Abstract

A simple theoretical framework is used to calculate specular reflection spectra in the vicinity of an absorption band in a solid. The energy of the reflectivity peak is shown to differ from the energy of the absorption band even at normal incidence with thick samples and with thin film samples supported on a substrate. By considering the absorption band system of solid CO, synthetic reflection spectra of the Fourth Positive System of solid CO at 45° incidence are obtained that successfully match the experimental results, including striking time-dependent changes.

© 1974 Optical Society of America

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    [CrossRef]
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  23. J. E. G. Wheaton, Appl. Opt. 3, 1247 (1964).
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    [CrossRef]
  25. M. Brith, O. Schnepp, Mol. Phys. 9, 473 (1965).
    [CrossRef]
  26. J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
    [CrossRef]
  27. S. R. Scharber, S. E. Webber, J. Chem. Phys. 55, 3977 (1971).
    [CrossRef]
  28. R. A. H. Buxton, W. W. Duley, Phys. Rev. Lett. 25, 801 (1970).
    [CrossRef]
  29. R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
    [CrossRef]
  30. E. Boursey, J.-Y. Roncin, Phys. Rev. Lett. 26, 308 (1971).
    [CrossRef]
  31. J. Daniels, Opt. Commun. 2, 352 (1970).
    [CrossRef]
  32. E. E. Koch, M. Skibowski, Chem. Phys. Lett. 14, 37 (1972).
    [CrossRef]
  33. R. A. H. Buxton, W. W. Duley, J. Chem. Phys. 56, 1783 (1972).
    [CrossRef]

1973

1972

D. M. Kolb, J. Opt. Soc. Am. 62, 599 (1972).
[CrossRef]

O. Hunderi, Appl. Opt. 11, 1573 (1972).

B. F. Armaly, J. G. Ochoa, D. C. Look, Appl. Opt. 11, 2907 (1972).
[CrossRef] [PubMed]

E. E. Koch, M. Skibowski, Chem. Phys. Lett. 14, 37 (1972).
[CrossRef]

R. A. H. Buxton, W. W. Duley, J. Chem. Phys. 56, 1783 (1972).
[CrossRef]

1971

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

E. Boursey, J.-Y. Roncin, Phys. Rev. Lett. 26, 308 (1971).
[CrossRef]

R. K. Ahrenkiel, J. Opt. Soc. Am. 61, 1651 (1971); J. Opt. Soc. Am. 62, 1009 (1972).
[CrossRef]

S. R. Scharber, S. E. Webber, J. Chem. Phys. 55, 3977 (1971).
[CrossRef]

1970

R. A. H. Buxton, W. W. Duley, Phys. Rev. Lett. 25, 801 (1970).
[CrossRef]

I. T. Steinberger, C. Atluri, O. Schnepp, J. Chem. Phys. 52, 2723 (1970).
[CrossRef]

J. Daniels, Opt. Commun. 2, 352 (1970).
[CrossRef]

1969

1967

D. W. Berreman, Appl. Opt. 6, 1519 (1967).
[CrossRef] [PubMed]

J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
[CrossRef]

1965

M. Brith, O. Schnepp, Mol. Phys. 9, 473 (1965).
[CrossRef]

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[CrossRef]

1964

1962

K. Dressler, J. Quant. Spectrosc. Rad. Trans. 2, 683 (1962).
[CrossRef]

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

1959

W. R. S. Garton, J. Sci. Instrum. 36, 11 (1959).
[CrossRef]

1951

Ahrenkiel, R. K.

Armaly, B. F.

Armstrong, K. R.

Atluri, C.

I. T. Steinberger, C. Atluri, O. Schnepp, J. Chem. Phys. 52, 2723 (1970).
[CrossRef]

Bell, E. E.

E. E. Bell, in Handbuch der Physik, S. Flugge, Ed. (Springer-Verlag, Berlin, 1961), Vol. 25/2a.

Bell, R. J.

Berreman, D. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Boursey, E.

E. Boursey, J.-Y. Roncin, Phys. Rev. Lett. 26, 308 (1971).
[CrossRef]

Bradley, R. W.

Brith, M.

M. Brith, O. Schnepp, Mol. Phys. 9, 473 (1965).
[CrossRef]

Buxton, R. A. H.

R. A. H. Buxton, W. W. Duley, J. Chem. Phys. 56, 1783 (1972).
[CrossRef]

R. A. H. Buxton, W. W. Duley, Phys. Rev. Lett. 25, 801 (1970).
[CrossRef]

R. A. H. Buxton, Ph.D Thesis , York University (1972).

Cardona, M.

