JOURNAL
ELSEVIER
OF
Journal of Non-Crystalline Solids 184 (1995) 9-20
Optical properties of fluoride glasses: a review
Fuxi Gan
*
Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, PO Box 800-211, Shanghai 201800, People's Republic of China
Abstract
Current research activities on optical properties of fluoride glasses are reviewed; emphasis is given to the refractive-index
dispersion and multiphonon absorption. The dependence of optical properties of fluoride glasses on their chemical
composition has been summarized and interpreted under consideration of fluoride glasses as ionic substances in nature. The
methods for calculating optical properties of fluoride glasses have been reviewed and a new calculation system for
refractive-index dispersion and multiphonon absorption of fluoride glasses is proposed.
1. Introduction
In recent years, an increasing interest has been
devoted to fluoride glasses, particularly heavy metal
fluoride glasses, because of their potential use for
making infrared optical components and fibers. The
optical properties of fluoride glasses are important
for accurately designing optical systems and optical
fiber waveguides. For practical applications, the optical properties are concerned with linear and non-linear refractive index, optical dispersion, material dispersion and zero-dispersion wavelength, as well as
ultraviolet (UV) and infrared (IR) absorption. A m o n g
these, the refractive-index dispersion and IR eigen
absorption and multiphonon absorption are the most
important. Because of the poor optical homogeneity
of fluoride glass samples, it is difficult to measure
precisely the optical properties of fluoride glasses;
hence so far only a small amount of refractive-index
dispersion and multiphonon process data for fluoride
* Corresponding author. Tel: + 86-21 952 8814. Telefax: + 8121 952 8812. E-mail: [email protected].
glasses have been reported. In this paper, we summarize the optical properties of fluoride glasses, analyze
the relationship between the optical properties and
chemical composition and present a new system for
calculating the optical properties of fluoride glasses.
2. Optical dispersion
2.1. R e f r a c t i v e index, na, a n d m e a n dispersion n F n C
The fluoride glasses are one group of optical
glasses with low refractive index and mean dispersion, as well as special partial dispersion. We have
discussed them in detail in Ref. [1]. This is shown in
the n o - vd diagram (see Fig. 1), where vd = ( n a 1 ) / ( n F - n c) is the Abbe value and no, n F and n c
are the refractive indices at the d, F and C spectral
lines, respectively (587.56, 486.13 and 656.27 nm).
The BeF2-based fluoride glasses possess lower refractive index ( n a = 1.4) and higher v ( v a = 95), and
are located at the lower left comer in the n o - v d
diagram. The ZrF4- and InF3-based fluoride glasses
0022-3093/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
SSDI 0022-3093(94)00592-3
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
10
nd
1.65
1.60
1.48
//
1.50
1.45
//
/"
/ / e3
/ / *1
1.40
////
5*
II
/
/ /~
/Bet +2
105 100
I
95
/
85
i
I
80
75 "--70
29 8.5
28 8.0
1,36
i~ _
90
Ca+2,~~Sr' 2
1,47
/q
/
110
(b)
30 9°0
1.55
1.25~
MV
1.49
65
i
~
i
(a)/
iS//
245.0
1.35 i,i g ~ A 2 ~ l /
1,34
I
55
234.5
Va
/
Fig. 1. Diagram of retractive index, n d versus the Abbe Number,
Cd: A, 55BeF2-NdF 3 - 4 4 R F [2]; B, 47BeF2-10AlFa-27KF2NdF3-14RF 2 [3]; C, 31.6BaF2-3.8GdF3-60.4ZrF4-4A1F 34RF 3 [4]; 1, 34BeFz-23AlF3-19MgF2-10CaF2-14BaF2; 2,
58BeF 2-40A1F3-2NdF3; 3, 35A1Fa-15YF3-50RF 2 [5]; 4,
60ZrF4-33ThF4-7LaF 3 [6]; 5, 57.5ZrF4-33.75BaF2-8.75ThF4;
6, 25AIF3-30YbF3-15PbF2-15ZnF2-15BaF 2 [7]; 7, 40InF 2 20ZnF2-20BaF2-20SrF2-5GdF3; I, oxide glasses; II, fluoride
224.0
1,33
I
0.5
I
1
1.0 1.5
r (I)
2,0
Fig. 2. Change of (1) refractive index, rid, (2) molar volume (MV)
and (3) molar refractivity (MR) with ionic radiusof akali earth
ions in fluoride glasses: (a) 47BeF2-IOA1F3-27KF-2NdF 3 -
14RF 2 [3]; (b) 20ALE3-20ThF 4-40ZnF 2 -20RF 2 [9].
glasses.
2.2. Refractive-index dispersion
have higher refractive indices and mean dispersion
(n a = 1.50-1.55, vd = 6 5 - 8 0 ) and are located at the
upper right side in the n d - v d diagram. The AIF 3based fluoride glasses are in the middle position
between the two above-mentioned glass systems. By
comparison with oxide optical glasses, all fluoride
glasses are located lower in the n d - vd diagram.
Since fluoride glasses have ionic bonds the influence of different fluoride components on the molecular refractivity (MR) and molecular volume (MV) of
fluoride glasses depends on their ionic radius [8].
Fig. 2 shows the increase of refractive index, molecular refractivity and molecular volume of RF2-containing glasses with increasing radius of R 2÷ ions.
