Supplementary Information
Observation of efficient population of the red emitting state from the green state
by non-multiphonon relaxation in Er3+–Yb3+ system
Jiahua Zhang*, Zhendong Hao, Jing Li, Xia Zhang, Yongshi Luo, and Guohui Pan
State Key Laboratory of Luminescence and Applications, Changchun Institute of Optics, Fine
Mechanics and Physics, Chinese Academy of Sciences, 3888 Eastern South Lake Road, Changchun
130033, China
*To whom correspondence should be addressed. E-mail: zhangjh@ciomp.ac.cn
This supplementary information contains:
A. Analysis of the increment in 1530 nm emission intensity
B. Description of the decay of the green emission
C. Derivation of R1/R2 ratio upon pulse infrared excitation
A. Analysis of the increment in 1530 nm emission intensity
There appears an intensity increase of Er3+ 1530 nm emission under 520 nm excitation with respect
to that under 650 nm excitation. The increment is due to extra populations by CRNB and the
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S3/2→4I13/2 radiative transition upon 520 nm excitation. If denote the excitation flow at 520 nm by 𝐹,
the emission efficiency at 1530 nm by 𝜂r1 , then the increment (𝐼1 − 𝑖1 ) in 1530 nm emission
intensity is
𝐼1 − 𝑖1 = F(𝜂CRNB + β𝜂r4 )𝜂r1
(S1)
𝐼4 = F 𝜂r4
(S2)
with
When x =0, then 𝜂CRNB = 0, combination of Eq.(S1) and (S2) gives
𝜂r1 = (
𝐼1 −𝑖1
1
𝛽𝐼4
)
(S3)
0
In experiment, we found the emission lifetimes at 1530 nm is independent on x, meaning
unchanged 𝜂r1 with x. Using Eq.(S1) - (S3), we obtain
𝜂CRNB
𝛽𝜂r4
=
𝐼1 −𝑖1
𝐼4
(𝐼
𝐼4
1 −𝑖1
) −1
(S4)
0
B. Description of the decay of the green emission
Under 520 nm excitation of Er3+ 2H11/2 + 4S3/2, we assume the decay pattern of the green emission
contains an undetected fast component and a detectable slow component, corresponding to the Er3+
ions in the nearest and distant Er3+ -Yb3+ pairs, respectively, as shown in Figure S1. The relative
efficiency 𝜂r4 ⁄𝜂r4,0 or intensity 𝐼4 ⁄𝐼4,0 of the green emission is the ratio of the area under the
decay curve in the presence (solid) of Yb3+ to that in its absence (dashed), and expresses as
𝜂r4 ⁄𝜂r4,0 = 𝐼4 ⁄𝐼4,0 = 𝑓𝜏4 /𝜏4,0
(S5)
𝑓 = (𝜂r4 ⁄𝜂r4,0 )(𝜏4,0⁄𝜏4 ) = (𝐼4 ⁄𝐼4,0 )(𝜏4,0 /𝜏4 )
(S6)
then
Figure S1 Decay pattern of the green emission in the presence of Yb3+ (solid) and in the absence of
Yb3+ (dashed).
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C. Derivation of R1/R2 ratio upon pulse infrared excitation
Figure S2 Diagram of energy transfer upconversion in Er3+–Yb3+ system.
As shown in Figure S2, the 4S3/2 is populated by a rapid MPR from the 4F7/2, and this state is excited
from 4I11/2 by ETU. In ETU the excitation is dominantly performed by energy transfer from excited
Yb3+. The high Yb3+ and low Er3+ concentrations of this work may allow the average rate of
migration between Yb3+ ions much larger than that of transfer to Er3+. One of the evidence is the
single exponential decay of Yb3+ emission. Hence, one can then describe energy transfer with an
average transfer rate. We assume the 4F7/2 population can completely relax down to the 4S3/2 state due
to a rapid MPR from the 4F7/2. After pulse excitation of Yb3+, we write the population of Er3+ 4I11/2 as
the same single exponential decay as Yb3+ emission because Er3+ 4I11/2 and Yb3+ 2F5/2 are thermally
coupled in case of rapid energy transfer between them. Then we have rate equations
𝑑𝑛1 ⁄𝑑𝑡 = 𝑊21 𝑛2 − 𝑛1 /τ1
(S7)
𝑛2 = 𝑛2 (0)exp(− 𝑡⁄𝜏d )
(S8)
𝑛d = 𝑛d (0)exp(− 𝑡⁄𝜏d )
(S9)
with
Substitution of Equation (S8) and (S9) into (S7) gives
𝑛1 =
𝑊21 𝑛2 (0)τ1 𝜏d
τ1 −τd
𝑡
𝑡
1
d
[exp (− 𝜏 ) − exp (− 𝜏 )]
(S10)
In the UCL measurement for pulse excitation, we detect upconversion luminescence yield over
time, therefore,
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∞
𝑅1 @pulse = 𝜂R ∫0 𝐶𝑑3 𝑛𝑑 𝑛1 𝑑𝑡
∞
𝑅4 @pulse = 𝜂R 𝜂43 ∫0 𝐶d5 𝑛d 𝑛2 𝑑𝑡
(S11)
(S12)
We insert Equations (S8)-(S10) into (S11) and (S12) and obtain,
(𝑅1⁄𝑅4 ) @pulse = [τd ⁄(𝜏1 + 𝜏d )](𝐶d3 /𝐶d5 )𝑊21 𝜏1 /𝜂43
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(S13)