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Pr3+-doped heavy metal germanium tellurite glasses for irradiative light source in minimally invasive photodynamic therapy surgery

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Abstract

Pr3+-doped medium-low phonon energy heavy metal germanium tellurite (NZPGT) glasses have been fabricated and the intense multi-peak red fluorescence emissions of Pr3+ are exhibited. Judd-Ofelt parameters Ω2 = 3.14 × 10−20cm2, Ω4 = 10.67 × 10−20cm2 and Ω6 = 3.95 × 10−20cm2 indicate a high asymmetrical and covalent environment in the optical glasses. The spontaneous emission probabilities Aij corresponding to the 1D23H4, 3P03H6, and 3P03F2 transitions are derived to be 1859.6, 6270.1 and 17276.3s−1, respectively, and the relevant stimulated emission cross-sections σem are 5.20 × 10−21, 14.14 × 10−21 and 126.77 × 10−21cm2, confirming that the effectiveness of the red luminescence in Pr3+-doped NZPGT glasses. Under the commercial blue LED excitation, the radiant flux and the quantum yield for the red fluorescence of Pr3+ are solved to be 219μW and 11.80%, respectively. 85.24% photons of the fluorescence in the visible region are demonstrated to be located in 600−720nm wavelength range, which matches the excitation band of the most photosensitizers (PS), holding great promise for photodynamic therapy (PDT) treatment and clinical trials.

©2013 Optical Society of America

1. Introduction

Minimally invasive photodynamic therapy (PDT) is a promising cancer treatment that combines the photosensitizing (PS) drugs and the suitable wavelength excitation light in the presence of oxygen to initiate photosensitivity reactions companied by a specific biological effect that generate a highly reactive product termed single oxygen (1O2) [13]. It can produce oxidation reaction when uniting the adjacent biological macromolecules and then rapidly cause significant toxicity leading to irreversible apoptosis and necrosis of tumor cells. The new technique possesses less aggressivity, reduced side effects and relatively short healing times compared with the surgery, the radiotherapy and the chemotherapy combating the obstinate cancer, thus it is becoming a popular palliative treatment for use in several different malignant and pre-malignant conditions, which includes esophageal, skin, lung, urinary bladder, alimentary canal and invasive intracranial tumors [4,5]. This procedure involves a PS agent accumulated in tumor tissue via intravenous injection, an irradiation light at a wavelength corresponding to an excitation band of the PS and a set of flexible fiber-optic device delivered the lights to diseased organs in human body. Evidently, the irradiation light source and light delivery devices play vital roles in PDT treatment. Based on most tissue modeling, red light in the 600−730nm spectral region penetrates through tissue 50−200% deeper than the blue and green lights, and has more sufficient energy to stimulate photodynamic reaction to generate 1O2 penetrated into tumor tissue by means of hemoglobin [6,7]. The absorbance of hemoglobin is strongly oxygen dependent, in particular, the absorbance of deoxyhemoglobin is almost six times greater than that of hemoglobin in the wavelength range between 600 and 700nm [8]. Therefore, high-directivity and high-brightness light source in 600−730nm region is exceedingly desirable in PDT surgery.

Both lasers with favorable directivity and light-emitting diodes (LEDs) with high fluence rates are well-accepted and increasingly matured as irradiation light sources in PDT treatment in recent years [5,7]. However, laser lights with tremendous power density may mis-locate from the target area and cause accidental damage to the normal tissue. Although LEDs can be coupled with optical fiber, the low coupling efficiency and narrow excited spectral bandwidth severely restrict their application in PDT treatment. Nowadays, new researches have been focused on the effective fluorescence and upconversion luminescence generated in rare-earth (RE) ions doped glass channel waveguides and glass fibers, which are considered to be new generation of high-quality irradiation light sources for PDT treatment [9,10]. As an active fluorescent center, Pr3+ exhibits favorable red fluorescence emissions in 600−720nm wavelength region [1125], which locates in the maximum absorption region of the PS currently used in PDT therapy or clinical trials, such as hematoporphyrin derivative, phthalocyanine, photofrin, acridine orange and chlorophyll derivative [26,27]. Favorable red fluorescence and foreseeable admirable amplified spontaneous emission (ASE) fluorescence from Pr3+-doped glass fibers with sufficient intensity and suitable directivity have the potential to be applied for light source in PDT treatment.

