Spectroscopic properties and energy transfers in Tm3+ singly- and Tm3+Ho3+ doubly-doped glasses

]OORHA L OF

ELSEVIER

Journal of Non-Crystalline Solids 195 (1996) 113-124

Spectroscopic properties and energy transfers in T m Tm3+/Ho 3+ doubly-doped glasses

3+

singly-and

Xuelu Zou *, Hisayoshi Toratani R & D Center, Hoya Corporation, 3-3-1 Musashino, Akishima-shi, Tokyo 196, Japan Received 8 February 1995; revised 18 July 1995

Abstract Spectroscopic measurements and analysis of energy transfer processes for Tm 3+ singly-and Tm3+/Ho 3+ doubly-doped glasses pumped with 790 nm diode laser have been performed. The emission cross-sections and the net gain have been determined from the measured absorption spectra for both the ions on the basis of principle of reciprocity. Tm 3+ singly-doped fluorozircoaluminate glass, which has a higher fluorescence efficiency at 1.82 ~m and a longer upper state lifetime, is a material suitable for Tm laser compared with oxide glasses. The quantum efficiency of H o 3+ fluorescence of 517-518 at 2.05 txm for the Tm3+/Ho 3+ doubly-doped glass is dominated by three energy transfer processes: Tm3+-Tm 3+ cross-relaxation, net Tm3+-Ho 3+ energy transfer, and energy transfer upconversion. The first process allows pumping efficiency to approach 2, and the second one contributes to population of the upper 5I 7 laser level, while the final process gives rise to a sublinear increase in upper state population with pump power. Optimum doping levels for laser performance are easily predicted based on spectroscopic measurements and are found to be 2-8Tm 3+ (102°/cm 3) for Tm 3+ singly-doped and 2-8Tin 3+/0.3-1Ho 3+(10m/cm 3) for Tm 3+/Ho 3+ doubly-doped systems, respectively.

1. Introduction The recent development of near-infrared tunable solid state lasers opens interesting perspectives for applications in several different fields, such as monitoring of atmospheric pollutants, medical surgery, high-resolution spectroscopy of low pressure gasses and eye-safe laser radar. In pursuit of efficient, compact and cheap sources of laser radiation for this wavelength region, thulium (Tm3÷) - or holmium (Ho 3÷ )-doped crystal and glass lasers are considered serious contenders.

* Corresponding author. Tel: +81-425 46 2748. +81-425 46 2742. E-mail: [email protected].

To achieve this objective, a complete knowledge of Tm 3+ and Ho 3+ fluorescence properties in laser materials seems necessary. Lasing characteristics, such as pumping efficiency, laser threshold and intrinsic slope efficiency, have been reported on Tm 3+ singly-and T m 3 + / H o 3÷ doubly-doped crystals and glasses [1-8]. By contrast, there are only a few spectroscopic measurements for the two ions in these materials which have been performed in terms of dopant concentrations. However, it is important to understand the spectroscopy of Tm 3+ or Ho 3+ laser systems to optimize laser performance. There are some spectroscopic properties that are important for understanding and modeling of Tm 3÷ and Ho 3+ lasers. Typical properties are the stimulated emission cross-section, upper state lifetime for the transition

0022-3093/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSD1 0 0 2 2 - 3 0 9 3 ( 9 5 ) 0 0 5 2 2 - 6

114

X. Zou, H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

and absorption spectra for diode laser pumping. Additional properties important for Tm 3+ and Ho 3+ lasers are T m 3 + - T m 3+ cross-relaxation, net energy transfer from Tm 3+ to Ho 3÷ and energy transfer upconversion which are dependent on dopant concentrations. In this work, we report the results of spectroscopic measurements for Tm 3÷- and Ho 3+doped glasses over wide dopant concentrations in order to assess their potential laser performance in diode laser pumped systems and to identify specific candidates for laser operation.

2. Experimental procedure Fluoride and fluorophosphate glasses were prepared by melting batch materials in glassy carbon crucibles at 950°C for 1 h in argon gas atmosphere in a fused silica enclosure. The glass melt in the crucible was rapidly cooled to the glass transition temperature and then annealed. Gallate and aluminate glasses were prepared by melting batch materials in a platinum crucible at 1500°C for 2 h in dry nitrogen gas atmosphere. The glass melts were poured into graphite molds and then annealed. The batch compositions of the glasses are listed in Table 1. Highly purified materials were employed for the batch preparation. Samples for the optical property measurements were fabricated to the size of 25 X 25 × 5 mm 3 and four surfaces were polished by the same process. Absorption spectra were recorded on spectrophotometer (Hitachi-330) at room temperature. Emission spectra were measured by exciting the samples with light from a diode laser operating around 790 nm. The light was chopped at 80 Hz and focused on the

Table 1 The compositions of base glasses in this

25 × 25 mm 2 face of sample. A position 0.5 mm from an edge of a sample was excited to minimize the re-absorption of the emission. Average beam size of pumping light through the sample was about 0.48 × 0.52 mm 2. The emission from the sample was focused onto a monochromator and detected by an InAs detector. The signal was intensified with a lock-in amplifier and processed by a computer. Errors in these measurements were estimated to be < 5%. Emission lifetimes were measured by exciting the samples with a Nd:YAG pumped dye laser (DMOTC) operating around 780 nm, and emissions were detected with the InAs detector and an S-1 photomultiplier tube. Emission decay curves were recorded and averaged with a computer-controlled transient digitizer. Errors in the lifetime measurements were estimated to be < 10%.

