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Material dispersion in heavy metal oxide glasses containing bi2o3
Journal of Non-Crystalline North-Holland. Amsterdam
Solids
92 (1987)
MATERIAL DISPERSION . CONTAINING BI 203
89-94
89
IN HEAVY METAL
OXIDE GLASSES
Richard N. BROWN Rome
Air
Received Revised
Development
Center,
4 November 1986 manuscript received
Solid
State
18 February
Sciences
Directorare.
Hanscom
AFB,
MA
01731.
USA
1987
The refractive index of PbO-Bi,O,-Ga,O, and CdO-Bi,O,-Ga,O, glasses has been measured between 0.5 and 5.0 pm. and their material dispersion has been evaluated. The cross-over wavelengths are near 3 am. Electronic and lattice dispersion parameters have been obtained, and compared with those of heavy metal fluoride glasses. The material dispersion values at 3.5 pm are comparable for the oxide and fluoride glasses, while the cross-over wavelength is larger in the oxide glass.
1. Introduction Much effort has been expended in the last decade in the search for glasses which not only transmit infrared radiation with very low absorption and scattering loss, but which also possess desirable mechanical and chemical properties [l-6]. Some of the glasses studied for this purpose include oxides, halides and chalcogenides comprising heavy metals because of their long wavelength cutoff. The oxides of lead and bismuth are particularly promising in this respect. Among the many applications awaiting the advent of such glasses are optical fibers operating at infrared wavelengths, where Rayleigh scattering is reduced relative to the visible region. An important design parameter for such a fiber is the material dispersion, which may be evaluated from spectral refractive index data. It is the purpose of this paper to present refractive index measurements for some recently developed heavy metal oxide glasses containing Bi,O,, and to discuss the relevant dispersion parameters.
2. Experimental The compositions of the glasses studied are shown in table 1. Refractive index measurements were made using the minimum deviation method. The apparatus is described elsewhere [7], where further references will also be found. Samples were in the form of polished prisms having 1 X 3 cm faces. 0022-3093/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
90
R.N.
Table Glass
1 compositions
Brown
/ Material
dispersion
in heavy metal oxide
glasses
(mol%)
BGP BGC
Bi 201
GaA
PbO
25 60.9
17.9 13
57.1
Cd0 26.1
The data appear in fig. 1. Absorption bands are responsible for the gaps in the upper spectrum, but, for the purpose of subsequent analyses, interpolations were made. By differentiating the index spectrum, the material dispersion is obtained [8]:
where A is the wavelength and c is the velocity of light. This is shown in fig. 2, where it can be seen that the cross-over wavelength (M = 0) is near 3 pm for these glasses. According to Wemple’s model [9], the dependence of the index, n, on photon energy, E, in the region between electronic and lattice resonances can be described by the following expression:
4,&
-- E:
Et-E=
E2’
n*-1=
(1)
Here E,, is’ an average excitation energy for the electrons, Ed represents the electronic oscillator strength, and E, is the lattice dispersion parameter. At sufficiently high energies that the lattice term may be neglected, eq. (1) may be rearranged as follows: 1 n*-1
En” --
=l$
Fig. 1. Refractive
E2
WG
index
.
vs wavelength.
Fig. 2. Material
dispersion
vs wavelength.
RN.
Brown
/ Material
dispersion
in heavy metal
oxide glasses
91
0 24 1
d-1 0 23
0.22
E2 WP Fig. 3. Dispersion
analysis parameters.
for electronic
Fig. 4. Dispersion
A2 ( ud analysis for lattice ters.
parame-
Plots of l/(n* - 1) vs E2 are shown in fig. 3, and straight lines are fitted to the data points [lo]. The electronic parameters, E, and E,, are obtained from the slopes and intercepts of these lines, and they appear in table 2 as measured values (also shown for comparison are some fluoride glass values). At low energies the electronic term in eq. (1) approaches a constant, yielding
where use is made of the expression E(eV) = 1.24/X(pm). Plots of n2 - 1 vs A* are shown in fig. 4 and straight lines are fitted to the data points [ll]. The lattice parameter, E,, is obtained from these lines, and is shown in table 2. Nassau [12] has shown how to calculate the electronic dispersion parameters for the glasses from a knowledge of the component crystal parameters. Some of these crystal values have been deduced from index data, by the above analysis [9], and the others can be estimated. They appear in table 3. The Cd0 parameters have been estimated as follows: from the measured value of E, for
Table Glass
BGP BGC ZBLA BZYT
2 dispersion
parameters
(ev)
Eo
Eo
Ed
El
El
(meas.)
