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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 20 — Oct. 1, 2007
  • pp: 13421–13433
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Analysis on fluorescence intensity reverse photonic phenomenon between red and green fluorescence of oxyfluoride nanophase vitroceramics

Xiaobo Chen, Zengfu Song, Lili Hu, Junjie Zhang, Ce Wang, Lei Wen, and Song Li  »View Author Affiliations


Optics Express, Vol. 15, Issue 20, pp. 13421-13433 (2007)
http://dx.doi.org/10.1364/OE.15.013421


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Abstract

An interesting fluorescence intensity reverse photonic phenomenon between red and green fluorescence is investigated. The dynamic range ∑ of intensity reverse between red and green fluorescence of Er(0.5)Yb(3):FOV oxyfluoride nanophase vitroceramics, when excited by 378.5nm and 522.5nm light respectively, is about 4.32×102. It is calculated that the phonon-assistant energy transfer rate of the electric multi-dipole interaction of {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer of Er(0.5)Yb(3):FOV is around 1.380×108s-1, which is much larger than the relative multiphonon nonradiative relaxation rates 3.20×105s-1. That energy transfer rate for general material with same rare earth ion’s concentration is about 1.194×105s-1. These are the reason to emerge the unusual intensity reverse phenomenon in Er(0.5)Yb(3):FOV.

© 2007 Optical Society of America

1. Introduction

Nano-technology has been developed rapidly since 1980’s [1–7

1. R. P. Feynman, “There’s plenty of room at the bottom,” Engineering and Science 23, 22–23 (1960).

]. It fast forms a new research fields which has splendid subject content and great application prospect. The particularities of nano-material structure, such as small sized particle and large specific surface area, and a series of new effects, including small size effect, interface effect, quantum size effect, and macroscopic quantum tunnel effect, decide that nanomaterials feature many unique properties. It makes them distinguished from traditional materials [2–6

2. P. N. Prasad, Nanophotonics, (N. J. Hoboken, Wiley-Interscience, 2004). [CrossRef]

]. Among these are the further enhanced optical properties of the material [7

7. B. K. Zhou, Y. Z. Gao, and Z. R. Chen, Laser Principle, (Beijing: National Press, 2004).

,8

8. A. Lin, D. H. Son, I. H. Ahn, G. H. Song, and W. T. Han, “Visible to infrared photoluminescence from gold nanoparticles embedded in germano-silicate glass fiber,” Opt. Express 15, 6374–6379 (2007). [CrossRef] [PubMed]

]. Photonics, following electronics, has become an important mainstay of modern science [9

9. Q. M. Wang, Photonics Technology, (Beijing,Tsinghua University Press, 2002).

]. Therefore the investigation on the photonics of nanomaterial is significant and valuable.

As is well known, rare earth luminescence nanomaterial can be widely used in the fields of luminescence, display, optical information transfer, solar energy photoelectric conversion, X-ray image, laser, scintillation etc [6

6. Y. Z. Shen, C. S. Friend, Y. Jiang, D. Jakubczyk, J. Swiatkiewicz, and P. N. Prasad, “Nanophotonics: Interactions, materials, and applications,” J. Phys. Chem. B 104, 7577–7587 (2000). [CrossRef]

,7

7. B. K. Zhou, Y. Z. Gao, and Z. R. Chen, Laser Principle, (Beijing: National Press, 2004).

]. Especially it is the supporting material for display, human medicine and health care, and illumination, and plays an increasingly important part in modern science and human society [2

2. P. N. Prasad, Nanophotonics, (N. J. Hoboken, Wiley-Interscience, 2004). [CrossRef]

,3

3. M. Grundmann, Nano-optoelectronics: concepts, physics, and advices, (Berlin: New York, Springer, 2002).

]. In recent years, the fluorescence properties of rare earth nanomaterial have been progressively studied worldwide [10

10. U. H. Kynast, M. M. Lezhnina, and H. Katker, “Potential of nano-sized rare earth fluorides in optical applications,” Solid State Phenomena 106, 93–102 (2005). [CrossRef]

]. So far, most of rare earth luminescence nanomaterials are powders in form. The nanophase vitroceramics material, in which the nano-crystals are inlaid in the matrix glass, has attracted much attention due to its characteristic properties and very stable structure. Rare earth ions-doped oxyfluoride nanophase vitroceramics is just one kind of valuable nanomaterials [11

11. Y. H. Wang and J. Ohwaki, “New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion,” Appl. Phys. Lett. 63, 3268–3270 (1993). [CrossRef]

,12

12. X. B. Chen, Y. L. Liu, and N. Sawanobori, “Raman and x-radiate diffraction study about material property of oxyfluoride vitroceramics and glass,” Proc. SPIE 4221, 83–87 (2000). [CrossRef]

].

In the present paper, the photonics process of the rare earth ions-doped oxyfluoride nanophase vitroceramics material is studied. A new interesting unusual fluorescence intensity reverse phenomenon between red and green fluorescence is found.

2. Samples

The oxyfluoride glass is manufactured first in high temperature. The oxyfluoride glass samples were made from the oxide of Silicon SiO2, and the fluoride of Plumbum PbF2, Zinc ZnF2, Lutetium LuF3, Ytterbium YbF3, and Erbium ErF3. All raw materials are high pure reagent and are put in platinum crucible to be heated 100 minutes at about 900°C. Then it is cooled fast at iron plate to get oxyfluoride glass. The oxyfluoride vitroceramics is obtained by 7 hours annealed at about the glass transition temperature Tg=389°C.

The samples used in our experiments are rare earth ions-doped oxyfluoride nanophase vitroceramics(FOV) and oxyfluoride glass(FOG). Three samples of oxyfluoride vitroceramics(FOV) are (1) Er(0.5)Yb(3):FOV, (2) Er(0.5)Yb(1):FOV, and (3) Er(0.5):FOV. Three samples of oxyfluoride glass(FOG) are (4) Er(0.5)Yb(3):FOG, (5) Er(0.5)Yb(1):FOG, and (6) Er(0.5):FOG. Among which Er(0.5)Yb(3):FOV is doped with Er3+ and Yb3+ ions at the concentrations of 0.5 mol % and 3 mol % respectively. For a comparison with conventional materials, the ZBLAN fluoride glass (7) Er(0.3)Yb(3):ZBLAN and (8) Er(0.3):ZBLAN were selected as representative samples to investigate their photonic phenomenon. All of samples are about 1 mm thick.