From Fig. 3 the spectacular behaviour of trivalent
ions can be seen; owing to the strong decline of MV,
the n d of glasses increases from YF3-containing to
AIF3-containing glasses. A quite different effect can
be seen in Fig. 4, i.e., when A1F3 is replaced by YF3,
the value of nd continuously increases. The main
reason can be attributed to the different structural
states of AI 3+ in ZrF4-based and A1F3-based glasses.
The AI 3+ ions are located at octahedral sites in
ZrF4-based glasses, but mainly in tetrahedral coordination in AIF3-based glasses.
Several reports have already been made on refractive-index dispersion for fluoride glasses, but the
data were quite insufficient [4,8,19]. Mitachi and
nv
~+3 ot
r+sd
°,
1.55
41 k
~
~~+31.531"54
2 oZr+4
413 ~A21+3OZr+4
13.5
I~
3
3
Lu+3
Zr+4 • 3~3~3Lff
,
13.0
/
39 '~AI+~
0.4
Fig. 3. Change
I
I
0.8
1.2
rs (.~)
112.5
1.6
of (1) refractive index, (2) molar volume and (3)
molar refractivity of fluoride glass series 50ZrF4-43ThF4-7RF 3
[10].
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
nd
~
11
ru~
1.5C
1.4.~
YA
Zm.*A
1.43
1.4~
1.41
1.~
0
1.3g
0
I
I
10
~
"
i
1.0
~
I
2.0
I
3.0
127
30
20
A~R
I
4.0
I
5,0
i
6.0
~.(~=)
Fig. 6. Optical dispersion curves of five fluoride glasses,
r~ 3 (z)
Fig. 4. Change of (1) refractive index, (2) molar volume and (3)
molar refractivity of glass series (50-x)A1F3 -50RF 2 -xYF 3
[51.
Miyashita [4] measured the refractive-index dispersion of BGZ glasses with different fluoride additives
by the minimum deviation method; the experimental
results are illustrated in Fig. 5. It can be seen that the
influence of fluoride additives is small, the characteristics of refractive-index dispersion are mainly dependent on the host fluorides. The optical dispersion
data of InF3-based glasses has also been reported
recently [11].
We measured the refractive-index dispersion of
five fluoride glasses with different chemical compositions by autocollimation and prism-coupled total
reflection methods. The requirement of a small glass
sample and lower optical glass quality is the main
advantage of both methods over the minimum deviation method. The measured data of refractive-index
L.47
1.53
FbF2
L.46
1.52
F2
L.45
dispersion in the 0.365-5.6 p~m wavelength range
are shown in Fig. 6. The chemical compositions of
measured glasses are listed in Table 1. It indicates
that the refractive-index dispersion curve for A1F3based glass is flatter in the UV region than that of
ZrFa-based glass, and the optical dispersion curve for
InF3-based glass is different from those for ZrF4based and AIF3-based glasses; it is flatter in the IR
region.
Using the optical dispersion equation shown below, we calculated the eigen absorption wavelengths,
A1, A2, in the UV and IR respectively, as well as the
corresponding oscillator strengths, fl, f2. The values, listed in Table 2, are calculated from
n 2 - 1 = f l A2/(~. 2 -- A~) q-f2 A2/(A 2 -- A~).
(1)
From the UV absorption and reflection spectra, as
well as the IR absorption and Raman spectra, the
peak values of UV absorption, Au, and IR absorption, AR, were measured (Table 2) [1]. The experimental values are in good agreement with calculated
ones.
L.44. ~,~
1.51
L.43
1.42
I. 49
1"30f
1.48
1.41
1.47
0
~
I
t
2
,
i
3
4
.40
%(pro)
Fig. 5. Optical dispersion curves of fluoride glasses ZBLAN and
ZBGA with different additives.
2.3. Material dispersion and zero-dispersion wavelength
The material dispersion of optical fibers is the
sum of bulk glass dispersion and waveguide dispersion, and can be expressed as
M(A) = ( A / c ) ( d Z n / d A 2 ) .
(2)
F. Gan/Journal of Non-CrystallineSolids 184 (1995) 9-20
12
Table 1
Chemical composition (tool%) of several fluoride glasses
Glass
ZrF4
ZBLAN
AYR
IZBS
ZBYA
ZBLA
53
ThF4
InF3
A1F3
3
40
5
LaF3
YF3
MgF2
CaF2
15
10
20
40
55
52
SrF2
4
5
5
20
23
10
20
BaF2
NaF
20
10
20
20
20
20
ZnF2
20
Table 2
Optical dispersion parameters of several fluoride glasses
Glass
ZBLAN
AYR
IZBS
fl
f2
/~1 ( I x m )
1.22514
1.01675
1.19200
1.52898
1.04228
1.20869
0.08969
0.07540
0.09166
Taking the quadratic differential of Eq. (1), we obtained
M ( A ) = ( A / c n ) ( a I + A 2 - A2),
(3)
where
A a =fIA2(A 2 +
3A2)(A 2 - A2) -3,
z2=f2a~(a~+3a2)(a2_a~
(4)
) 3,
+f2h~A(h 2 - A 2 ) - 2 ] ,
(6)
and M ( A ) is the material dispersion, h is the wavelength, n is the refractive index and c is the speed of
light.
