of light, e, the electron charge, h, the Planck's constant, and N0 is the Er 31 ions concentration. k l is the absorption coef®cient, which is de®ned as k l ln I0 =I=l: Where l is the thickness of the sample and I0 is the intensity of the input light, I the intensity of output light. The measured line strength can then be used to calculated the J±O intensity parameters V 2, V 4 and V 6 by solving a set of equations for the corresponding transitions between initial u S; LJl and terminal u S 0 ; L 0 J 0 l manifolds expressed by Judd and Ofelt in the form [10,11] X S cal J ! J 0 V t uk S; LJuuU t uu S 0 ; L 0 J 0 lu2 2 t2;4;6
where the elements k¼iU t i¼l are the reduced matrix elements of unit tensor operator U t of rank t. Since the 4f 3 electron are well shield by other layers in trivalent rare earth ions (Re 31), the reduced matrix elements k¼iU t i¼l are virtually independent of the ligand species surrounding the Re ions [16]. Numerous sets of reduced matrix elements data calculated through various approaches in the literature con®rm this fact [17,18] and thus can be readily applied in intensity analysis. The three phenomenological parameters V 2, V 4 and V 6, on the other hand, exhibit the in¯uence of the host on the radiative transition probabilities, since they contain implicitly the effects of the odd-symmetry crystal®eld terms, intercon®gurational radical integrals and energy denominators. Nine absorption bands lying between 300 and 900 nm regions were selected and numerically integrated. Values of the doubly reduced matrix elements k¼iU t i¼l of the unit tensor operators for these bands were taken from the set of values for Er 31 ions listed by Kaminskii et al. When two or more absorption manifolds overlapped, the matrix element was taken to be the sum of the corresponding squared matrix elements. The best set of V t (t 2; 4 and 6) parameters was determined by a least squared ®tting of the calculated S values given by Eq. (2) to the experimental ones given by Eq. (1). All these values (V 2,4,6, Scal and Sexp) were in Table 1.
2013
In order to estimate the quality of our ®tting, rms deviation were evaluated: rms
q X S cal 2 Sexp 2 q2p i1
!1=2 3
where q is the number of transitions taken in the ®tting, nine in our case, and p is the number of adjustable parameters, three in our case. The value obtained for such deviation (0.29) remarks the consistency of our ®tting. The radiative transition rates and the branching ratios of the electro±dipole transitions inter the excited states and the ground state now can be calculated from V t parameters. The transition rate from initial J manifold u S; LJl to the terminal J 0 manifold u S 0 L 0 J 0 l is given by [19] 0 Aed JJ
64p4 e2 n n2 1 22 ed SJJ 0 9 3h 2J 1 1l3
4
where n n2 1 22 =9 is the local-®eld correction for the Er 31 ion in the initial J manifold. The ¯uorescence branching ratios for transitions originating on a speci®c initial manifold u S; LJl are de®ned by [19] A S; LJ; S 0 ; L 0 J 0 b S; LJ; S 0 ; L 0 J 0 X A S; LJ; S 0 ; L 0 J 0
5
S0L0J 0
where the sum is over all possible terminal manifolds u S 0 ; L 0 J 0 l: The sum represents the total transition probability for radiative decay from the initial manifold. The radiative lifetime of a level is related to the total transition probability as [19] ( )21 X tcrad A S; LJ; S 0 ; L 0 J 0 A21 6 total S0L0J 0
The integrated emission cross section can be obtained from the spontaneous emission probability:
s
l2 AJJ 0 8pn2 c
7
The total 9 spontaneous emission transition rates A and the branching ratio b for the Er 31 ion in the NYW crystal are listed in Table 2, together with the total spontaneous emission probability (Atotal). The radiative lifetime tcrad ; computed as the reciprocal of the total transition probability Atotal, also is given in Table 2. This radiative lifetime calculated from J±O intensity parameters is inversely proportional to a linear combination of V t parameters. 3.2. Fluorescence measurements The upconversion luminescence spectra at room temperature excited by 974 nm laser diode were measured by using Model F111AI ¯ouro-meter. It should be emphasized that