3. Experiment setup

The Stokes fluorescence spectra were measured by using a fluorescence spectrophotometer equipped with a double-grating monochromator (JY-ISA, Fluorolog-Tau-3). A traditional Xe lamp was used as the light source of the fluorescence spectrophotometer. The observation direction of the fluorescence was nearly along the incident direction of the pumping light. The experimental conditions were held unchanged to ensure that the measured results are comparable.

4. Excitation dynamics

The cross-energy-transfer nonlinear photonic effect of Yb3+Er3+ co-doped and Er3+ mono-doped oxyfluoride nanophase vitroceramics materials was studied first [11

11. Y. H. Wang and J. Ohwaki, “New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion,” Appl. Phys. Lett. 63, 3268–3270 (1993). [CrossRef]

,14

14. S. Hinjosa, M. A. Meneses-Nava, O. Barbosa-Garcia, L. A. Diaz-Torres, M. A. Santoyo, and J. F. Mosino, “Energy back transfer, migration and energy transfer (Yb-to-Er and Er-to-Yb) processes in Yb,Er : YAG,” J. Lumin. 102, 694–698(2003). [CrossRef]

].

The Stokes excitation spectra were measured in the experiments. Figure 1(a) shows the excitation spectra of 543.7nm 4S3/24I15/2 and 667.1nm 4F9/24I15/2 fluorescence of (1) Er(0.5)Yb(3):FOV Figure 1(b) shows the excitation spectra of 543.7nm and 667.1nm fluorescence of (3) Er(0.5):FOV. It was found that there are several excitation peaks of 2G7/2, 4G9/2, 4G11/2, (2G4F2H)9/2, 4F3/2, 4F5/2, 4F7/2, and 2H11/2, which are positioned at the wavelengths of 355.3nm, 363.7nm, 378.5nm, 405.0nm, 441.0nm, 449.0nm, 486.5nm, and 522.5nm, respectively. The wavelengths of excitation peaks of other samples are quite near to those of Er(0.5)Yb(3):FOV.

Fig. 1. The excitation spectra of 667.1nm and 543.7nm fluorescence of (a) Er(0.5)Yb(3):FOV and (b) Er(0.5):FOV oxyfluoride nanophase vitroceramics.

All the relative excitation spectral peak intensities F of 543.7nm 4S3/24I15/2 and 667.1nm 4F9/24I15/2 fluorescence for all samples are measured. First, it is found that the ratios of obtained energies from 2G7/2, 4G9/2, 4G11/2, (2G4F2H)9/2, 4F3/2, 4F5/2, 4F7/2, and 2H11/2 levels are basically constant for the 543.7nm and 667.1nm fluorescence of samples (3) Er(0.5):FOV, (5) Er(0.5)Yb(1):FOG, (6) Er(0.5):FOG, (7) Er(0.3)Yb(3):ZBLAN and (8) Er(0.3):ZBLAN. Their luminescence dynamics is the very obvious linear luminescence dynamic processes.

It is interesting to note that the ratios of obtained energies from 2G7/2, 4G9/2, 4G11/2, (2G4F2H)9/2, 4F3/2, 4F5/2, 4F7/2, and 2H11/2 levels are quite different for the 543.7nm and 667.1nm fluorescence of Er(0.5)Yb(3):FOV. For the 543.7nm fluorescence it is easy to obtain energies from 4F7/2 and 2H11/2 levels, while for the 667.1nm fluorescence it is easy to obtain energies from 4G9/2 and 4G11/2 levels. It is illustrated that the luminescence dynamics of Er(0.5)Yb(3):FOV is a very clear nonlinear luminescence dynamic process.

Surprisingly, however, the extent of nonlinear luminescence dynamics for the (2) Er(0.5)Yb(1):FOV is reduced by a factor of 500 relative to Er(0.5)Yb(3):FOV. Even when the concentrations of Er3+ or Yb3+ ions and their base-matrix are entirely the same, the extent of nonlinear luminescence dynamics of Er(0.5)Yb(3):FOG is reduced by more than one hundredfold relative to Er(0.5)Yb(3):FOV. They are basically the linear luminescence dynamics for (2) Er(0.5)Yb(1):FOV and (4) Er(0.5)Yb(3):FOG.

These mean that the conventional Er3+Yb3+ co-doped materials do not at all have the nonlinear luminescence dynamic process which is only found in Er(0.5)Yb(3):FOV.

5. Experiment and results of the fluorescence intensity reverse property between red and green fluorescence

In succession, the Stokes emission spectra of Yb3+Er3+ co-doped and Er3+ single-doped oxyfluoride nanophase vitroceramics Er(0.5)Yb(3):FOV and Er(0.5):FOV were measured. As is shown in Fig. 2, the Stokes emission spectra of 4G11/2 level has several fluorescence transitions, (2G4F2H)9/24I15/2, 2H11/24I15/2, 4S3/24I15/2 and 4F9/24I15/2, whose peak wavelengths are (406.9nm, 411.1nm), (522.5nm, 528.7nm), (543.7nm, 550.2nm), and (655.2nm, 667.1nm), respectively. It was found that the Stokes emission spectra of 2H11/2 level has only two fluorescence transitions, 4S3/24I15/2 and 4F9/24I15/2. Table 1 lists the relative intensities of Stokes emission spectra of all the eight samples.

