Quantitative Analysis of Energy Transfer and Origin of Quenching in

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Quantitative Analysis of Energy Transfer and Origin of Quenching in Er3+/Ho3+ Codoped Germanosilicate Glasses Tao Wei, Ying Tian, Cong Tian, Muzhi Cai, Xufeng Jing, Bingpeng Li, Rong Chen, Junjie Zhang, and Shiqing Xu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b04537 • Publication Date (Web): 10 Jun 2015 Downloaded from http://pubs.acs.org on June 19, 2015

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The Journal of Physical Chemistry

Quantitative Analysis of Energy Transfer and Origin of Quenching in Er3+/Ho3+ Codoped Germanosilicate Glasses Tao Weia, Ying Tiana,∗, Cong Tianb, Muzhi Caia, Xufeng Jingc, Bingpeng Lia, Rong Chena, Junjie Zhanga, Shiqing Xua,∗ a College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, PR China b College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, PR China c Institute of Optoelectronic Technology, China Jiliang University, Hangzhou 310018, PR China Abstract The energy transfer mechanism between Ho3+ and Er3+ ions has been investigated in germanosilicate glass excited by 980 nm LD. A rate equation model was developed to demonstrate the energy transfer from Er3+ to Ho3+ ions, quantitatively. Energy transfer efficiency from Er3+: 4I13/2 to Ho3+: 5I7 level can reach as high as 75%. Such high efficiency was attributed to the excellent matching of host phonon energy with the energy gap between Er3+: 4I13/2 and Ho3+: 5I7 levels. In addition, the energy transfer microparameter (CDA) from Er3+: 4I13/2 to Ho3+: 5I7 level was estimated to (4.16±0.04)×10-40 cm6·s-1 via the host assisted spectral overlap function, coinciding with the CDA (2.88×10-40 cm6·s-1) from decay analysis of Er3+: 4I13/2 level which also indicated hopping migration assisted energy transfer. Furthermore, concentration quenching of Ho3+: 5I7→5I8 transition was the dipole-dipole interaction in diffusion-limited regime and quenching concentration of Ho3+ reached up to 4.13×1020 cm-3. 1. Introduction Recently, Ho3+/Er3+ codoped glasses operating at 2 µm have been attracting enormous attention because of their promising civil and military applications including remote sensing, laser surgery, environmental monitoring and eye-safe light detection and ranging (LIDAR) 1-3. Appropriate host material is indispensible to achieve mid-infrared emissions. The past decades have witnessed great progress in glass hosts for mid-infrared emissions such as germanate glass4, 5, tellurite glass6, 7, bismuthate glass8 and silicate glass9. Germanosilicate glass is a potential candidate for 2 µm laser material since it has the merits of higher refractive index of germanate glass and low cost as well as higher thermal stability of silicate glass10, 11. Previous studies have demonstrated that germanosilicate glass is a promising optical material for fiber amplifier at 1.53 µm 11-13 . It is expected that efficient 2 µm radiations can also be achieved from Ho3+ activated germanosilicate glass for laser and amplifier. *

Corresponding author. Tel.: +86 571 8683 5781; fax: +86 571 2888 9527 E-mail address: [email protected] (Y. Tian), [email protected] (S. Xu) 1

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The multiple absorption bands of Ho3+ ion in the range from ultra-violet, visible to near-infrared provide a variety of pumping options for its 2 µm emissions. However, the lack of efficient absorption bands at 980 nm wavelength suggest that Ho3+ ions cannot be pumped by high-power and commercial 980 nm laser diodes (LDs). Fortunately, Yb3+ or Er3+ ions can be codoped to improve absorption band of Ho3+ ions at 980 nm. Compared with Yb3+ ions, Er3+: 4I13/2 level can match better with Ho3+:5I7 level, which is more beneficial for 2 µm emissions14. Hence, Ho3+/Er3+ codoping is a good dopant method to realize 2 µm fluorescence. However, the energy transfer processes between Er3+ and Ho3+ ions are complicated due to their substantial energy level structures. Therefore, other unwanted and detrimental energy transfer processes (such as cross relaxation in Ho3+:5I7 level and back energy transfer from Ho3+ to Er3+ ions) can take place, which weakens 2 µm emissions. In this case, a detailed investigation on energy transfer mechanism and ion-ion interactions between Er3+ and Ho3+ ions can be useful for the final desired applications. Reports on 2 µm emissions of Er3+/Ho3+ codoped systems are less and they are mainly focused on the investigation of spectroscopic properties14. Therefore, the knowledge and quantification of energy transfer mechanism between Ho3+ and Er3+ based on the built rate equation model and phonon assisted energy transfer analysis is helpful to optimize and assure the technological applications of the codoped materials. In addition, the concentration quenching at 2 µm in the concentration range is also calculated by the measured fluorescence spectra and decay curves to unravel 2 µm fluorescence behaviors. This work may provide useful guide for the design of mid-infrared laser material. 2. Experimental Host glasses have the following compositions (in mol %): 30SiO2-30GeO2-8CaO12Li2O-5Nb2O5-15BaO. At the same time, 1 mol % Er2O3 and x mol % Ho2O3 (x=0.25; 0.5; 0.75; 1) were added in the prepared samples. High purity of SiO2 (99%), GeO2 (99.999%), CaO(99%), Li2O(99%), Nb2O5(99%), BaO(99.9%) were used and the samples were prepared by melting-quenching technique. In addition, Er3+ singly doped sample was also prepared for a comparison. Raw materials of 20 g were mixed homogeneously and melted in a platinum crucible with a SiC-resistance electric furnace at the temperature of 1450 ºC for 45 min. Then the melts were quenched on preheated stainless steel plate and annealed at 10 °C below the glass transition temperature for 4 h before they were cooled to room temperature. Finally, the annealed samples were fabricated and optically polished to the size of 10 mm×10 mm×1.5 mm for the optical property measurement. The densities of samples were measured by Archimedes’ liquid-immersion method in distilled water with the error of ±0.01 g/cm3. The refractive indexes of samples at 633 nm wavelength were recorded on a prism coupling apparatus (Metricon Model 2010) with the error of ±0.003. Fourier transform infrared (FTIR) spectroscopy of germanosilicate glass was carried out using a FTIR Nicolet 5700 in the range of 400-1300 cm-1. Absorption spectra were determined by means of a Perkin Elmer Lambda 900UV-VIS-NIR spectrophotometer in the range of 350-2200 nm with the resolution of 1 nm. Fluorescence spectra (500-700 nm, 1400-1700 nm and 1800-2200 2