From the above calculations, the material dispersion at different wavelengths of three types of fluo-
1.0
0.8
0.6
0°4
~
0.2
,
v
~, \\"4
,
3,
)tu (Ixm)
0.09
0.08
0.09
)tR (Ixm)
18.2
15.3
20.5
ride glass are shown (Fig. 7). The zero-dispersion
wave-length, A0, (defined as the wavelength at
M ( A ) = 0) is easy to obtain from Fig. 7. The A0
values for five types of fluoride glass are presented
in Table 3.
2.4. Calculation of refractive-index dispersion
(5)
A 3 = ( I / n ) [ f l A Z A ( A 2 - A 2 ) -2
~
)t2 (Ixm)
21.3825
17.2567
25.0933
,
In glass melting, for modifying glass composition
and developing new types of glass, it is necessary to
estimate various properties of a glass produced from
its chemical composition in advance. In order to
avoid large numbers of complicated experiments, it
is of great practical significance to establish a correct
calculating system for optical properties of fluoride
glasses.
Fluoride glasses differ significantly from oxide
glasses in their higher degree of ionic bonding, and
their structure may be attributed to disordered ion
packing. Based on this concept we recently developed a method for calculating the refractive index
nd, and density, d, of fluoride glasses from the ionic
refractivity and ionic volume [13,14]. It is well known
that the molecular volume (MV) and molecular re-
4
-0.2
-11.4
-'0.6
Fig. 7. Material dispersion of three fluoride glass fibers.
Table 3
Zero-dispersion wavelength, )to, of several fluoride glasses
Glass sample: ZBLAN AYR IZBS ZBYA ZBLA
)to (ixm):
1.724
1.494 1.989 1.69
1.65
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
13
fractivity (MR) are additive properties, and in fluoride glasses can be expressed by
glasses, a calculation system was set up using the
following additive formula:
R M = ~_, R c i X i + X F - R F-
(7)
a = E
(8)
where G is the physical property, gi is the partial
property with respect to the fluoride component i in
the glass, and r i is the molar concentration of the
fluoride component in the glass.
On the basis of the bond refractivity concept, we
derived the partial refractivities at different wavelengths, Rd, RF, R c, as well as the cut-off wavelength in UV, As, of the fluoride components in
glasses, which are listed in Appendix 1.
In order to check whether the values given in
Appendix 1 are correct, the refractive index and
mean dispersion of 230 samples in 10 different
fluoride glass systems have been calculated and the
results are compared with the measured values, the
average calculation errors are as follows: n d - 1 ×
10-2; (n F - n c) - 3 × 10 -4.
Considering the similarity of chemical bond characteristics of fluoride components in glasses and in
crystals, we carefully derived the partial properties of
f l , f2 and 41, A2 of fluoride components in glasses,
which are listed in Appendix 2 [15]. If we neglect the
girl
(11)
i
vM = E VciXi + XF-VF-,
i
where Rci, Vci and X i are the refractivity, volume
and concentration of cations in the glasses, and R F
and Vv are the refractivity and volume of the F
anion. The determination of ionic refractivity and
ionic volume of cations and fluorine ions in glasses
has been discussed in detail in Refs. [13,14].
The values of Vm and R m are related in the
Lorentz-Lorenz optical dispersion equation,
R M= [(n 2 - 1)/(n 2 + 2)]M/d
= [ ( n 2 - 1 ) / ( n 2 + 2)] VM,
(9)
where M is the average molecular weight of the
glass, and d is its density. From Eq. (9), we have
n = ( V M + 2 R M ) ' / Z / ( V M --RM) 1/2.
(10)
After extensive studies of the relationship between
the optical properties and compositions of fluoride
~1.5011"5248 "'"
BGZ
".
r< 1'50
fl.481'52
1.'°t
f
.
.
.
.
.
0
I
2
3
4
5
*
" " ~ ,
q 1.501"52
. . . . .
0
i
2
3
BGZA-Cd e 1.501"52
[ ~ .....
' ~..,
"
1.48
1.4o f
11:46 E
4
5
0
1
2
3
4
5
O
J
1
~(l~m)
. . . .
2
3
4
1.54 ,
1.
(4)
I.
1.__
0
.
1
.
.
2
.
3
1.52
1.52
1.48
1.48
1.46[
,
0
1
.
4
5
0
1
~,(~m)
1.5
n .
*
2
3
4
5
X(I~m)
1481
-
1.52
q 1.
1
~
2
3
X(tint)
4
5
0
1
2
3
~(Itm)
,
,
,
,
3
4
5
0
ZBLA
I
2
3
4
5
~,(I~m)
-'Cs
1.48
,
1.44
q 1.42
1.40
1.38[
ZB~Iq
~ 1.46
1.44
1.
0
1.52
ql.50
BGZA-y
2
5
7~(~tm)
1.42
4
5
0
1
2
3
X(t~m)
Fig. 8. Optical dispersion curves of several fluoride glasses: - -
4
5
0
CB¥A
1
2 3 4
7~(ILm)
5
, calculated; . . . . . . ,measured.