It can be seen from Fig. 2(a) that an interesting unusual phenomenon for the (1) Er(0.5)Yb(3):FOV oxyfluoride nanophase vitroceramics occurs. When the 2H11/2 level was excited by 522.5nm visible light, a common fluorescence phenomenon was observed that the 543.7nm green fluorescence of 4S3/2 level is strong, while the 667.1nm red fluorescence of 4F9/2 level is weak. However, when the 4G11/2 level was excited by 378.5nm ultraviolet light, an interesting unusual red and green fluorescence intensity reverse phenomenon was seen, showing that the 667.1nm red fluorescence of 4F9/2 level is strong, while the 543.7nm green fluorescence of 4S3/2 level is weak. We use F[4S3/2](4G11/2), F[4F9/2](4G11/2), F[4S3/2](2H11/2) and F[4F9/2](2H11/2) to represent the fluorescence intensities of 4S3/2, and 4F9/2 levels when the 4G11/2 and 2H11/2 levels are excited, respectively. It is easy to identify the common intensity ratio between green and red fluorescence as α=[F(4S3/2)/F(4F9/2)](2H11/2), which is the ratio of F[4S3/2](2H11/2) to F[4F9/2](2H11/2), when the 2H11/2 level is excited. It is convenient to identify the unusual intensity reverse ratio between red and green fluorescence as γ=[F(4F9/2)/F(4S3/2)](4G11/2), which is the ratio of F[4F9/2](4G11/2) to F[4S3/2](4G11/2), when the 4G11/2 level is excited. The dynamic range ∑ of intensity reverse between red and green fluorescence can be expressed as ∑=γ×α. It was found that the dynamic range ∑ of (1) Er(0.5)Yb(3):FOV reached the level of ∑=4.32×102.

It can be seen from Fig. 2(b) that there is not at all an intensity reverse phenomenon between red and green fluorescence for the (3) Er(0.5):FOV. Whenever the 2H11/2 level is excited by 522.5nm visible light or the 4G11/2 level is excited by 378.5nm ultraviolet light, both of them exhibit the common fluorescence phenomenon, namely the 543.7nm green fluorescence of 4S3/2 level is strong, while the 667.1nm red fluorescence of 4F9/2 level is weak. The dynamic range ∑ of (3) Er(0.5):FOV was calculated to be about ∑=4.05×10-1, which is obviously 1000 times smaller than that of (1) Er(0.5)Yb(3):FOV.

Fig. 2. The emission spectra of 378.5nm and 522.5nm absorption energy levels of (a) Er(0.5)Yb(3):FOV and (b) Er(0.5):FOV oxyfluoride nanophase vitroceramics.

Table 1. Relative fluorescence intensity F of Stokes emission spectra, the common intensity ratio α=[F(4S3/2)/F(4F9/2)](2H11/2) between green and red fluorescence when the 2H11/2 level is excited, the unusual intensity reverse ratio γ=[F(4F9/2)/F(4S3/2)](4G11/2) between red and green fluorescence when the 4G11/2 level is excited, and the dynamic range ∑=γ×α of fluorescence intensity reverse between red and green fluorescence. The samples number N represent the used samples (1) Er(0.5)Yb(3):FOV, (2) Er(0.5)Yb(1):FOV, (3) Er(0.5):FOV, (4) Er(0.5)Yb(3):FOG, (5) Er(0.5)Yb(1):FOG, (6) Er(0.5):FOG, (7) Er(0.3)Yb(3):ZBLAN and (8) Er(0.3):ZBLAN respectively.

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Table 1 lists the relative fluorescence intensity F of Stokes emission spectra and the dynamic range ∑ of intensity reverse between red and green fluorescence of all the eight samples. Clearly, there is not obvious fluorescence intensity reverse between red and green fluorescence for the 7 samples, (2) Er(0.5)Yb(1):FOV, (3) Er(0.5):FOV, (4) Er(0.5)Yb(3):FOG, (5) Er(0.5)Yb(1):FOG, (6) Er(0.5):FOG, (7) Er(0.3)Yb(3):ZBLAN and (8) Er(0.3):ZBLAN. It is only the (1) Er(0.5)Yb(3):FOV oxyfluoride nanophase vitroceramics that exhibits the clear unusual phenomenon. The dynamic range ∑ of (1) Er(0.5)Yb(3):FOV is 100 to 1000 times larger than those of other materials or samples.

6. Mechanism analysis

A careful analysis of the luminescence dynamics of Er3+Yb3+ codoped system can reveal the physical mechanism behind the intensity reverse between red and green fluorescence of (1) Er(0.5)Yb(3):FOV. When samples are excited by 378.5nm ultraviolet light, the Er3+ ions are excited to the 4G11/2 level. There are primarily two kinds of population relaxation passages for the 4G11/2 level [15

15. J. Frenkel, “On the Transformation of light into Heat in Solids,” Phys. Rev. 37, 17–44(1931). [CrossRef]

]. One is multi-phonon nonradiative relaxation, a step by step downward process. The relaxation rate can be calculated by the theory of multi-phonon nonradiative relaxation [16–19

16. L. A. Riseberg, W. B. Gandrud, and H. W. Moos, “Multiphonon Relaxation of Near-Infrared Excited States of LaCl3:Dy3+,” Phys. Rev. 159, 262–266 (1967). [CrossRef]

]. The smaller the energy gap between two adjacent levels, the larger the multi-phonon nonradiative relaxation. Both the 4S3/2 and 4F9/2 levels may gain population by multi-phonon nonradiative relaxation. Another population relaxation passage is cross energy transfer which is governed by the energy transfer theory of rare earth [20–23

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

]. The mechanism behind this process is electric multipole interaction and exchange interaction. The energy transfer rate would be higher if the energy match between a pair of energy levels is better, and the J-O intensity parameters Ωt and the doubly reduced matrix elements of tensor operators U(t) are greater. Because the concentration of Er3+ ions is low, the energy cross transfer between Er3+ ions can be neglected in order to simplify the problem. However, since the concentration of Yb3+ ions is high, the energy cross transfer between Yb3+ and Er3+ ions can be intense. It is revealed from a careful research that there are two apparent cross energy transfer passages, {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} and {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} for Yb3+ and Er3+ ions co-doped systems, respectively. The schematic diagram of cross-energy-transfer processes in Yb3+ and Er3+ co-doped systems is shown in Fig. 3. These cross energy transfer passages can cause part of the populations at 4G11/2 and (2G4F2H)9/2 levels to jump over 2H11/2 and 4S3/2 levels, and subsequently enter the 4F9/2 level directly. As a result, the luminescence dynamics of the Yb3+ and Er3+ ions co-doped system is different to some extent from the Er3+ ions mono-doped system.