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nm) were measured with a computer-controlled Triax 320 type spectrometer upon excitation by 980 nm LD with the maximum power of 2 W. Fluorescence lifetimes of Er3+: 4I13/2 (1.53 µm) and Ho3+: 5I7 (2 µm) level were recorded with light pulses of the 980 nm LD and HP546800B 100-MHz oscilloscope. All the measurements were carried out at room temperature and in the same condition. 3. Results Fig. 1 displays the upconversion fluorescence spectra of Er3+ singly and Er3+/Ho3+ codoped germanosilicate glasses pumped by 980 nm LD. For Er3+ singly doped sample, two emission peaks at 548 nm and 658 nm occur, which correspond to 4 S3/2→4I15/2 and 4F9/2→4I15/2 transitions, respectively. However, the enhanced 548 nm and 658 nm emission peaks can be observed in Er3+/Ho3+ codoped system. The 548 nm emission peak is considered to Er3+: 4S3/2 →4I15/2 and Ho3+: 5S2 (5F4) →5I8 transitions, whereas the 658 nm peak is ascribed to Er3+: 4F9/2→4I15/2 and Ho3+: 5 F5→5I8 transitions. It is well known that 980 nm pumping energy cannot be absorbed by Ho3+ ion due to its absence of efficient absorption band. Therefore, there must be the existence of energy transfer processes between Er3+ and Ho3+. The phenomenon is also observed in Er3+/Ho3+ co-doped tellurite glasses15, 16. The inset of Fig.1 plots the dependence of Ho3+ concentration on fluorescence intensities at 548 nm and 658 nm, respectively. It can be seen that the intensities of 548 nm and 658 nm emissions both increase with the increment of Ho3+ concentration then reach to the maximum emissions with the Ho3+ concentration of 0.5 mol% subsequently the upconversion emission intensity decreases with the further increase of Ho3+ concentration. Fig. 2 shows near-infrared emission spectra in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm. The emission peak centered at 1530 nm is attributed to Er3+:4I13/2→4I15/2 transition. It is found that the emission intensity reduces monotonically with the increment of Ho3+ concentration, also indicating the efficient energy transfer between Er3+ and Ho3+ ions. Fig.3 gives the mid-infrared fluorescence spectra in Er3+/Ho3+ codoped germanosilicate glasses at the excitation of 980 nm LD. All the samples were measured in the same condition. No emission peaks can be observed for Er3+ singly and Ho3+ singly doped samples. However, obvious emission peaks at 2 µm can be found in Er3+/Ho3+ codoped system, which is ascribed to Ho3+:5I7→5I8 transition. This is due to the presence of energy transfer process between Er3+ and Ho3+ ions. It can be found that the 2 µm emissions become stronger with increasing Ho3+ concentration and then become weaker with the further enhancement of Ho3+ ions. When Ho3+ concentration is 1.5 mol%, mid-infrared emissions reach to the maximum value. The decreased 2 µm emissions are owing to the concentration quenching. The inset of Fig.3 shows the dependence of Ho3+ concentration on 2 µm lifetime. With the increment of Ho3+ concentration, the lifetime at 2 µm reduces, monotonically.

