The refractive index, the temperature coefficient of the refractive index, and the optical transparency ofgadolinium gallium garnet are reported as a function of wavelength from the near UV to the middle IR. Thematerialis transparent enough for good optical components between 0.36 and 6.0 ,um, and the refractive indexranges from 2.0 at the UV end to 1.8 at theIR end of the spectrum. The wavelength dependence of index is ex-pressed as a three-term Sellmeier formula with agreement better than two parts in the fourth decimal betweencalculated and experimental values. Variations in composition depending on growth from various melts (e.g.,stoichiometric vs congruent) have no effect on the optical parameters at this level of precision. Keywords:Garnets, gadolinium gallium garnet, refractive index, optical properties.
1. Introduction
Gadolinium gallium garnet (GGG) is a useful mate-rial for substrates on which to grow epitaxial layers forintegrated optical devices.1-5 It can be produced inlarge single crystal form6-8 and cut and polished wellusing standard'optical finishing techniques. 9-"1 Itscrystal lattice matches that of several materials fromwhich bubble memory films are made.12 However, avariation of lattice parameter can exist depending onhow GGG is grown,13 and it is not known if this varia-tion is severe enough to affect optical properties signif-icantly. We have measured the refractive index vswavelength and vs temperature as well as the opticaltransparency of a range of GGG samples, and the re-sults are reported here as an aid for the design ofoptical devices.
II. Experimental
Four different crystals of Czochralski-pulled GGGwere used. One of these crystals (MCL-52) is knownto have been grown from a stoichiometric melt, i.e.,Gd3Ga5Ol 2, while another (33) was grown fromGd3.03 Ga4.9 7 012 [i.e., Gd3(Ga4 .97 Gdo.03 )O12] close to thecongruent, i.e., maximum melting composition.Nothing is known about the other two crystals.Prisms were cut with apex angles near 30° suitable formeasurement of index of refraction with a computer-ized machine previously described.14 The deviationsof radiations of various wavelengths passing through
The authors are with AT&T Bell Laboratories, Murray Hill, NewJersey 07974.
Received 20 November 1989.0003-6935/90/253704-04$02.00/0.
the prism were converted to index, and the index vswavelength data were fitted to a three-term Sellmeierformula. For index vs temperature, the deviation ofeleven emission lines of mercury between 0.365 and1.813 Asm was measured with the prism in an ovenfitted with transparent windows as previously de-scribed.14 The optical transparency was measured ona Hitachi model 330 UV-visible-near IR or a Perkin-Elmer model 683 IR spectrophotometer for severalthicknesses cut and polished from one of the crystals.
Ill. Transparency Results
The region of optical transparency of GGG extendsfrom the UV near 0.38,um through the visible into theIR beyond -6.0,m as Fig. 1 shows. The points in thefigure were calculated from measurements of the ab-sorbances of several samples of thicknesses varyingbetween 0.5 and 90 mm using a reflection correctionderived from the measured refractive indices. If t isthe sample thickness, Io the incident radiation intensi-ty, and I the transmitted intensity, the specific absor-bance a in Fig. 1 is given by
The range of transparency for practical use in opti-cal devices can be expressed as the wavelength intervalover which the absorption is <50% for a thickness of 1cm (a < 0.30), and this interval is between 0.38 and 6.0,gm, as suggested above and as Fig. 1 indicates.
On closer examination of the absorption spectrum inthe UV one finds several relatively strong narrow linesin the steeply rising absorption edge. These are shownin Fig. 2 and arise from the well known 4f - 4f elec-tronic transitions of trivalent gadolinium'5- 7 indicat-ed in the figure. The relative intensities of the linegroups vary rather drastically with the environment ofthe rare earth, but the intensities we observe are simi-lar to those found in aqueous solutions of Gd3+.l8
Fig. 1. Transparency of gadolinium gallium garnet as specific ab-sorbance in cm-' vs wavelength in microns. Note the break in theabscissa between 0.6 and 4,gm where the absorption was too small to
be measured.
12
10
8
6
4
2
00.25 0.30 0.35
x,,um
Fig. 2. Detail of the optical absorption of gadolinium gallium gar-net near the absorption edge in the UV. The relatively narrow lines
are due to 4f - 4f transitions of gadolinium as noted.
2.1w020z
-2.0
> 0.4 0.6 0.8 1.0
< 1.9
a1.8 L
Lu_
1.8
1.7 I 1 1 1
0 1 2 3 4 5 6 7 8
, /Fm
Fig. 3. Refractive index as a function of wavelength for gadoliniumgallium garnet over the useful range of transparency.