3. Experimental results 3.1. Fluorescence properties o f Tm 3+ singly-and Tm 3 +/ Ho 3 + doubly-doped samples T h e 3H4-3H 6 fluorescences around 1.82-1.86 Izm were observed for Tm 3÷ singly-doped samples under diode laser excitation of the 3F4 level at 790 nm. For understanding of concentration dependences of these fluorescences, we plot the output fluorescences normalized to the absorbed pump power in Fig. 1 as a function of Tm 3÷ concentrations. Here it is noteworthy that the relative fluorescence intensities of the Tm 3÷ singly-doped phosphate, silicate and germanate glasses are too weak to be presented in Fig. 1. The maximum values of the relative intensities occur at concentrations between 3 and 7 ×

study

Glass

Compositions (mol%)

Fluoride Gallate Aluminate Fluorophosphate Germanate Silicate Phosphate

25AIF3-13ZrF4-(I 1 - x - y)YF3-45.4(MgF 2 + CaF 2 + SrF~ + BaF2)-5.6NaF-xTmF3-yHoF 3 50GaOi,5-8KO0.5-14CaO- 19SrO-9BaO-xTmOi.5-yHoOt.5 48AIO15-36CaO-8MgO-8BaO-xTmOl.~ HoOl. 5 10POz~-33AIF3-(4 - x - y)YF3-48(MgF 2 + CaF 2 + SrF 2 + BaF2)-5NaF-xTmF3-yHoF 3 57.5GEO 2-16.5BaO-26.0KO0.5-xTmO~ .5-yHoOi.5 50SiO2-5AIOI.s-9SrO-24LiO0.5-12NaOo. ~-xTmOt. 5-yHoOI.5 65POzs-9AIOi.5-8(MgO + BaO)- 18KOo.5-xTmOi,5-yHoOi.5

X. Zou, H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

8.0 ..............

5

:

7.0 F"

t~ •

[ [

~

.

.

.

.

Oallate

Alumirmtc Fluorophosphate

o~o\

6.0 ~

e~ 5.0

/ /

,0 , j

" ~

,o

~x

-,\\

e~

30

.... ~

/

/ .E

,o

~-~

2.0

',~

t--

o

E

1.0

'o

0.0

,~,,D

0

....

5

, .... I0

= 15

....

I

....

20

25

Concentration of T m 3+ (102°/cm 3) Fig. 1. Concentrational dependence of the Tm 3+ 3H,I-3H 6 emission intensity normalized to the absorbed pump power for Tm 3+ singly-doped glass systems excited at 790 nm. Lines are a guide to the eye.

102°/cm 3 of Tm 3+ for the oxide samples and 8 and 15 × 102°//cm3 of Tm 3+ for the fluoride samples. The Tm 3+ concentration at which the maximum value of the fluorescence intensity occurred is higher for the fluoride sample than those for the oxide samples. This behavior may be due to a higher quantum efficiency of the excited 3F4 level (see Fig. 5 in the Discussion) of Tm 3+ in the fluoride sample. According to our observation, the quantum efficiency of the 3F4 level of Tm 3+ in the fluoride samples is nearly 1, but those in the oxide samples are less than 0.3. One observation also reveal that a great portion of the excited ions in the 3F4 for the oxide samples non-radiatively relaxes to the emitting 3H 4 level through the 3H 5 level, while the excited

115

ions in the 3F4 level for the fluoride samples can transfer their energies to the emitting 3H 4 level by the cross-relaxation of 3F4- 3H 4(Tm): 3H 63~ 3H 4(Tm). Clearly, one photon excites one ion into H 4 for the former process but two ions into t h e 3H 4 for the latter process. Increasing the Tm 3+ concentration, the quantum efficiency o f 3F4-3Ha(Tm):3H 63Ha(Tm) energy transfer increases, causing concentration quenching of the fluorescence intensity for the fluoride sample shifted to a higher Tm 3+ concentration. In other words, the maximum intensity of the 3Ha-3H 6 fluorescence will take place at a higher Tm a÷ concentration, after the cross-relaxation of 3F4-3H4(Tm):3H6-3H4(Tm) is saturated at a certain Tm 3÷ concentration. In addition, according to phonon energy measurements that have been performed for the samples by Raman spectroscopy, the observed maximum intensities tend to increase in the order of decreasing phonon energies of the glass hosts. Since quantum efficiency of the emitting level is strongly affected by the phonon energy of glass host, the fluorescence intensities are expected to be determined by quantum efficiencies of t h e 3H4-3H 6 transition of Tm 3÷. To evaluate the quantum efficiencies, "qq, we calculated the spontaneous-emission probabilities, Arad, of the 3H 4 level using the Judd-Ofelt theory [9-11] and measured the lifetimes, 7f, of that level. Based on these data, r/q is calculated for the samples in which the maximum values of fluorescence intensities were observed, The results are tabulated in Table 2 where we also present the emission cross-section, tre, measured peak wavelength, Aep , of the emission spectrum and the absorption cross-section, %, at the pumping wavelength.

Table 2 Spectroscopic properties of various Tm3+-dope d glasses Glass

Gallate Fluoride Aluminate Fluorophosphate Germanate Silicate Phosphate

NT a ( 1 0 2 ° / c m 3)

Aap (nm)

Ora ( 1 0 -20 c m 2)

Aep (nm)

O"e ( 1 0 -20 cm 2)

Arad

Tf

(S-l)

(ms)

~q (%)

(YeTf ( 1 0 - 2 0 cm 2 ms)

5.75 15.50 6.20 8.95 2.50 3.52 2.35

789 790 789 790 788 788 789

0.60 0.27 0.61 0.28 0.41 0.40 0.57

1860 1820 1860 1820 1840 1835 1835

0.63 0.32 0.59 0.43 0.68 0.61 0.84

344 113 300 152 201 158 200

2.44 6.40 1.52 1.12 0.60 0.25 -

83.90 72.10 45.60 17.00 12.10 0.060 -

1.54 2.05 0.90 0.48 0.41 0.15 -

a NT represents the Tm 3+ concentration.