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4. Discussions 4.1 Energy transfer mechanism between Er3+ and Ho3+ According to upconversion, near-infrared and mid-infrared fluorescence spectra in Ho3+/Er3+ codoped germanosilicate glasses, the energy level diagram and energy transfer mechanism are proposed as shown in Fig.4. The left hand of Fig.4 displays the absorption spectrum of Ho3+/Er3+ codoped sample. An absorption peak centered at 10246 cm-1 (~976 nm) can be observed from absorption spectrum, suggesting that the prepared germanosilicate glasses can be pumped by commercially available 980 nm LD. Based on previous reports15-17, the energy transfer mechanism between Er3+ and Ho3+ is as follows: (1) The ions in Er3+:4I15/2 level are pumped to higher 4I11/2 level via ground state absorption (GSA: Er3+:4I15/2+a photon→4I11/2) when excited by commercial 980 nm LD. (2) On one hand, the ions in 4I11/2 level are populated to higher 4F7/2 level by excited state absorption (ESA: 4I11/2+ a photon→4F7/2) or energy transfer upconversion (ETU: 4 I11/2+ 4I11/2→4I15/2+4F7/2) process. (3) The ions in 4F7/2 level relax non-radiatively to lower 2H11/2, 4S3/2 and 4F9/2 levels due to the small energy gaps among them. (4) Subsequently, Er3+: 4S3/2 and 4F9/2 levels radiate their energy to the ground state (4I15/2), generating 548 nm and 658 nm light emissions ((4a) 4S3/2→4I15/2+548 nm; (4b) 4 F9/2→4I15/2+658 nm). (5) Owing to small energy mismatch between Er3+:2H11/2 (4S3/2) and Ho3+:5F4 (5S2) levels along with the equal energy between Er3+:4F9/2 and Ho3+:5F5 levels, energy transfer processes ((5a) ET1: Er3+:2H11/2 (4S3/2)+Ho3+:5I8→Er3+:4I15/2+Ho3+:5F4 (5S2); (5b) ET2: Er3+:4F9/2+ Ho3+:5I8→ Er3+:4I15/2+ Ho3+:5F5) between Er3+ and Ho3+ can happen. Thus, the ions in Ho3+:5F4 (5S2) and 5F5 levels are accumulated. (6) Meanwhile, the ions in Ho3+:5F4 (5S2) level can also decay quickly to lower 5F5 level by multiphonon relaxation process. (7) Afterwards, Ho3+:5F4 (5S2) and 5F5 levels depopulate their energy to the ground state (5I8) by radiative transition processes, leading to 548 nm and 658 nm emissions ((7a): 5F4 (5S2)→5I8+548 nm; (7b): 5F5→5I8+658 nm). (8) On the other hand, the ions in Er3+:4I11/2 level can relax to lower 4I13/2 level by nonradiative process. (9) Er3+:4I11/2 level can also transfer its energy to Ho3+:5I6 level via ET3 (Er3+:4I11/2+ Ho3+:5I8→Er3+:4I15/2+ Ho3+:5I6) process. (10) Then the ions in 5I6 level decay to lower 5I7 level because of multi-phonon relaxation process thus the ions in 5I7 level are accumulated. (11) In addition, some ions in 4I13/2 level radiate to ground state (4I15/2) resulting in 1.53 µm emissions. 4


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(12) The 4I13/2 level transfer a part of its energy to adjacent Ho3+:5I7 level (ET4: Er3+:4I13/2+ Ho3+:5I8→Er3+:4I15/2+ Ho3+:5I7) making this energy level populated. (13) 2 µm emissions take place via radiative transition of Ho3+:5I7→5I8. From Fig.1, one can see the enhanced 548 nm and 658 nm emissions after the addition of Ho3+ ions, indicating the existence of (5a) and (5b) processes. The decreased 1.53 µm emissions and occurrence of 2 µm fluorescence demonstrate the existence of (12) process. 4.2 Rate equation analysis On the basis of energy level diagram from Fig.4, the energy transfer parameters from Er3+ to Ho3+ ions are determined via a rate equation model to better understand luminescent behavior. The rate equations are built as follows

dn 0 = −Rn 0 + C ETU n 22 + W 40n 4 + W 30n3 + W 20n2 + W 10n1 dt

(1)

dn1 = W 41n 4 + W 31n 3 + W 21n 2 − C ET 3n1n5 − W 10n1 dt

(2)

dn 2 = Rn 0 − 2C ETU n 22 + W 42n 4 + W 32n3 − W 21n 2 − W 20n 2 dt

(3)

dn3 = W 43n 4 − W 31n 3 − W 32n 3 − C ET 2n3n5 − W 30n3 dt

(4)

dn 4 = C ETU n 22 − C ET 1n 4 n5 − W 43n 4 − W 42n 4 − W 41n 4 − W 40n 4 dt

(5)

dn5 = W 85n 8 + W 75n 7 + W 65n 6 dt

(6)

dn 6 = C ET 3n1n 5 + W 86n 8 + W 76n7 − W 65n 6 dt

(7)

dn7 = C ET 2n 3n5 + W 87n 8 − W 76n 7 − W 75n7 dt

(8)

dn 8 = C ET 1n 4 n5 − W 87n 8 − W 86n 8 − W 85n 8 dt

(9)

n0 + n1 + n2 + n3 + n 4 = nEr

(10) 5



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n5 + n6 + n7 + n8 = n Ho

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(11)

where n0, n1, n2, n3, n4, n5, n6, n7 and n8 are the time dependent population numbers of Er3+: 4I15/2, 4I13/2, 4I11/2, 4F9/2, 2H11/2(4S3/2) and Ho3+: 5I8, 5I7, 5F5, 5F4(5S2) levels, respectively. nEr and nHo are total Er3+ and Ho3+ concentrations, respectively. R is the pumping rate18. Wij is the total transition rates from i to j level, which contains radiative transition (it is determined by Judd-Ofelt theory19, 20) and multiphonon relaxation contributions (it is calculated by energy gap law21) as listed in Table 1. CET1, CET2, CET3 are energy transfer rates from Er3+:2H11/2(4S3/2) to Ho3+:5F4(5S2), Er3+:4F9/2 to Ho3+:5F5 and Er3+:4I13/2 to Ho3+:5I7 level, respectively. Finally, the CETU is energy transfer upconversion parameter corresponding to Er3+:4I11/2 level. It is noted that several approximations have been made to develop rate equations. The population numbers (ni) of selected energy level can be determined by the emission intensity from its level (Ii) using the equation as follows22

I i = hυijWij ni

(12)

where hνij is the emission energy. According to Eq.(12) and Fig.1, the fluorescence intensity ratio for 548 nm and 658 nm emissions can be expressed, respectively, as

I Er548/ Ho W n + W 85n8 = 40 4 548 W 40n 4 I Er

(13)

I Er658/ Ho W n + W 30n3 = 75 7 658 W 30n3 I Er

(14)

