A Fluorescence-Based Determination of Quantum Efficiency

by Scott Melis

ARL-CR-0726 December 2013

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Army Research Laboratory

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ARL-CR-0726 December 2013

A Fluorescence-Based Determination of Quantum Efficiency

Scott Melis

American Society for Engineering Education

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Washington, DC 20036-2479

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A Fluorescence-Based Determination of Quantum Efficiency

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14. ABSTRACT

This work attempts to apply the method of determining quantum efficiency described by de Mello et al. in order to verify that 

it is accurate and can be used to measure unknown samples in the future. This method takes direct spectra of the fluorescence 

of a sample excited by an incoming excitation laser beam in an integrating sphere. Three scenarios are considered: a sphere 

with no sample inside such that only the laser light is scattered, a sphere with the sample inside but not in the direct path of the 

laser, and a sample inside and in the direct path of the laser. Samples of 1% ceramic neodymium (Nd): yttrium aluminum 

garnet (YAG) and 10% crystal ytterbium (Yb):YAG (chosen after the poor result achieved for Nd:YAG) were tested, since 

both are thought to have high quantum efficiencies of close to 1. In this experiment, the quantum efficiency values determined 

were 0.54 and 0.99, respectively. These results forced a consideration of all possible sources of error in this method; future 

work will be needed to determine if the technique is still viable.

15. SUBJECT TERMS

Quantum efficiency, fluorescence, Nd, Yb, YAG, integrating sphere

16. SECURITY CLASSIFICATION OF:

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OF 

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Larry D. Merkle

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iii

Contents

Lift of Figures iv

List of Tables iv

1. Background 1

2. Introduction 1

3. Equipment 1

4. Experiment 2

5. Results 3

6. Analysis 5

7. Retrial With 10% Yb:YAG 6

8. Conclusions 8

9. References 9

Appendix A. System Response Curves 11

Appendix B. Example of the Data Analysis 13

Appendix C. Transmission Spectra of Samples 15

Appendix D. Data for Reabsorption Determination for Yb:YAG 17

Distribution List 18
iv

Lift of Figures

Figure 1. Diagram showing the three scenarios for the quantum efficiency measurement. 

(1) The sphere is empty. (2) The sample is in the sphere but out of the beam. (3) The 

sample is in the sphere and in the beam.....................................................................................3

Figure 2. This is the raw spectrum produced by the 1% Nd:YAG sample located directly in 

the beam. The out of the beam case produced a similar spectrum with smaller 

fluorescence values and a larger laser line.................................................................................5

Figure 3. Raw spectrum produced by the 10% Yb:YAG sample located directly in the beam. 

The out of the beam case produced a similar spectrum with smaller fluorescence values 

and a larger laser line. The laser line for this scenario peaked at 9.5 on this scale and has 

been cut off for clarity of the fluorescence spectrum. ...............................................................7

Figure A-1. Normalized system response curve generated for the aluminum holder in the 

integrating sphere in conjunction with the 2.2-μm InGaAs detector and the 1-μm blazed 

grating. .....................................................................................................................................11

Figure A-2. Normalized system response curve obtained when the same method was applied 

to the coated sample holder in conjunction with the 2.2-μm InGaAs detector and the 

1-μm blazed grating.................................................................................................................12

Figure B-1. True fluorescence spectrum of 1% ceramic Nd:YAG................................................13

Figure B-2. Photon flux of 1% ceramic Nd:YAG. ........................................................................14

Figure C-1. Transmission spectrum for the 1% ceramic Nd:YAG sample used in this 

experiment................................................................................................................................15

Figure C-2. Transmission spectrum for the 10% Yb:YAG sample used in this experiment.........16

Figure D-1. Photon flux scaled for the detection system for the powdered sample and the 

bulk sample measured directly in the spectrometer.................................................................17

List of Tables

Table 1. Values for Le, Lo, Li, Fo, and Fi using the 1% Nd:YAG sample........................................5

Table 2. Values for Le, Lo, Li, Fo, and Fi using the 10% Yb:YAG sample......................................7
1

1. Background

The quantum efficiency of a material is an important measurement in laser applications. It is 

defined as the percentage of incident photons that a material converts to fluorescence, with the 

energy of the unconverted photons being wasted as heat. A high quantum efficiency value would 

therefore allow the material to waste little energy when it is lased. This makes the material more 

useful as a laser for three reasons. First, there is no risk of overheating the laser material, since 

little energy is converted to heat. Heating it by too much could degrade the material or the beam 

quality, making the laser less effective at whatever tasks are required. Second, the lowered 

heating means that the laser is easier to construct and operate because it requires simpler cooling 

processes. Finally, a highly efficient laser material would require less power to operate, since the 

input power is more readily converted to light. With these goals in mind, a determination of 

whether or not a material possesses a high value of quantum efficiency is very necessary in laser 

applications and laser material research.