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
14
effect of fluoride components on one another in the
glass, the eigen absorption wavelength in the ultraviolet and infrared regions and corresponding oscillator strength of fluoride glasses can be calculated by
Eq. (11). The material dispersion of fluoride glasses
can also be estimated by Eq. (3).
If we let M(A) = 0, the expression of zero-dispersion wavelength can be obtained as
Ao = (3fl
h2h2/f 2)1/4.
(12)
To confirm the validity of the parameters listed in
Appendix 2, the optical dispersion curves of 11
fluoride glass samples have been drawn (Fig. 8).
Clearly the calculated results agree well with experimental ones.
MacNamara [16] applied the values of fl, f 2 and
)tl, A 2 of fluoride components in glasses proposed
by us and derived the zero-dispersion wavelength
A0, refractive index n2.55, (dn/dA)z55 and material
dispersion M2.55 at 2.55 Ixm wavelength of fluoride
components in glasses. The calculation parameters
are shown in Appendix 3 [16]. It is worthwhile
pointing out that the values of fl, f2 A1, A2 proposed by us are correct and applicable when compared with the experimental values.
Wemple [17] and Nassau [18] have proposed the
following formula to calculate the zero-dispersion
wavelength, A0 via the average electron gap E 0, and
oscillator, f:
h o -= 2.96( d3fo u/E3ZA
)1/4
(13)
where d is the distance between cation and anion, u
is the reduced mass of the cation-anion pair and ZA
is the anion valence. For multi-component fluoride
glasses, the value of A0 of fluoride components in
the glass should be calculated first, then the value of
h 0 of the glass can be obtained by an additive
formula similar to Eq. (11). The comparison of
calculation results from Nassan's method and by us
is shown in Table 4. The experimental data were
taken from Ref. [11]. It can be seen that the calculation errors of Nassan's method are larger than that of
ours.
3. Infrared absorption and multiphonon processes
The infrared absorption of glass is raised by the
vibration of different chemical bonds in the glass.
Generally it can be measured by IR absorption and
reflection spectroscopies, which we have discussed
in detail previously [1].
The multiphonon process is rather important for
evaluation of fluoride glasses in applications. Because of multiphonon absorption, the IR cut-off
wavelength is much shorter than the IR eigen absorption wavelength. The decrease of emission quantum
efficiency of rare earth ions in doped glasses is
mainly caused by a multiphonon non-radiative energy transition. All multiphonon processes are dependent on the phonon energy of the glass, which
can easily be determined by Raman spectroscopy.
3.1. Phonon energy
In comparison with oxide glasses, fluoride glasses
possess much lower phonon energy. Fig. 9 shows the
Table 4
Measured and calculated values of h 0 of several fluoride glasses
Glass
BGZ
TGZA (2)
BGZA (4)
BGZA (6)
BGZA-Li
BGZA-Cs
BGZA-Cd
BGZA-Pb
ZBLAN
Measured Ao (Ixm)
[11]
Calculated Ao (~m)
Gan and Zhang [15]
Nassau [18]
1.62
1.682
1.675
1.670
1.670
1.668
1.681
1.704
1.62
1.643
1.707
1.700
1.667
1.643
1.693
1.707
1.714
1.617
1.853
1.841
1.830
1.819
1.823
1.861
1.846
1.868
1.748
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
lO~
weakly with a transverse optical mode, which decays
into two or more lower-energy phonons of frequencies corresponding to fundamental vibrational modes.
Therefore the multiphonon absorption coefficient
a(~o, T) is given by [22]
lO7
~w
15
lO5
o~(to,T) = a o [ N (w0) + 1]'°/'°r[N(wo) + 1 ] - t
Xexp(-Aw),
lO1
10~
. . . . . .
2000
3000
,6"-,5
~
(15)
where N is the Bose-Einstein function:
5000
N( X ) = [exp( X / k B r ) - 1 ] - t
Energy gap ( c1-1 )
(16)
Fig. 9. Non-radiative decay rate versus energy gap for rare-earth
ions in various glasses: (1) borate glass, (2) phosphate glass, (3)
silicate glass, (4) germanate glass, (5) tellurite glass, (6) fluoride
glass.
Here x represents w or w 0, kg is the Boltzmann
constant, a 0 is the oscillator strength of IR absorption of the vibration center, w 0 is the frequency of
the vibration center, A is the magnitude of anharmonic vibration and A a 1 / w 0. Eq. (15) is rewritten
non-radiative energy transition probability, W,r, of
rare-earth ions caused by the multiphonon process in
different glass hosts. Depending on the phonon energy of the glass, the decrease of W,r is clearly in
the order of oxide, oxyfluoride to fluoride glasses.
According to the Raman spectra, the highest frequency is located at 600, 580 and 500 cm -t, respectively, for AIF3-, ZrF4- and InF3-based glasses [20].
The main peak in the IR reflection spectra is at 650,
500 and 480 cm 1 respectively [21]. The highest
vibraitonal frequency of the multi-component fluoride glasses depends on the bond constant, K, and
reduced mass, /x, of the host fluoride. The relationship is
as
v=
( K/4"rrZlx) '/2.
