Z-scan Measurement of the Upconversion Coefficient in 

Er:YAG

by Jeffrey O. White, Robert Dibiano, Alexander B. Fick, 

and John E. McElhenny

ARL-TR-4994 September 2009

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Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TR-4994 September 2009

Z-scan Measurement of the Upconversion Coefficient in 

Er:YAG

Jeffrey O. White, Robert Dibiano, Alexander B. Fick, 

and John E. McElhenny

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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4. TITLE AND SUBTITLE

Z-scan Measurement of the Upconversion Coefficient in Er:YAG

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Jeffrey O. White, Robert Dibiano, Alexander B. Fick, and John E. McElhenny

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U.S. Army Research Laboratory

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Adelphi, MD 20783-1197

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14. ABSTRACT

Solid-state laser research at the U.S. Army Research Laboratory (ARL) is currently emphasizing techniques for power scaling 

and achieving wavelengths in the eye-safer spectral region. We are studying erbium-doped yttrium aluminum garnet 

(Er:YAG), because it can be operated with a low quantum defect and has transitions around 1.6 μm. However, it suffers from 

cooperative pair upconversion, which can raise the lasing threshold, and thus lower the output power. In this report, we 

demonstrate how to measure the upconversion coefficient Cup using the z-scan technique with a continuous wave source. We 

find Cup to be proportional to [Er], for concentrations ranging from 0.5–5%. The value we find at 1% is 3.6×10-17 cm3

/s, 

approximately eight times larger than a value reported previously in the literature.

15. SUBJECT TERMS

ER:YAG, upconversion, z-scan

16. SECURITY CLASSIFICATION OF: 

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 ABSTRACT

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19a. NAME OF RESPONSIBLE PERSON

Jeffrey O. White

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(301) 394-0069

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iii

Contents

List of Figures iv

Summary 1

1. Introduction/Background 3

2. Experiment/Calculations 4

3. Results and Discussion 8

4. Summary and Conclusions 9

5. References 10

Symbols, Abbreviations, and Acronyms 11

Distribution List 12
iv

List of Figures

Figure 1 Energy levels in the lowest four manifolds of Er:YAG. The scale on the right is 

magnified. ..................................................................................................................................3

Figure 2. Experimental setup. .........................................................................................................4

Figure 3. Absorption cross section of Er:YAG for a range of crystal temperatures.......................5

Figure 4. Beam radius data and a least squares theoretical fit for the 20-cm lens..........................6

Figure 5. (a) Beam radius as a function of z, (b) transmission as a function of z, and (c) 

effective absorption coefficient as a function of peak intensity. Three runs at 1, 2, and 3 

W are combined on the bottom two graphs. ..............................................................................8

Figure 6. Losses due to upconversion as a function of both erbium doping and beam peak 

intensity. Increasing either [Er] or peak intensity will cause more upconversion until a 

maximum upconversion rate has been reached. ........................................................................9
1

Summary

In a solid-state laser, cooperative upconversion can be beneficial or deleterious, i.e., it can 

populate or de-populate the upper laser level, depending on the ion and transitions involved. In 

the case of erbium-doped yttrium aluminum garnet (Er:YAG), at excitation densities typically 

occurring in our lasers, the dominant upconversion process occurs when two ions in the first 

excited manifold 4

I13/2 are in close proximity. This competes with stimulated emission from the 

4

I13/2 manifold. The coefficient that characterizes this process has been measured in the past with 

pulsed sources by examining the non-exponential decay of fluorescence from the various levels 

involved. We propose a steady-state technique for measuring the upconversion coefficient that 

uses the same continuous wave (CW) source that is used to pump an Er:YAG laser. We find that 

Cup is proportional to [Er], as expected, but approximately eight times larger than previously 

reported values.
2

INTENTIONALLY LEFT BLANK.
3

1. Introduction/Background

Er:YAG is a promising material for eye-safer lasers because emission from the 4I13/2 manifold is 

in the 1.6-μm spectral region. Er:YAG can also address the need for a low quantum defect, 

because the crystal field splitting is large enough at 300 K that one can pump and lase between 

the lowest two manifolds. The energy levels in the lowest four manifolds are shown in figure 1. 

4

I 15/2

4

I 13/2

4

I 11/2

4

I 9/2

N1

N2

N3

N4

Pump

upconversion

W43

W32

W21 300°K

300°K

Figure 1 Energy levels in the lowest four manifolds of Er:YAG. The scale on the 

right is magnified.