Fig. 3. The schematic diagram of cross-energy-transfer processes in Yb3+ and Er3+ co-doped systems. The solid line is absorption or energy transfer. The dashed straight line is fluorescence.

It is well known for the electric multipole interaction that the energy transfer rate is governed by the J-O intensity parameters Ωt, the doubly reduced matrix elements of tensor operators U(t), the distance R between the rare earth ions, the energy match between a pair of energy levels, and so forth. For the Er3+ ion doped material, the doubly reduced matrix elements of tensor operators U(t) are exactly the same, and the J-O intensity parameters Ωt are similar. Therefore, the distance R between the rare earth ions is a key factor. In fact, Ref. [24

24. S. L. Zhao and Z. Xu, “Donor concentration dependence of upconversion luminescence in YLiF4:Er3+Yb3+,” Spectrosc. Spect. Anal. 25, 1933–1937 (2005).

] finds that for YLiF4 crystal the energy transfer between Yb3+ and Er3+ ions is enhanced greatly when the concentration of Yb3+ ions is higher than 6%.

It is known that the relation [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

] between the concentration ρ of the doping rare earth ions and the distance R between the doping rare earth ions is ρ ∝ R-3, so the energy transfer rate WET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions can be described as follows [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

]

WET(dd)=231gigkπ2e4h2cχR6t=2,4,6ΩtΨiU(t)ΨJ2×t=2,4,6ΩtΨkU(t)Ψe2SR6ρ2
(1)
WET(dq)=11.41gigkπ2e4h2cχR8t=2,4,6ΩtΨiU(t)ΨJ2×49[4fC(2)4frΨkU(2)Ψe]2SR8ρ83
(2)
WET(qq)=48.71gigkπ2e4h2cχR1049[4fC(2)4frΨiU(2)ΨJ]2
×49[4fC(2)4frΨkU(2)Ψe]2SR10ρ103
(3)
χ=(n2+23n)4
(4)
fc2f=(2815)1/2
(5)
S=ΓΓ2+Δυ2
(6)
ΨlrΨk2=ΩλΨlU(λ)Ψk2
(7)
ΨlrtrtΨk2=49[fc2fr2ΨlU(2)Ψk]2
(8)

Where Ωλ is the Judd-Ofelt parameter, n is the refractive index, Γ is the line width, S is the overlap integral, Δυ is the mismatch between the two energy transfer.

Formulas (1–8) mean that the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions are proportional to ρ2, ρ8/3 and ρ10/3 respectively. In general [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

], when distance R = 0.8nm, the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions possess a near and similar energy transfer probability [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

]. On the contrary, when R > 1.0nm, the dipole-dipole interaction is obviously stronger than the dipole-quadruple and quadruple-quadruple interactions [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

], whereas when R becomes smaller than 0.8nm, the quadruple-quadruple interaction will gradually become stronger than the dipole-dipole and dipole-quadruple interactions. Taking account of the exchange interaction, the energy transfer probability would increase sharperly when the distance R decreases further [20

20. R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

,25

25. S. Y. Zhang, Theory of Rare Earth spectroscopy, (Chang Chun: Jilin Science Press, 1991).

].

In our experiment, the absorption of Er(0.5):FOV oxyfluoride nanophase vitroceramics has been measured. According to the well-known J-O theory of Prof. Judd [26

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

] and Ofelt [27

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

], the spectrum line strength S, spontaneous radiative transition rate A, and oscillator strength f can be calculated for both electric-dipole and magnetic-dipole transition.

Sed(aJ,bJ′)=e2t=2,4,6ΩtΨU(t)Ψ′2
(9)
AED=64π4v3e23h(2J+1)c3×n(n2+2)29t=2,4,6ΩtΨUtΨ′2
(10)
Smd(ΨJ,Ψ′J)=e24m2c2fNΨJL+2SfNΨ′J2
(11)
AMD(ΨJ,Ψ′J)=64π4v̄33hc3(2J+1)n3Smd(aj,bj′)
(12)
f(aj,bj′)=mc2Nπe2OD(λ)×2.303d×λ2dλ
(13)
f(aj,bj′)=8π2mv3hn2e2(2J+1)[χedSed(aj,bj′)+χmdSmd(aj,bj′)]
(14)
τ=1A+W
(15)

Combining Judd-Ofelt calculation and the measured value of oscillator strength from the ground state, the J-O parameters Ωt(t=2,4,6) can be deduced by general fitting method. The calculated J-O parameters are Ω2=2.168×10-20cm2, Ω4=1.276×10-20cm2, Ω6=1.705×10-20cm2; rms=0.307×10-6. It is easy to calculate the whole spontaneous radiative transition rate A between all excited states. Then the lifetime τ of the several luminescent energy levels of Er(0.5):FOV was measured out in our experiment. It is also easy to calculate the multiphonon nonradiative relaxation rates W of these several luminescent energy levels based on the above mentioned J-O theory.