(14)
In a = In a o + (~o/o%) l n [ N ( w o ) + 1]
- ln[g(w)
+ 1] - A w
(17)
At room temperature and to > 1300 cm -~, N ( w ) =
0; thus l n ( N ( w ) + 1)-= 0. a 0 and ~oo are definite
values for a glass. Therefore, Eq. (17) can be simplified as
In a ( o ) ) = B - A w ,
(18)
where B is a constant and the value of A determines
the slope of the IR absorption curve.
The intersection point between multiphonon absorption and Rayleigh scattering curves is the theoretical minimum loss wavelength, Ami", of glass
If the force between the cation and the fluoride ion is
simply determined by Coulomb interactions, its magnitude is in accordance with the order of the highest
vibrational frequency:
10
AI-F(600-650 cm ' ) > Z r - F ( 5 0 0 - 5 8 0 c m - ' )
lO3
/ 1
/
/ , /
~.514 0.633
/
2 ? /
/ // //
/ / /
Il 1/
> In-F(480-500 cm- 1).
3.2. Multiphonon absorption
~"7-~
i0-3
The IR absorption decreases as the frequency
becomes greater than the fundamental absorption and
overtone frequencies in glasses. There also exists the
exponential tail, which is caused by the multiphonon
processes. In glasses, multiphonon processes couple
o.~
i i i Li
,.o ,:~.;
3' ,: ; '6~,;;;o
,;
X(~m)
Fig. 10. Multiphonon absorption and Rayleigh scatering curves of
fluoride glasses: (1) SiO 2, (2) B a - L a - A I - Z r - F , (3) L i - B a - A I La-Zr-F, (4) B a - Z r - T h - F , (5) B a - Z n - Y b - Y h - F .
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
16
3.0
8O
A¥
F " 1250cm- I
ZBLA
2.5
70
p - 1300o~-I
I-0.12~
I -- 0,34611
60
2.0
--0.551
~
1.5
/ J - 133oc.~- 1
1.0
v
0.5
P "l~Ocm-I
~ 40
0
0.5
~ I ffi 0.794mm
~I-1.57~
~I - 2.53~
3O
20
0800
1.5
2.0
2.5
l
3.0
I, ( m )
Fig. 12. Plot of In(l/T) versus thickness, L, of fluoride glasses at
different wavelengths.
/
lo
1.0
I000
1200
I
I
1400
1600
Frequency (can-l)
Fig. 11. IR absorption edge of fluoride glass of different thicknesses.
/~min
fibers, as shown in Fig. 10 [23]. The value of
is
1.55 tzm for fused silica fibers and 2 . 5 - 4 txm for
fluoride glass fibers.
Fig. 11 shows the IR absorption edge of fluoride
glasses with different thickness. According to the
L a m b - B e e r equation In l / T = aL, where T is the
transmittance, a is the absorption coefficient and L
is the thickness. A plot of In 1 / T versus L of
fluoride glasses at different wavelength is shown in
Fig. 12. The slope of the straight line is the absorption coefficient at a definite wavelength and is independent of the sample thickness. Then the plot of IR
absorption coefficients versus frequency of fluoride
glasses can be derived from Fig. 13. The exponential
tail is clearly demonstrated.
Using computer calculation and fitting Fig. 13
with Eq. (15), the IR multiphonon absorption parameters of fluoride glasses can be obtained and are
listed in Table 5. The estimated values of IR multiphonon absorption at 2.5 and 3.5 I.Lm are also shown
in Table 5.
mass, ~, and vibration force constant, k. For a
diatomic molecule force constant can be expressed
as
k
=
a N ( x a x b / d 2 ) 3/4 + b,
(19)
where a and b are constants, N is the number of
valence bonds in the molecule ( N = Z c, for fluorides), d is the bond length, x a and x b are the
electronegativities of atoms a and b ( x F -- 4.10 for
fluorides).
After systematic analysis of the frequency dependence of the muliphonon absorption coefficient, we
proposed an empirical equation to estimate the value
of A for fluoride components in glasses:
a = [23.565(tx/Zc)
X
10 -4
1/2(d6/x
3
)1/8 + 6.570]
(20)
.
18
16
14
12
I0
AY
3.3. Calculation of multiphonon absorption
As shown in Eq. (15), there are three unknown
parameters, c~0, too and A. In Section 2.4. we have
already derived the IR eigen absorption wavelength,
A2, and oscillator strength, f2, of fluoride components in glasses, which correspond to oJ0 and c% in
Eq. (15). The parameter, A, depends on the reduced
1200
1300
1400
1500
1600
Frequency (cm- I )
Fig. 13. Plot of infrared absorption coefficients versus frequency
with fluoride glasses.
17
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
Table 5
IR multiphonon absorption parameters of fluoride glasses
Glass
a o (10 -5 cm -1)
w0 (cm -1)
AY
ZBLA
ZBYA
A(10 -3 cm 1)
a (10 -4 dB/km)
fitted
calc
fitted
calc
fitted
calc
2.5 Ixm
3.5 ixm
11.102
9.367
5.684
3.586
2.513
2.737
518.41
517.84
512.36
536.27
563.07
543.89
9.358
9.131
9.267
8.797
9.085
9.285
1.37
2.93
1.06
3.78
6.13
2.61
2
~¥bT
1
o
-I
-2
2
1
c.alc
ZBT
0
-1
-2
2
~
ZBLk
o
-1
-2
2
1
0
-1
-2
2
ZBTA
elllc
A¥
1
0
-1
-2
12
13
14
15
16
£( 102can-I )
Fig. 14. Frequency dependence of IR multiphonon absorption of
several fluoride glasses.