X. Zou, H. Toratani / Journal of Non-Crystalline Solids" 195 (1996) 113-124

116

It is evident from Table 2 and Fig. 1 that the 3H4-3H 6 fluorescence intensities are related to the quantum efficiencies compared with the spontaneous-emission probabilities. The fluoride and gallate samples with lower phonon energies are found to have much longer lifetimes and higher quantum efficiencies than the other samples. Although the gallate sample has the highest quantum efficiency among the samples, it is not realistic to use this samples as a laser material unless its chemical durability is improved. By contrast, the fluoride sample possesses a higher chemical durability compared with the gallate glass and to ZBLAN glass. Moreover, this glass can be doped with relatively high concentration of Tm 3+ with high fluorescence efficiency and long lifetime, as shown in Fig. 1 and Table 2. High doping not only leads to strong Tm 3+ absorption (NTO-a) at the pumping wavelength but also gives rise to efficient energy transfer from the excited level of 3F4 to the laser level of 3H 4 [12]. Although this fluoride sample possesses a small emission crosssection, the product of the emission cross-section and the upper state lifetime that plays the key role for cw operation [13] is the largest among the samples. These parameters indicate that fluoride sample may be a useful material for a Tm laser. In the following sections, therefore, we describe the spectroscopic measurements of Tm 3+ singly-and Tm 3+//H03+ doubly-doped fluoride sample only, followed by analysis of the results and discussion. Fig. 2 shows fluorescence spectra near 2 tzm of the 3H4-3H 6 transition of Tm 3+ and 517-5I 8 transi-

100 .~.

ltoa~(~ lr~s Ia)

"~ 50

E m

0 1500

~r"~"- I 1660

I 1820 1980 Wavelength (nm)

2140

Fig. 2. Fluorescence spectra of Tm 3 + / H o 3+ doubly-doped fluorozircoaluminate glasses excited at 790 nm. The dopant concentrations are 15.5X 102°/cm 3 of Tm 3+ ions and (a) 0, (b) 2.1, (c) 1.05, (d) 2.1 and (e) 4.15X 102°/cm 3 of rio 3+ ions.

tion of Ho 3+ in Tm3+/Ho 3+ doubly-doped fluoride sample excited by the 790 nm diode laser. Based on energy level positions of the 3H 4 and the 517, the emission at wavelengths shorter than 1.82 Ixm is due to the Tm 3+ transition and that at wavelengths longer than 1.85 ixm is mainly due to the Ho 3+ emission. It can be seen from Fig. 2 that the static fluorescence of Tm 3+ rapidly decreases with increasing the Ho 3+ concentration due to effective energy transfer between the two ions. Incorporating about 2.1 × 102°/cm 3 of Ho 3+ into the Tm 3+ (15.5 × 102°/cm3)-dope d system, for examsple, the transfer efficiency is so high as to cause the I7-518 fluorescence to be more intense than the 3Ha-3H 6 fluorescence in the Tm 3+ singly-doped system. However, the fact that there are emissions from both ions indicates that there is not a complete energy transfer from Tm 3+ to Ho 3+. Strong fluorescences for the 3H4-3H 6 transition of Tm 3+ can still be observed at lower Ho 3+ concentrations.

3.2. Absorption and emission cross-sections, tra(h) and O-e(h) The cross-sections of the absorption and emission processes arising from the upper and lower states in a strongly phonon-coupled system can be related by [141

=

exp

kT

"

( 1)

where Z u, Z~, A, k and Exl denote the partition functions of the upper and lower states, wavelength of the transition, Boltzmann's constant, and the energy of so-called 'zero line', respectively. This equation is useful, since it suggests that the emission spectrum can, in principle, be obtained from the measured absorption cross-section lineshape. The major additional information required includes the ratio of the partition functions of the lower and upper states, Z I / Z u, and Ezj. In the hightemperature limit, the Z~/Zo simply becomes the degeneracy weighting of the two states. This approximation is available for Tm3 + (Ho 3+ )_doped sampies, since only one broad absorption band, corresponding to the 3Hn-3H 6 (517-518) transition of

117

X. Zou, H. Toratani /Journal of Non-Crystalline Solids 195 (1996) 113-124 4.0

....

3.5

i ....

! ....

J ....

i ....

i ....

i ....

......... Absorptioncross s e c t i o n •Emissioncross section

5.0

i ....

. . . .

i . . . .

, . . . .

i . . . .

i . . . .

i . . . .

......... Absorptioncross section

lil"Uo3. )

Emissioncross section

"~L~m3+ ") 4.0

3.0 2.5

0

3.0

v

0

2.0

0

o

1.5 o {J

2.0

1.0 ~-) 1.0 0.5 0.~,40 On

/ 0.0 1700

1500 1600 1700 1800 1900 2000 2100 2200

1800

1900

2000

2100

2200

2300

Wavelength (nm)

Wavelength(nm)

Fig. 3. Absorption cross-sections and the derived emission cross-sections versus wavelengths of the 3H6-3H a transition of Tm 3÷ and the 518-5I 7 transition of Ho 3+ in fluorozircoaluminate glasses.

Tm 3+ (Ho 3+ ), was observed even at low temperature and, therefore, the levels can be represented as two continuous sets of levels [15]. Another parameter, the 'zero line' energy Ezl, can be determined by matching the magnitude of actual emission spectra to that of the derived emission result of Eq. (1), since the derived and actual emission spectra agree reasonably well in lineshape [16]. The values of Ezl were found to be 5778 cm -z for the 3H~-3H4 transition of Tm 3÷ and 5136 cm -~ for the I8-517 transition of

I.,,~

....

I ....

I ....

I ....

I ....

I ....

I . . . .

Ho 3+. The measured absorption spectra and the derived emission spectra are shown in Fig. 3 plotted on an absolute cross-section scale for the Tm3+-and Ho3+-doped fluoride samples. It can be seen from Fig. 3 that the absorption and emission spectra are generally in good agreement; both spectra have the same features and similar bandwidths. We believe that the essential features in the spectra are adequately resolved. These spectra are useful for designing and modeling of cw or pulsed pump lasers.