M. Cardona, in Optical Properties of Solids, S. Nudelman, S. S. Mitra, Eds. (Plenum, New York, 1969), p. 137.
[CrossRef]

Damany, N.

J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
[CrossRef]

Daniels, J.

J. Daniels, Opt. Commun. 2, 352 (1970).
[CrossRef]

Dressler, K.

K. Dressler, J. Quant. Spectrosc. Rad. Trans. 2, 683 (1962).
[CrossRef]

Duley, W. W.

R. A. H. Buxton, W. W. Duley, J. Chem. Phys. 56, 1783 (1972).
[CrossRef]

R. A. H. Buxton, W. W. Duley, Phys. Rev. Lett. 25, 801 (1970).
[CrossRef]

Ehrenreich, H.

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Garton, W. R. S.

W. R. S. Garton, J. Sci. Instrum. 36, 11 (1959).
[CrossRef]

Gautschi, W.

W. Gautschi, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Segun, Eds. (Dover, New York, 1965).

Haensel, R.

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

Hale, G. M.

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

Holland, W. E.

Hunderi, O.

O. Hunderi, Appl. Opt. 11, 1573 (1972).

Hunter, W. R.

Koch, E. E.

E. E. Koch, M. Skibowski, Chem. Phys. Lett. 14, 37 (1972).
[CrossRef]

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

Kolb, D. M.

Kosuch, N.

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

Look, D. C.

Nichols, C. S.

Nielsen, U.

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

Ochoa, J. G.

Philipp, H. R.

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Querry, M. R.

Rashba, E. I.

E. I. Rashba, Thesis, University of Kiev (1955).

Romand, J.

J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
[CrossRef]

Roncin, J.-Y.

E. Boursey, J.-Y. Roncin, Phys. Rev. Lett. 26, 308 (1971).
[CrossRef]

J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
[CrossRef]

Scharber, S. R.

S. R. Scharber, S. E. Webber, J. Chem. Phys. 55, 3977 (1971).
[CrossRef]

Schnepp, O.

I. T. Steinberger, C. Atluri, O. Schnepp, J. Chem. Phys. 52, 2723 (1970).
[CrossRef]

M. Brith, O. Schnepp, Mol. Phys. 9, 473 (1965).
[CrossRef]

Simon, I.

Skibowski, M.

E. E. Koch, M. Skibowski, Chem. Phys. Lett. 14, 37 (1972).
[CrossRef]

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

Steinberger, I. T.

I. T. Steinberger, C. Atluri, O. Schnepp, J. Chem. Phys. 52, 2723 (1970).
[CrossRef]

Stone, J. M.

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1965).

Webber, S. E.

S. R. Scharber, S. E. Webber, J. Chem. Phys. 55, 3977 (1971).
[CrossRef]

Wheaton, J. E. G.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Appl. Opt.

Chem. Phys. Lett.

R. Haensel, E. E. Koch, N. Kosuch, U. Nielsen, M. Skibowski, Chem. Phys. Lett. 9, 548 (1971).
[CrossRef]

E. E. Koch, M. Skibowski, Chem. Phys. Lett. 14, 37 (1972).
[CrossRef]

J. Chem. Phys.

R. A. H. Buxton, W. W. Duley, J. Chem. Phys. 56, 1783 (1972).
[CrossRef]

S. R. Scharber, S. E. Webber, J. Chem. Phys. 55, 3977 (1971).
[CrossRef]

I. T. Steinberger, C. Atluri, O. Schnepp, J. Chem. Phys. 52, 2723 (1970).
[CrossRef]

J. Mol. Spectrosc.

J.-Y. Roncin, N. Damany, J. Romand, J. Mol. Spectrosc. 22, 154 (1967).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Rad. Trans.

K. Dressler, J. Quant. Spectrosc. Rad. Trans. 2, 683 (1962).
[CrossRef]

J. Sci. Instrum.

W. R. S. Garton, J. Sci. Instrum. 36, 11 (1959).
[CrossRef]

Mol. Phys.

M. Brith, O. Schnepp, Mol. Phys. 9, 473 (1965).
[CrossRef]

Opt. Commun.

J. Daniels, Opt. Commun. 2, 352 (1970).
[CrossRef]

Phys. Rev.

H. Ehrenreich, H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[CrossRef]

Phys. Rev. Lett.

R. A. H. Buxton, W. W. Duley, Phys. Rev. Lett. 25, 801 (1970).
[CrossRef]

E. Boursey, J.-Y. Roncin, Phys. Rev. Lett. 26, 308 (1971).
[CrossRef]

Other

R. A. H. Buxton, Ph.D Thesis , York University (1972).

E. I. Rashba, Thesis, University of Kiev (1955).

L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Addison-Wesley, Reading, Mass., 1960).