The parameters of fluoride c o m p o n e n t s in glasses for
calculating the m u l t i p h o n o n absorption are s u m m a rized in A p p e n d i x 4. By m e a n s of the a b o v e - m e n tioned parameters, we calculated the frequency dep e n d e n c e of m u l t i p h o n o n absorption of fluoride
glasses and compared them with measured results, as
s h o w n in Fig. 14. The calculated and measured
curves are very close. This indicates that the proposed method for calculating the m u l t i p h o n o n absorption is correct. As s h o w n in Fig. 14, the measured values are a little higher than those of the
calculated ones. This m a y be due to the impurity
absorption and scattering loss in tested fluoride
glasses.
4. Conclusion
The experimental results of investigations on optical properties of fluoride glasses have b e e n s u m m a -
rized. The dependence of the optical properties of
fluoride glasses on their chemical composition can
be interpreted in the framework of the consideration
of fluoride glass as an ionic substance. The optical
properties of fluoride glasses, such as optical dispersion and eigen absorption in the U V and IR regions,
are d e p e n d e n t on the optical properties of the cations
and fluorine anions and the characteristics of the
chemical bonds M - F . Based on these considerations,
the proposed system for calculating refractive-index
dispersion and m u l t i p h o n o n absorption of fluoride
glasses is basically correct. Hence it can be used to
quantitatively estimate the optical properties of
m u l t i - c o m p o n e n t fluoride glasses the chemical composition of which is k n o w n , or to guide designing the
chemical composition of fluoride glasses with special optical properties.
References
[1] F. Gan, Optical and Spectroscopic Properties of Glass,
(Springer, Berlin, 1992) pp. 62-96.
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1093.
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58; L. Zhang and F. Gan, Special Glasses 5 [1] (1988) 10.
18
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
Appendix I
Values of R o, Rv, Rc, A~, a and VM of fluoride components in glasses
MFn
R0
(cm3/mol)
RF
(cm3/mol)
Rc
(cm3/mol)
As
(Ixm)
a
VM
(cm3/mol)
LiF
NaF
KF
RbF
CsF
BeF 2
MgF2
CaF2
SrF2
BaF2
MnFe
CuF 2
ZnF2
CdF 2
PbF2
CrF3
FeF3
AIF3
GaF 3
InF3
ScF3
YF3
LaF3
CeF3
PrF3
NdF3
SmF3
EuF3
GbF3
TbF3
DyF3
HoF3
ErF3
TmF3
YbF3
LuF3
ZrF4
HfF4
ThF4
2.482
2.898
4.759
6.264
8.998
4.086
4.894
6.184
7.429
9.509
6.109
5.784
6.872
7.752
13.608
10.047
8.152
6.392
7.924
9.465
9.450
8.992
11.971
11.951
11.930
11.920
11.772
11.728
11.537
11.406
11.229
11.058
10.975
10.965
10.576
10.581
12.527
12.981
13.813
2.4974
2.9171
4.7913
6.3071
9.0635
4.1105
4.9239
6.2236
7.4791
9.5754
6.1881
5.8622
6.9446
7.8460
13.8942
10.1765
8.2688
6.4367
7.9858
9.6012
9.5298
9.0741
12.0955
12.0735
12.0517
12.0404
11.8912
11.8467
11.6538
11.5199
11.3401
11.1670
11.0832
11.0731
10.6803
10.6854
12.6195
13.0769
13.9164
2.4754
2.8899
4.7453
6.2456
8.9701
4.0756
4.8813
6.1672
7.4077
9.4807
6.0756
5.7510
6.8412
7.7122
13.4885
9.9922
8.1027
6.3730
7.8977
9.4076
9.4160
8.9571
11.9182
11.8991
11.8785
11.8681
11.7215
11.6776
11.4875
11.3578
11.1817
11.0118
10.9291
10.9191
10.5318
10.5368
12.4876
12.9402
13.7689
67.5
69.5
70.5
71.0
73.0
66.3
67.0
68.5
70.3
71.5
96.5
98.5
87.5
93.5
121.5
96.3
101.3
71.5
75.5
101.5
78.5
81.5
86.8
86.2
86.0
85.8
85.7
85.7
85.7
85.1
84.8
84.6
84.6
84.6
84.6
84.6
73.5
73.5
74.0
2.4492
2.8575
4.6905
6.1725
8.8591
4.0340
4.8304
6.1000
7.3227
9.3682
5.9543
5.6215
6.7196
7.5557
13.0262
9.7771
7.9097
6.2974
7.7932
9.1826
9.2813
8.8190
11.7098
11.6938
11.6745
11.6653
11.5216
11.4785
11.2916
11.1668
10.9950
10.8288
10.7475
10.7377
10.3568
10.3617
12.3310
12.7779
13.5939
10.176
13.088
19.964
24.614
32.430
23.675
16.973
21.361
23.458
28.981
25.214
22.053
24.320
24.211
26.413
39.304
32.493
30.542
33.019
36.029
35.342
31.258
34.421
34.203
33.929
33.709
33.474
33.162
32.451
31.085
30.891
30.333
30.013
29.807
29.732
29.724
42.113
41.689
41.692
[14] L. Zhang and F. Gan, Glass Technol 33 (1992) 23.