2. Introduction

The goal of this project was to interpret the method used by de Mello et al. (1) for calculating 

quantum efficiency and apply it to enable accurate measurements of bulk materials. Doing so 

would validate this method as well as create a setup that could be used to analyze future samples 

of unknown efficiency. To do this, a standard sample was needed to validate the technique. For 

this, a sample of 1% ceramic neodymium (Nd): yttrium aluminum garnet (YAG) was chosen. In 

addition, when the results with Nd:YAG proved to be incorrect, a sample of 10% ytterbium 

(Yb):YAG was also selected. Both samples were chosen due to their well-known and accepted 

high quantum efficiency values of close to 1.

3. Equipment

The following equipment was used:

• Spectra-Physics titanium sapphire laser

• Horiba Fluorolog 3 fluorescence spectrometer

○ With a nominally 2.6-μm indium gallium arsenide (InGaAs) detector and 1-μm blazed 

grating
2

○ With a nominally 2.2-μm InGaAs detector and 1-μm blazed grating

• Stanford Research Systems SR830 lock-in amplifier

• Thorlabs M37L02 multimode fiber with a 550-μm core and a 0.22 numerical aperture

• Edmund Optics integrating sphere

• Avian Technologies Avian-B barium sulfate white reflectance coating

○ Applied to an aluminum sample holder 

• Optronic Laboratories OL220IR spectral standard lamp

• Varian Cary 6000i ultraviolet (UV)-visible (Vis)-near infrared (NIR) spectrophotometer

• 1% ceramic Nd-doped Nd:YAG sample provided by Dr. Larry Merkle

• 10% crystal Yb-doped Yb:YAG sample borrowed from Dr. Alex Newburgh

4. Experiment

The experiment relies upon being able to measure a value for the photon flux in an integrating 

sphere. An integrating sphere is a hollow sphere made of a highly reflective material such that 

light in the sphere is scattered evenly throughout. The sphere used in this experiment was one 

purchased from Edmund Optics. The Spectra-Physics titanium sapphire laser was chopped at 

100 Hz and then allowed to shine through one opening of the sphere while a sample holder was 

positioned at another. Finally, a M37L02 fiber was attached to the sphere so that the light could 

be guided out of the sphere and into the Fluorolog spectrometer.

In replicating the method of de Mello et al. (1), the integrating sphere was used to capture light 

from three different scenarios, as shown in figure 1. The first scenario involved only an empty 

sample holder in the sphere. This was used to measure only the spectrum of the laser line for 

determining a value of its photon flux, labeled here as Le to reflect that it is the value for the laser 

line when the sphere was empty. The second scenario involved the sample being placed in the 

sphere such that it was not hit by the laser beam directly but was allowed to fluoresce from the 

scattered laser light. Measuring the photon flux of the fluorescence and the scattered laser beam 

produced values for Fo and Lo, labeled to reflect that the sample was out of the beam. Finally, the 

third scenario involved putting the sample directly in the laser beam path and again measuring 

the photon flux, labeled Fi and Li for the fact that the sample is in the beam.
3

(1 )

( )

o

i

e

o

o

i

i

L

L

L

F

L

L

F





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Figure 1. Diagram showing the three scenarios for the quantum efficiency measurement. (1) The sphere is empty.

(2) The sample is in the sphere but out of the beam. (3) The sample is in the sphere and in the beam.

With these data, it is possible to determine a value for the quantum efficiency of the material in 

question using the equation derived by de Mello et al. (1). Through assessing their derivation, 

their equation for the quantum efficiency, η, was found to be a believable answer when 

considering a simple model of the integrating sphere system. Therefore, the equation used for 

this experiment was

(1)

5. Results

In order to validate the experimental method, a reference sample was needed as a standard. The 

sample would need to be one with a well-known quantum efficiency value and, preferably, 

limited reabsorption. Because of these requirements, a sample of 1% ceramic Nd:YAG was used 

due to its well-known quantum efficiency value of close to 1.