According to the Ref [18

18. T. Miyakawa and D. L. Dexter, “Phonon Sidebands, Multiphonon Relaxation of Excited States, and Phonon-Assisted Energy Transfer between Ions in Solids,” Phys. Rev. B 1, 2961–2969 (1970). [CrossRef]

,21

21. T. Miyakawa and D. L. Dexter, “Cooperative and Stepwise Excitation of Luminescence: Trivalent Rare-Earth Ions in Yb3+-Sensitized Crystals,” Phys. Rev. B 1, 70–80 (1970). [CrossRef]

] of Prof. T. Miyakawa and Prof. D. L. Dexter, the multiphonon nonradiative relaxation rates Wp can be expressed as

Wp=W0eαΔE
(16)

The phonon-assistant energy transfer rate WPET can be expressed as

WPET=WETeβΔE
(17a)
β=αγ
(17b)
γ=1ħωln(1+gAgD)
(17c)

where ΔE is the energy gap between two adjacent energy levels, W0 is the transition probability when the energy gap equals zero, p is the number of phonons, ħω is the energy of phonon, g is the coupling constant between electron and phonon, gA and gD is the coupling constant of acceptor and donor. According to formula (16), W0 and α can be deduced by general fitting method. Finally, it is easy to calculate all the multiphonon nonradiative relaxation rates Wp of all energy levels of Er3+ ion. It is found that the multiphonon nonradiative relaxation rates Wp from 4G11/2(Er3+) to lower levels (2G4F2H)9/2(Er3+) and 4F3/2(Er3+) are 3.20×105s-1 and 1.41×103s-1 respectively. That for (2G4F2H)9/2(Er3+) to lower levels 4F3/2(Er3+) and 4F5/2(Er3+) are 2.08×105s-1 and 6.61×104s-1 respectively.

As is well known, the electric multi-dipole interaction exists for all kinds of materials. It is significant to compare the energy transfer rates of electric multi-dipole interaction with the multiphonon nonradiative relaxation rates. It is reasonable to adopt that the energy transfer {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} will outstrip the multiphonon nonradiative relaxation {4G11/2(Er3+) ⇒ (2G4F2H)9/2(Er3+)} to play main action when the energy transfer rates of electric multi-dipole interaction equal 10.00×105s-1. It is also reasonable to consider that the energy transfer {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} will outstrip the multiphonon nonradiative relaxation {(2G4F2H)9/2(Er3+)⇒4F3/2(Er3+)} to play main action when it equal 7.00×105s-1. In addition, it is easy to find that the squares of the matrix elements of the unit tensor operators {U 2(2), U 2(4), U 2(6)} for 4G11/2(Er3+)→4F9/2(Er3+) transition are {0.4283, 0.0372, 0.0112}. Those for (2G4F2H)9/2(Er3+)→4F9/2(Er3+) are {0.0075, 0.0261, 0.0469}. And those for 2F7/2(Yb3+)→2F5/2(Yb3+) are {0.1225, 0.4082, 0.8571}. According to the formulas (1) to (8) and (17), the variation of the phonon-assistant energy transfer rate WPET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions that depend on the distance R can be calculated. Fig. 4(a) gives the results of the phonon-assistant energy transfer rate WPET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions for {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer, while Fig. 4(b) gives the results for {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer. It is interesting to note that the energy transfer rate is small and nearly unchanged when the distance R is larger than 1nm. However, when R is smaller than 1nm, the energy transfer rate will increase very rapidly. For the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions of {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer, the points at which the phonon-assistant energy transfer rate WPET is about 10.00×105s-1 are positioned at 0.22nm, 0.45nm and 0.47nm. For the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions of {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer, the points at which the phonon-assistant energy transfer rate WPET is about 7.00×105s-1 are positioned at 0.22nm, 0.36nm and 0.39nm. Their variation of energy transfer rates are all about 100 times as much when distance R is enlarged for 0.3nm.

Fig. 4. The variation of the phonon-assistant energy transfer rate WPET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions dependent on the distance R for (a) {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} and (b) {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} energy transfer.
Fig. 5. The variation of the distance R between Er3+ and Yb3+ ions dependent on the mole concentration of Yb3+ ions when the mole concentration of Er3+ ion is fixed at 0.5%. The solid line, dash line and dotted line represent that their crystal volume fraction of nanocrystal phase to whole material is 10%, 1% and 30%.
Fig. 6. The typical variation of the phonon-assistant energy transfer rate WPET of the electric multi-dipole interaction of {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)}(Solid line) and {(2GF2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)}(Dash line) energy transfers dependent on mole concentration of Yb3+ ions when the crystal volume fraction equals to (a) 10% and (b) 100%, meanwhile the mole concentration of Er3+ ion is fixed at 0.5%.

The structure of rare earth ion-doped oxyfluoride nanophase vitroceramics has been investigated intensively. And remarkable progress has been made. The nature of the nanocrystalline phase is the low crystal volume fraction in the residual glass. However, the real environment in which the Er3+ ion is situated is not yet well defined. As a result, it is now generally accepted that the nanocrystals are Er3+-doped PbF2, which is about 20nm large[11

11. Y. H. Wang and J. Ohwaki, “New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion,” Appl. Phys. Lett. 63, 3268–3270 (1993). [CrossRef]

,12

12. X. B. Chen, Y. L. Liu, and N. Sawanobori, “Raman and x-radiate diffraction study about material property of oxyfluoride vitroceramics and glass,” Proc. SPIE 4221, 83–87 (2000). [CrossRef]

]. The average size of the crystal cell is measured out with a lattice parameter a=0.573 nm [28

28. M. Beggiora, I. M. Reaney, and M. S. Islam, “Structure of the nanocrystals in oxyfluoride glass ceramics,” Appl. Phys. Lett. 83, 467–469 (2003). [CrossRef]

]. There is 60 at% Er3+ substituted for Pb in cubic PbF2 with F-1 interstitial compensation. Thus if more than one rare earth ion is entered into a nanocrystal cell when the concentration of rare earth ions is high enough, the distance between rare earth ions would be smaller than the lattice parameter a=0.573 nm [28

28. M. Beggiora, I. M. Reaney, and M. S. Islam, “Structure of the nanocrystals in oxyfluoride glass ceramics,” Appl. Phys. Lett. 83, 467–469 (2003). [CrossRef]

]. In this case, the energy transfer rates of electric multi-dipole interaction would increase very rapidly and outstrip multiphonon nonradiative relaxation very much. It results in the very strong cross energy transfer passages {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} and {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} to produce the interesting phenomenon of unusual red and green fluorescence intensity reverse phenomenon.