In this work, Pr3+-doped fiber-adaptive medium-low maximum phonon energy heavy metal germanium tellurite (NZPGT) glasses have been fabricated and characterized. Intense red fluorescence emissions generated from the emitting levels 3P0 and 1D2 of Pr3+ that can be used as excitation lights for minimally invasive PDT treatment are captured in the glass samples under the excitation of short-wavelength visible lights. The radiant flux and the quantum yield for the red fluorescence of Pr3+ are solved to be 219μW and 11.80%, respectively, under the excitation of commercial blue LED, using an integrating sphere in the absolute measurements. 85.24% photons of the fluorescence in visible region are demonstrated to be located in 600−720nm wavelength range and the large stimulated emission cross-sections of the emission transitions indicate that the intense red emitting in 600−720nm region can be efficiently achieved in Pr3+-doped NZPGT glasses under appropriate excitation conditions, such as commercial blue laser diode, blue and blue-greenish LEDs, and Ar+ optical laser.

2. Experiments

Pr3+-doped NZPGT core and cladding glasses were prepared from high-purity Na2CO3, ZnO, PbO, GeO2 and TeO2 powders according to the molar host composition 14Na2O−10ZnO− 7PbO−19GeO2−50TeO2 (NZPGT core glasses) and 14Na2O−11ZnO−6PbO−19GeO2−50TeO2 (NZPGT cladding glasses), respectively. Additional 1.0wt% and 0.2wt% Pr6O11 were introduced in the core glasses based on the host weight, respectively. The glasses were melted in pure Pt crucibles and the preparation procedure is described in Ref.28. For optical measurements, the annealed glass samples were sliced and polished into pieces with two parallel sides.

The density of 1.0wt% Pr6O11 doped NZPGT glass sample was obtained to be 5.075g⋅cm−3 by the Archimedes method, and the number density of Pr3+ ions was calculated to be 1.778 × 1020cm−3. Using the Metricon 2010 prism coupler, the refractive indices of 1.0wt% Pr6O11 doped glass samples were identified to be 1.9326 and 1.8829 at 632.8 and 1536nm, respectively. The refractive indices of the sample at all other wavelengths can be obtained by the Cauchy’s equation n=A+B/λ2 with A = 1.8727 and B = 23970nm2 for the coming Judd-Ofelt analysis.

Absorption spectrum of the Pr3+-doped NZPGT glasses is detected by a Perkin-Elmer UV−vis−NIR Lambda 19 double beam spectrophotometer. Differential thermal analysis (DTA) scan of the Pr3+-doped NZPGT glasses was carried out by a WCR-2D differential thermal analyzer at the rate of 10°C/min from room temperature to 700°C. Visible fluorescence and excitation spectra were measured using a Jobin Yvon Fluorolog-3 spectrophotometer equipped with an R928 photomultiplier (PMT) tube as detector and a CW Xe-lamp as pump source. Fluorescence decay curve for 1D21G4 transition emission was recorded under the same setup using a NIR PMT detector and a flash Xe-lamp. The spectral power distribution was measured using an integrating sphere of 30cm diameter, which was connected to a CCD detector (Ocean Optics, USB4000) with a 400μm-core optical fiber. The current of the exciting blue light emitting diode (LED) was fixed at 20mA. A standard halogen lamp (EVERFINE D062) was used for calibrating this measurement system, and its spectral power distribution was obtained through fitting the factory data based on the blackbody radiation law. The pumping source (457nm blue LED) rounded by a black tape except the emitting surface was mounted in the integrating sphere. The 0.2wt% Pr6O11 doped NZPGT glass sample with dimensions of 8.0 × 7.4 × 3.2mm3 was put on the blue LED and it covered the topside completely. The luminescence pictures of the samples were taken using a Sony α200 digital camera. All the measurements were carried out at room temperature.