Therefore, the obtained ratios of n8/n4 and n7/n3 are 0.85 and 2.87, respectively, for Er3+/0.5Ho3+ co-doped samples. In the steady-state process, dn3/dt=0, dn7/dt=0 and dn8/dt=0. Moreover, it is reasonable that the n5 is equal to nHo due to much larger population numbers in 5I8 level than those of other levels. Thus, Eqs.(4), (8) and (9) can be simplified as

n8 C ET 1n Ho = n4 W 87 + W 86 + W 85

(15)

n7 C n C n W (C n + W 30 + W 31 + W 32 ) = ET 2 Ho + ET 1 Ho 87 ET 2 Ho n3 W 76 + W 75 (W 76 + W 75 )W 43 (W 87 + W 86 + W 85 )

(16)

Combining Table 1, Eqs.(15) and (16) , the CET1 is equal to 6.42×10-15 cm3/s and CET2 reach 4.99×10-17 cm3/s, indicating the existence of energy transfer processes (5a) and (5b). In addition, the parameter CET1 is much larger than CET2 value, signifying the faster energy transfer process from Er3+:2H11/2(4S3/2) to Ho3+:5F4(5S2) level than that

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from Er3+:4F9/2 to Ho3+:5F5 level. This is due to good energy match between Er3+:2H11/2(4S3/2) and Ho3+:5F4(5S2) levels as shown in Fig.4. According to Eq.(2), the time dependent population of Er3+:4I11/2 level can be determined as

n1(t ) = n1(0)e [− (W

10

+ C ET 3 n Ho )t ]

(17)

where n1(0) is the excited population of Er3+:4I13/2 level after the pump source turns off (t=0). It is noted from Table 1 that W21 is significantly larger than W41 and W31. Thus, it is reasonable to neglect excited state absorption or energy transfer upconversion process in Er3+:4I11/2 level and populations of this level relax quickly to lower Er3+:4I13/2 level in purpose of obtaining Eq.(17) from Eq.(2). The decay curve at 1.53 µm in Er3+/0.5Ho3+ codoped germanosilicate glass and fitting results via Eq.(17) are shown in Fig.5(a). It is found that the fitting curve can match well to 1.53 µm decay curve and the fitted CET3 is 9.78×10-18 cm3/s, revealing the existence of energy transfer process (12). 4.3 Energy transfer efficiency analysis In order to estimate the energy transfer efficiency from Er3+:4I13/2 to Ho3+:5I7 level, the decay curves monitoring at 1.53µm in Er3+ singly (τEr) and Er3+/1.5 mol% Ho3+ codoped (τEr/Ho) samples are measured as shown in Fig.5(b). The lifetimes are determined by single exponential fitting procedure as listed in the inset of Fig.5(b) as well as the energy transfer efficiency (η) which is expressed as23

η =1−

τ Er / Ho τ Er

(18)

It is calculated from Fig.5(b) that the η can reach 75%, confirming the highly efficient energy transfer process from Er3+:4I13/2 to Ho3+:5I7 level. Such high efficiency will be elucidated in the next section. 4.4 Non-resonant energy transfer analysis Fig. 6(a) displays the FTIR spectrum of undoped germanosilicate glass in the region of 400-1200 cm-1 with the aim to understand the glassy nature. Four infrared absorption peaks can be observed. It has been reported that the peak at ca. 1080 cm-1 is attributed to the Si-O stretching mode of one non-bridging atom24. The peak at ca. 630 cm-1 is assigned to Ge–O–Ge stretching vibration in GeO6 units while the peak at ca. 780 cm-1 is ascribed to Ge-O bond vibrations in GeO4 units25, 26. In addition, the peak at ca.455 cm-1 may come from bending vibrations of the silicate network27. It is worth mentioning that the maximum phonon vibrations at 1080 cm-1 may have an important influence on fluorescence emissions and lead to weak luminescence due to high multi-phonon relaxation rate. The extent of energy transfer from Er3+: 4I13/2 to Ho3+:5I7 level is dependent on the spectral overlap of donor’s emission (Er3+) with acceptor’s absorption (Ho3+). In case 7



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of Er3+-Ho3+ doped system, the spectral overlap between 1.53 µm emissions of Er3+ and 2 µm absorption of Ho3+ is very poor with the energy gap of about 1400 cm-1. However, the observed efficient energy transfer with η of 75 % suggests that the energy transfer process in the prepared glass system may be assisted by host phonons. For such non-resonant energy transfer, the energy transfer probability (PET) can be estimated by the phonon modified spectral overlap integral, I(Eph) as follows28

PET ∝ I (E ph ) =

e e

E ph k B T

E ph k B T

∫ −1

fD (E − E ph )fA (E ) dE E2

(19)

where Eph is the phonon energy of host. kB is Boltzmann constant and T is absolute temperature. According to the 1.53 µm emission cross section of Er3+ and 2 µm absorption cross section of Ho3+, the normalized energy transfer probability has been calculated as a function of phonon energy in the region of 0-2400 cm-1 as presented in Fig.6(b). It can be seen that PET increases firstly with increasing phonon energy and it reaches a maximum for the phonon energy of 1550 cm-1. The PET decreases and diminishes with further increase of phonon energy. Hence, the energy gap between Er3+: 4I13/2 and Ho3+:5I7 levels can be bridged by host phonons for efficient energy transfer. From Fig.6(a), about one phonon is required to bridge the energy gap. Although the hosts with high phonon energy such as borate glass can promote energy transfer from Er3+ to Ho3+ with assistance of less phonons, they also lead to high multi-phonon relaxation rates from Ho3+:5I7 level and weaken the mid-infrared emissions. Hence, suitable host material with moderate phonon energy is important for highly efficient mid-infrared emissions. To understand more intuitively and clearly the phonon assisted energy transfer mechanism from Er3+ to Ho3+, emission cross sections of Er3+:4I11/2→4I15/2, 4 I13/2→4I15/2 transitions with the participation of m phonons (m=0, 1 and 2) and absorption cross sections of Ho3+:5I8→5I6, 5I8→5I7 transitions in prepared sample are depicted in Fig.6 (c) and (d). The emission cross section with the participation of m phonons can be determined by following equation29