During the first attempt at the experiment, a spectrum of the Nd:YAG sample was measured in 

the three integrating sphere scenarios using the nominally 2.2-μm detector and 1-μm blazed 

grating. The sample was held in the sphere using a bare aluminum sample holder of unknown 

reflectivity. The titanium sapphire laser was tuned to a wavelength of 808.6 nm so that the 

Nd:YAG would be able to absorb the incoming laser light without interfering with the 

fluorescence. These data were initially inconclusive since a calibration of the sphere and the 

sensitivity of the InGaAs detector had not been performed. However, it was still believed that it 

would most likely be incorrect due to the sample holder being made of bare, machined aluminum 

instead of a material of high reflectivity.
4

To adjust the data for the system’s sensitivity changes at different wavelengths, the OL220IR 

standard lamp was shone into the integrating sphere in hope of correcting for the system as a 

whole. The spectrum produced by the integrating sphere system was then divided by the 

accepted values for the standard lamp’s spectrum and normalized. A graph of this system 

response curve can be found in appendix A. The data set could then be divided by this calibration 

curve to scale the data relative to the system’s highest sensitivity at roughly 1330 nm. Applying 

this system response curve to the data set and multiplying each data point by its corresponding 

wavelength to convert to a value of the photon flux in relative units produced the necessary 

graph for this experiment. When integrated, this graph produced a quantum efficiency value of 

0.46. 

Since this initial value for the quantum efficiency was far from what was expected, it was 

decided to first correct the issue of the aluminum holder. To do this, the Avian-B barium sulfate 

white reflectance coating was purchased and applied to the aluminum holder. Doing this caused 

the holder to more closely resemble the reflectivity of the integrating sphere. In addition, the 

nominally 2.2-μm InGaAs detector was replaced with the 2.6-μm detector due to the belief that 

the longer wavelength detector actually had a slightly higher sensitivity at shorter wavelengths 

and a higher signal-to-noise ratio. This is reflected when comparing its system response curve to 

the one previously used. The system response curve for the 2.6-μm detector and 1-μm blazed 

grating with the coated holder can be found in appendix A.

With these concerns addressed, it was decided to take one more data set for Nd:YAG using the 

new coated sample holder. Taking this new data set produced the spectrum shown in figure 2 for 

the case of the sample not in the beam.
5

Figure 2. This is the raw spectrum produced by the 1% Nd:YAG sample located directly in the beam. The out of 

the beam case produced a similar spectrum with smaller fluorescence values and a larger laser line.

Again, these data were corrected by dividing by the appropriate calibration curve. They were

then multiplied by wavelength in order to convert from values proportionate to energy to ones 

proportionate to the photon flux. The process is shown in figure 2 for the out of the beam data set 

in figure 2. Doing this and then integrating gave the following values for Le, Lo, Li, Fo, and Fi

(table 1).

Table 1. Values for Le, Lo, Li, Fo, and Fi using the 1% Nd:YAG sample.

Le = 33376 Lo = 29327 Li = 4631 Fo = 2047 Fi = 15404

For these new data, a quantum efficiency value of 0.54 was obtained. In light of these low 

results, reabsorption was not considered at this time. In Nd:YAG, reabsorption can occur in the 

850-nm region of fluorescence but it should have a small effect on the fluorescence, making it 

dwarfed by the apparent larger discrepancy. In addition, the calculated branching ratios for the 

Nd:YAG were within 4% of the accepted values, so it was clear that reabsorption was not 

impacting the data greatly.

6. Analysis

These results of 0.46 and 0.54, respectively, were obviously much lower than expected for a 1% 

ceramic Nd:YAG sample and prompted much discussion about possible sources of error. The 

first thing that was considered was the possibility that the shortest wavelength section of the 

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1% Ceramic Nd:YAG Located Directly In The Laser Beam
6

system response curve could have an error due to the system’s obviously weak detection ability 

in the region. To test this, it was decided to move further up the curve and excite the Nd:YAG 

sample at 869 nm. Doing this would avoid some of the system’s poorer detection range at the 

cost of making some of the weaker fluorescence peaks disappear into the laser line. However, 

doing this produced a result of 0.45 for the quantum efficiency. This was again close to the 

experiment’s previously incorrect answers, shedding no light on the source of the discrepancy.