(talc.)
(meas.)
&.)
(meas.)
(Elk.)
5.5 5.6
22.6 21.7 17.7 18.4
21.2 19.7
0.125 0.116 0.079 0.074
0.084 0.090
5.5 5.5 13.7 13.8
92
R.N.
Table 3 Crystal dispersion
parameters
Cd0 PbO Bi,O, GM3
Brown
/ Material
dispersion
in heavy metal oxide
glasses
(eV) Eo
Ed
El
4.1 4.7 5 9.5
18.5 23 21 16
0.086 0.071 0.084 0.125
the CdO-containing glass, E, for Cd0 is estimated to be 4.7 eV. The ratio, I&/E,, is estimated from the refractive index at visible wavelengths, using [13] and Ed is obtained from this ratio and the previous estimate of E,. The values of Ed for Bi,O, and Ga,O, are similarly obtained from known indices [14] and E,, values [12]. The remaining parameters have been obtained from measured values appearing in the literature [9]. The calculated values of the electronic parameters for the glasses, also appearing in table 2, are the sums of these crystal parameters weighted by the mole fractions [12]. The lattice parameter, E,, is obtained from the following expression, also due to Wemple [15]: E: = NAh2Z2e2/sp, (2) where NA is the anion density, Z is the formal anion valence, p is the reduced mass, and h is Planck’s constant. Again, Nassau [12] has shown how to calculate the anion density and reduced mass for the glasses from the crystal values. The calculated values of the lattice parameter appearing in the table 2 were obtained in this way. 3. Discussion The material dispersion in the PbO-containing glass shown in fig. 2 is seen to be larger at wavelengths beyond A, than it is in the Cd0 glass. This is caused by a larger lattice parameter, E,, in the former (see table 2) [15]. Table 4 shows the values of material dispersion at a wavelength of 3.5 pm, as well as the cross-over wavelengths and the slope of M at ha. These are important parameters for the design of optical communication fibers operating in this region (161. Also included in the table are some fluoride glass data for comparison. Although the material dispersions for these oxide glasses are comparable to those for the fluoride glasses at 3.5 pm, the cross-over wavelengths and slopes at X0 are significantly larger in the former. As shown by Wemple [15], the cross-over wavelengths can be calculated from the dispersion parameters, according to the expression
R.N. Table 4 Material dispersion,
Brown
/ Material
cross-over M at 3.5 gm @s/l--W
BGP BGC ZBLA BZYT
-
24.2 16.6 27.5 23.0
wavelength
dispersion
and slope
in heavy meral oxide
for oxide
and fluoride
(w)
dM/dh (PO-~-v)
2.9 3.0 1.7 1.8
-46.3 - 46.6 -28 -24
A0
glasses
93
glasses at ho
Thus the fluoride glasses generally have smaller cross-over wavelengths due to their larger excitation energies and smaller electronic oscillator strengths, as can be seen in table 2 [7]. Comparing the measured dispersion parameters for the two oxide glasses studied here, table 2 shows that they are much alike. This is to be expected, because, with the exception of Ga,O,, all the component parameters, appearing in table 3, are similar. Furthermore, the contribution of Ga,O, to each composite glass parameter is small. If we compare the oxide glasses with fluoride glasses, we see that the excitation energies in the fluorides are larger because of their larger energy gaps. The electronic oscillator strengths, E,,, in the fluorides are about 75% of the oxide values. This can be understood by reference to Wemple’s expression [15]: Ed = fn,ZNAd3.
where f is proportional to the microscopic oscillator strength, n, is the number of valence electrons per anion, and d is the nearest neighbor bond length. The dimensionless factor, NAd3, which is a measure of the packing of anions, is about 50% larger in the fluorides than it is in the oxides. On the other hand, the anion valence is half as great in fluorides. Since the product, fn.3 is comparable in both oxides and fluorides, the net result is that the electronic oscillator strengths are about three-fourths as great in the fluorides. When comparing lattice oscillator strengths, we find that they are about 50% higher in oxide glass then in fluoride glass. This is understood by reference to eq. (2). Compensating for the larger anion valence in the oxide glasses are the lower anion densities and larger reduced masses relative to the fluorides. In spite of the uncertainties in estimating the dispersion parameters for the component crystals, fairly good agreement with the measured values of table 2 is achieved for the electronic parameters, being within 2% for the excitation energies, E,, and within 10% for the oscillator strengths, Ed. However, agreement is poor for the lattice parameter, E,, Not only are the calculated values between 67 and 78% of the measured values, but the relative sizes for the two glasses are in the wrong order. Similarly low estimates have been obtained for the fluoride glasses [17].