σ em

Stokes

= σ em

 1 S 0me − S  + 1  hν k B T m! e −1  0

m

(20)

where σem is the emission cross section which is equal to the one with zero-phonon calculated by the McCumber equation29. S0 is the Huang-Rhys factor, which is 0.31 for rare earth ions28. It is worth noting that there is almost no spectral overlapping between Er3+:4I11/2→4I15/2 and Ho3+:5I8→5I6 transitions as well as that between Er3+: 4 I13/2→4I15/2 and Ho3+:5I8→5I7 transitions without the participation of phonons. However, a larger spectral overlap among them is determined after the matrix absorbs one or two phonons as indicated in Fig.6 (c) and (d). In this case, energy transfer microscopic parameter (CDA) from Er3+ to Ho3+ can be obtained by following expression28, 31, 32

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C DA =

3c 8π 4n 2

∫ σ em (λ )σ abs (λ )dλ D

A

(21)

According to Eq.(21) and Fig.6(c),(d), the energy transfer microparameter from Er3+:4I11/2 to Ho3+:5I6 level is (0.76±0.05)×10-40 cm6·s-1, significantly lower than that from Er3+:4I13/2 to Ho3+:5I7 level ((4.16±0.03)×10-40 cm6·s-1). Results indicate the dominant energy transfer process from Er3+:4I13/2 to Ho3+:5I7 level other than that from Er3+:4I11/2 to Ho3+:5I6 level. To further understand the interaction mechanism from Er3+:4I13/2 to Ho3+:5I7 level, the quenching rates (1/τ-1/τR) of Er3+:4I13/2→4I15/2 transition as a function of the product of Er3+ and Ho3+ concentration (NEr×NHo) are calculated based on decay curves of 1.53 µm emissions with various Ho3+ concentrations according to the following equation33,34

1

τ

−

1

τR

= KN A N D

(22)

where τR is intrinsic decay time. K is the constant containing donor-donor and donor-acceptor transfer constants. NA and ND are acceptor and donor concentrations, respectively. The obtained results are shown in Fig.7(a). As can be observed, the quenching rate depicts a good linear dependence on the product of Er3+ and Ho3+ concentrations (NEr×NHo) in the present concentration range. The behavior indicates a dipole-dipole quenching mechanism in the framework of a limited-diffusion energy transfer from Er3+ to Ho3+ ions33. Taking into account of the energy migration process among donors (Er3+) and the dipole-dipole interaction between Er3+ and Ho3+ ions, Burshtein expression is utilized to fit the fluorescence decay of Er3+ for an energy transfer assisted by donor migration, which is given as follows33, 35









I (t ) = I 0 exp − W +

 1 4 t − π 1.5N AC DA0.5t 0.5   τ0  3 

(23)

where τ0 is the intrinsic lifetime of donor Er3+ ions. W is the migration parameter. NA and CDA represent the concentration of acceptor Ho3+ ions and energy transfer microparameter, respectively. According to Eq.(23), the good agreement between experimental data and theoretical fit is obtained and Fig.7(b) shows the fitting results for Er3+/0.5Ho3+ codoped system. Results demonstrate the energy transfer mechanism is the dipole-dipole interaction in a diffusion-limited framework. Moreover, the energy transfer microparameter (CDA) is determined to 2.88×10-40 cm6·s-1, which is in good agreement with the value ((4.16±0.04)×10-40 cm6·s-1) obtained from Eq.(21). The energy migration rate is found to (1102±12) s-1.

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For further confirmation of hopping mechanism, the theoretical energy transfer rates have been estimated via the following expressions35, 36

γ DD2 =

16π 3 C DD N D2 9

(24)

γ DA2 =

16π 3 C DA N A2 9

(25)

where CDD and CDA are donor-donor energy migration and donor-acceptor energy transfer rates (here, CDD and CDA are 88.39×10-40 cm6·s-1 and 4.16×10-40 cm6·s-1, respectively, via Eq.(21)). NA and ND are acceptor (Ho3+) and donor (Er3+) ion concentration, respectively. For Er3+/0.5Ho3+ codoped system, γDD (335 s-1) is significantly larger than γDA (18 s-1), further confirming the existence of hopping migration assisted energy transfer between Er3+ and Ho3+ ions35, 36. 4.5 Concentration quenching at 2 µm In view of 2 µm emissions, the relative luminescent intensity increases firstly then decreases while the lifetime at 2µm reduces monotonically with Ho3+ concentration as depicted in Fig.3. This behavior is mainly considered as the diffusion towards unidentified impurities such as OH- groups presented in prepared glasses. It is reported that the problem can be separated into two cases: fast diffusion and diffusion-limited regime. As one can see, in diffusion-limited situation, the quenching rate is proportional to the product of concentrations of acceptor and donor. It is shown from Fig.7(c) that the quenching rate of Ho3+:5I7 level shows a linear behavior as a function of the product of Er3+ and Ho3+ ion concentrations. Results signify that concentration quenching of Ho3+ ions is the dipole-dipole interaction in diffusion-limited regime. In such a case, the quenching behavior at 2µm can be described as33