[15] L. Zhang and F. Gan, in: Extended Abstracts 5th Int. Symp.
on Halide Glasses, Japan, 1988, p. 70.
[16] P. McNamara, in: Extended Abstracts 6th Int. Symp. on
Halide Glasses, Germany, 1989, p. 357.
[17] S.H. Wemple, Appl. Opt. 18 (1979) 31.
[18] K. Nassau and M.E. Lines, SPIE 484 (1984) 7.
[19] F. Gan and F. Lin, Acta Opt. Sin. 1 (1981) 481.
[20] H. Chen and F. Gan, Acta Opt. Sin. 8 (1988) 791.
[21] L. Zhang, F. Gan and Y. Jing, Mater. Sci. Progr. 3 (1989)
360.
[22] C.H. Perry, D.J. McCarthy and G. Rupprecht, Phys. Rev. 138
(1965) A1537.
[23] L.G. Van Uitert and A.J. Bruce, in: Extended Abstracts 3th
Int. Syrup. on Halide Glasses, 1985, p. 596.
[24] B. Bendow, M.G. Drexhage and H.G. Lipson, J. Appl. Phys.
52 (1981) 1460.
[25] A.C. Pastor, J.A. Harrington, L.E. Gorre and R.K. Chew,
Mater. Res. Bull. 14 (1979) 543.
[26] L.G. Van Uitert, H.J. Guggenheim, H.M. O'Bryan, A.W.
Warner, J.D. Bromlow, J.L. Bernstein, G.A. Pasteur and L.F.
Johnson, Mater. Res. Bull. 11 (1976) 669.
19
F. Gan / J o u r n a l of Non-Crystalline Solids 184 (1995) 9 - 2 0
Appendix 2
Values o f f l , ]'2 and Ai, A2 o f fluoride c o m p o n e n t s in glasses
MF,
]'1
]'2
A,
A2
LiF
NaF
KF
RbF
CsF
BcF 2
MgF 2
CaF 2
SrF 2
BaF2
MnF 2
CuF 2
ZnF 2
CdF 2
PbF 2
CrF 2
FeF 3
A1F 3
GaF 3
InF 3
0.9470
0.8043
0.9572
0.9895
1.1130
0.6123
1.1893
1.1961
1.3434
1.3855
1.2069
1.1305
1.3562
1.3652
2.2679
0.8954
0.9727
0.7069
0.7318
0.9428
0.0738
0.1170
0.1260
0.1280
0.1315
0.0692
0.0855
0.1000
0.1025
0.1050
0.1125
0.1205
0.0975
0.1015
0.1510
0.1213
0.1236
0.0728
0.0892
O. 1151
3.2705
4.6856
4.5935
4.5531
5.2235
1.1792
3.0834
2.6825
2.6935
2.7631
2.5862
2.3274
3.3023
2.0241
2.5211
2.0245
1.5121
1.2665
1.8523
2.3158
32.7912
40.5731
55.5514
63.2953
78.7452
13.1620
23.4602
32.8954
37.4431
44.4379
26.1061
24.1528
28.5939
31.2532
35.5892
18.0538
18.1871
15.6344
18.0476
23.7538
ScF 3
YF 3
LaF 3
CeF 3
PrF 3
NdF 3
SmF 3
EuF 3
GdF 3
TbF 3
DyF 3
HoF 3
ErF 3
TmF 3
YbF3
LuF 3
Z r F4
H f F4
T h F4
1.0713
1.1854
1.5805
1.5737
1.5667
1.5543
1.5461
1.5393
1.5257
1.5563
1.5457
1.5250
1.5112
1.4907
1.4772
1.4637
1.2429
1.2018
1.4544
0.0795
0.0855
0.0900
0.0914
0.0892
0.0890
0.0889
0.0889
0.0889
0.0883
0.0880
0.0878
0.0878
0.0878
0.0878
0.0878
0.0735
0.0803
0.0828
2.3585
2.6049
3.4296
3.1147
3.0794
3.1165
3.1165
2.9384
3.0081
2.9483
2.9416
2.9375
2.9493
2.9482
3.0310
2.9281
1.4821
1.3945
1.4069
20.8631
27.1789
30.1871
30.6809
30.5252
30.4302
30.4161
31.1069
31.0279
29.8546
29.7545
29.6254
29.4889
29.5233
29.7332
28.9131
17.5479
22.2641
25.2953
Appendix 3
Values o f d n / d A ,
A0, M a n d n of fluoride c o m p o n e n t s in glasses
MFn
dn/dA
(2.55 ~xm)
Ao
(~m)
n
(0.5 ~ m )
n
(2.55 txm)
n
(5 p~m)
M
(P s / k m nm)
AIF 3
GaF 3
MgF 2
BeF 2
FeF 3
ScF3
InF 3
LiF
CrF 3
MnF 2
ZrF4
CuF e
YF 3
ZnF 2
YbF 3
TmF 3
CaF2
LuF3
ErF 3
TbF 3
DYF 3
HoF3
0.0259
0.0177
0.0157
0.0148
0.0141
0.0136
0.0133
0.0122
0.0114
0.0106