R=0.62(NEr+NYb)(1/3)
(18)
Nre=ρM1Nay
(19)

where NEr and NYb is the number density of Er3+ and Yb3+ ions in units volume respectively, ρ is mass density, M is mole mass, Na is Avogadro’s constant, y is mole concentration. Figure 5 plots the variation of the distance R between Er3+ and Yb3+ ions dependent on the mole concentration of Yb3+ ions when the mole concentration of Er3+ ion is fixed at 0.5%. The three line denoted as 1%, 10% and 30% corresponding to that their crystal volume fraction [28

28. M. Beggiora, I. M. Reaney, and M. S. Islam, “Structure of the nanocrystals in oxyfluoride glass ceramics,” Appl. Phys. Lett. 83, 467–469 (2003). [CrossRef]

] of nanocrystal phase to whole material, including nanophase crystalline and residual glass, is 1%, 10% and 30%. It is clear that the distance R between Er3+ and Yb3+ ions is fall into the sensitive area to have large energy transfer rates when the mole concentration of Yb3+ ions is large. The Fig. 6(a) plot the typical variation of the phonon-assistant energy transfer rate WPET of the electric multi-dipole interaction dependent on the mole concentration of Yb3+ ions when the crystal volume fraction of nanocrystal phase to whole material is adopted to equal to 10% and the mole concentration of Er3+ ion is fixed at 0.5% [28

28. M. Beggiora, I. M. Reaney, and M. S. Islam, “Structure of the nanocrystals in oxyfluoride glass ceramics,” Appl. Phys. Lett. 83, 467–469 (2003). [CrossRef]

,30

30. F. Bao, Y. S. Wang, and Z. J. Hu, “Influence of Er3+ doping on microstructure of oxyfluoride glass-ceramics,” Mater. Res. Bull. 40, 1645–1653 (2005). [CrossRef]

]. It is clear that the energy transfer rate of the electric multi-dipole interaction increase very rapidly when the mole concentration of Yb3+ ions enhances. Especially at 3% mole concentration of Yb3+ ions, the phonon-assistant energy transfer rate WPET of {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} is about 1.380×108s-1, that of {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} is about 1.495×107s-1, which is much larger than the relative multiphonon nonradiative relaxation rates. It illustrates that the Er(0.5)Yb(3):FOV can have the unusual intensity reverse phenomenon between red and green fluorescence. However for general material which can be represented by 100% crystal volume fraction, the WPET of {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} is about 1.194×105s-1, that of {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} is about 0.151×105s-1, as is shown in Fig. 6(b). It illustrates that the general material could not have the unusual intensity reverse phenomenon between red and green fluorescence.

7. Conclusions

An interesting unusual red and green fluorescence intensity reverse phenomenon was observed for (1) Er(0.5)Yb(3):FOV. The dynamic range ∑ of intensity reverse between red and green fluorescence of (1) Er(0.5)Yb(3):FOV is 100 to 1000 times larger than those of other materials. Careful analysis proves that the mechanism behind this process is that because of the special nanometer microcrystal structure of oxyfluoride nanophase vitroceramics, the cross energy transfer {4G11/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} and {(2G4F2H)9/2(Er3+)→4F9/2(Er3+), 2F7/2(Yb3+)→2F5/2(Yb3+)} are largely enhanced, resulting in the unusual fluorescence intensity reverse phenomenon between red and green fluorescence.

Acknowledgments

This project was supported mainly by the Free Applying Project Foundation of the National Natural Science Foundation of China through Grant No. 10674019. The authors would like to thank Prof. Gang Hu, Prof. Guojian Yang, Prof. Jing Zhou, Prof. Zheng Zhao, Prof. Dahe Liu, Prof. Zhigang Zheng, Prof. Yafei Wang, Prof. Yuhua Liu, Prof. Yihong Wang, Prof. Guoan Cheng at Beijing Normal University; Prof. Jinguang Wu, Prof. Zizhao Gang, Prof. Chenjia Chen, Prof. Suitang Zhao, Prof. Guowen Wang, Prof. Q. H. Gong, Prof. Daohen Sun, Prof. Yinghua Zou at Peking University; and Prof. Pingxiang Wu at Fuzhou University.

References and links

1.

R. P. Feynman, “There’s plenty of room at the bottom,” Engineering and Science 23, 22–23 (1960).

2.

P. N. Prasad, Nanophotonics, (N. J. Hoboken, Wiley-Interscience, 2004). [CrossRef]

3.

M. Grundmann, Nano-optoelectronics: concepts, physics, and advices, (Berlin: New York, Springer, 2002).

4.

H. Masuhara, Nanophotonics: Integrating Photochemistry, Optics and Nano/Bio Materials Studies, (Elsevier, 2004).

5.

E. L. Wolf, Nanophysics and nanotechnology: an introduction to modern concepts in nanoscience, (Weinheim :Wiley-VCH Verlag, 2004).

6.

Y. Z. Shen, C. S. Friend, Y. Jiang, D. Jakubczyk, J. Swiatkiewicz, and P. N. Prasad, “Nanophotonics: Interactions, materials, and applications,” J. Phys. Chem. B 104, 7577–7587 (2000). [CrossRef]

7.

B. K. Zhou, Y. Z. Gao, and Z. R. Chen, Laser Principle, (Beijing: National Press, 2004).

8.

A. Lin, D. H. Son, I. H. Ahn, G. H. Song, and W. T. Han, “Visible to infrared photoluminescence from gold nanoparticles embedded in germano-silicate glass fiber,” Opt. Express 15, 6374–6379 (2007). [CrossRef] [PubMed]

9.

Q. M. Wang, Photonics Technology, (Beijing,Tsinghua University Press, 2002).

10.

U. H. Kynast, M. M. Lezhnina, and H. Katker, “Potential of nano-sized rare earth fluorides in optical applications,” Solid State Phenomena 106, 93–102 (2005). [CrossRef]

11.

Y. H. Wang and J. Ohwaki, “New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion,” Appl. Phys. Lett. 63, 3268–3270 (1993). [CrossRef]

12.