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Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
Table 2 Calculated radiative transition rates and branching ratios of Er 31 in Er/Yb codoped NaY(WO4)2 crystal Transitions
Wavelength (nm)
AJJ 0 (s 21)
b
t 0 (ms)
s (10 218cm 2)
4
1537 974 2750 797 1690 4384 653 1152 1981 3614 542 846 1222 1694 3189 521 487 451 442 405 554 693 823 1066 378 504 618 719 898 1377 364 480
239 423 45.4 398 88 2 424 218 176 22.9 2020 818 69.2 126 1.03 40,000 5900 2340 2050 2930 4990 1460 233 103 13,4000 8800 247 1290 4350 78.7 7670 91,300
1 0.903 9.7 0.815 0.18 0.005 0.891 0.057 0.046 0.006 0.666 0.269 0.029 0.041 <0 0.965 0.713 0.392 0.409 0.251 0.539 0.158 0.025 0.011 0.899 0.059 0.002 0.009 0.029 0.001 0.069 0.819
4190 2140
1.99 1.47 1.26 0.93 0.92 0.16 5.37 1.06 2.54 1.1 2.19 2.15 0.38 1.32 0.038 39.9 5.15 1.75 1.48 1.40 5.64 2.58 0.58 0.43 70.4 8.22 0.35 2.46 12.9 0.55 3.74 77.3
I13/2 ! 4I15/2 I11/2 ! 4I15/2 4 I13/2 ! 4I13/2 4 I9/2 ! 4I15/2 4 I9/2 ! 4I13/2 4 I9/2 ! 4I11/2 4 F9/2 ! 4I15/2 4 F9/2 ! 4I13/2 4 F9/2 ! 4I11/2 4 F9/2 ! 4I9/2 4 S3/2 ! 4I15/2 4 S3/2 ! 4I13/2 4 S3/2 ! 4I11/2 4 S3/2 ! 4I9/2 4 S3/2 ! 4F9/2 2 H11/2 ! 4I15/2 4 F7/2 ! 4I15/2 4 F5/2 ! 4I15/2 4 F3/2 ! 4I15/2 2 H9/2 ! 4I15/2 2 H9/2 ! 4I13/2 2 H9/2 ! 4I11/2 2 H9/2 ! 4I9/2 2 H9/2 ! 4F9/2 4 G11/2 ! 4I15/2 4 G11/2 ! 4I13/2 4 G11/2 ! 4I11/2 4 G11/2 ! 4I9/2 4 G11/2 ! 4F9/2 4 G11/2 ! 2H11/2 4 G9/2 ! 4I15/2 4 G9/2 ! 4I13/2 4
the strong green light can be easily seen with naked eyes when the 974 nm diode laser (even only a few milliwatts) is focus on the sample. The upconversion ¯uorescence near 552 and 530 nm is very intense, which were associated with the relaxation of 4S3/2 ! 4I15/2 and 4H11/2 ! 4I15/2; and the emissions peaked 650 and 796 nm is relatively weak, which were associated with the transition of 4F9/2 ! 4I15/2 and 4I9/2 ! 4I15/2.The intensity of green light is about 50 times more intense than the red light at 655 nm. When the pump light become more intense, 407 nm emission and 450 nm were detected, which correspond to transition of 2 H9/2 and 4F5/2 to the ground state. The crystal also emits ¯uorescence at IR±red band centered at 1537 nm, which associated with 4I13/2 ! 4I15/2 transition (Fig. 2). The dependence of the green and red lights emission intensities on the pumping light intensity was measured and the log±log plot was shown in Fig. 3. The slope for 552, 530 nm green light and 655 red lights are 1.99, 2.05 and 1.91, respectively, which indicated that two-photon processes populates the 2H11/2, 4S13/2 and 4F9/2 levels. Even
2050 260
329
24.1 121 168 199 108
6.7
8.97
as the pump power increases, no three-photon process was observed. But the slope for 407 nm emission was 2.50, which indicates a three-photon process populates 2H9/2 energy levels. The energy transfer from Yb 31 to Er 31 can be described with the help of the energy level diagram sketched in Fig. 4. The process were indicated here: the energy overlap between the 2F5/2(Yb 31) and 4I11/2(Er 31) energy level was the basic fact that allows the ef®cient resonant energy transfer between both ions [20]. Nevertheless, the absorption (associated with the 2F7/2 ! 2F5/2 transition) of Yb 31 transitions is broader than the corresponding Er 31 transitions. In this way it is possible to perform selective excitation of the Yb 31 ions (in the wavelength range 900±950 nm) and realize energy transfer from Yb 31 ions to Er 31 ions after excitation of the Yb 31 ions. After the selective excitation of the 2F5/2(Yb 31) level, it may relax radiatively to 2F7/2 ground state, producing luminescence in the range 920±1100 nm, or transfer energy to Er 31 ions and excited it to 4I11/2 level from ground state,
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
2015
Fig. 2. Fluorescence spectrum of Er/Yb codoped NaY(WO4)2 crystal upon excitation at 974 nm (LD).
