Optical constants of magnesium oxide in far ultraviole

Roessler, D. M.

Walker, W. C.

English

NASA Technical Reports Server

Optical Constants of Magnesium oxide 
in the Far Ultraviolet* 
j L6-J 9 
b. M. Roessler and W. C. Walker 
Department of Physics 
'Ltniversity of California, Santa Bar a a 2Jrn 
,-& #F I 209 WUOd A I l l 1 3 V d  
.a 
The refractive indices of many crystals are well known in those 
spectral regions where the materials are transparent. On the other 
hand, very few data exist on either the refractive index, n, or the 
absorption index, k, for these materials beyond their ultraviolet 
transmission limits. 
spectrum of crystalline magnesium oxide included the intermediate 
derivation of the optical properties as far as 28 eV. 
Part of our research program on the electronic 
The experimental procedure consisted of the measurement of the 
near-normal-incidence reflectance spectrum of freshly cleaved 
crystals of magnesium oxide from 4 to 28 eV. If the-ratio of the ' 
reflected and incident light intensities is denoted by r , then it , 2 
is possible to derive the following relationships, via the Fresnel 
equations: 
2 1 - r  
h =  2 1 + I: -2r COS 8 
I 2r 
2 k =  1 + r -2r cos 8 
$Work supported by the National Aeronautics and Space Administration 
https://ntrs.nasa.gov/search.jsp?R=19670008806 2020-03-16T18:56:57+00:00Z
t 
c 
The determination of 8 ,  the phase change'on reflection, is 
achieved by use of a Kramers-Kronig integral transformation of the 
reflectance data. 
given elsewhere (1, 2 and references therein). In practice, the 
determination of the phase angle involves an approximation procedure 
which thereby introduces an uncertainty in the computed values of 
n and k. The errors, from this cause, can become important only near 
the end-points of the experimental data energy range (2). 
optical behavior at the long-wavelength end is known (because the 
crystal is transparent here), only the data beyond 26 eV is likely 
to be in error from the computation procedure. 
A detailed discussion of this technique has been 
Since the 
The experimental measurements of the reflectance are accurate 
to about 5%, as estimated from the scatter of the original data points 
and the reproducibility of the spectrum. In any reflectance measure- 
ments however, only the surface Payers of the material are examined 
and it is difficult to assess how nearly even a freshly cleaved surface 
resembles the bulk crystal in its optical properties. Since any defects 
or surface contamination tend to decrease the sharpness and intensity of 
ultraviolet reflectance structure, only data from surfaces exhibiting 
the highest reflectance at the 7.58 eV peak (about 27.5% at 300'K) 
were used in the final computation. In practice, the variations 
in peak reflectance from different freshly cleaved surfaces were 
less than 5%. It is doubtful if the true reflectance, intrinsic 
to the bulk crystal, is more than 5% different from that measured, 
because of the above and also because the Pow energy tail of the first 
reflectance band could be smoothly matched onto the near ultraviolet 
- 2 -  
r 
reflectance as  computed from known va lues  of the refractive index i n  
t h i s  region ( 3 ) .  
The spectral dependence of both n and k La shown i n  figure 1. 
Since there is  some variation i n  the l i t e ra ture  i n  the  use of 
symbols for  absorption, it should be noted tha t  the absorption index,. 
denoted here by k, is related t o  the absorption coefficient, a, 
through the expression a = 4Vk/X. 
dependence of the optical  properties, par t icular ly  near the first 
A discussion of the temperature 
band, has been described previously ( 4 ) .  The electronic t ransi t ions 
responsible for  the observed spectral structure w i l l  be discussed 
elsewhere. 
The values of n and k a t  given photon energies are presented 