94
R.N.
Brown
/ Material
dispersion
in heavy metal oxide glasses
4. Conclusion It has been shown that the material dispersion and the cross-over wavelength as well as the IR edge for these heavy metal oxide glasses are all favorable for low loss optical fibers operating near 3 pm. Because of the X4 dependence of the Rayleigh scattering, the large cross-over wavelengths of the oxide glasses relative to the fluoride glasses would tend to make the former more favorable for such applications. Wemple’s model [9] accounts well for the electronic contributions to the dielectric constant, but good agreement is not achieved between calculated and measured lattice effects.
References [l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [ll] [12] (131
W.H. Dumbaugh, Phys. Chem. Glasses 19 (1978) 121. W.H. Dumbaugh, in: Emerging Optical Materials, SPIE 297 (1981) 80. W.H. Dumbaugh. in: Advances in Optical Materials, SPIE 505 (1984) 97. W.H. Dumbaugh. Opt. Eng. 24 (1985) 257. W.H. Dumbaugh, in: Infrared Optical Materials and Fibers IV, SPIE 618 (1986) 160. W.H. Dumbaugh. Phys. Chem. Glasses 27 (1986) 119. R.N. Brown and J.J. Hutta, Appl. Opt. 24 (1985) 4500. D.N. Payne and W.A. Gambling, Electron. Lett. 11 (1975) 176. S.H. Wemple, J. Chem. Phys. 67 (1977) 2151. S.H. Wemple and M. DiDomenico, Jr., Phys. Rev. B3 (1971) 1338. H. Poignant, Electron. Lett. 17 (1981) 973. K. Nassau, Bell Sys. Tech. J. 60 (1981) 327. Given the dispersion parameters in table 2, it can be shown that the index at X =X0 is approximately equal to the asymptote approached by the index at long wavelengths in the absence of lattice effects. Thus, at X = X,, n = ,/‘m. [14] K.-S. Sun, J. Am. Ceram. Sot. 30 (1946) 282. (151 S.H. Wemple, Appl. Opt. 18 (1979) 31. [16] K. Nassau and S.H. Wemple, Electron. Lett. 18 (1982) 450. [17] R.N. Brown and M.J. Suscavage, J. Non-Cryst. Solids 89 (1987) 282.
Solids
92 (1987)
MATERIAL DISPERSION . CONTAINING BI 203
89-94
89
IN HEAVY METAL
OXIDE GLASSES
Richard N. BROWN Rome
Air
Received Revised
Development
Center,
4 November 1986 manuscript received
Solid
State
18 February
Sciences
Directorare.
Hanscom
AFB,
MA
01731.
USA
1987
The refractive index of PbO-Bi,O,-Ga,O, and CdO-Bi,O,-Ga,O, glasses has been measured between 0.5 and 5.0 pm. and their material dispersion has been evaluated. The cross-over wavelengths are near 3 am. Electronic and lattice dispersion parameters have been obtained, and compared with those of heavy metal fluoride glasses. The material dispersion values at 3.5 pm are comparable for the oxide and fluoride glasses, while the cross-over wavelength is larger in the oxide glass.
1. Introduction Much effort has been expended in the last decade in the search for glasses which not only transmit infrared radiation with very low absorption and scattering loss, but which also possess desirable mechanical and chemical properties [l-6]. Some of the glasses studied for this purpose include oxides, halides and chalcogenides comprising heavy metals because of their long wavelength cutoff. The oxides of lead and bismuth are particularly promising in this respect. Among the many applications awaiting the advent of such glasses are optical fibers operating at infrared wavelengths, where Rayleigh scattering is reduced relative to the visible region. An important design parameter for such a fiber is the material dispersion, which may be evaluated from spectral refractive index data. It is the purpose of this paper to present refractive index measurements for some recently developed heavy metal oxide glasses containing Bi,O,, and to discuss the relevant dispersion parameters.
2. Experimental The compositions of the glasses studied are shown in table 1. Refractive index measurements were made using the minimum deviation method. The apparatus is described elsewhere [7], where further references will also be found. Samples were in the form of polished prisms having 1 X 3 cm faces. 0022-3093/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
90
R.N.