2.0

I ' ' '

. . . .

Tm~*=3.5 (10z° ions/cm3) 1.0

~

I

. . . .

l

'

'

',

l

. . . .

....

I

I'11"

H@÷=3.5 (10 z° ions/cm3) 1.5

~

_,'-" 1.0 E

O.S

o

o.s ¢)

~

o.o

~,,

8

~%f

.~ -0.5

/.." .... ,Z

0.0

/""

......... ....... ..... .....

:.,-

-I.0

- -

-

P=0 P=0.2 P=0.4 P---0.6

•~ -0.5

"..".: ....."

.........

~-o

.......

P=o.2

! :"

. . . . .

})=-0.4

".:

. . . . . 1:'=0.6

', " -I .0

- P=0.8

- -

--P=I.0 -1.S

..I

1400

. . . .

I . . . .

1600

I . . . .

I . . . .

1800

1 . . . .

-1.5

I . ~ , / i s l

2000

Wavelength (nrn)

2200

. i

1700

i

.

I

. . . .

1800

I

•

1900

.

.

i

I

i

2000

i

i

i

-

-

-

I

i

- P=0.8 P=-1.0

i

2100

i

.

[

. . . .

2200

2300

Wavelength (nm)

Fig. 4. The calculated net gain coefficient versus wavelengths of the 3H6-3H 4 transition of Tm 3+ and the 518-5I 7 transition of Ho 3+ in fluorozircoaluminate glasses.

118

X. Zou, H. Toratani / Journal of Non-Crystalline Solids" 195 (1996) 113-124

While we have chosen the reciprocity method of Eq. (1) to obtain the emission cross-sections, we will utilize the Fuchtbauer-Ladenburg (FL) equation as a method of checking the reasonableness of our resuits. The FL equation is commonly used to estimate the emission cross-section from the normalized lineshape function, g(A), of the actual emission spectrum [17]: A4g(A)

~(A)

8'rrcn 2 araa,

(2)

where n is the refractive index of medium, c is the velocity of light and Arad is the spontaneous-emission probability including the contributions of the electric-dipole and magnetic-dipole transitions. We have calculated the values of Ar~d that, when substituted into Eq. (2), give good agreement with the cross-sections obtained from the derived emission spectrum of Eq. (1). The maximum discrepancies between the two values are about 11% for the 3H 43H 6 transition of Tm 3+ and about 13% for the 517-sI 7 transition of Ho 3+. These errors represent the combined uncertainty in the absorption and emission lineshape functions and in the assignment of the electronic state energy levels. It is interesting to calculate, using the measured absorption and derived emission cross-sections, the wavelength dependence of net gain as a function of population inversion for the upper laser level, in order to determine the gain property qualitatively. If we assume that Tm 3+ or Ho 3+ ions are either in the ground state or in the upper laser level, the gain, G(A), can be calculated by G(A) = N [ P ~ ( A ) - (1 - P)o'a(A)],

4. D i s c u s s i o n

In this section, we discuss the concentration dependences of the energy transfer efficiencies in both the Tm 3+ singly-and Tm3+/Ho3+-doubly doped fluoride systems and describe how to estimate absorbed pump power for their laser performances. There are at least three energy transfer processes of importance in both the systems. One is spatial energy migration of excitation among Tm 3+ ions followed by the cross-relaxation of 3F4-3H4(Tm):3H 63H4(Tm) that can enhance the pump quantum efficiency for both the systems. The second process is nearly resonant energy transfer from the 3H 4 level of Tm 3+ to the 517 level of Ho 3+. As the third process, there is an energy transfer upconversion o f 3H 43H6(Tm):5IT-5Is(Ho) which impacts laser threshold [5]. In order to describe these processes and find their concentration dependences, energy transfer paths need to be identified, and the microscopic probabilities for energy transfer between the ions in each step of the transfer also need to be known. If these are known, then the energy transfer can be described macroscopically, from which the pumping efficiency can also be estimated quantitatively. We illustrate these energy transfer processes and the transition paths, including radiative and non-radiative relaxations, in Fig. 5 for the Tm 3+- and Tm3+/Ho3+-doped glass systems. In this section, Energy (103cmq ) 15

(3)

where P stands for the population of the upper laser level, N 2, divided by the total Tm 3+ or Ho 3+ concentrations, N. Fig. 4 shows the calculated gain coefficients versus wavelengths of the 3H4-SH 6 and 517-518 transitions of Tm 3+ and Ho 3+ in the fluoride samples. The peak wavelength at which the maximum values of the gain occur shifts to longer wavelengths with decreasing population inversion for both Tm 3+- and Ho3+-doped systems; i.e., the laser performance wavelength with the maximum gain varies as the pump power is increased. This variation may be a typical feature of the quasi-threelevel laser system.

10

~

Ic,2

!t

Ho~

!p~l

4

"

!

Td ÷

0

~¢ ~¢ 13H6 Td ÷

Fig. 5. Energy level scheme of Tm 3+ and Ho 3+ in a fluoride glass showing energy transfer and energy transfer upconversion processes (dotted lines represent radiative and non-radiative decays).