3. Results and discussion

As shown in the inserted photo of Fig. 1 , Pr3+-doped NZPGT glasses exhibit bright orangish-red fluorescence under 488nm laser excitation, which is promising to be used for diagnosis and localization of cancer cells in PDT treatment. Under 488nm radiation, seven emission bands corresponding to 3P03H5, 1D23H4, 3P03H6, 3P03F2, 1D23H5, 3P03F3 and 3P03F4 transitions, respectively [2931], have been observed, as presented in Fig. 1, among which 3P03F2 transition is a hypersensitive transition [32,33]. The excitation spectra monitored at the wavelengths of (a) 645 and (b) 613nm are shown in Fig. 2 . The excitation spectrum for 645nm emission consists of three excitation bands peaking at 447, 472 and 485nm due to the absorption transitions 3H4→(3P2, 1I6), 3H43P1 and 3H43P0, severally, indicating that the emissions originating from the emitting state 3P0 can be achieved under the excitation of commercial blue laser diode, blue and blue-greenish LEDs, and Ar+ optical laser. Compared with the former, one more band peaking at ~595nm is recorded in the excitation spectrum for 613nm emission, demonstrating that the 613nm red emission component is not only the result of the 3P03H6 transition but also owes much to the contribution from the emission assigned to 1D23H4 transition, which join together to present the intense red fluorescence under the long-wavelength visible light excitation.

 figure: Fig. 1

Fig. 1 Emission spectrum of 0.2wt% Pr6O11 doped NZPGT glasses under 488nm wavelength excitation. Inserted photo: fluorescence of 0.2wt% Pr6O11 doped NZPGT glasses under the excitation of 488nm wavelength laser pumping.

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 figure: Fig. 2

Fig. 2 Excitation spectra of Pr3+-doped NZPGT glasses monitored at the wavelength of (a) 645 and (b) 613nm. Emission cross-section profiles of Pr3+ for (c) 3P03F2 and (d) 3P03H6 and 1D23H4 transition emissions in 0.2wt% Pr6O11 doped NZPGT glasses.

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The stimulated emission cross-section σem is an important parameter to evaluate the energy extraction efficiency for optical materials [34]. From the experimental luminescence spectrum, the σem for the transition emissions of Pr3+ can be evaluated via the Fuchtbauer−Ladenburg (FL) formula

σem=Aiβij8πcn2×λij5I(λij)λijI(λij)dλ=Aij8πcn2×λij5I(λij)λijI(λij)dλ,
where Ai is the radiation transition probability from the i state, βij is the branching ratio for the given transition from i to j which leads to the fluorescence I(λij), Aij = Aiβij is the radiation transition probability from i to j state, c is the light speed in vacuum, n is the refractive index and the limits of the integration cover the spectral region associated with the ij transition. The obtained σem profiles of Pr3+ doped NZPGT glasses in visible region are shown as Fig. 2(c) and 2(d), and the maximum values of σem for 3P03F2, 3P03H6 and 1D23H4 emission transitions are 126.77 × 10−21, 14.14 × 10−21 and 5.20 × 10−21cm2, respectively. The large emission cross-sections for the emission transitions indicate that the intense red emitting in 580−660nm region can be achieved in Pr3+-doped NZPGT glasses under appropriate excitation conditions, such as commercial blue laser diode, blue and blue-greenish LEDs, and Ar+ optical laser, and the admirable red lights generated from Pr3+ ions are promising to be used for diagnosis and location of cancer cells in PDT treatment.

The thermodynamic properties of the Pr3+-doped NZPGT core and the NZPGT cladding glasses are presented by DTA curves in Fig. 3 . The transition temperatures of the core and the cladding glasses are derived to be Tg1 = 288°C and Tg2 = 290°C, which are close to the value of 290°C reported in TeO2-ZnO-Na2O glasses [35]. The crystallization onset temperatures of the core and the cladding glasses are Tx1 = 396°C and Tx2 = 391°C, respectively. Typically, the temperature difference values (ΔT=TxTg) of the glasses should be as large as possible to be considered good candidates for fiber drawing, and a ΔT value lager than 100°C suggests favorable glass stability. The ΔT of the core and cladding glasses are calculated to be 108 and 101°C, respectively, indicating that the NZPGT glasses exhibit good ability against crystallization. In addition, the transition temperatures of the core and the cladding glasses are similar, confirming that they can be melted under the identical condition of the temperature in the fiber drawing process. Here, another two new critical thermal parameters — the thermal stability parameter (H) and the Saad-Poulain criterion (S) are introduced to further evaluate the stability of glass samples against crystallization [36]. The thermal stability parameter is identified by H=(TxTg)/Tg and the Saad-Poulain criterion is expressed as S=(TxTg)(TcTx)/Tg. The crystallization temperatures of the NZPGT core and cladding glasses are identified as Tc1 = 413°C and Tc2 = 400°C, and thus, the H and S values of the core and cladding glasses are derived to be H1 = 0.375, H2 = 0.348, S1 = 6.375°C and S2 = 3.134°C, respectively. The S values of the core and cladding glasses are similar to the value of 4.87°C reported in TeO2-ZnO-Na2O glasses, suggesting that the addition of heavy-metal elements into tellurite glasses can improve both chemical and thermal stability for fiber drawing [36].

 figure: Fig. 3

Fig. 3 DTA curves of 1.0wt% Pr6O11 doped NZPGT core (a) and cladding (b) glasses.