It was then decided that the concentration of the sample should be checked. This was done by 

placing the sample in the Cary spectrophotometer and taking a transmission spectrum. Upon 

doing this, the transmission spectrum was found to agree with accepted values for a 1% ceramic 

Nd:YAG sample, so a possibility of there being a mislabeling of the concentration was ruled out.

The transmission spectrum of the Nd:YAG sample can be found in appendix C.

Finally, a brief experiment was performed to determine the scattering ability of the sphere. To do 

this, the angle of the incoming beam was changed multiple times and, in a separate experiment, 

the location of the sample holder was changed multiple times in the case where the sample is not 

in the beam. The spectra of these measurements allowed us to conclude that the sphere was 

indeed highly uniform in its scattering as they did not differ significantly.

7. Retrial With 10% Yb:YAG

After considering the difficulties with the 1% Nd:YAG, it was then determined that the 

experiment should again be performed with a new sample. For this, a sample of 10% Yb:YAG 

was obtained for its similarly high quantum efficiency. The experiment was repeated by exciting 

Yb:YAG at 914 nm, with this excitation wavelength chosen in order to interfere with as little of 

the material’s fluorescence as possible. A transmission spectrum of this sample can be found in 

appendix C. Doing this produced the spectrum in figure 3 for the sample in the beam case.

Repeating the previous method of dividing by the system response, multiplying by wavelength, 

and integrating, these data produced the results in table 2.
7

1 ( )

observed

observed

true

a a 





 



Figure 3. Raw spectrum produced by the 10% Yb:YAG sample located directly in the beam. The out of the beam 

case produced a similar spectrum with smaller fluorescence values and a larger laser line. The laser line 

for this scenario peaked at 9.5 on this scale and has been cut off for clarity of the fluorescence spectrum.

Table 2. Values for Le, Lo, Li, Fo, and Fi using the 10% Yb:YAG sample.

Le = 32087 Lo = 29786 Li = 20157 Fo = 1416 Fi = 11200

In addition, applying the quantum efficiency equation to these data produce a result of 0.98. In 

contrast to the Nd:YAG sample, this answer agreed with what was expected.

Since the sample was a 10% concentration, reabsorption did indeed have to be reconsidered in 

this case. To do this, a piece of the sample was cut off and ground into a powder. Then, the 

powder’s spectrum was excited at 914 nm and its spectrum was measured directly by the 

Fluorolog spectrometer without using the integrating sphere. In addition, the remaining bulk 

sample also had its spectrum measured directly. Both of these spectra can be found in 

appendix D. Both sets of data were multiplied by wavelength to convert to photon flux and 

integrated as described in Ahn et al.’s paper (2) on correcting for a sample’s reabsorption. The 

ratio of the area of the bulk sample’s curve to the powder’s curve was found and subtracted from 

1 to find a value of 0.45 for a, the probability of reabsorption. Then, it was possible to apply their 

equation

(2)

Their equation was derived by modeling the reabsorption as a geometric series. This method is a 

reasonable technique for considering the reabsorption and has the added benefit of not being able 

to produce a value over 1. With this in mind, it adjusted the previously observed quantum 

efficiency value to a new value of 0.99. It is believable that this reabsorption only made a small 

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10% Yb:YAG Located Directly In The Laser Beam
8

change in the previous result because a high efficiency material would, in theory, lose little light 

over multiple reabsorption processes since nearly all of the light that is reabsorbed is converted 

back into fluorescence that would be detected in the integrating sphere.

8. Conclusions

Unfortunately, the problem with this experiment was not solved during this summer’s 

experiments. It was previously thought that the problem had to have been either systematic or 

theoretical, yet the new results for Yb:YAG have complicated that idea. What remains currently 

are several possibilities. One of these possibilities is that there is an error in the calibration curve, 

either in the steep fall off of the systems sensitivity at shorter wavelengths or in our inability to 

properly calibrate for the fluorescence light originating inside the sphere. This has prompted a 

presently unfinished critical discussion of the equations used and whether or not they accurately 

take these factors into account. In addition, the 1% Nd:YAG will most likely be retested using 

the 940-nm excitation wavelength to further ignore the lowest parts of the detectors sensitivity.

