1. Introduction

Nano-technology has been developed rapidly since 1980’s [1–7]. 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]. Among these are the further enhanced optical properties of the material [7,8]. Photonics, following electronics, has become an important mainstay of modern science [9]. 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 [6,7]. 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 [2,3]. In recent years, the fluorescence properties of rare earth nanomaterial have been progressively studied worldwide [10]. 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 [11,12].

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 T_g=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 [11,14].

The Stokes excitation spectra were measured in the experiments. Figure 1(a) shows the excitation spectra of 543.7nm ⁴S_3/2→⁴I_15/2 and 667.1nm ⁴F_9/2→⁴I_15/2 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 ²G_7/2, ⁴G_9/2, ⁴G_11/2, (²G⁴F²H)_9/2, ⁴F_3/2, ⁴F_5/2, ⁴F_7/2, and ²H_11/2, 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.

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All the relative excitation spectral peak intensities F of 543.7nm ⁴S_3/2→⁴I_15/2 and 667.1nm ⁴F_9/2→⁴I_15/2 fluorescence for all samples are measured. First, it is found that the ratios of obtained energies from ²G_7/2, ⁴G_9/2, ⁴G_11/2, (²G⁴F²H)_9/2, ⁴F_3/2, ⁴F_5/2, ⁴F_7/2, and ²H_11/2 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 ²G_7/2, ⁴G_9/2, ⁴G_11/2, (²G⁴F²H)_9/2, ⁴F_3/2, ⁴F_5/2, ⁴F_7/2, and ²H_11/2 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 ⁴F_7/2 and ²H_11/2 levels, while for the 667.1nm fluorescence it is easy to obtain energies from ⁴G_9/2 and ⁴G_11/2 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 ⁴G_11/2 level has several fluorescence transitions, (²G⁴F²H)_9/2→⁴I_15/2, ²H_11/2→⁴I_15/2, ⁴S_3/2→⁴I_15/2 and ⁴F_9/2→⁴I_15/2, 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 ²H_11/2 level has only two fluorescence transitions, ⁴S_3/2→⁴I_15/2 and ⁴F_9/2→⁴I_15/2. 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 ²H_11/2 level was excited by 522.5nm visible light, a common fluorescence phenomenon was observed that the 543.7nm green fluorescence of ⁴S_3/2 level is strong, while the 667.1nm red fluorescence of ⁴F_9/2 level is weak. However, when the ⁴G_11/2 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 ⁴F_9/2 level is strong, while the 543.7nm green fluorescence of ⁴S_3/2 level is weak. We use F[⁴S_3/2](⁴G_11/2), F[⁴F_9/2](⁴G_11/2), F[⁴S_3/2](²H_11/2) and F[⁴F_9/2](²H_11/2) to represent the fluorescence intensities of ⁴S_3/2, and ⁴F_9/2 levels when the ⁴G_11/2 and ²H_11/2 levels are excited, respectively. It is easy to identify the common intensity ratio between green and red fluorescence as α=[F(⁴S_3/2)/F(⁴F_9/2)](²H_11/2), which is the ratio of F[⁴S_3/2](²H_11/2) to F[⁴F_9/2](²H_11/2), when the ²H_11/2 level is excited. It is convenient to identify the unusual intensity reverse ratio between red and green fluorescence as γ=[F(⁴F_9/2)/F(⁴S_3/2)](⁴G_11/2), which is the ratio of F[⁴F_9/2](⁴G_11/2) to F[⁴S_3/2](⁴G_11/2), when the ⁴G_11/2 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 ²H_11/2 level is excited by 522.5nm visible light or the ⁴G_11/2 level is excited by 378.5nm ultraviolet light, both of them exhibit the common fluorescence phenomenon, namely the 543.7nm green fluorescence of ⁴S_3/2 level is strong, while the 667.1nm red fluorescence of ⁴F_9/2 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.

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Table 1. Relative fluorescence intensity F of Stokes emission spectra, the common intensity ratio α=[F(⁴S_3/2)/F(⁴F_9/2)](²H_11/2) between green and red fluorescence when the ²H_11/2 level is excited, the unusual intensity reverse ratio γ=[F(⁴F_9/2)/F(⁴S_3/2)](⁴G_11/2) between red and green fluorescence when the ⁴G_11/2 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 ⁴G_11/2 level. There are primarily two kinds of population relaxation passages for the ⁴G_11/2 level [15]. 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]. The smaller the energy gap between two adjacent levels, the larger the multi-phonon nonradiative relaxation. Both the ⁴S_3/2 and ⁴F_9/2 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]. 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 Ω_t 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, {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} and {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(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 ⁴G_11/2 and (²G⁴F²H)_9/2 levels to jump over ²H_11/2 and ⁴S_3/2 levels, and subsequently enter the ⁴F_9/2 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.