Fig. 3. log±log plot of upconversion luminescence (the slope for 552, 530 nm green light and 655 red lights are 1.99, 2.05 and 1.91, respectively).
Fig. 4. Schematic energy level diagram of Er/Yb codoped NaY(WO4)2 crystal.
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Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017
Fig. 5. Emission spectra of Yb/Er codoped NaY(WO4)2 crystal.
according to the energy cross-transfer mechanism: 2
F5=2 Yb31 1 4 I15=2 Er31 ! 2 F7=2 Yb31 1 4 I11=2 Er31
shown as process a From the 4I11/2 erbium level the energy can be transferred back to the Yb 31 or relax within the Er 31 ions. This relaxation produces luminescence at around 1000 nm (associated with the 4I11/2 ! 4I15/2 transition), and at around 1500 nm (associated with the 4I13/2 ! 4I15/2 transition) after population of the metastable erbium level ( 4I13/2) via a nonradiative connection. The emission of 1.5 mm can be easily measured. The 1.0 mm is very weak and easily is hidden by the broader Yb 31 emission within similar wavelength range. Er 31 ions at 4I13/2 can absorb another photon from Yb 31 and be excited to 4F9/2 (shown as process b), then red light near 650 nm produced through 4 F9/2 ! 4I15/2 transition. Er 31 at 4I11/2 also can absorb energy from adjacent Yb 31 again and be excited to 2H11/2 according to the energy crosstransfer mechanism: 2
F5=2 Yb31 1 4 I11=2 Er31 ! 2 F7=2 Yb31 1 2 H11=2 Er31
shown as process c 4 H11/2 ! 4I15/2(Er 31) transitions generates 530 nm green light. Parts of erbium ions excited to the 4H11/2 also relaxed nonradiatively to the 4S3/2 level and then relaxed to ground state from where green emission at around 552 nm is observed. In NYW crystal, 4S3/2 level has relative long energy level lifetime and 4S3/2 ! 4I15/2 transition has relative larger integral emission cross section, which are suitable for the accumulating of population of 4S3/2 level. The above analysis showed that red light and green light all are two-photon process. Er 31 at 4F9/2 also can absorb energy from adjacent Yb 31 again and be excited to 4H9/2 according to the energy cross-
transfer mechanism: 2
F5=2 Yb31 1 4 F9=2 Er31 ! 2 F7=2 Yb31 1 2 H9=2 Er31
shown as process d Er 31 ions at 2H9/2 level relax to the ground state and emit 407 nm light. Some ions will nonradiatively decay to the 4 F3/2 and then transit to ground state with 450 nm luminescence. For the 407 nm emission, it is a three-photon process. In order to understand the mechanism of the luminescence, we measured the photoexcited luminescence spectra. When emission wavelength was ®xed at 530 nm, and the excitation wavelength is tuned from 250 to 500 nm, the signal at 363, 406, 450, and 488 nm are observed (Fig. 5). The signal at 363 nm is the most intense. As indicate that the ions at 4G11/2, 4H9/2, 4F5/2, 4F7/2 levels can nonradiatively decay to the 2H11/2 levels. Also the below cross-relaxation process is indicated: 4
I9=2 Er31 1 4 G11=2 Er31 ! 22 H11=2 Er31