Another possibility is that the 1% Nd:YAG ceramic is somehow damaged or defective and thus 

produces a smaller quantum efficiency value than expected. This is again highly unlikely due to 

the fact that Nd:YAG is incredibly well studied and this particular sample is believed to be of 

high quality and to have been stored and handled properly. However, it would explain the results 

and could possibly be verified by comparing this sample’s fluorescence lifetime to accepted 

values or finding another 1% Nd:YAG sample. These and other possibilities will be tested 

further by Dr. Larry Merkle.

With this in mind, it is important to note that the experiment still has great potential. Several 

papers (3, 4) have reported positive results with this method. In addition, it seems to have 

correctly measured 10% Yb:YAG and has provided fairly precise results, despite yielding most 

likely inaccurate ones for 1% Nd:YAG. Because of this, the conclusion is that this method still 

could be an incredibly useful one for finding the quantum efficiency of unknown materials 

provided that the issues with the previously measured standard samples can be sorted out.
9

9. References

1. de Mello, J. C.; Wittmann, H. F.; Friend, R. H. Adv. Materials. (Weinham Ger) 1997, 9, 230.

2. Ahn, T.; Al-Kaysi, R. O.; Muller, A. M.; Wentz, K. M.; Bardeen, C. J. Rev. Sci. Instrum.

2007, 78, 086105.

3. Porres, L.; Holland, A.; Palsson, L.-O.; Monkman, A. P.; Kemp, C.; Beeby, A. J. 

Fluorescence 2006, 16 (2), 267.

4. Dong, X.; Du, X.; Liu, Y.; Ren, L.; Jin, L.; Lei, X.; Chen, W. Proc. SPIE 2012, 8560, 

85600O.
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Normalized System Response vs Wavelength

For Aluminum Holder

Appendix A. System Response Curves

This first graph (figure A-1) shows the normalized system response curve generated for the 

aluminum holder in the integrating sphere in conjunction with the 2.2-μm InGaAs detector and 

the 1-μm blazed grating.

Figure A-1. Normalized system response curve generated for the aluminum holder in the integrating sphere in 

conjunction with the 2.2-μm InGaAs detector and the 1-μm blazed grating. 

This second graph (figure A-2) shows the normalized system response curve obtained when the 

same method was applied to the coated sample holder in conjunction with the 2.2-μm InGaAs 

detector and the 1-μm blazed grating.
12

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Normalized System Response vs Wavelength

For Coated Holder

Figure A-2. Normalized system response curve obtained when the same method was applied to the coated sample 

holder in conjunction with the 2.2-μm InGaAs detector and the 1-μm blazed grating 
13

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Fluorescence Spectrum 1% Ceramic Nd:YAG

Appendix B. Example of the Data Analysis

Taking the raw dataset in figure 2 as a starting point, it was then divided by the system response 

curve to produce a true fluorescence spectrum. This spectrum is shown in figure B-1.

Figure B-1. True fluorescence spectrum of 1% ceramic Nd:YAG.

The laser line at 808.6 nm actually extends to roughly 9.35 on this scale and has been cut off to 

better show the fluorescence. This true fluorescence spectrum would then be multiplied by 

wavelength so that the data would become proportionate to the photon flux. Doing this produced 

the graph in figure B-2.
14

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Photon Flux of 1% Ceramic Nd:YAG

Figure B-2. Photon flux of 1% ceramic Nd:YAG.

Again, the laser line was cut off and really reaches roughly 7500 on this scale. It is this graph 

that was then integrated to get the necessary values for the quantum efficiency equation.
15

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%Transmission of 1% Ceramic Nd:YAG vs Wavelength

Appendix C. Transmission Spectra of Samples

This first graph (figure C-1) shows the transmission spectrum for the 1% ceramic Nd:YAG 

sample used in this experiment.

Figure C-1. Transmission spectrum for the 1% ceramic Nd:YAG sample used in this experiment

This second graph (figure C-2) shows the transmission spectrum for the 10% Yb:YAG sample 

used in this experiment.
16

Figure C-2. Transmission spectrum for the 10% Yb:YAG sample used in this experiment.

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17

Appendix D. Data for Reabsorption Determination for Yb:YAG

Figure D-1 shows the graph of the photon flux scaled for the detection system for the powdered 

sample and the bulk sample measured directly in the spectrometer. The area underneath the bulk 

curve was divided by the area underneath the powdered curve and subtracted from 1 to calculate 

the probability of reabsorption.

Figure D-1. Photon flux scaled for the detection system for the powdered sample and the bulk sample measured 

directly in the spectrometer.

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Scaled Photon Flux vs Wavelength

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18

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