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The absorption spectrum of Pr3+-doped NZPGT glasses shows nine absorption bands peaking at 447.5, 473.0, 485.5, 594.5, 1024.5, 1448.0, 1540.0, 1953.0 and 2339.0nm, which associate with the absorption transitions from the 3H4 ground state to the excited states, as labeled in Fig. 4(a) . The radiative transitions within the 4f2 configuration of Pr3+ can be analyzed by the Judd-Ofelt theory based on the absorption of Pr3+ [3740]. Judd-Ofelt intensity parameters Ωt (t = 2, 4, 6) are derived to be 3.14 × 10−20, 10.67 × 10−20 and 3.95 × 10−20cm2 by a least-squares fitting approach, respectively. The intensity parameter Ω2 has been identified to be associated with the asymmetry and the covalency of the lanthanide sites, and Ω4 and Ω6 are related to the bulk property and rigidity of the samples, respectively [11]. In the NZPGT glass system, Ω2 is larger than the values of 2.34 × 10−20 and 2.09 × 10−20cm2 in lithium silicate and lithium borate glasses, respectively, showing a strong asymmetrical and covalent environment around Pr3+ ions [41,42]. Using the Ωt values, some important radiative properties including spontaneous transition probabilities (Aij), branching ratios (β), and radiative lifetime (τrad) for the optical transitions of Pr3+ in NZPGT glasses were calculated and listed in Table 1 . The predicated spontaneous emission probability Aij for the transitions 3P03F2, 3P03H6 and 1D23H4 are derived to be 17276.3, 6270.1 and 1859.6s−1, respectively, and the relevant branching ratios are obtained to be 13.24%, 4.81% and 25.85%. The quantum efficient (η) of the 1D2 level is calculated to be 49.6% from the equation η=τexp/τrad, where τexp is the experimental lifetime, which is derived to be 69.0μs by fitting the fluorescence decay curve for the 1D21G4 transition emission, and τrad is the radiative lifetime, which is obtained to be 139.0μs from Judd-Ofelt analysis.

 figure: Fig. 4

Fig. 4 (a) Absorption spectrum of 1.0wt% Pr3+-doped NZPGT glasses. (b) Energy level diagram of Pr3+ ion in NZPGT glasses.

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Tables Icon

Table 1. Predicted emission probabilities, fluorescence branching ratios and radiative lifetimes of Pr3+ in NZPGT glasses

The emission efficiencies of the RE ions are related to the nonradiative rates (WNR) from relative excited states. According to the Miyalawa−Dexter theory [43], the multiphonon decay rate (WMP), which is dominant for the nonradiative decay rates, is expressed by

WMP=W0exp(αΔE/ω),
where α is a positive host-dependent constant, ΔE is the energy gap to the next lower level, W0 is the decay rate when ΔE = 0, and ω is the phonon energy. According to Eq. (2), WNR in NZPGT glasses should be lower than those in silicate, phosphate and borate glasses, which hold higher maximum phonon energies (ω of ~1100, ~1300 and ~1400cm−1, respectively), and the lower WNR will be helpful to achieve some seductive emissions in RE ions, which is impossible to be captured in high phonon energy glasses. In the NZPGT glass system, at least 5-phonon bridging is needed to complete the multiphonon relaxation processes from 3P0 state to 1D2 state because of the low energy gap of 3700cm−1 between the two levels and the medium-low maximum phonon energy 793cm−1 of the host matrix. In this case, the transition emissions from the emitting states 1D2 and 3P0 can be recorded in Pr3+-doped NZPGT glasses simultaneously, due to the presence of abundant population distribution in the both levels. Moreover, the effective fluorescence emissions springing from 3P0 level like 3P03F2 and 3P03H6 transitions are dominant in the emissions, owing to the lager predicted emission probabilities of 3P0 level than those of 1D2 level. The energy level diagram and the predicted emissions are schematically illustrated in Fig. 4(b).