0.0099
0.0098
0.0086
0.0080
0.0068
0.0067
0.0066
0.0065
0.0065
0.0064
0.0064
0.0064
1.1086
1.3100
1.2231
1.0747
1.7800
1.3660
1.6826
0.9390
1.7780
1.7800
1.4432
1.7930
1.5488
1.7394
1.6752
1.6866
1.1636
1.6663
1.6970
1.7110
1.7093
1.7093
1.5561
1.4933
1.3544
1.2817
1.5735
1.5789
1.6215
1.3943
1.5787
1.5282
1.6068
1.5184
1.5142
1.5844
1.5238
1.5241
1.2617
1.5224
1.5248
1.5277
1.5266
1.5255
1.5159
1.4596
1.3269
1.2596
1.5237
1.5511
1.5805
1.3724
1.5388
1.4911
1.5849
1.4831
1.4920
1.5577
1.5030
1.5035
1.2448
1.5020
1.5043
1.5071
1.5062
1.5052
1.4091
1.3898
1.2664
1.1972
1.4709
1.4990
1.5316
1.3264
1.4962
1.4529
1.5466
1.4478
1.4603
1.5290
1.4784
1.4795
1.2206
1.4786
1.4809
1.4841
1.4833
1.4823
91.54
63.64
56.83
60.23
37.77
39.48
38.11
41.52
28.93
22.46
31.82
19.74
22.46
20.42
23.14
15.65
15.65
15.65
11.91
14.97
18.04
14.97
F. Gan /Journal of Non-Crystalline Solids 184 (1995) 9-20
20
Appendix 3 (continued)
M Fn
dn/dh
(2.55 I.tm)
Ao
(Ixm)
n
(0.5 tzm)
n
(2.55 izm)
n
(5 p.m)
M
(P s / k m nm)
SmF 3
CeF 3
NdF 3
EuF 3
GdF3
LaF3
PrF 3
H f F4
SrF 2
NaF
T h F4
PbF 2
CdF 2
BaF 2
KF
RbF
CsF
0.0063
0.0063
0.0063
0.0063
0.0062
0.0062
0.0062
0.0059
0.0051
0.0045
0.0042
0.0042
0.0041
0.0038
0.0033
0.0028
0.0025
1.7403
1.8276
1.7300
1.7303
1.7300
1.7460
1.7400
1.7314
1.3463
1.6248
1.8786
3.0301
1.6260
1.9576
1.7900
2.1936
2.3352
1.5322
1.5369
1.5330
1.5312
1.5296
1.5346
1.5334
1.6215
1.3419
1.1064
1.5607
1.7812
1.5703
1.3501
1.1452
1.2539
1.2651
1.5116
1.5132
1.5122
1.5106
1.5090
1.5137
1.5127
1.6022
1.3241
1.1472
1.5438
1.7238
1.5475
1.3330
1.1331
1.2365
1.2471
1.4890
1.4909
1.4897
1.4883
1.4867
1.4914
1.4906
1.5806
1.3063
1.3098
1.5289
1.7135
1.5341
1.3200
1.1216
1.2275
1.2395
18.04
18.04
11.23
11.23
14.29
18.04
14.29
16.68
10.21
11.91
7.49
- 9.87
6.81
12.93
7.83
2.72
1.36
Appendix 4
Values o f a o , to o and A o f fluoride c o m p o n e n t s in glasses
MFn
ao(10-3cm
Wo(Cm-1)
A(10
LiF
6.967
1)
305.0
10.821
3cm)
MFn
a o (10 - 3 cm - 1 )
to o (cm
NaF
KF
RbF
CsF
BeF 2
MgF 2
CaF 2
SrF 2
BaF2
MnF 2
CuF 2
ZnF2
CdF 2
PbF 2
CrF2
FeF 3
AIF 3
GaF 3
lnF3
3.182
3.600
4.550
5.920
1.179
4.380
3.359
3.410
3.500
3.886
3.027
3.701
2.024
2.030
2.024
2.513
3.589
3.150
4.315
246.5
194.0
158.0
127.0
759.8
427.2
304.0
267.1
225.0
383.1
414.0
349.8
320.0
281.0
553.9
549.8
639.6
554.1
421.0
13.389
17.012
20.887
25.984
4.343
7.724
10.855
12.356
14.665
8.615
7.970
9.433
10.313
11.745
5.958
6.002
5.519
5.956
7.839
ScF3
YF 3
LaF3
CeF 3
PrF 3
NdF3
SmF 3
EuF 3
GdF 3
TbF 3
DyF3
HoF3
ErF 3
TmF 3
YbF3
LuF 3
Z r F4
H f F4
ThF4
3.454
3.536
3.126
3.211
3.176
3.213
3.213
3.335
3.308
3.145
3.108
3.074
3.116
3.196
3.328
3.205
1.782
1.694
1.476
479.3
367.9
331.3
325.9
327.6
328.6
328.8
321.5
322.3
335.0
336.1
337.6
339.1
338.7
336.3
345.9
569.9
449.2
395.2
1)
A (10 - 3 c m )
6.885
8.969
9.962
10.125
10.073
10.042
10.037
10.265
10.239
9.852
9.819
9.776
9.731
9.743
9.812
9.541
5.791
7.347
8.347