X. Zou, H. Toratani/Journal of Non-Crystalline Solids 195 (1996) 113-124

119

tO0

the energy transfer processes will be described based on this model and the spectroscopic measurements. Some conclusions can be drawn from the upper state lifetime and spectral measurements. The first observation is that the lifetimes measured for the 3F4 level of Tm 3÷ singly-doped system rapidly decrease as the Tm 3÷ concentration is increased, as shown in Table 3, because of the effective cross-relaxation of 3F4-3H4(Tm):3H6-3H4(Tm). In Table 3, we also present the quantum efficiencies for this energy transfer that are evaluated by the relation of T/I = 1 - z / r o, where r and r 0 are the measured lifetime and the intrinsic lifetime of the 3F4 level, respectively. The transfer efficiency approaches nearly 100% if the Tm 3÷ concentration is higher than 8 × 102°/cm 3. This energy transfer can be expressed in the framework of a diffusion limited regime and the cross-relaxation occurs only between nearby ions, as proved by our previous work [12]. At lower dopant concentrations, the excited energy diffusion among donor ions is low enough to make a great part of the excited Tm 3÷ ions in the 3F4 level emit directly to the ground state before they diffuse their energy into the vicinity of an acceptor ion. High doping is, therefore, required for a Tm 3÷ laser emitting around 1.82 Ixm pumped with currently available diode laser to obtain relatively high pumping efficiency. The second interesting observation is that the emission spectrum of Tm 3÷ and the absorption spectrum of rio 3+ near 1.9 Ixm overlap well, as shown in Fig. 6. This spectral overlap gives rise to effective cross-relaxation of 3H4-3H6(Tm):5Is-5IT(HO) as expected. However, the lifetime measurements show that the f l u o r e s c e n c e s 3H4-3H 6 of Tm 3÷ near 1.8 Ixm and 517-5I 8 of Ho 3+ near 2 ixm decay identically and exponentially. Rapid decrease of the 3H 4 lifetimes with increasing Ho 3+ concentration, as usually expected, was not observed in the systems, indicating that the energy transfer between ions is

4.8

==

_.-... Tn 3 . r~

2.4.8

50 g"

÷

m

<

0 1500

1660

1820 1980 Wavelength (nm)

2140

Fig. 6. Spectral overlaps of Tm 3- 3 H 4 - 3 H 6 fluorescence and H03+518-517 absorption for 7.95x102°/cm3 Tm 3+ and 1.05× 102°/cm 3 Ho 3+ singly-doped fluorozircoaluminate glasses.

very fast compared with their upper state lifetimes and the two excited states are in quasi-thermal equilibrium, so that they must be treated as a coupled system. The quantum efficiency for this energy transfer is impossible to evaluate from the lifetime measurements. However, it is often possible to formulate a macroscopic description of an energy transfer process without knowing the microscopic probability of the transfer, although it is difficult to derive the intrinsic energy transfer rate between the ions. If the 3Ha(Tm3+) and 517(H03+) levels are treated as being in quasi-thermal equilibrium under cw excitation, we can see that their relative populations can be related to the corresponding fluorescence intensities as [181 hc

IT=

hc

AVp

W T n I and

IH =

hHp

(4)

WHn 5

and the net transfer efficiency, r/I 5, can be expressed as 12 I

rh5 = 1

nI + n5

1 = 1 + (IT/I.)(W./WT)(ATJh,p)

Table 3 Lifetimes of the 3F4 level and quantum efficiencies of energy transfer from

the

3F4

to

'

3H 4 levels

Concentration of Tm 3+ ions ( 102°/cm 3)

Lifetime (ms): Transfer efficiency (%):

0

0.21

0.43

1.10

2.10

4.20

7.95

15.50

1.92 0

1.92 0

1.82 5.21

1.38 28.00

0.74 61.46

0.17 91.15

0.021 99.89

0.0019 99.90

(5)

120

X. Zou, H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

where n I and n 5 are the populations of 3H4(Tm3+) and 517(H03+) levels, respectively, Wv and W H a r e the transition probabilities, h c / A v p and hc/AHp are the transition energies and I T and I H are the integrated intensities, for the 3H4-3H 6 and 517-5I 8 fluorescences, respectively. The quantum efficiencies for energy transfer to Ho 3+ from Tm 3+, calculated using this equation, are 0.175, 0.48, 0.62, 0.715, 0.81 and 0.84 for 0.21, 0.56, 1.05, 2.1, 3.15 and 4.15 × 102°/cm 3 Ho 3+, respectively, in the Tm 3+ (15.5 × 102°/cm3)-doped system. The results indicate that the net energy transfer is sensitive to the Ho 3+ concentration. When the Ho 3+ concentration is small, only a small fraction of the excited Tm 3+ ions in the 3H 4 can transfer their energies to the emitting 5I 7 level and a large fraction of the excited Tm 3+ ions emits to their ground state, thereby leading to relatively s t r o n g 3H4-3H 6 fluorescences of Tm 3-, as shown in Fig. 2. With increasing Ho 3+ concentration, however, the net transfer efficiencies become so efficient as to make a great part of the excited Tm 3+ ions transfer their energies to the emitting 5I 7 level. The final item of interest from the lifetime measurements is that, as the incident pump power is increased, the relaxation time from the coupled upper states decreases. This decrease is a sign of energy transfer upconversion between two nearby ions in excited states in which one ion gives up energy to a second ion causing the second ion to be excited to the higher energy level of 515, i.e., 3H 43H6(Tm):5IT-5Is(Ho). This energy transfer upconversion acts as a loss by draining excitations from the u p p e r 5I 7 level and gives rise to lower emission intensities at high pumping powers, as shown in Fig. 7. The induced fluorescence from the u p p e r 5I 7 level increases sublinearly as expected if the upconversion occurs, indicating that t h e 5I 7 population increases at a slower rate than the pump power because the upconversion provides an additional channel for the population to be lost from the initial excited state. The upconversion process is illustrated in Fig. 5. It is most likely because it is reasonable and the populations of both t h e 3H4(Tm3+) a n d 517(H03+) levels are relatively high. In this work, we have proved this process by looking for upconverted fluorescences from the 5I 5 and 5I 6 levels of Ho 3+. The 5I 5 level shows little fluorescence due to fast non-radiative decay to t h e 5I 6 level, but t h e 5I 6 level emits,

200

....

, ....

t ....

i ....