i n  table 1, w h e r e  the choice of photon energies was determined by 
the need t o  define the original reflectance spectrum suff ic ient ly  
for  a re l iab le  Kramers-Kronig analysis 
I 
- 3 -  
. .  
”- 
REFERENCES 
1 .  D .  M.  R o e s s l e r ,  B r i t .  J. A p p l .  Phys., - 16, 1119 (1965) 
2. D. M. R o e s s l e r ,  B r i t .  J. A p p l .  Phys., 1 7 8  1313 (1966) 
3. J. Strong,and R .  T .  Brice, J. O p t .  SOC. Am. ,  2 5 8  207 (1935) 
4. D. M. R o e s s l e r  and W. C .  Walker, P h y s .  R e v .  Letters, l7, 
319 (1966) 
TABLE CAPTIONS 
Table 1 .  Values of the refractive and absorption indices ,  
n and k, for magnesium.:oxide a t  photon eGergies 
i n  the range 5 - 28 e V .  
TABLE I w 
n k k h o ( e V )  h w ( e v )  n 
5.00 1.86 0.00 7.68 2.29 0.88 (5) 
5.50 
6.00 
6.50 
7.00 
1.91 
1.97 
2.07 
2.20 
0.00 7.70 2.24 0.84 
0.00 7.75 2.16 0.75 
0.00 7.80 2.11 0.67(5) 
0.01 7.83 2.11 0.63 
7.20 2.31 0.02 7.85 2.11 0.61 
7.30 
7.35 
7.40 
7.45 
7.48 
7.50 
7.52 
7.53 
7.54 
7.55 
7.56 
7.57 
7.58 
7.59 
7.60 
7.61 
7.62 
7.63 
2.41 
2.47 
2.54 
2.65 
2.73 
2.79 
2.89 
2.94 
3.01 
3,06 (5) 
3.06(5) 
3.03 
2.97 
2.89 
2.81 
2.70 
0.03 7.90 2.12 0.58 
0.04 7.95 2.13 0.56 
0.05 (5) 
0.09 
0.13 
0.17 
0.22 
0.27 
0.33 
0.45 
0.58 
0.70 
0.80 
0.89 
0.95 (5) 
1.00 
2.60 
2.52 
1.01, 
1.00 
8.00 
8.10 
8.20 
8.50 
9.00 
9.30 
9.50 
9.70 
9.80 
10.20 
10.50 
10.80 
10.90 
11.00 
2.14 
2.15 (5) 
2.16 
2.15 
2.12 
2.09 
2.08 
2.06 (5) 
2.06 
2.03 
1.98 
1.86 
1.79(5) 
1.72 
0.55 
0.55 
0.56 
0.60 
0.69 
0.74 
0.77 
0.81 
0.83 
0.93 
1.05 
1.17 
1.20(5) 
1.23 
11 .,lo 1.63 1.23 
11.15 1.59 1.22 
7.64 2.45 (5) 0 .97 (5 )  11.20 1.54 1.21 
7.66 2.35 0.92 11.30 1.46 1.16 
11.40 
11.50 
11.65 
11.80 
11.90 
12.00 
12.10 
12.40 
12.60 
12.80 
12.95 
13.00 
13.25 
13.30 
13.40 
13.45 
13.50 
13.55 
13.60 
13.75 
13.80 
1.40 
1.36 
1.39 
1.46 
1.51 
1.55 
1.59 
1.68 
1.73 
1.77 
1.78 
1.78 
1.58. 
1.50 
1.34 
1.25 
1.16 
1.08 
1.02 
0.98 
0.98 (5) 
13.90 1.02 
14.00 1.05 
14.10 1.08 
14.30 1.11 
14.80 1.13 
1.08 
1.00 
0.84 
0.79 
0.77 
0.77 
0.77(5) 
0.83 
0.90 
1.00 
1.11 
1.16 
1.44 
1.47 
1.49 
1.48(5) 
1.45 (5) 
1.40 
1.32 
1.13 
1.07 
15.10 
15.30 
15 . 50 
15.70 
15.80 
15.90 
16.00 
16.20 
16.40 
16.60 
16.80 
16.90 
17.00 
17.20 
17.40 
17.50 
17.60 
17.65 
17.70 
17.80 
17.98 
1.13 
1.13 
1.15 
1.17 
1.19 
1.21 
1.23 
1.25 (5) 
1.28 
1.30 
1.27 
1.23 
1.20 
1.17 
1.09(5) 
1.04 
0.99 
0.97 
0.95 
0.93 
0.91(5) 
0.82 
0.80 
0.77 
0.75 
0.75 
0.76 
0.77 
0.79 (5)  
0.83 
0.88 
0.98 
1.01 
1.01 
1.04 
1.10 
l.lO(5) . 
1.10 
1.09 
1.07 
1.04 
1.02 
0.99 18.00 0.90 1.02 
0.95 18.20 0.87 1.00 
0.92 18.50 0.81 0.98 
0.89 18.60 0.79 0.97 
0.84 18.70 0.78 0.95 
t 
n k h w ( e v )  n 
~ 
k 
18.90 
19.00 
19.20 
19.30 
19.60 
19.70 
19.80 
19.90 
20.00 
20.10 
0.75 
0.73 
0.71 
0.69 
0.64 
0.62 
0.60 (5) 
0.59 
0.58 
0.58 
0.93 
0.92 
0.89 
0.88 (5) 
0.85 
0.83 
0.81 
0.79 
0.76 
0.73 
21.70 
22.00 
22.50 
22.90 
23.00 
23.10 
23.20 
23.60 
23.80 
24.00 
0.46 
0.47 
0.52 
0.58 
0.59 
0.60 
0.61 
0.62 
0.62 
0.62 
0.50 
0.42 
0.33 
0.29 
0.28 (5) 
0.29 
0.29 
0.27 
0.26 
0.25 
20.20 0.59 (5) 0.71 24.20 0.63 0.24 
20.30 
20.40 
20.50 
20.60 
20.80 
20.90 
21.00 
21.10 
21.20 
21.30 
21.40 
21.50 
0.61 
0.61 
0.61 
0.60 
0.56 
0.54 
0.52 
0.50 
0.49 
0.48 
0.47 
0.46 
0.70 
0.70 
0.70 
0.70 (5) 
0.70 
0.69 
0.67 
0.65 
0.62 (5) 
0.60 
0.57 (5) 
0.55 
24.30 
24.40 
24.60 
24.70 
24.80 
24.90 
25.50 
26.00 
26.50 
27.00 
27.50 
28.00 
0.63 
0.63 
0.62 
0.61 
0.61 
0.62 
0.64 
0.67 
0.70 
0.73 
0.75 
0.78 
(5 1 0.24 
0.24 
0.23 (5) 
0.22 
0.21 
0.20 
0.14 
0.11 
0.08 
0.06 
(5 1 0.04 
0.03 
I, 
,- 
FIGURE CAPTIONS 
Figure 1. The spectral dependence of n and k, at room temperature, 
for single-crystal magnesium oxide. 
\ / / 
1 
I 
1 
I 
/ S/ 
0 cv 
U’ 


Optical Constants of Magnesium Oxide in the Far Ultraviolet

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