shown as process e When the emission wavelength was ®xed at 552 nm, and the excitation wavelength is turned from 250 to 530 nm, the signal at 363, 406, 450, 488 and 533 nm are observed. The signal at 363 and 533 nm are the most intense. As indicate that 4S3/2 level was populated mainly through nonradiative decaying of 2H11/2 level and the crossrelaxation of 4G11/2 level also produce population of 4S3/2. The 530 nm emission at 363 nm excitation was more intense than emissions at 450 and 407 nm excitations, also for the 552 nm emission. Otherwise the 552 nm emission at 363 nm excitation and 488 nm excitation show the almost the same intensity. As is impossible if only nonradiative relaxation exist. When the emission was located at 650 nm, no excitation signal was found in 250±630 nm. As indicated 650 nm emission was mainly from the transit of lower levels to 2 F9/2 level, not from the cross-relaxation of higher energy
Z.X. Cheng et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2011±2017 2
levels to F9/2 level. When the sample was excitated by 363, 406, and 450 nm, no red light was detected, which indicated no three-photon process exist for 650 nm emission. 4. Conclusions Er/Yb codoped NaY(WO4)2 crystals with good optical quality can be grown by using CZ pulling method. The optical parameters of Er 31 ions in the codoped NaY(WO4)2 crystals were obtained as V 2 18:1 £ 10220 cm2 ; V 4 2:59 £ 10 2 20 cm2 and V 6 1:21 £ 10220 cm2 : Upconversion luminescences of 552 nm green light, 530 nm red light and 407 nm violet light were obtained when the sample was pumped by 974 nm LD. The red light and green light emissions all were two-photon processes and the 407 nm emission is three-photon process. Acknowledgements The author would like to thank Prof. Zhaohe Yang for transmittance measurements. References [1] S. Tacheo, P. Laporta, S. Longhi, O. Svelto, C. Svelto, Appl. Phys. B 63 (1996) 425. [2] N.P. Bames, W.J. Rodriguez, B.M. Walsh, J. Opt. Soc. Am. B 13 (1996) 2872.
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[3] A.G. Antipenko, N.V. Aetem'ev, A.A. Betim, V.R. Kamenskii, W.P. Novikov, V.G. Plotnichenko, I.V. Skipachev, G.E. Snopatim, Quant. Elect. 25 (1995) 498. [4] D.W. Nam, R.G. Waarts, Laser Focus World, August 49 (1994). [5] A.J. Silversmith, W. Leth, R.M. Macfarlane, J. Opt. Soc. Am. A3 (1996) 128. [6] Z. Cheng, S. Zhang, H. Chen, J. Cryst. Growth 222 (2001) 797. [7] K. Hirao, S. Todoroki, N. Sogan, J. Non-Cryst. Solids 40 (1992) 143. [8] A.A. Kaminskii, H.J. Eichler, K. Ueda, N.V. Klassen, B.S. Redkin, et al., Appl. Opt. 38 (1999) 4533. [9] Z. Cheng, S. Zhang, H. Chen, Jpn. J. Appl. Phys. (2001) 40. [10] B.R. Judd, Phys. Rev. 127 (1962) 750. [11] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. [12] J.L. Adm, M. Matecki, H. L'hegoualch, B. Jacuquier, Eur. J. Solid State Inorg. Chem. 31 (1994) 337. [13] A.A. Kaminskii, Crystalline Laser: Physical Processes and Operating Schemes, CRC Press, Boca Raton, FL, 1996. [14] R. Reis®eld, C.K. Jorgenson, Lasers and Excited States of Rare Earth, Springer, Berlin, 1977. [15] L.J.F. Broer, C.J. Gorter, J. Hoogschagen, Physica 11 (1945) 231. [16] G. Gashurov, O.J. Sovers, J. Chem. Phys. 50 (1969) 429. [17] W.T. Carnall, P.R. Fields, K. Rajnak, J. Chem. Phys. 49 (1968) 4424. [18] A.A. Kaminskii, G. Boulon, M. Buoncristiani, B. Dibartolo, A. Kornienko, V. Mironov, Phys. Stat. Sol. A 141 (1994) 471. [19] W.F. Krupke, IEEE J. Quant. Electron. Q E-10 (1974) 450. [20] E. Cantelar, F. Cusso, Appl. Phys. B 69 (1999) 29.