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It is well known for the electric multipole interaction that the energy transfer rate is governed by the J-O intensity parameters Ω_t, 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 Ω_t are similar. Therefore, the distance R between the rare earth ions is a key factor. In fact, Ref. [24] 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] 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 W_ET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions can be described as follows [20]

Where Ω_λ 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, ρ^8/3 and ρ^10/3 respectively. In general [20], when distance R = 0.8nm, the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions possess a near and similar energy transfer probability [20]. On the contrary, when R > 1.0nm, the dipole-dipole interaction is obviously stronger than the dipole-quadruple and quadruple-quadruple interactions [20], 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 [20,25].

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] and Ofelt [27], 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.

Combining Judd-Ofelt calculation and the measured value of oscillator strength from the ground state, the J-O parameters Ω_t(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 [18,21] of Prof. T. Miyakawa and Prof. D. L. Dexter, the multiphonon nonradiative relaxation rates W^p can be expressed as

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

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, g_A and g_D 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 W^p of all energy levels of Er³⁺ ion. It is found that the multiphonon nonradiative relaxation rates W^p from ⁴G_11/2(Er³⁺) to lower levels (²G⁴F²H)_9/2(Er³⁺) and ⁴F_3/2(Er³⁺) are 3.20×10⁵s^-1 and 1.41×10³s^-1 respectively. That for (²G⁴F²H)_9/2(Er³⁺) to lower levels ⁴F_3/2(Er³⁺) and ⁴F_5/2(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 {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} will outstrip the multiphonon nonradiative relaxation {⁴G_11/2(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⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} will outstrip the multiphonon nonradiative relaxation {(²G⁴F²H)_9/2(Er³⁺)⇒⁴F_3/2(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 ⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺) transition are {0.4283, 0.0372, 0.0112}. Those for (²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺) are {0.0075, 0.0261, 0.0469}. And those for ²F_7/2(Yb³⁺)→²F_5/2(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 W_PET 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 W_PET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions for {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} energy transfer, while Fig. 4(b) gives the results for {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(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 {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} energy transfer, the points at which the phonon-assistant energy transfer rate W_PET 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⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} energy transfer, the points at which the phonon-assistant energy transfer rate W_PET 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 W_PET of the dipole-dipole, dipole-quadruple and quadruple-quadruple interactions dependent on the distance R for (a) {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} and (b) {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} energy transfer.

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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%.

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Fig. 6. The typical variation of the phonon-assistant energy transfer rate W_PET of the electric multi-dipole interaction of {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)}(Solid line) and {(²GF²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(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%.

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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[11,12]. The average size of the crystal cell is measured out with a lattice parameter a=0.573 nm [28]. 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]. 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 {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} and {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} to produce the interesting phenomenon of unusual red and green fluorescence intensity reverse phenomenon.

The energy transfer rates are tightly and sensitively related with the distance between rare earth ions. According to the Ref [29], the distance R between Er³⁺ and Yb³⁺ ions in Er³⁺Yb³⁺ codoped system can be express as :

where N_Er and N_Yb is the number density of Er³⁺ and Yb³⁺ ions in units volume respectively, ρ is mass density, M is mole mass, N_a 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] 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 W_PET 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% [28,30]. 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 W_PET of {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} is about 1.380×10⁸s^-1, that of {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(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 W_PET of {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} is about 1.194×10⁵s^-1, that of {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(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.

Therefore, it is easy to explain the experiment facts of that the unusual intensity reverse ratio γ and the dynamic range ∑ of intensity reverse between red and green fluorescence of (1) Er(0.5)Yb(3):FOV are about 909 and 1067 times larger than those of (3) Er(0.5):FOV respectively, and are about 244 and 279 times larger than those of (2) Er(0.5)Yb(1):FOV, respectively. This phenomenon is tight related with the excellent material and optical property, in particular, the nanometer characteristics of oxyfluoride nanophase vitroceramics. Because of the special nanometer microcrystal structure of oxyfluoride nanophase vitroceramics, rare earth ions are enriched within the nanocrystal, leading to a significant reduction of the distance R between rare earth ions. The electric multipole interaction is then strengthened greatly, resulting in a large enhancement of energy transfer. Thus, the cross energy transfer passages {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} and {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} are very strong [31,32], giving rise to the emergence of the fluorescence intensity reverse between red and green fluorescence in (1) Er(0.5)Yb(3):FOV oxyfluoride nanophase vitroceramics.

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 {⁴G_11/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} and {(²G⁴F²H)_9/2(Er³⁺)→⁴F_9/2(Er³⁺), ²F_7/2(Yb³⁺)→²F_5/2(Yb³⁺)} are largely enhanced, resulting in the unusual fluorescence intensity reverse phenomenon between red and green fluorescence.