That is, the group of transitions 8S7 /2 -6Pj and 8S 7 /2
6Dj are weak, while those for 8S7/2 - 4 Ij are muchstronger. These transitions are in the absorption edgeof the garnet crystal itself, where the transparency ofappreciable thicknesses of material is greatly reduced,but they still could be important in some optical de-vices.
IV. Refractive Index Results
The index of refraction vs wavelength measure-ments are plotted in Fig. 3, and the Sellmeier coeffi-cients Ai, Li in the expression
(2)n 2 1 = EAiX2/(X2 _
i=1
are given in Table I for prisms cut from the four differ-ent crystals. Using these coefficients, some usefuldispersion values are given in Table II together withthe indices for some standard wavelengths used inoptical designing and the dispersion value. Severalvalues for the indices of GGG have been given in the
Table 1. Sellmeler Coefficients of GGG
Sellmeier Crystal Crystal Crystal Crystalcoefficients MCL-52 644 645 33 Average
literaturel9-24 but not for the entire region of transpar-ency and not with the accuracy achieved here. It is notpossible to fit the experimental values of index vswavelength to a single term Sellmeier formula over theentire range of transparency, as attempted in thesereferences, and our three-term formula with the con-stants in Table I should be used instead.
The results for each specimen were separately fitted,and the number of individual wavelengths used in thefit varied from forty-seven for crystal 644 to sixty for 33as noted in the table. These individual fits gave therms deviations entered in the next line of the table andwere of the order of 1 in the fourth decimal placebetween experimental and calculated index values. Ifthe Sellmeier parameters for the individual fits of allfour crystals are averaged, giving the values in the lastcolumn of Table I, the rms deviation is increased toalmost 2 X 10-4 as the last line of the table shows.Since the four crystals from which the four sampleswere cut had provenances widely differing in time andwere grown in different conditions of melt stoichio-metry, we can conclude that the indices obtained fromthe averaged parameters will give values for any pro-duction material which are correct to 2 X 10-4. Withinone crystal the index can be expected to vary less thanthat. Using published x-ray diffraction data,13 thelattice parameter change in going from stoichiometricto congruent melts in crystal growth corresponds to thechange from 12.383 to 12.3845 A, i.e., less than 2 partsin 104. Accordingly it is reasonable that the opticalproperties should remain constant within the accuracyof our measurements. This range of crystals encom-passes essentially any GGG likely to be encounteredoutside a GGG research laboratory.
3.0
2.8 -
2.6
,,2.4To
i 2.2
2.0
1.8
1.60.2 0.6 1.0 1.4 1.8
X,p/Jm
Fig. 4. Temperature coefficient of refractive index of gadoliniumgallium garnet for the wavelength range from 0.365 to 1.8 gm.
It was found that the index of refraction of GGGbetween 18 and 1400C varies linearly with tempera-ture, and the slopes of the curves for various wave-lengths gave the temperature coefficients dn/d T listedin Table III. The values obtained are plotted in Fig. 4,where it can be seen that the coefficients in the IR arenearly constant, while those at the short wavelengthend of the visible and in the UV increase rapidly withdecreasing wavelength. This is the expected behav-ior,25with two competing mechanisms determining thevalues of the coefficients. The density of most materi-als decreases with increased temperature, producing adecrease in refractive index. The absorption edge onthe other hand shifts to longer wavelength with in-creasing temperature and thus produces an increase inrefractive index with temperature. The latter effect isclearly dominant in GGG, especially for the shorterwavelengths.
For calculating values of the temperature coefficientof index for any wavelength between 0.35 and 1.8,um,the following relation is convenient, although it has nophysical basis:
dnldT = 1.69 + 0.06/ . (3)
V. Summary
Single crystal gadolinium gallium garnet is transpar-ent between 0.38 and 6.0 Am and has a refractive indexbetween 2.027 and 1.838 in this range. The dispersionNF - NC is 0.02046. The index as a function of wave-length for four crystals of differing origin is represent-ed by a three-term Sellmeier formula to within 2 X 10-4over the entire range of transparency. The tempera-ture coefficient of refractive index between 18 and1400C was found to increase from 1.7 X 10-5/OC in theIR to 2.8 X 10- 5/OC at 0.38 m.
The authors are grateful for helpful discussions withR. L. Barns, A. J. Valentino, and C. H. Henry.
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