, ....

rio "~ 15o

jo NH= 1-05x 10~°/cm3

100

.~_

/ o

•~

f

.~.~"~

/

0

•

NH--0.21Xl01/¢m

t3- ''c~"

,

,

I

,

i

i

•

....

I

. . . .

)

. . . .

i

. . . .

so 100 1so zoo Absorbed power (mW)

zso

Fig. 7. Induced fluorescences at 2.05 Ixm corresponding to the Ho3+S17-518 transition as a function of pump power at 790 nm for 15.5× 102°//cm 3 Tm 3+ and 0.21 and 1.05× 102°/cm3 Ho 3+ codoped fluorozircoaluminate glasses. N H denotes the Ho 3+ concentration. The lines are a guide for the eye.

observably, to t h e 517 level at 2.85 ixm for systems with low dopant concentrations. This fluorescence is sensitive to the Tm 3+ concentration; its lifetime decreases when the Tm 3+ concentration is increased, as shown in Table 4. The easiest way to describe this energy transfer upconversion is to utilize rate equations in steady state. The simplest rate equations derived from the model proposed in Fig. 5 are (6)

d n 3 1 d t ~ - ~bp - C31n3n o - "r3'n3, dnl/dt-~

2C31n3n 0 - Cisnln4 - Wupnln5

(7)

+TI62Wup n l n 5 _ z ~ l n l ,

dns/dt=

Ci5nln 4 -

(8)

Wupnln 5 -- ~'~ I n 5,

where ~bp is the pumping rate of the 3F4 level of Table 4 Lifetimes of the 5I 6 level and quantum efficiencies of the Ho 3+ (516)-Tm3+ (3H 5) energy transfer in the system codoped with 2.1 × 102°/cm 3 Ho 3+ ions Concentration of Tm 3 + ions (102°/cm3)

Lifetime (ms): Transfer efficiency (%):

0

1.10

2.10

4.20

7.95

3.20 0

0.82 74.38

0.41 87.19

0.18 94.38

0.034 98.94

X. Zou, H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

Tm 3+, n i and "r~ are the population and the intrinsic lifetime of level i, Cij is the rate constant for energy transfer between levels i and j, r/~i is the quantum efficiency for the energy transfer between levels i and j and Wup is the rate constant for the energy transfer upconversion. In writing these equations, we have assumed that any excitation lost from 515 level by multiphonon relaxation to the 5I 6 transfers to the 3H 5 and non-radiatively relaxes to the 3H 4 level. This approximation is good, as the 5I 6 fluorescence is substantially quenched when Ho 3+ is codoped with relatively high concentration of Tm 3÷ in this material, as shown in Table 4. The term -Wupn ~n 5 in Eq. (7) represents the upconversion rate, and the following term, h62Wupn]ns, approximately equal to C62n6no, is the relaxation of the upconverted ions back to the initial state. Owing to the high Tm 3÷ concentration, the term "r31n3 can be ignored compared with the term C31n3n O. Then the rate equations can be simplified to be

0 = 2~p - "r-ln

-

Wupr/15( I

-

1/15)(2 - r/62) n2

and/or

121

the high Ho 3+ concentration gives rise to a smaller Wup. However, our interest is to obtain quantum efficiency for the energy transfer upconversion from spectroscopic measurements and then to determine excitation loss due to this upconversion. According to the rate equations, the competition between the upconversion rate (including two relaxation rates from the 3H 4 to the 3H 6 state and from the 517 tO the 5I 5 level) and the emission rate from the upper coupled 3H4-5I 7 levels will determine the upconversion efficiency, r/up, and can be quantified as Wup nl n5

r/up = 2Wupnln5 + r_ln Wup(1 - ,r/15) n 5 = 2Wup(1 _ r/,5)n 5 + "r- l •

(11)

It can be seen from this equation that the upconversion efficiency is generally smaller than 50%. If we assume that the Ho 3+ ions are either in the ground state or in the emitting level, Eq. (11) can be related to the Ho 3+ concentration, N H, with Eq. (3) and

p = n s / N H: O = 2 0 p _ "r-i - n5 - - W u p ( 2 - r/62)f l -r/,5r/~5 )

1

r/t5

(9) where n is the sum of upper state populations of n 1 and n 5, in which n~ can be related to n 5 by the relation n I = (1 - r/15)ns/r/15, as they are in thermal equilibrium, and "r is the measured lifetime of the coupled system and can be expressed approximately as [5] 1 --

"r

r/15 =

- -

"r5

1 - r/15 +

-

-

rl

(lO)

The r/62 has been evaluated from the 5I 6 lifetime measurements, as shown in Table 4, and it approaches nearly 100% when the T m 3÷ concentration is more than 8 × 102°/cm 3. Then the Wup Can be found by fitting the data in Fig. 7 to Eq. (9). The values are 9.89, 7.53, 6.17, 5.32, 4.72 and 4.67 × 10 -17 c m 3 / s for 0.21, 0.56, 1.05, 2.1, 3.15 and 4.15 × 102°/cm 3 Ho 3÷, respectively, in the Tm 3+ (15.5 × 102°/cm3)-dope d system. The upconversion rate decreases as the n o 3+ concentration increases, especially at low concentrations. It is not clear why

r/uP=

"r- 1[ ~ ( A ) + ~ ( A ) ]

(12)

2+ Wup(1 - r/,5) [ G ( A ) N . o'a( A)] This assumption is available since the relaxation rates from the 5I 5 and 5I 6 levels of higher energies are larger than the emission rate from the 5I 7 level of Ho 3+.

