Kramers-Kronig Analysis of Solid Xenon Reflectivity Data I. T. Steinberger

Racah Institute of Physics, Hebrew University, Jerusalem, Israel. Received 6 November 1972 In a recent paper1 Scharber and Webber published

reflectivity and absorptivity data of solid xenon and kryp­ton in the VUV region. Their elegant method of mea­surement and evaluation was published in this journal, 2

and it was applied to solid CO and O2 as well.3 As point­ed out by Scharber and Webber, 1 their e1 curve for xenon is similar to their reflection spectrum, while this similari­ty is entirely lacking in the e1 curve presented previously.4

Moreover, the value of e1 and of n is larger than 1—ac­cording to Scharber and Webber—throughout the spectra of all materials studied, even at the short wavelength side of very strong reflectivity peaks (50% reflectivity in Kr and 25% in Xe). Kramers-Kronig analysis, applied to in­dependent measurements4 revealed, however, that in xenon the value of ε1 as well as that of n drops well below 1 in several spectral regions.

Webber kindly sent us his reflectivity data on solid xenon, and we applied to them a self-consistent method4

of Kramers-Kronig analysis. In Fig. 1 the e1 and ε2 curves thus obtained are represented together with the evalua­tion of the same quantities by Scharber and Webber. 1 It is seen that according to the Kramers-Kronig analysis the value of ε1 becomes less than 1 in several regions: espe­cially prominent is the dip around 6800 c m - i , at a fre­quency somewhat above that of the first peak of the ε2 spectrum. At the frequency of this first ε2 peak the value of e1 is approximately 1 in our analysis, while it is about 5 according to Scharber and Webber. The oscillator strengths of the Γ(3/2) and Γ(½) (n = 1) excitons are, ac­cording to the Kramers-Kronig analysis, 0.23 and 0.13, re­spectively, while their values, as given by Scharber and Webber, were 0.12 and 0.08.

In our opinion the chief reason for the discrepancy be­tween the two sets of results lies in the analysis employed by Scharber and Webber. These authors used a graphical method to find n from the observed R and k values. In principle, this solution is double valued, since

Fig. 1. The real part ε1 and the imaginary part ε2 of the dielec­tric constant as a function of wavenumber as obtained by the Kramers-Kronig analysis (full lines) and by Scharber and Web­

ber (dotted lines; see Ref. 1).

The present case emphasizes the necessity of checking proposed values of optical data by independent methods of analysis, especially in the difficult VUV region.

The author is indebted to S. E. Webber for submitting his data for analysis and for permission to publish the re­sults; he does not agree1 with the above interpretation.

References 1. S. R. Scharber, Jr., and S. E. Webber, J. Chem. Phys. 55,

3985(1971).

Webber informed us5 that in their analysis they had chosen the + sign throughout.

However, for a single resonance frequency V0 Maxwell's equations approximately yield (for |vo2 - v2| » g2, where g is the half-width of the band)

2. S. E. Webber and S. R. Scharber, Jr., Appl. Opt. 10, 338 (1971).

Thus for VO > v, n > 1 and ε1 > 1, and for VO < v, n < I and ε1 < 1. In other words, one has to switch over from the + branch to the - branch of eq. (1) at the frequency where the square root becomes zero.

In the particular case of Scharber and Webber1 the square root never became zero,5 and accordingly these au­thors did not switch over from' one branch to the other. Since the Kramers-Kronig analysis is not affected at all by these sign ambiguities, it follows that the experimental errors of the reflectivity and absorptivity data of Scharber and Webber were too large for the successful use of the graphical equivalent of Eq. (1).

3. S. R. Scharber and S. E. Webber, J. Chem. Phys. 55, 3977 (1971).

4. I. T. Steinberger, C. Atluri, and O. Schnepp, J. Chem. Phys. 52,2723(1970).

5. S. E. Webber, University of Texas, Austin, private communi­cation.

614 APPLIED OPTICS / Vol. 12, No. 3 / March 1973