M. Cardona, in Optical Properties of Solids, S. Nudelman, S. S. Mitra, Eds. (Plenum, New York, 1969), p. 137.
[CrossRef]

W. Gautschi, in Handbook of Mathematical Functions, M. Abramowitz, I. A. Segun, Eds. (Dover, New York, 1965).

N. J. Harrick, Internal Reflection Spectroscopy (Interscience, New York, 1967).

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955).

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1965).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

E. E. Bell, in Handbuch der Physik, S. Flugge, Ed. (Springer-Verlag, Berlin, 1961), Vol. 25/2a.

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Figures (12)

Fig. 1
Fig. 1

Real part (right) of the dielectric constant computed from a Guassian shape in the imaginary part (left) using the Kramers-Kronig relations.

Fig. 2
Fig. 2

Specular reflection profile at normal incidence of the interface between vacuum and a medium with a single Gaussian-shaped absorption band centered at E0. 2 max of the band varies from 1 (lowest peak reflectivity) to 5 (highest peak reflectivity).

Fig. 3
Fig. 3

Shift of the energy of the peak reflectivity (Ep) from E0 in units of the absorption band FWHM (W).

Fig. 4
Fig. 4

Reflection profiles at 45° incidence of a thin film on a substrate. Film: 2 max of absorption band = 3.0; d0 ≥ 1. Substrate: 1 = 0.80, 2 = 1.65.

Fig. 5
Fig. 5

Shift of the energy of the peak reflectivity at 45° incidence caused by a thin surface layer of constant thickness. Layer is dispersionless and has parameters as shown. Underlying material contains an absorption band at 10.0 eV with strength 2 max and a FWHM of 0.1 eV. Shift is measured from the normal location of the reflection peak. δE is the size of the energy step in the calculations = 1 meV.

Fig. 6
Fig. 6

Shift of the energy of the peak reflectivity at 45° incidence caused by a thin surface layer of variable thickness d0. Otherwise, as in Fig. 5.

Fig. 7
Fig. 7

Schematic arrangement of the experimental apparatus.

Fig. 8
Fig. 8

Reflection spectrogram of α-CO at 20 K. Lower spectrum: normal bands of the Fourth Positive System. Upper spectrum: the abnormal bands.

Fig. 9
Fig. 9

Imaginary part of the dielectric constant of α-CO calculated from a sum of Gaussian curves for the (v′, O) bands of the A1Π − X1+ transition: (O,O) band at left. Experimentally derived spectrum of Scharber and Webber shown by dashed line where different from calculated spectrum.

Fig. 10
Fig. 10

Experimental (dots) and calculated [(c) and scale on right)] reflection spectrum of α-CO for normal bands. Wavelengths marked (a) are absorption results of Brith and Schnepp. Wavelengths marked (b) are experimental band reflectivity peaks where outside negative density calibration range.

Fig. 11
Fig. 11

Microdensitometer traces of α-CO at 20 K. Lowest trace: spectrum following deposition. Center trace: spectrum following the deposition of a second layer onto the layer providing the lowest trace. Top trace: spectrum made following the exposure producing the center trace.

Fig. 12
Fig. 12

Experimental (dots and dashed line) and calculated (solid line and scale on right) reflection spectrum of α-CO for abnormal bands. v′ series at top are the experimental normal band reflectivity peaks.

Equations (8)

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E c = E 0 c exp [ i ( K c · r - ω t ) ] ,
K 1 = ω 2 c [ ( 1 2 + 2 2 · cos - 2 θ ) 1 / 2 + 1 ] 1 / 2
K 2 = ω 2 c [ ( 1 2 + 2 2 · cos - 2 θ ) 1 / 2 - 1 ] 1 / 2 .
sin θ 2 = { α 1 sin 2 θ 1 + 2 12 - [ α 1 sin 2 θ 1 - 2 12 ) 2 + 4 22 2 ] 1 / 2 12 α 1 sin 2 θ 1 - ½ 22 2 } × ( α 1 ) 1 / 2 sin θ 1 ,
2 ( E ) = j A j exp ( - x j 2 ) ,
x j = [ 2 ( ln 2 ) 1 / 2 ( E - E j ) ] / W j ,
1 ( E ) = 1 + C + 2 π j A j exp ( - x j 2 ) 0 x j exp ( t 2 ) d t .
b 1 Π u - X 1 Σ g +

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