Table Glass
1 compositions
Brown
/ Material
dispersion
in heavy metal oxide
glasses
(mol%)
BGP BGC
Bi 201
GaA
PbO
25 60.9
17.9 13
57.1
Cd0 26.1
The data appear in fig. 1. Absorption bands are responsible for the gaps in the upper spectrum, but, for the purpose of subsequent analyses, interpolations were made. By differentiating the index spectrum, the material dispersion is obtained [8]:
where A is the wavelength and c is the velocity of light. This is shown in fig. 2, where it can be seen that the cross-over wavelength (M = 0) is near 3 pm for these glasses. According to Wemple’s model [9], the dependence of the index, n, on photon energy, E, in the region between electronic and lattice resonances can be described by the following expression:
4,&
-- E:
Et-E=
E2’
n*-1=
(1)
Here E,, is’ an average excitation energy for the electrons, Ed represents the electronic oscillator strength, and E, is the lattice dispersion parameter. At sufficiently high energies that the lattice term may be neglected, eq. (1) may be rearranged as follows: 1 n*-1
En” --
=l$
Fig. 1. Refractive
E2
WG
index
.
vs wavelength.
Fig. 2. Material
dispersion
vs wavelength.
RN.
Brown
/ Material
dispersion
in heavy metal
oxide glasses
91
0 24 1
d-1 0 23
0.22
E2 WP Fig. 3. Dispersion
analysis parameters.
for electronic
Fig. 4. Dispersion
A2 ( ud analysis for lattice ters.
parame-
Plots of l/(n* - 1) vs E2 are shown in fig. 3, and straight lines are fitted to the data points [lo]. The electronic parameters, E, and E,, are obtained from the slopes and intercepts of these lines, and they appear in table 2 as measured values (also shown for comparison are some fluoride glass values). At low energies the electronic term in eq. (1) approaches a constant, yielding
where use is made of the expression E(eV) = 1.24/X(pm). Plots of n2 - 1 vs A* are shown in fig. 4 and straight lines are fitted to the data points [ll]. The lattice parameter, E,, is obtained from these lines, and is shown in table 2. Nassau [12] has shown how to calculate the electronic dispersion parameters for the glasses from a knowledge of the component crystal parameters. Some of these crystal values have been deduced from index data, by the above analysis [9], and the others can be estimated. They appear in table 3. The Cd0 parameters have been estimated as follows: from the measured value of E, for
Table Glass
BGP BGC ZBLA BZYT
2 dispersion
parameters
(ev)
Eo
Eo
Ed
El
El
(meas.)
(talc.)
(meas.)
&.)
(meas.)
(Elk.)
5.5 5.6
22.6 21.7 17.7 18.4
21.2 19.7
0.125 0.116 0.079 0.074
0.084 0.090
5.5 5.5 13.7 13.8
92
R.N.
Table 3 Crystal dispersion
parameters
Cd0 PbO Bi,O, GM3
Brown
/ Material
dispersion
in heavy metal oxide
glasses
(eV) Eo
Ed
El
4.1 4.7 5 9.5
18.5 23 21 16
0.086 0.071 0.084 0.125
the CdO-containing glass, E, for Cd0 is estimated to be 4.7 eV. The ratio, I&/E,, is estimated from the refractive index at visible wavelengths, using [13] and Ed is obtained from this ratio and the previous estimate of E,. The values of Ed for Bi,O, and Ga,O, are similarly obtained from known indices [14] and E,, values [12]. The remaining parameters have been obtained from measured values appearing in the literature [9]. The calculated values of the electronic parameters for the glasses, also appearing in table 2, are the sums of these crystal parameters weighted by the mole fractions [12]. The lattice parameter, E,, is obtained from the following expression, also due to Wemple [15]: E: = NAh2Z2e2/sp, (2) where NA is the anion density, Z is the formal anion valence, p is the reduced mass, and h is Planck’s constant. Again, Nassau [12] has shown how to calculate the anion density and reduced mass for the glasses from the crystal values. The calculated values of the lattice parameter appearing in the table 2 were obtained in this way. 3. Discussion The material dispersion in the PbO-containing glass shown in fig. 2 is seen to be larger at wavelengths beyond A, than it is in the Cd0 glass. This is caused by a larger lattice parameter, E,, in the former (see table 2) [15]. Table 4 shows the values of material dispersion at a wavelength of 3.5 pm, as well as the cross-over wavelengths and the slope of M at ha. These are important parameters for the design of optical communication fibers operating in this region (161. Also included in the table are some fluoride glass data for comparison. Although the material dispersions for these oxide glasses are comparable to those for the fluoride glasses at 3.5 pm, the cross-over wavelengths and slopes at X0 are significantly larger in the former. As shown by Wemple [15], the cross-over wavelengths can be calculated from the dispersion parameters, according to the expression
R.N. Table 4 Material dispersion,
Brown
/ Material
cross-over M at 3.5 gm @s/l--W
BGP BGC ZBLA BZYT
-
24.2 16.6 27.5 23.0
wavelength
dispersion
and slope
in heavy meral oxide
for oxide
and fluoride
(w)
dM/dh (PO-~-v)
2.9 3.0 1.7 1.8
-46.3 - 46.6 -28 -24
A0
glasses
93
glasses at ho
Thus the fluoride glasses generally have smaller cross-over wavelengths due to their larger excitation energies and smaller electronic oscillator strengths, as can be seen in table 2 [7]. Comparing the measured dispersion parameters for the two oxide glasses studied here, table 2 shows that they are much alike. This is to be expected, because, with the exception of Ga,O,, all the component parameters, appearing in table 3, are similar. Furthermore, the contribution of Ga,O, to each composite glass parameter is small. If we compare the oxide glasses with fluoride glasses, we see that the excitation energies in the fluorides are larger because of their larger energy gaps. The electronic oscillator strengths, E,,, in the fluorides are about 75% of the oxide values. This can be understood by reference to Wemple’s expression [15]: Ed = fn,ZNAd3.