In order that critical inversion may be continuously maintained, the loss by fluorescence and upconversion from the upper laser level must be supplied by the pump energy. As a result, the absorbed pump power is defined as [19] Pab = hcN2/XAex'rf,

(13)

where hc/aex is the pumping energy, "re is the lifetime of upper laser level and X is the pump quantum efficiency; X is related to the energy transfer efficiencies and is defined as P3, +q3, + P 3 2 [ P z l ( P 2 o + P 2 , ) XT =

P30 "F P31 "[- P32 + q31

-'] dr- r/31

(14)

122

X. Zou. H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

for the Tm 3+ singly doped system, where P30, P3,, P32. P20 and P2, are the sum of the radiative and non-radiative transition probabilities from the Tm 3÷ 3F4 and 3H 5 levels to their lower levels, as shown in Fig. 5, and q31 = "1''03,~ - T - I - - T O ' is the 3F43H 4(Tm): 3H 6- 3H 4(Tm) cross-relaxation rate. Since p21 >>P20 and the multiphonon relaxation rate of the 3F4 level is approximately zero, P21(P20 + p 2 , ) - ' = 1 and P30 + P 3 , + P 3 2 is equal to the total radiative transition probability from the 3F4 level of Tm3+, ?o '. Then Eq. (14) can be rewritten as XT = 2'031 + (1 -- '03,)( ]33, "['-]332)'

(15)

where ]331 = 0.14 and ]332 = 0.02 are the branching ratios [12]. It can be seen from Eq. (15) that the pumping efficiency reaches 2 only if '03, = 1. For the T m 3 + / H o 3+ doubly-doped system, there are three important energy transfer processes that must be taken into account: Tm3+-Tm 3+ cross-relaxation, net T m 3 + - H o 3+ energy transfer, and energy transfer upconversion, so the pumping efficiency can be defined as -)(H ~-" XT"0T"015( 1 -- "loss)'

(16)

where '0T is the quantum efficiency of the 3H 4 level of Tm 3+ and also denotes the fractional population of the excited Tm 3+ ions in the 3H 4 level that can transfer their energy to Ho3+; the term 1 - '0~o~ is the compensation parameter for excitation loss, "0,oss, by the upconversion: "0loss is discussed below. Substituting Eqs. (3), (15) and (16) into Eq. (13), we obtain the absorbed pump power

he[ G(h) + N wOta(h)] Pao(Tm) = [2"03, + (1 - "03,)( ]33, +]332)] 1

x [~Te(/~) + O.a(/~)]Aexrf(3n4 )

(17)

for the Tm 3+ singly-doped system, and

hc[G(A) + NH O'a(h)] Pab(H°) =

wavelength, threshold pump power can be also calculated by these equations. We now discuss the effect of excitation loss by upconversion on the laser performance. Clearly, if the upconversion rate, Wu_n ln 5, is much smaller than the 517 emission rate, r - f n 5, its effect on the system performance can be ignored. For our glass system, r -~ is about 100 s - ' so, if a Ho 3÷ population inversion of 0.1 × 102°/cm 3 is desired, Wup must be less than 1 × 10-'Tcm3/s if upconversion is not to be the dominant loss factor. It is obvious that this value is much smaller than the evaluated values of Wop for the glass system. Thus, if the population inversion is larger than or even comparable to a value of NHO'a(h)/(O'a(h)+ O'e(h)) which must be excited to have net gain at the laser wavelength, the upconversion rate will be greater than the 5I 7 emission rate, so the upconversion will have a substantial effect on the system performance. By considering the relaxation processes from the 515 level of Ho 3+, however, we can see that not all upconverted energy is lost. Any excitation that returns from the 5I 5 level via multiphonon relaxation and cross-relaxation to the upper coupled 3H4-5I 7 levels (as shown in Fig. 5) does not act as a loss on the system. Based on the rate equations, therefore, the excitation loss from the upper coupled 3H4-5I 7 levels due to the upconversion can be given as Wup(2-

"062)(1

-

"0,5)"0,5n 2

"01°ss= 2Wup(l -- 77,5)'1"/15n2 + T - ' n

"

Obviously, this excitation loss can be associated with the upconversion efficiency, "0up, by a factor of (2 - '062) as "0loss= (2 - "062)'0up-For the high Tm 3÷ concentration, approximately 100% of the upconverted energy in the 515 level of Ho 3+ can be back-transferred to the upper 3H4-5I 7 levels, i.e., "q62 = 1, so the excitation loss can be expressed as Wup( 1 - '015)'qjsn 2 "0,oss = '0up = 2Wup(1- '0,5)'015n2 + . r _ t n .

)(T"0T"015( 1 -- "/']loss)

(19)

(20)

1

× [o.a(h)+~(A)]hexrf(517 )

(lS)

for the T m 3 + / H o 3+ doubly-doped system. As the gain coefficient, G(A), is set equal to the intrinsic loss originating from base-glass medium at laser

If desired population inversion increases up to N H Ora()t)//(Ora(h) + Cre()t)) at the Ho 3+ concentration >_ 2.5 × 1 0 ' 9 / c m 3, the excitation loss will be approximately 0.5 due to Wupn >> r - '. In this case, the upconversion can be calculated on the basis of Eqs.

X. Zou, H. Toratani/Journal of Non-Crystalline Solids 195 (1996) 113-124 I0

z

.

.

.

.

.

.

.

.

,

.

.

.

.

.

.

.

.

z

'

'

~'E3-- "O1 10 ~ t'L

E

&

O Tm3+singlydopedsystem r3 Tm3÷,fflo3+doublydopedsystem

< ~°'~o"

'

......

i'o °

'

......

i'o'

'

'

Concentrations of Tm 3+ and Ho 3÷(102°/cm3) Fig. 8. The calculated absorbed pump power normalized to the net gain coefficient as a function of concentrations of Tm 3+ and Ho 3+ for Tm 3+ singly-doped and T m 3 + / H o 3+ (Tm3+: 15.5X 102°/cm 3) doubly-doped fluorozircoaluminate glasses. Lines are guides to the eye.

