Abstract

It is shown that (Al-MgF2)-interference filters of better performance than have been predicted and obtained previously are possible in the uv below 2500 Å. Experimental results are given for conventional filters of first and higher order and for new filter designs that use multilayer structures for the two mirrors of the filter. All discrepancies between theoretical and experimental results are explained by a coupling of light into the surface plasmon of aluminum via a surface roughness of the MgF2 films.

© 1974 Optical Society of America

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References

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  1. D. J. Schroeder, J. Opt. Soc. Am. 52, 1380 (1962).
    [CrossRef]
  2. B. Bates, D. J. Bradley, Appl. Opt. 5, 971 (1966).
    [CrossRef] [PubMed]
  3. R. L. Maier, Thin Solid Films 1, 21 (1967).
    [CrossRef]
  4. G. Baldini, L. Rigaldi, Thin Solid Films 13, 143 (1972).
    [CrossRef]
  5. E. Spiller, Optik 39, 118 (1973).
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 51.
  7. Ref. 6, p. 348.
  8. G. Hass, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), Chap. 6.
  9. H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, (1967), Vol 4, p. 1.
  10. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
    [CrossRef]
  11. A. Otto, Z. Phys. 216, 398 (1968), Z. Phys. 219, 227 (1669).
    [CrossRef]
  12. W. Steinmann, Phys. Stat. Sol. 28, 437 (1968).
    [CrossRef]
  13. J. G. Endriz, W. E. Spicer, Phys. Rev. B4, 4144 (1971).
  14. B. P. Feuerbacher, W. Steinmann, Opt. Commun. 1, 81 (1969).
    [CrossRef]

1973 (1)

E. Spiller, Optik 39, 118 (1973).

1972 (1)

G. Baldini, L. Rigaldi, Thin Solid Films 13, 143 (1972).
[CrossRef]

1971 (1)

J. G. Endriz, W. E. Spicer, Phys. Rev. B4, 4144 (1971).

1969 (1)

B. P. Feuerbacher, W. Steinmann, Opt. Commun. 1, 81 (1969).
[CrossRef]

1968 (2)

A. Otto, Z. Phys. 216, 398 (1968), Z. Phys. 219, 227 (1669).
[CrossRef]

W. Steinmann, Phys. Stat. Sol. 28, 437 (1968).
[CrossRef]

1967 (1)

R. L. Maier, Thin Solid Films 1, 21 (1967).
[CrossRef]

1966 (1)

1963 (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

1962 (1)

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Baldini, G.

G. Baldini, L. Rigaldi, Thin Solid Films 13, 143 (1972).
[CrossRef]

Bates, B.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, (1967), Vol 4, p. 1.

Bennett, J. M.

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, (1967), Vol 4, p. 1.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 51.

Bradley, D. J.

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Endriz, J. G.

J. G. Endriz, W. E. Spicer, Phys. Rev. B4, 4144 (1971).

Feuerbacher, B. P.

B. P. Feuerbacher, W. Steinmann, Opt. Commun. 1, 81 (1969).
[CrossRef]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Hass, G.

G. Hass, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), Chap. 6.

Maier, R. L.

R. L. Maier, Thin Solid Films 1, 21 (1967).
[CrossRef]

Otto, A.

A. Otto, Z. Phys. 216, 398 (1968), Z. Phys. 219, 227 (1669).
[CrossRef]

Rigaldi, L.

G. Baldini, L. Rigaldi, Thin Solid Films 13, 143 (1972).
[CrossRef]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Schroeder, D. J.

Spicer, W. E.

J. G. Endriz, W. E. Spicer, Phys. Rev. B4, 4144 (1971).

Spiller, E.

E. Spiller, Optik 39, 118 (1973).

Steinmann, W.

B. P. Feuerbacher, W. Steinmann, Opt. Commun. 1, 81 (1969).
[CrossRef]

W. Steinmann, Phys. Stat. Sol. 28, 437 (1968).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 51.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

B. P. Feuerbacher, W. Steinmann, Opt. Commun. 1, 81 (1969).
[CrossRef]

Optik (1)

E. Spiller, Optik 39, 118 (1973).

Phys. Rev. (1)

J. G. Endriz, W. E. Spicer, Phys. Rev. B4, 4144 (1971).

Phys. Rev. Lett. (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, R. N. Hamm, Phys. Rev. Lett. 21, 1530 (1963); M. L. Dakss, L. Kuhn, P. F. Heidrich, B. A. Scott, Appl. Phys. Lett. 16, 523 (1970).
[CrossRef]