where f is proportional to the microscopic oscillator strength, n, is the number of valence electrons per anion, and d is the nearest neighbor bond length. The dimensionless factor, NAd3, which is a measure of the packing of anions, is about 50% larger in the fluorides than it is in the oxides. On the other hand, the anion valence is half as great in fluorides. Since the product, fn.3 is comparable in both oxides and fluorides, the net result is that the electronic oscillator strengths are about three-fourths as great in the fluorides. When comparing lattice oscillator strengths, we find that they are about 50% higher in oxide glass then in fluoride glass. This is understood by reference to eq. (2). Compensating for the larger anion valence in the oxide glasses are the lower anion densities and larger reduced masses relative to the fluorides. In spite of the uncertainties in estimating the dispersion parameters for the component crystals, fairly good agreement with the measured values of table 2 is achieved for the electronic parameters, being within 2% for the excitation energies, E,, and within 10% for the oscillator strengths, Ed. However, agreement is poor for the lattice parameter, E,, Not only are the calculated values between 67 and 78% of the measured values, but the relative sizes for the two glasses are in the wrong order. Similarly low estimates have been obtained for the fluoride glasses [17].
94
R.N.
Brown
/ Material
dispersion
in heavy metal oxide glasses
4. Conclusion It has been shown that the material dispersion and the cross-over wavelength as well as the IR edge for these heavy metal oxide glasses are all favorable for low loss optical fibers operating near 3 pm. Because of the X4 dependence of the Rayleigh scattering, the large cross-over wavelengths of the oxide glasses relative to the fluoride glasses would tend to make the former more favorable for such applications. Wemple’s model [9] accounts well for the electronic contributions to the dielectric constant, but good agreement is not achieved between calculated and measured lattice effects.
References [l] [2] [3] [4] [5] [6] [7] [S] [9] [lo] [ll] [12] (131
W.H. Dumbaugh, Phys. Chem. Glasses 19 (1978) 121. W.H. Dumbaugh, in: Emerging Optical Materials, SPIE 297 (1981) 80. W.H. Dumbaugh. in: Advances in Optical Materials, SPIE 505 (1984) 97. W.H. Dumbaugh. Opt. Eng. 24 (1985) 257. W.H. Dumbaugh, in: Infrared Optical Materials and Fibers IV, SPIE 618 (1986) 160. W.H. Dumbaugh. Phys. Chem. Glasses 27 (1986) 119. R.N. Brown and J.J. Hutta, Appl. Opt. 24 (1985) 4500. D.N. Payne and W.A. Gambling, Electron. Lett. 11 (1975) 176. S.H. Wemple, J. Chem. Phys. 67 (1977) 2151. S.H. Wemple and M. DiDomenico, Jr., Phys. Rev. B3 (1971) 1338. H. Poignant, Electron. Lett. 17 (1981) 973. K. Nassau, Bell Sys. Tech. J. 60 (1981) 327. Given the dispersion parameters in table 2, it can be shown that the index at X =X0 is approximately equal to the asymptote approached by the index at long wavelengths in the absence of lattice effects. Thus, at X = X,, n = ,/‘m. [14] K.-S. Sun, J. Am. Ceram. Sot. 30 (1946) 282. (151 S.H. Wemple, Appl. Opt. 18 (1979) 31. [16] K. Nassau and S.H. Wemple, Electron. Lett. 18 (1982) 450. [17] R.N. Brown and M.J. Suscavage, J. Non-Cryst. Solids 89 (1987) 282.