In order to understand the red fluorescence characteristic essentially, spectral power distribution of the fluorescence in Pr3+-doped NZPGT glasses was recorded using an integrating sphere with a blue LED excitation. Under the excitation of a 457nm blue LED, the investigated spectral region of the Pr3+-doped NZPGT glasses is 380−780nm, whose spectral power distribution P(λ) is shown as curve 1 in Fig. 5(a) . To obtain the absorption extent of the pumping energy, P(λ) of the blue LED is also derived when the glass sample is located on the side of the blue LED (curve 2 in Fig. 5(a)). The total radiant flux, ΦE, of the luminescence is calculated by

ΦE=380nm780nmP(λ)dλ.
In the spectral region of 380−780nm, the total radiant flux, ΦE, of Pr3+-doped NZPGT glasses under the excitation of the blue LED was obtained to be 7896μW by Eq. (3). In the spectral region of 570−720nm for orangish-red fluorescence emission, it was solved to be 219μW, and occupied 2.77% of the whole.

 figure: Fig. 5

Fig. 5 (a) Spectral power distribution (curve 1, sample on the top of LED; curve 2, sample on the side of LED) of luminescence in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: detail of spectral power distribution in the spectrum region of 510−780nm. (b) Photon distribution of luminescence (curve 1, sample on the top of LED; curve 2, sample on the side of LED) in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: detail of photon distribution in the spectral region of 19700−13300cm−1.

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Based on the absolute spectral power distribution P(λ) of Pr3+-doped NZPGT glasses, the photon distribution N(ν¯) has been derived by

N(ν¯)=λ3hcP(λ),
where λ is the wavelength, ν¯ is the wavenumber, h is the Plank’s constant, and c is the vacuum light velocity. The derived photon distribution profiles are presented in Fig. 5(b).

Quantum yield (QY) is being used as a selection criterion of the luminescence materials for potential use in solid-state lighting applications [44,45], and is defined as the ratio of the number of photons emitted to that of photons absorbed. From the Fig. 5(b), the obtained spectrum can be deconvoluted into two components — the transmitted blue light from the excitation LED and the fluorescence from the sample. In the whole visible spectral region, the photon distribution of the Pr3+-doped NZPGT glasses under the excitation of a 457nm blue LED is shown as curve 1. To show the absorption extent of the pumping energy, the photon distribution of the blue LED is also presented as curve 2. By subtracting the Nside blue component of the LED composite from the Non of the blue LED as shown in Fig. 6(a) , the absorbed photon number, LsideLon, can be estimated by integrating the photon distribution with the wavenumber and the emitted photon number, EonEside, can also be evaluated by the integrating the fluorescence component of the LED composite derived by Gaussion multi-peaks fitting [46]. Namely, the QY is defined by

QY=emittedphotons/absorbedphotons=(EonEside)/(LsideLon),
where Eon and Eside are the emitted photon numbers, respectively, when the sample located on the top and the side of blue LED; Lon and Lside are the recorded photon numbers emitted from blue LED, respectively, when the sample located on the top and the side of the blue LED. The total QY of the Pr3+-doped NZPGT glasses under the excitation of the blue LED was calculated to be 11.80%, which is larger than those values of other RE ions doped glass systems, for instance, the value of 7.55% in Sm3+ doped heavy metal tellurite glasses (Li2O-K2O-BaO-Bi2O3-TeO2) [47], due to the intense absorption peaks of Pr3+ presented in the 400−500nm wavelength region.

 figure: Fig. 6

Fig. 6 (a) Net emission and absorption photon distribution in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: fluorescence photograph of the Pr3+-doped NZPGT glass sample under the excitation of blue LED in an integrating sphere. (b) Histogram of photon percentage of the photon numbers in each wavelength interval to that in the whole wavelength region of 570−720nm.