Phys. Stat. Sol. (1)

W. Steinmann, Phys. Stat. Sol. 28, 437 (1968).
[CrossRef]

Thin Solid Films (2)

R. L. Maier, Thin Solid Films 1, 21 (1967).
[CrossRef]

G. Baldini, L. Rigaldi, Thin Solid Films 13, 143 (1972).
[CrossRef]

Z. Phys. (1)

A. Otto, Z. Phys. 216, 398 (1968), Z. Phys. 219, 227 (1669).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 51.

Ref. 6, p. 348.

G. Hass, in American Institute of Physics Handbook, D. E. Gray, Ed. (McGraw-Hill, New York, 1972), Chap. 6.

H. E. Bennett, J. M. Bennett, in Physics of Thin Films, G. Hass, R. E. Thun, Eds. (Academic, New York, (1967), Vol 4, p. 1.

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Figures (7)

Fig. 1
Fig. 1

Optical constants n and k of Al used throughout this paper and the phase shift for reflection at the MgF2-Al boundary.

Fig. 2
Fig. 2

Peak transmission vs resolution of first-order interference filters for wavelengths around λ = 1900 Å. Curve A is the theoretical curve using the correct theory, curve B is the theoretical curve derived according to Ref. 2. xxx: experimental points. □ □ □: experimental points from Ref. 2.

Fig. 3
Fig. 3

Calculated transmission curves for interference filters. Curve a: Conventional interference filter substrate-Al-MgF2-Al-MgF2 with layer thicknesses of 282.5 Å, 352.7 Å, 282.5 Å, 205.5 Å. Curve b: twelve-layer structure of Al and MgF2 with the following layer thicknesses: 105.7, 572.5, 105.7, 572.5, 105.7, 379.4, 105.7, 572.5, 105.7, 572.5, 105.7, 795 Å. Curve c: twelve-layer structure of Al andl MgF2 with the following layer thicknesses: 196, 575.9, 70.6, 575.9, 49, 409.9, 49, 575.9, 70.6, 575.9, 196, 810.7 Å.

Fig. 4
Fig. 4

Peak transmission vs resolution of first-order interference filters using high quality mirrors made of six layers of Al and MgF2. The curve for conventional filters is given for comparison. All points are experimental. x: First-order conventional filters as in Fig. 1; ○: calculated from the experimental performance given in Ref. 5; *: experimental performance of a twelve-layer filter deposited in one run.

Fig. 5
Fig. 5

Ratio of the measured reflectivity of an Al film deposited on a thick (d = 4100-Å) MgF2 film divided by the reflectivity of the same film deposited on a smooth glass slide (full curve). The dashed curve is the same ratio calculated for ordinary scattering (Ref. 9) from a rough surface with a rms roughness of 48 Å.

Fig. 6
Fig. 6

Scanning electron micrograph of the surface of an Al film coated on MgF2 with the following thicknesses:

Fig. 7
Fig. 7

Calculated dispersion curves of the plasma surface oscillation in Al. The full curves are for zero coupling; the dashed curves in (a) are for stronger coupling and are characterized by the width of the gap between the incident medium and the Al. The gap is MgF2 on both sides for (a) and (b) and vacuum or air on the top and MgF2 at the bottom for (c). (a) is for an opague Al film, curve (b) and (c) are for films of 100-Å thickness. Plotted is the wavelength of the surface plasmon λsp vs the period in the roughness needed to couple into that surface plasmon.

Tables (1)

Tables Icon

Table I Comparison of the Measured and Calculated Resolution λ0/Δλ of Four-Layer (Substrate-Al-MgF2-Al-MgF2) Interference Filters of Different Orders with a Peak Transmission of 25% at a Wavelength Around 1850 Å

Equations (6)

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λ 0 / Δ λ = F m - ( 1 / π ) [ ( / λ 0 ) ( ϕ λ 0 ) λ 0 ] ,
F = ( π R ) / ( 1 - R )
T max = 1 / ( 1 + A / T ) 2 ,
λ 0 / Δ λ = F [ m - ( ϕ / π ) - ( λ 0 / π ) ( ϕ / λ 0 ) ] ,
n d = ( λ 0 / 2 ) [ m - ( ϕ / π ) ] .
( d MgF 2 500 Å )

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