(12) and (18) to cause an increase in the threshold pump power by a factor of two. This evaluated value is in good agreement with the calculated result by Fan et al. for a T m / H o : Y A G crystal [5]. Fig. 8 shows the calculated absorbed pump power normalized to the laser gain coefficient as a function of the dopant concentrations using Eqs. (12) and (18). Here it must be first stated that this calculation is designed to give a method of using the measured spectroscopic properties and the derived energy transfer efficiencies to find 'optimum' doping levels for the laser performance, but not to give absolute absorbed pump power for the laser operation. It is clear from Fig. 8 that the optimum doping levels at which the minimum absorbed pump power are observed for deriving the same gain are 2-8 X 102°/cm 3 Tm 3+ for the Tm 3+ singly-dopedand 0.3-1 X 102°//cm3 Ho 3+ for the T m a + / H o 3+ doubly-doped fluoride glasses, respectively. If the Tm 3÷ concentration is lower than 2 × 102°/cm 3 for the Tm 3÷ singly-doped system, the Tm3+-Tm 3÷ crossrelaxation will be so slow as to make a great part of the excited ions in the 3F4 emit directly to the ground state. The pumping efficiency is, therefore, decreased and gives rise to higher excitation intensity. By contrast, if the Tm 3÷ concentration is higher than 8 X 102°/cm 3, since the Tm3+-Tm 3+ cross-relaxa-

123

tion has been saturated, the absorbed pump power will become larger with decreasing the quantum efficiency of the emitting level. For the Tm3+/Ho 3+ doubly-doped system, when the Ho 3÷ ion density is less than 0.3 X 102°/cm 3, a small fractional population of Ho 3÷ in the upper 5I 7 level followed by a high upconversion rate gives rise to relatively low pump quantum efficiency. However, if the Ho 3+ ion density is more than 1 × 102°/cm 3, owing to relatively high absorption coefficient at the laser wavelength, a high pumping energy is needed to maintain a population inversion to derive the same gain, although the upconversion efficiency decreases with increasing the Ho 3+ concentration. For this system, we have realized that the Tm 3÷ concentration is too high, causing not only an increase in upconversion coefficient but also a decrease in the net energy transfer from Tm 3÷ to Ho 3+. For example, a sample doped with 8Tm3+/0.5Ho3+(102°/cm 3) has been measured experimentally and calculated to cause a decrease, by a factor of 48%, in the absorbed pump power compared with the sample doped with 15.5Tm 3+/0.5Ho 3+ (102°/cm3).

5. Summary The Tm3+-doped fluorozircoaluminate glass which has relatively high fluorescence efficiency at 1.82 ixm and long upper state lifetime has been found to be a good material suitable for Tm laser as compared with oxide glasses. The 517-518(H03+) fluorescence efficiency for this Tm 3+ / H o 3+ codoped glass is dominated by three energy transfer processes: the Tm 3+-Tm3+ cross-relaxation, net Tm3+-Ho 3+ energy transfer, and energy transfer upconversion from the upper coupled 3 H 4 - 5 I 7 l e v els. The first process allows the pump quantum efficiency to approach 2, and the second process contributes to populate its upper laser level, while the final process leads to a sublinear increase in upper state population with pump power. The upconversion that has been analyzed based on rate equations causes an increase in threshold pump power by a factor of 2, as the upconversion rate is much higher than the emission rate from the upper coupled 3H 4517 levels.

124

X. Zou, H. Toratani / Journal of Non-Crystalline Solids 195 (1996) 113-124

The emission cross-section and the net gain were determined from the measured absorption spectra for both the systems based on the principle of reciprocity. Using these spectroscopic properties followed by the energy transfer efficiencies, the optimum doping levels for laser performance can be predicted, and the absorbed pump power needed to maintain a certain population inversion can also be estimated. The optimum Tm 3+ and Ho 3+ concentrations for their laser operations are found to be 2-8 × 102°/cm 3 Tm 3+ for Tm 3+ singly-doped and 0.3-1 x 102°/cm3 Ho 3+ for Tm3+/Ho 3+ doubly-doped fluoride glasses, respectively.

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[4] G.J. Kinkz, L. Esterowitz and R. Allen, Electron. Lett. 23 (1987) 616. [5] T.Y. Fan, G. Huber, R.L. Byer and P. Mitzscherlich, IEEE J. Quantum Electron. 24 (1988) 924. [6] T.Y. Fan, G. Huber, R.L. Byer and P. Mitzscherlich, Opt. Lett. 12 (1987) 678. [7] R.M. Percival, D. Szebesta and S.T. Davey, 28 (1992) 671. [8] P. Myslinscki, X. Pan, C. Bamard, J. Chrostowski, B.T. Sullivan and J.F. Bayon, Opt. Eng. 32 (1993) 2025. [9] B.R. Judd, Phys. Rev. 127 (1962) 750. [10] G.S. Ofelt, J. Chem. Phys. 37 (1962) 511. [11] W.T. Carnall, P.R. Fields and B.G. Wyboume, J. Chem. Phys. 42 (1965) 3797. [12] X. Zou and T. Izumitani, J. Non-Cryst. Solids 162 (1993) 58. [13] L.D. DeLoach, S.A. Payne, L.K. Smith, W.L. Kway and W.F. Krupke, J. Opt. Soc. Am. BII (1994) 269. [14] D.E. McCumber, Phys. Rev. 136 (1964) A954. [15] A. Brenier, C. Pedrini and B. Moine, Phys. Rev. B41 (1990) 5364. [16] S.A. Payne, L.L. Chase, L.K. Smith, W.L. Kway and W.F. Krupke, IEEE J. Quantum Electron. 28 (1992) 2619. [17] P.F. Moulton, J. Opt. Soc. Am. B3 (1986) 125. [18] J.C. Wright, Top. Appl. Phys. 15 (1976) 239. [19] W. Koechner, Solid-State Laser Engineering (Springer, Berlin, 1988) p. 84.