X. B. Chen, Y. L. Liu, and N. Sawanobori, “Raman and x-radiate diffraction study about material property of oxyfluoride vitroceramics and glass,” Proc. SPIE 4221, 83–87 (2000). [CrossRef]

13.

E. De la Rosa, P. Salas, L. A. Diaz-Torres, A. Martinez, and C. Angeles, “Strong visible cooperative up-conversion emission in ZrO2 : Yb3+ nanocrystals,” J. Nanosci. Nanotechnol. 5, 1480–1486 (2005). [CrossRef] [PubMed]

14.

S. Hinjosa, M. A. Meneses-Nava, O. Barbosa-Garcia, L. A. Diaz-Torres, M. A. Santoyo, and J. F. Mosino, “Energy back transfer, migration and energy transfer (Yb-to-Er and Er-to-Yb) processes in Yb,Er : YAG,” J. Lumin. 102, 694–698(2003). [CrossRef]

15.

J. Frenkel, “On the Transformation of light into Heat in Solids,” Phys. Rev. 37, 17–44(1931). [CrossRef]

16.

L. A. Riseberg, W. B. Gandrud, and H. W. Moos, “Multiphonon Relaxation of Near-Infrared Excited States of LaCl3:Dy3+,” Phys. Rev. 159, 262–266 (1967). [CrossRef]

17.

E. Cohen, L. A. Riseberg, and H. W. Moos, “Effective Density of Phonon States for NdCl3 from Vibronic Spectra and Applications to Ion-Lattice Interactions,” Phys. Rev. 175, 521–525 (1968). [CrossRef]

18.

T. Miyakawa and D. L. Dexter, “Phonon Sidebands, Multiphonon Relaxation of Excited States, and Phonon-Assisted Energy Transfer between Ions in Solids,” Phys. Rev. B 1, 2961–2969 (1970). [CrossRef]

19.

L. A. Riseberg and M. J. Weber, “Relaxation phenomena in rare earth luminescence,” in Progress in Optics, (Amsterdam, North Holland Publishing Co. 1975) Vol. 14.

20.

R. ReisfeldLasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]

21.

T. Miyakawa and D. L. Dexter, “Cooperative and Stepwise Excitation of Luminescence: Trivalent Rare-Earth Ions in Yb3+-Sensitized Crystals,” Phys. Rev. B 1, 70–80 (1970). [CrossRef]

22.

D. L. Dexter, “A Theory of Sensitized Luminescence in Solids,” J. Chem. Phys. 21, 836–850 (1953). [CrossRef]

23.

M. Inokuti and F. Hirayama, “Influence of Energy Transfer by the Exchange Mechanism on Donor Luminescence,” J. Chem. Phys. 43, 1978–1989 (1965). [CrossRef]

24.

S. L. Zhao and Z. Xu, “Donor concentration dependence of upconversion luminescence in YLiF4:Er3+Yb3+,” Spectrosc. Spect. Anal. 25, 1933–1937 (2005).

25.

S. Y. Zhang, Theory of Rare Earth spectroscopy, (Chang Chun: Jilin Science Press, 1991).

26.

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

27.

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

28.

M. Beggiora, I. M. Reaney, and M. S. Islam, “Structure of the nanocrystals in oxyfluoride glass ceramics,” Appl. Phys. Lett. 83, 467–469 (2003). [CrossRef]

29.

M. Tsuda, K. Soga, H. Inoue, and A. Makishima, “Comparison between the calculated and measured energy transfer rates of the 4S3/2 state in Er3+-doped fluorozirconate glasses,” J. Appl. Phys. 88, 1900–1906 (2000). [CrossRef]

30.

F. Bao, Y. S. Wang, and Z. J. Hu, “Influence of Er3+ doping on microstructure of oxyfluoride glass-ceramics,” Mater. Res. Bull. 40, 1645–1653 (2005). [CrossRef]

31.

Q. Song, X. Y. Wang, H. Chen, J. S. Gao, T. T. Wang, X. M. Zheng, C. R. Li, and C. L. Song, “Photoluminescence enhancement in Yb3+: Er3+ co-doped eutectic Al2O3 : SiO2 thin films by 980nm excitation,” Opt. Express 15, 3948–3954 (2007). [CrossRef] [PubMed]

32.

J. R. DiMaio, B. Kokuoz, and J. Ballato, “White light emissions through down-conversion of rare-earth-doped LaF3 nanoparticles,” Opt. Express 14, 11412–11417 (2006). [CrossRef] [PubMed]

OCIS Codes
(160.5690) Materials : Rare-earth-doped materials
(250.5230) Optoelectronics : Photoluminescence
(300.6280) Spectroscopy : Spectroscopy, fluorescence and luminescence
(300.6420) Spectroscopy : Spectroscopy, nonlinear
(160.4236) Materials : Nanomaterials

ToC Category:
Spectroscopy

History
Original Manuscript: August 14, 2007
Revised Manuscript: September 17, 2007
Manuscript Accepted: September 18, 2007
Published: September 28, 2007

Citation
Xiaobo Chen, Zengfu Song, Junjie Zhang, Lili Hu, Lei Wen, Ce Wang, and Song Li, "Analysis on fluorescence intensity reverse photonic phenomenon between red and green fluorescence of oxyfluoride nanophase vitroceramics," Opt. Express 15, 13421-13433 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-20-13421