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The efficient orangish-red fluorescence emissions are located in the wavelength region of 570−720nm. In order to investigate the luminescence effects of Pr3+-doped NZPGT glasses, the spectral region is divided into five equal parts, with 30nm for a step length. The photon numbers of each wavelength interval are obtained by integrating the photon distribution illustrated in Fig. 6(a), and the photon number percentages based on the photon numbers in the whole wavelength region of 570−720nm are presented in Fig. 6(b). The photon ratios of the wavelength range of 570−600nm, 600−630nm, 630−660nm, 660−690nm and 690−720nm are derived to be 14.76%, 40.30%, 32.22%, 5.43% and 7.29%, respectively. Thus, 85.24% photons of the fluorescence in the visible region are located in 600−720nm wavelength range, which matches the effective excitation bands of many PS agents currently used in clinical treatment, and the foreseeable admirable red amplified spontaneous emission (ASE) fluorescence generated in the Pr3+-doped NZPGT glass fibers under the proper excitation conditions can deliver enough energy to molecular oxygen (O2) to create singlet oxygen (1O2) and rapidly cause significant toxicity leading to cancer cell death via apoptosis or necrosis in the PDT treatment.

4. Conclusion

Pr3+-doped heavy metal germanium tellurite (NZPGT) glasses with the medium-low maximum phonon energy of 793cm−1 was prepared, and the derived Judd-Ofelt parameters indicate a high asymmetrical and covalent environment in the glass host. Intense red fluorescence emissions are observed in the glasses under the excitation of short-wavelength visible lights and the large emission cross-sections of the emission transitions indicate that the intense red emitting can be efficiently achieved in Pr3+-doped NZPGT glasses. The radiant flux for the visible emission bands of Pr3+ was solved to be 219μW, using an integrating sphere in the absolute measurements, and the quantum yield of the red fluorescent is derived to be 11.80%, which is larger than Sm3+ doped heavy metal tellurite glasses. 85.24% photons of the luminescence in visible region are demonstrated to be located in 600−720nm wavelength range, which matches the effective absorption band of the most photosensitizers (PS), holding great promise for photodynamic therapy (PDT) treatment and clinical trials.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (61275057) and the Science and Technology Foundation of Liaoning Province, China (201202011).

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Figures (6)

Fig. 1
Fig. 1 Emission spectrum of 0.2wt% Pr6O11 doped NZPGT glasses under 488nm wavelength excitation. Inserted photo: fluorescence of 0.2wt% Pr6O11 doped NZPGT glasses under the excitation of 488nm wavelength laser pumping.
Fig. 2
Fig. 2 Excitation spectra of Pr3+-doped NZPGT glasses monitored at the wavelength of (a) 645 and (b) 613nm. Emission cross-section profiles of Pr3+ for (c) 3P03F2 and (d) 3P03H6 and 1D23H4 transition emissions in 0.2wt% Pr6O11 doped NZPGT glasses.
Fig. 3
Fig. 3 DTA curves of 1.0wt% Pr6O11 doped NZPGT core (a) and cladding (b) glasses.
Fig. 4
Fig. 4 (a) Absorption spectrum of 1.0wt% Pr3+-doped NZPGT glasses. (b) Energy level diagram of Pr3+ ion in NZPGT glasses.
Fig. 5
Fig. 5 (a) Spectral power distribution (curve 1, sample on the top of LED; curve 2, sample on the side of LED) of luminescence in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: detail of spectral power distribution in the spectrum region of 510−780nm. (b) Photon distribution of luminescence (curve 1, sample on the top of LED; curve 2, sample on the side of LED) in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: detail of photon distribution in the spectral region of 19700−13300cm−1.
Fig. 6
Fig. 6 (a) Net emission and absorption photon distribution in Pr3+-doped NZPGT glasses under the excitation of blue LED. Inset: fluorescence photograph of the Pr3+-doped NZPGT glass sample under the excitation of blue LED in an integrating sphere. (b) Histogram of photon percentage of the photon numbers in each wavelength interval to that in the whole wavelength region of 570−720nm.

Tables (1)

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Table 1 Predicted emission probabilities, fluorescence branching ratios and radiative lifetimes of Pr3+ in NZPGT glasses

Equations (5)

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σ em = A i β ij 8πc n 2 × λ ij 5 I( λ ij ) λ ij I( λ ij )dλ = A ij 8πc n 2 × λ ij 5 I( λ ij ) λ ij I( λ ij )dλ ,
W MP = W 0 exp(αΔE/ω),
Φ E = 380nm 780nm P(λ)dλ .
N( ν ¯ )= λ 3 hc P(λ),
QY=emitted photons/absorbed photons=( E on E side )/( L side L on ),
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