When pumped at 1532 nm at room temperature, Er:YAG lases at 1645 nm, representing a 

quantum defect of about 7%. A small quantum defect is advantageous for high average power 

lasers, where heat generation is proportional to the input power and quantum defect. However 

the upper laser level can be depleted by cooperative pair upconversion (CPU), because the 4I9/2

manifold in Er:YAG is at 12301–12760 cm–1

, about twice the energy of the 4I13/2 manifold at 

6544–6879 cm–1

. In this (lowest order) process, the electron in one ion jumps to the 4I9/2

manifold and the electron in the other ion returns to the ground state 4I15/2 manifold.

Higher order upconversion also occurs. For example, when Er:YAG is pumped at 1532 nm, 

green light is emitted at ~500 nm. Although it is possible for multiple photons to excite a single 

ion in stepwise fashion before it relaxes, the majority of Er ions above the 4

I13/2 manifold arrive 

there through a cooperative process (1).
4

2. Experiment/Calculations

The schematic for the experimental setup is shown in figure 2. A 5-MHz linewidth distributed 

feedback Bragg (DFB) laser diode is temperature tuned to resonance with the 1532-nm Er 

absorption line (figure 3). It seeds the Er fiber amplifier with 14 mW. The 1–3 W output of the 

amplifier is collimated, chopped, and focused, then passes through the sample before falling on 

an indium gallium arsenide (InGaAs) photodiode connected to a lock-in amplifier (LIA). The 

optical chopper reduces the duty cycle to 10%, to minimize sample heating. The intensity can be 

varied over a factor of 10 by changing the power of the beam, but it can be varied by 3–4 orders 

of magnitude by translating the sample axially through the focus. The Er concentration was 

varied from 0.5–5% by using different samples of 1-mm thickness and 10-mm diameter (2). The 

samples are anti-reflection coated on both sides.

Figure 2. Experimental setup.

With the sample removed, the photodiode measures the incident power. With the sample in 

place, the motorized stage moves in the z-direction through the focus with steps of 2 mm, under 

computer control. Focal lengths of 15 and 20 cm were used. The computer also reads from an 

analog-to-digital converter connected to the analog output of the LIA. Room light and 

upconversion fluorescence light are blocked by a long-wave-pass filter. A diffuser and a series 

of neutral density filters in front of the photodiode reduce the current to ~0.2 μA, a level that can 

be handled by the LIA. 
5

Figure 3. Absorption cross section of Er:YAG for a range of crystal temperatures.

A preliminary run is made to determine the intensity profile of the beam at each z position. 

These data were obtained by measuring the transmitted power when a razor blade was translated 

across the beam in the x direction. The transmitted power corresponds to an integral over a halfspace of the two-dimensional Gaussian intensity profile. This reduces to the cumulative 

distribution function, equation 1 (3). The beam radius, w, is obtained by fitting the experimental 

data to equation 2. P is the total incident power. 

( ) dt

w

t

w

p F x| μ w x

∫−∞

− − = = ]

2

( ) exp[ 21 , 2

2 μ

π

(1)

q = P[1− F(x| μ,w)] (2)

The theoretical equation for a TEM00 Gaussian beam radius in homogeneous media (4) was then 

fit to the data (figure 4). The good fit indicates a fundamental Gaussian beam. 
6

Figure 4. Beam radius data and a least squares theoretical fit for the 20-cm lens.































 = ⋅ +

2

0

2

0

2( ) 1

z

z

w z w (3)

Next, a nominal upconversion value Cup

~ was obtained from the literature (1). For each sample 

Cup

~ is calculated from equation 4. The relation is simply a proportionality constant relating the 

upconversion rate to the density of Er ions.

up ErNY C f 38 3.6 10 ~ − = × 

Y Al O

YAG

Y Av M M M

N N

3 5 12

3

+ + = ρ (4)

The theoretical transmission curve as a function of z was calculated for a few multiples of Cup

~ . 

The model that follows assumes a uniform intensity (plane wave); therefore, the Gaussian profile 

has to be simulated as a superposition of different intensities, each propagated separately through 

the sample. 
7

The plane wave model includes rate equations for the lowest four manifolds of Er3+, grouping 

together the population of each manifold.