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References

  1. R. P. Feynman, "There's plenty of room at the bottom," Engineering and Science 23, 22-23 (1960).
  2. P. N. Prasad, Nanophotonics, (N. J. Hoboken, Wiley-Interscience, 2004). [CrossRef]
  3. M. Grundmann, Nano-optoelectronics: concepts, physics, and advices, (Berlin: New York, Springer, 2002).
  4. H. Masuhara, Nanophotonics: Integrating Photochemistry, Optics and Nano/Bio Materials Studies, (Elsevier, 2004).
  5. E. L. Wolf, Nanophysics and nanotechnology: an introduction to modern concepts in nanoscience, (Weinheim :Wiley-VCH Verlag, 2004).
  6. Y. Z. Shen, C. S. Friend, Y. Jiang, D. Jakubczyk, J. Swiatkiewicz, and P. N. Prasad, "Nanophotonics: Interactions, materials, and applications," J. Phys. Chem. B 104, 7577-7587 (2000). [CrossRef]
  7. B. K. Zhou, Y. Z. Gao, Z. R. Chen, Laser Principle, (Beijing: National Press, 2004).
  8. A. Lin, D. H. Son, I. H. Ahn, G. H. Song, and W. T. Han, "Visible to infrared photoluminescence from gold nanoparticles embedded in germano-silicate glass fiber," Opt. Express 15, 6374-6379 (2007). [CrossRef] [PubMed]
  9. Q. M. Wang, Photonics Technology, (Beijing,Tsinghua University Press, 2002).
  10. U. H. Kynast, M. M. Lezhnina, and H. Katker, "Potential of nano-sized rare earth fluorides in optical applications," Solid State Phenomena 106, 93-102 (2005). [CrossRef]
  11. Y. H. Wang, and J. Ohwaki, "New transparent vitroceramics codoped with Er3 + and Yb3 + for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993). [CrossRef]
  12. X. B. Chen, Y. L. Liu, and N. Sawanobori, "Raman and x-radiate diffraction study about material property of oxyfluoride vitroceramics and glass," Proc. SPIE 4221, 83-87 (2000). [CrossRef]
  13. E. De la Rosa, P. Salas, L. A. Diaz-Torres, A. Martinez, and C. Angeles, "Strong visible cooperative up-conversion emission in ZrO2 : Yb3+ nanocrystals," J. Nanosci. Nanotechnol. 5, 1480-1486 (2005). [CrossRef] [PubMed]
  14. S. Hinjosa, M. A. Meneses-Nava, O. Barbosa-Garcia, L. A. Diaz-Torres, M. A. Santoyo, and J. F. Mosino, "Energy back transfer, migration and energy transfer (Yb-to-Er and Er-to-Yb) processes in Yb,Er : YAG, " J. Lumin. 102, 694-698(2003). [CrossRef]
  15. J. Frenkel, "On the Transformation of light into Heat in Solids," Phys. Rev. 37, 17-44(1931). [CrossRef]
  16. L. A. Riseberg, W. B. Gandrud, and H. W. Moos, "Multiphonon Relaxation of Near-Infrared Excited States of LaCl3:Dy3+," Phys. Rev. 159, 262-266 (1967). [CrossRef]
  17. E. Cohen, L. A. Riseberg, and H. W. Moos, "Effective Density of Phonon States for NdCl3 from Vibronic Spectra and Applications to Ion-Lattice Interactions," Phys. Rev. 175,521-525 (1968). [CrossRef]
  18. T. Miyakawa and D. L. Dexter, "Phonon Sidebands, Multiphonon Relaxation of Excited States, and Phonon-Assisted Energy Transfer between Ions in Solids," Phys. Rev. B 1, 2961-2969 (1970). [CrossRef]
  19. L. A. Riseberg, and M. J. Weber, "Relaxation phenomena in rare earth luminescence," in Progress in Optics, (Amsterdam, North Holland Publishing Co. 1975) Vol. 14.
  20. R. Reisfeld, Lasers and excited states of rare-earth, (New York : Springer-Verlag, Berlin Heidelberg, 1977). [CrossRef]
  21. T. Miyakawa and D. L. Dexter, "Cooperative and Stepwise Excitation of Luminescence: Trivalent Rare-Earth Ions in Yb3+-Sensitized Crystals," Phys. Rev. B 1, 70-80 (1970). [CrossRef]
  22. D. L. Dexter, "A Theory of Sensitized Luminescence in Solids," J. Chem. Phys. 21, 836-850 (1953). [CrossRef]
  23. M. Inokuti and F. Hirayama, "Influence of Energy Transfer by the Exchange Mechanism on Donor Luminescence," J. Chem. Phys. 43,1978-1989 (1965). [CrossRef]
  24. S. L. Zhao and Z. Xu, "Donor concentration dependence of upconversion luminescence in YLiF4:Er3+Yb3+, " Spectrosc. Spect. Anal. 25, 1933-1937 (2005).
  25. S. Y. Zhang, Theory of Rare Earth spectroscopy, (Chang Chun: Jilin Science Press, 1991).
  26. B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127,750-761 (1962). [CrossRef]
  27. G. S. Ofelt, "Intensities of crystal spectra of rare-earth ions," J. Chem. Phys. 37,511-520 (1962). [CrossRef]
  28. M. Beggiora, I. M. Reaney, and M. S. Islam, "Structure of the nanocrystals in oxyfluoride glass ceramics," Appl. Phys. Lett. 83, 467-469 (2003). [CrossRef]
  29. M. Tsuda, K. Soga, H. Inoue, and A. Makishima, "Comparison between the calculated and measured energy transfer rates of the 4S3/2 state in Er3+-doped fluorozirconate glasses," J. Appl. Phys. 88, 1900-1906 (2000). [CrossRef]
  30. F. Bao, Y. S. Wang, and Z. J. Hu, "Influence of Er3+ doping on microstructure of oxyfluoride glass-ceramics," Mater. Res. Bull. 40, 1645-1653 (2005). [CrossRef]
  31. Q. Song, X. Y. Wang, H. Chen, J. S. Gao, T. T. Wang, X. M. Zheng, C. R. Li, and C. L. Song, "Photoluminescence enhancement in Yb3+: Er3+ co-doped eutectic Al2O3 : SiO2 thin films by 980nm excitation," Opt. Express 15, 3948-3954 (2007). [CrossRef] [PubMed]
  32. J. R. DiMaio, B. Kokuoz, and J. Ballato, "White light emissions through down-conversion of rare-earth doped LaF3 nanoparticles," Opt. Express 14, 11412-11417 (2006). [CrossRef] [PubMed]

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