τ(N ) =

τR 1 + 9N 2 2πN 02

(26)

where τR and N0 are the intrinsic lifetime at 2µm and critical concentration for luminescent quenching. Fig.7(d) gives the experimental values and the fit to Eq.(26). It is found that Eq.(26) gives a good description of the experimental results. The fitted τR and N0 are 1.92 ms and 4.13×1020 cm-3, respectively. The determined N0 indicates that the fluorescent quenching occur when Ho3+ concentration reaches up to 4.13×1020 cm-3, which coincides with the results of Fig.3. 5. Conclusions In summary, upconversion, 1.53 µm and 2 µm fluorescence spectra as well as their decay curves were measured in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm LD. The energy transfer mechanism was proposed according to the energy level diagram between Ho3+ and Er3+ ions. Moreover, a rate equation model was 10


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developed to further confirm the energy transfer processes from Er3+ to Ho3+ ions. Energy transfer efficiency from Er3+: 4I13/2 to Ho3+: 5I7 level can reach as high as 75%. Such high energy transfer efficiency was attributed to the excellent matching of host phonon energy with the energy gap between Er3+: 4I13/2 and Ho3+: 5I7 levels. In addition, the microscopic energy transfer parameter (CDA) from Er3+: 4I13/2 to Ho3+: 5I7 level was estimated via the host assisted spectral overlap function and was found to be (4.16±0.04)×10-40 cm6·s-1, coinciding with the CDA (2.88×10-40 cm6·s-1) determined from decay analysis of Er3+: 4I13/2 level. Hopping migration assisted energy transfer is also proofed. Furthermore, concentration quenching of Ho3+: 5I7→5I8 transition is the dipole-dipole interaction in diffusion-limited regime and quenching concentration of Ho3+ reaches up to 4.13×1020 cm-3. This work may provide a beneficial guide for optimizing mid-infrared laser material. Acknowledgment The authors are thankful to Zhejiang Provincial Natural Science Foundation of China (Nos. LY15E020009, LY13F050003, and LR14E020003,), National Natural Science Foundation of China (Nos. 61308090, 61405182, 51372235, 51172252, and 51272243), overseas students preferred funding of activities of science and technology project, International S&T Cooperation Program of China (2013DFE63070), Research project of Zhejiang Province Education Department (No. Y201224887) and Public Technical International Cooperation project of Science Technology Department of Zhejiang Province(2015c340009). References 1. Wen, X.; Tang, G.; Wang, J.; Chen, X.; Qian, Q.; Yang, Z., Tm3+ doped barium gallo-germanate glass single-mode fibers for 2.0 µm laser. Opt. Express 2015, 23, 7722-7731. 2. Lagatsky, A. A.; Sun, Z.; Kulmala, T. S.; Sundaram, R. S.; Milana, S.; Torrisi, F.; Antipov, O. L.; Lee, Y.; Ahn, J. H.; Brown, C. T. A.; Sibbett, W.; Ferrari, A. C., 2 µm solid-state laser mode-locked by single-layer graphene. Appl. Phys. Lett. 2013, 102, 013113. 3. Geng, J.; Wang, Q.; Jiang, Z.; Luo, T.; Jiang, S.; Czarnecki, G., Kilowatt-peak-power, single-frequency, pulsed fiber laser near 2 µm. Opt. Lett. 2011, 36, 2293-2295. 4. Fang, Y.; Zhao, G.; Xu, J.; Zhang, N.; Ma, Z.; Hu, L., Energy transfer and 1.8µm emission in Yb3+/Tm3+ co-doped bismuth germanate glass. Ceramics International 2014, 40, 6037-6043. 5. Xu, R.; Xu, L.; Hu, L.; Zhang, J., Structural origin and laser performance of thulium-doped germanate glasses. J. Phys. Chem. A 2011, 115, 14163-7. 6. Yuan, J.; Shen, S. X.; Chen, D. D.; Qian, Q.; Peng, M. Y.; Zhang, Q. Y., Efficient 2.0 µm emission in Nd3+/Ho3+ co-doped tungsten tellurite glasses for a diode-pump 2.0 µm laser. J. Appl. Phys. 2013, 113, 173507. 7. Gao, G.; Wang, G.; Yu, C.; Zhang, J.; Hu, L., Investigation of 2.0µm emission in Tm3+ and Ho3+ co-doped oxyfluoride tellurite glass. J. Lumin. 2009, 129, 1042-1047. 11