( ) 2

2 1 2 21 3 31 4 41 2

1 f N f N N W N W N W C N

h

I

dt

dN

ep ap up

p

p p = + − + + + +

ν

σ . (5)

( ) 2

2 1 2 21 3 32 4 42 2

2 f N f N N W N W N W 2C N

h

I

dt

dN

ep ap up

p

p p = − − − + + − ν

σ

(6)

( ) 4 43 3 32 31

3 N W N W W

dt

dN = − + (7)

( ) 4 43 42 41

2

2

4 C N N W W W

dt

dN = up − + + (8)

Here, N1 is the population of the lowest 4I15/2 level, IP is the pump intensity, σP is the absolute 

cross section, fep (fap) is the probability that an electron is in a state that can emit (absorb) a pump 

photon, Wij is the relaxation rate from level i to level j, and Cup is the upconversion parameter. 

Also included in the model is a propagation equation for the pump beam:

( ) p p ep ap p p

p I f N f N I

d z

d I = σ 2 − 1 = −α . (9)

Equations 5–9 are solved in steady state using MATLAB®. The effective absorption coefficient 

αeff is calculated from the transmission data, using equation 10:

I L I ( ) ( L) p = p −αeff ( ) 0 exp (10)

There are a number of assumptions made in this experiment and its analysis. First, the beam 

radius is assumed to be constant throughout the 1-mm thickness of the sample. This makes the 

intensity and transmission calculations much easier, and is supported by all samples having a 

thickness smaller than the confocal parameter, or Rayleigh range. Another assumption is that 

scattering losses were negligible. This is well-justified by the excellent optical quality of the 

sample. As stated previously, the mathematical model only accounts for CPU to the 4

I9/2

manifold; we neglect the effect of multiple photons exciting a single ion or CPU occurring to 

higher energy states. The model is also “local” in the sense that the populations at any point in 

space are determined by the intensity at that point. This assumes that the excitations only 

migrate distances that are short compared to the beam diameter.
8

3. Results and Discussion

The z-scan results for transmission as a function of z show a peak where the beam intensity is 

highest, due to saturation of the absorption (figure 5b). The effect of upconversion is to shift the 

onset of saturation to higher intensities, because it depletes the 4I13/2 manifold. The shift of 

saturation can be seen more clearly in a plot of αeff versus peak intensity (figure 5c). The 

experimental data indicate a value of Cup that is approximately eight times larger than that 

reported in the literature. We estimate the accuracy to be a factor of two.

Figure 5. (a) Beam radius as a function of z, (b) transmission as a function of z, and (c) effective absorption 

coefficient as a function of peak intensity. Three runs at 1, 2, and 3 W are combined on the bottom two 

graphs. 
9

Using the simulation and Cup Cup

~ = 8 , it is possible to plot the losses due to upconversion as a 

function of both intensity and erbium concentration. Increasing either intensity or [Er] resulted 

in more loss, as seen in figure 6. The upconversion seems to scale linearly with [Er], although its 

relationship with peak intensity is more complicated.

Figure 6. Losses due to upconversion as a function of both erbium doping and beam peak intensity. Increasing 

either [Er] or peak intensity will cause more upconversion until a maximum upconversion rate has been 

reached. 

4. Summary and Conclusions

In an Er:YAG laser operating at 1645 nm, no upconversion would ideally take place, and the 

pump photons would have a 1:1 ratio with emitted photons. The only non-negligible heat 

generation would be from phonons that make up the quantum defect. The presence of 

upconversion causes more heat generation and lowers the power of the emitted laser beam, 

putting an upper bound on the allowable pump beam intensity and [Er], both of which introduce 

limits in creating a high energy laser. The results of the experiment show that the assumptions 

made were justified, that the experimental setup is effective at producing reliable information 

about the behavior of upconversion in Er:YAG, and that upconversion increases with [Er] and 

beam intensity. 
10

5. References

1. Iskandarov, M. O.; Nikitichev, A. A.; Stepanov, A. I. J. Opt. Technol. 2001, 68, 885.

2. Scientific Materials, Inc., Bozeman, MT.

3. NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.6.7.1, 2006.

4. Yariv, A. Quantum Electronics 1975, 111.

5. White, J. O.; Dubinskii, M.; Merkle, L. D.; Kudryashov, I.; Garbuzov, D. J. Opt. Soc. Am. 

B. 2007, 24, 2454.
11

Symbols, Abbreviations, and Acronyms

CPU cooperative pair upconversion

CW continuous wave

DFB distributed feedback Bragg (laser)

Er erbium

InGaAs indium gallium arsenide

LIA lock-in amplifier

TEM00 transverse electromagnetic, fundamental mode

YAG yttrium aluminum garnet
12

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