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8. Heo, J.; Kim, K. Y.; Kwon, Y. K., Populations and Emission Properties of the5I6 and 5I7 Levels in Ho3+ Doped into PbO–Bi2O3–Ga2O3 Glasses. J. Am. Ceram. Soc. 2008, 91, 938-941. 9. Liu, X.; Wang, X.; Wang, L.; Kuan, P.; Li, M.; Li, W.; Fan, X.; Li, K.; Hu, L.; Chen, D., Realization of 2µm laser output in Tm3+-doped lead silicate double cladding fiber. Mater. Lett. 2014, 125, 12-14. 10. Plotnichenko, V. G.; Sokolov, V. O.; Dianov, E. M., Hydroxyl groups in germanosilicate glasses. J. Non-Cryst. Solids 2000, 278, 85-98. 11. Wei, T.; Chen, F.; Tian, Y.; Xu, S., Broadband 1.53µm emission property in Er3+ doped germa-silicate glass for potential optical amplifier. Opt. Commun. 2014, 315, 199-203. 12. Wei, T.; Chen, F.; Tian, Y.; Xu, S., Broadband near-infrared emission property in Er3+/Ce3+ co-doped silica–germanate glass for fiber amplifier. Spectrochim. Acta, Part A 2014, 126, 53-58. 13. Tian, Y.; Wei, T.; Cai, M.; Chen, F.; Wang, F.; Jing, X.; Zhang, J.; Zhang, Q.; Xu, S., Enhancement of 1.53 µm emission in erbium/cerium-doped germanosilicate glass pumped by common 808 nm laser diode. Appl. Opt. 2014, 53, 6148-6154. 14. Huang, F.; Liu, X.; Hu, L.; Chen, D., Optical properties and energy transfer processes of Ho3+/Er3+- codoped fluorotellurite glass under 1550 nm excitation for 2.0 µm applications, J. Appl. Phys. 2014, 116, 033106. 15. Li, X.; Zhang, W., The microscopic interaction parameters for Er3+/Ho3+ energy transfer in tellurite glasses. Physica B 2008, 403, 2714-2718. 16. Zhang, X.; Xu, T.; Dai, S.; Nie, Q.; Shen, X.; Lu, L.; Zhang, X., Investigation of energy transfer and frequency upconversion in Er3+/Ho3+ co-doped tellurite glasses. J. Alloys Compd. 2008, 450, 306-309. 17. Kumarsingh, A.; Rai, S.; Rai, A., Optical properties and upconversion in Er3+ and Ho3+ doped in lithium tellurite glass. Prog. Cryst. Growth Charact. Mater. 2006, 52, 99-106. 18. Wang, X.; Fan, S.; Li, K.; Zhang, L.; Wang, S.; Hu, L., Compositional dependence of the 1.8 µm emission properties of Tm3+ ions in silicate glass. J. Appl. Phys. 2012, 112, 103521. 19. Judd, B., Optical Absorption Intensities of Rare-Earth Ions. Phys. Rev. 1962, 127, 750-761. 20. Ofelt, G. S., Intensities of Crystal Spectra of Rare-Earth Ions. J. Chem. Phys.1962, 37, 511-520. 21. van Dijk, J. M. F., On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f–4f transitions in rare-earth ions. J. Chem. Phys. 1983, 78, 5317-5323. 22. Li, X.; Nie, Q.; Dai, S.; Xu, T.; Lu, L.; Zhang, X., Energy transfer and frequency upconversion in Ho3+/Yb3+ co-doped bismuth-germanate glasses. J. Alloys Compd. 2008, 454, 510-514. 23. Gao, G.; Wondraczek, L., Near-infrared downconversion in Pr3+/Yb3+ co-doped boro-aluminosilicate glasses and LaBO3 glass ceramics. Opt. Mater. Express 2013, 3, 633-644. 12


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24. Yang, Z.; Xu, S.; Hu, L.; Jiang, Z., Density of Na2O–(3 − x)SiO2–xGeO2 glasses related to structure. Mater. Res. Bull. 2004, 39, 217-222. 25. Pascuta, P.; Culea, E., FTIR spectroscopic study of some bismuth germanate glasses containing. Mater. Lett.2008, 62, 4127–4129. 26. Hwa, L. G.; Chang, Y. R.; Chao, W. C., Infrared spectra of lanthanum gallogermanate glasses. Mater. Chem. Phys.2004, 85, 158-162. 27. Ahlawat, N.; Sanghi, S.; Agarwal, A.; Bala, R., Influence of SiO2 on the structure and optical properties of lithium bismuth silicate glasses. J. Mol. Struct. 2010, 963, 82-86. 28. Balaji, S.; Sontakke, A. D.; Sen, R.; Kalyandurg, A., Efficient ~2.0 µm emission from Ho3+ doped tellurite glass sensitized by Yb3+ ions: Judd-Ofelt analysis and energy transfer mechanism. Opt. Mater. Express 2011, 1, 138-150. 29. Zhang, W.-J.; Chen, Q.-J.; Qian, Q.; Zhang, Q.-Y.; Ballato, J., The 1.2 and 2.0 µm Emission from Ho3+ in Glass Ceramics Containing BaF2 Nanocrystals. J. Am. Ceram. Soc. 2012, 95, 663-669. 30. Gao, G.; Hu, L.; Fan, H.; Wang, G.; Li, K.; Feng, S.; Fan, S.; Chen, H.; Pan, J.; Zhang, J., Investigation of 2.0µm emission in Tm3+ and Ho3+ co-doped TeO2– ZnO–Bi2O3 glasses. Opt. Mater. 2009, 32, 402-405. 31. Sontakke, A. D.; Biswas, K.; Mandal, A. K.; Annapurna, K., Concentration quenched luminescence and energy transfer analysis of Nd3+ ion doped Ba-Al-metaphosphate laser glasses. Appl. Phys. B 2010, 101, 235-244. 32. Balaji, S.; Mandal, A. K.; Annapurna, K., Energy transfer based NIR to visible upconversion: Enhanced red luminescence from Yb3+/Ho3+ co-doped tellurite glass. Opt. Mater. 2012, 34, 1930-1934. 33. Balda, R.; Fernández, J.; García-Revilla, S.; Fernández-Navarro, J. M., Spectroscopy and concentration quenching of the infrared emissions in Tm3+-doped TeO2-TiO2-Nb2O5 glass. Opt. Express 2007, 15, 6750-6761. 34. Peng, M.; Zhang, N.; Wondraczek, L.; Qiu, J.; Yang, Z.; Zhang, Q., Ultrabroad NIR luminescence and energy transfer in Bi and Er/Bi co-doped germanate glasses. Opt. Express 2011, 19, 20799-20807. 35. Sontakke, A. D.; Annapurna, K., Phonon assisted effective non-resonant energy transfer based 1µm luminescence from Nd3+–Yb3+ codoped zinc–boro–bismuthate glasses. J. Lumin. 2013, 138, 229-234. 36. Zhou, J.; Moshary, F.; Gross, B. M.; Arend, M. F.; Ahmed, S. A., Population dynamics of Yb3+, Er3+ co-doped phosphate glass. J. Appl. Phys. 2004, 96, 237-241.

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Table 1 The total transition rates (s-1) for several levels in Er3+ and Ho3+ doped germanosilicate glass determined by Judd-Ofelt theory and energy gap law. W75

W30

W76

W43

W85

W86

W87

W32

W31

W30

W21

W31

W41

2802.48

1888.23

699.29

1.54×106

1462.88

1117.71

1.05×106

175.99

98.94

1888.23

5.25×104

84

900

14


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Figure captions Fig.1.Upconversion emission spectra of Er3+ singly and 0.5Ho3+/Er3+ co-doped germanosilicate glasses at 980 nm LD excitation (The inset is Ho3+ concentration dependent on upconversion emission intensity). Fig.2.Near-infrared emission spectra in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm. Fig.3.Mid-infrared fluorescence spectra in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm (The inset is the dependence of Ho3+ concentration on 2µm lifetime). Fig.4.Energy level diagram and energy transfer mechanism among Er3+ and Ho3+ ions (The left hand is the absorption spectrum of Er3+/Ho3+ codoped germanosilicate glass). Fig.5(a). The decay curve at 1.53 µm in Er3+/0.5Ho3+ codoped germanosilicate glass and fitted curve determined by Eq.(17); (b) the decay curves at 1.53 µm in Er3+ singly and Er3+/Ho3+ codoped germanosilicate glasses (The inset is lifetimes (τ) from single exponential fitting and energy transfer efficiency (η)). Fig.6(a). FTIR spectrum of undoped germanosilicate glass; (b) Energy transfer probability as a function of phonon energy in Er3+/Ho3+ codoped germanosilicate glass calculated by Eq.(19); (c) Emission cross sections assisted by m (m=0, 1 and 2) phonons for Er3+: 4I11/2→4I15/2 transition and absorption cross section for Ho3+:5I8→5I6 transition; (d) Absorption cross section of Ho3+:5I8→5I7 transition and emission cross sections of Er3+: 4 I13/2→4I15/2 transition with the participation of m (m=0, 1 and 2) phonons in prepared sample. Fig.7(a). Quenching rates (1/τ-1/τR) of the Er3+:4I13/2→4I15/2 transition as a function of the product of Er3+ and Ho3+ concentration (NEr×NHo); (b) The fluorescence decay curve at 1.53 µm in Er3+/0.5 mol% Ho3+ codoped system with theoretical fitting generated by hopping model; (c) Quenching rates (1/τ-1/τR) of the Ho3+:5I7→5I8 transition as a function of the product of Er3+ and Ho3+ concentration (NEr×NHo); (d) Experimental lifetimes of 5I7 level as a function of Ho3+ concentration and the fitted curve with Eq. (26).

15



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Table of Contents graphic

16


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Fig.1.Upconversion emission spectra of Er3+ singly and 0.5Ho3+/Er3+ co-doped germanosilicate glasses at 980 nm LD excitation (The inset is Ho3+ concentration dependent on upconversion emission intensity). 289x202mm (300 x 300 DPI)



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Fig.2.Near-infrared emission spectra in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm. 297x210mm (300 x 300 DPI)


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Fig.3.Mid-infrared fluorescence spectra in Ho3+/Er3+ codoped germanosilicate glasses pumped at 980 nm (The inset is the dependence of Ho3+ concentration on 2µm lifetime). 289x202mm (300 x 300 DPI)



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Fig.4.Energy level diagram and energy transfer mechanism among Er3+ and Ho3+ ions (The left hand is the absorption spectrum of Er3+/Ho3+ codoped germanosilicate glass). 289x202mm (300 x 300 DPI)


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Fig.5(a). The decay curve at 1.53 µm in Er3+/0.5Ho3+ codoped germanosilicate glass and fitted curve determined by Eq.(17); (b) the decay curves at 1.53 µm in Er3+ singly and Er3+/Ho3+ codoped germanosilicate glasses (The inset is lifetimes (τ) from single exponential fitting and energy transfer efficiency (η)). 289x202mm (300 x 300 DPI)



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Fig.6(a). FTIR spectrum of undoped germanosilicate glass; (b) Energy transfer probability as a function of phonon energy in Er3+/Ho3+ codoped germanosilicate glass calculated by Eq.(19); (c) Emission cross sections assisted by m (m=0, 1 and 2) phonons for Er3+: 4I11/2→4I15/2 transition and absorption cross section for Ho3+:5I8→5I6 transition; (d) Absorption cross section of Ho3+:5I8→5I7 transition and emission cross sections of Er3+: 4I13/2→4I15/2 transition with the participation of m (m=0, 1 and 2) phonons in prepared sample. 289x202mm (300 x 300 DPI)


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Fig.7(a). Quenching rates (1/τ-1/τR) of the Er3+:4I13/2→4I15/2 transition as a function of the product of Er3+ and Ho3+ concentration (NEr×NHo); (b) The fluorescence decay curve at 1.53 µm in Er3+/0.5 mol% Ho3+ codoped system with theoretical fitting generated by hopping model; (c) Quenching rates (1/τ-1/τR) of the Ho3+:5I7→5I8 transition as a function of the product of Er3+ and Ho3+ concentration (NEr×NHo); (d) Experimental lifetimes of 5I7 level as a function of Ho3+ concentration and the fitted curve with Eq. (26). 289x202mm (300 x 300 DPI)


Quantitative Analysis of Energy Transfer and Origin of Quenching in

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