Abstract

Transparent heat mirrors of the antireflecting metal type with a dielectric/metal/dielectric structure are studied. It is found that dielectrics of lower refractive index give a higher cutoff wavelength, but the transition becomes more gradual. The angular behavior of these mirrors is also analyzed. The optimum mechanical efficiency obtainable with a plain collector and a carnot engine is given for different concentrations and refractive indices. Moreover it appears that using Al instead of Ag introduces appreciable absorption losses (~25–35%).

© 1981 Optical Society of America

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References

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  1. A. B. Meinel, M. P. Meinel, Applied Solar Energy: An Introduction (Addison-Wesley, Reading, Mass., 1977).
  2. B. O. Seraphin, Solar Energy Conversion (Springer, Berlin, 1979).
    [CrossRef]
  3. J. C. C. Fan, F. J. Bachner, Appl. Opt. 15, 1012 (1976).
    [CrossRef] [PubMed]
  4. F. Abeles, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).
  5. G. Haas, “Mirror Coatings,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, London, 1965), Vol. 3.
  6. P. B. Johnson, R. W. Christy, Phys. Rev. B: 6, 4370 (1972).
    [CrossRef]
  7. G. Hass, J. B. Ramsey, R. Thun, J. Opt. Soc. Am. 48, 324 (1958).
    [CrossRef]
  8. G. Hass, J. B. Ramsey, R. Thun, J. Opt. Soc. Am. 49, 116 (1959).
    [CrossRef]
  9. L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, London, 1966).
  10. Landolt-Böernstein, Physikalisch-Chemische Tabellen (Springer, Berlin, 1931).

1976 (1)

1972 (1)

P. B. Johnson, R. W. Christy, Phys. Rev. B: 6, 4370 (1972).
[CrossRef]

1959 (1)

1958 (1)

Abeles, F.

F. Abeles, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).

Bachner, F. J.

Christy, R. W.

P. B. Johnson, R. W. Christy, Phys. Rev. B: 6, 4370 (1972).
[CrossRef]

Fan, J. C. C.

Haas, G.

G. Haas, “Mirror Coatings,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, London, 1965), Vol. 3.

Hass, G.

Holland, L.

L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, London, 1966).

Johnson, P. B.

P. B. Johnson, R. W. Christy, Phys. Rev. B: 6, 4370 (1972).
[CrossRef]

Landolt-Böernstein,

Landolt-Böernstein, Physikalisch-Chemische Tabellen (Springer, Berlin, 1931).

Meinel, A. B.

A. B. Meinel, M. P. Meinel, Applied Solar Energy: An Introduction (Addison-Wesley, Reading, Mass., 1977).

Meinel, M. P.

A. B. Meinel, M. P. Meinel, Applied Solar Energy: An Introduction (Addison-Wesley, Reading, Mass., 1977).

Ramsey, J. B.

Seraphin, B. O.

B. O. Seraphin, Solar Energy Conversion (Springer, Berlin, 1979).
[CrossRef]

Thun, R.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Phys. Rev. B (1)

P. B. Johnson, R. W. Christy, Phys. Rev. B: 6, 4370 (1972).
[CrossRef]

Other (6)

A. B. Meinel, M. P. Meinel, Applied Solar Energy: An Introduction (Addison-Wesley, Reading, Mass., 1977).

B. O. Seraphin, Solar Energy Conversion (Springer, Berlin, 1979).
[CrossRef]

L. Holland, Vacuum Deposition of Thin Films (Chapman and Hall, London, 1966).

Landolt-Böernstein, Physikalisch-Chemische Tabellen (Springer, Berlin, 1931).

F. Abeles, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).

G. Haas, “Mirror Coatings,” in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic, London, 1965), Vol. 3.

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Figures (14)

Fig. 1
Fig. 1

Selective reflectivity of thin silver films of different thicknesses immersed between two half-spaces of CeO2 (n = 2.2, λ = 600 nm).

Fig. 2
Fig. 2

Vector diagrams for qualitative descriptions of the behavior of the mirror.

Fig. 3
Fig. 3

Normal incidence reflectivities and transmissivities for different selective mirrors with various thicknesses of the metal layer: CeO2/Ag/CeO2/glass. The refractive index of CeO2 at 600 nm is n = 2.2. The thicknesses of the layers are 40, 12, and 40 nm for the continuous line; 40, 9, and 40 nm for the dashed line; and 40, 6, and 40 nm for the dotted line.

Fig. 4
Fig. 4

Normal incidence characteristics for mirrors with the same height of the ridge in the reflection curve but different refractive indices of the dielectrics:

Fig. 5
Fig. 5

Mirrors with the same width of transparency region but different refractive indices (see Table I):

Fig. 6
Fig. 6

Angular dependence of the reflectivity of a silver layer (7 nm thick) between two half-spaces of CeO2 (n = 2.2), where ϕ is the incidence angle in the dielectric and ϕ′ the corresponding angle in air:

Fig. 7
Fig. 7

Angular dependence of a mirror n = 2.2/Ag/n = 1.5 38 nm/8 nm/38 nm/∞ for different incidence angles:

Fig. 8
Fig. 8

Angular dependence of the same mirror as in Fig. 7 for large incidence angles:

Fig. 9
Fig. 9

Selective mirrors with AR films of relatively low refractive index n = 1.95; n = 1.95 43 nm/Ag 7 nm/n = 1.95 43 nm reflectivity and transmissivity for different incidence angles:

Fig. 10
Fig. 10

Theoretical transmission (continuous line) curve and experimental curves for two mirrors with ZnS as the dielectric material 50, 8, and 50 nm.

Fig. 11
Fig. 11

Reflectivity and transmissivity of a selective mirror with aluminum as the metal layer (normal incidence) and CeO2 (n = 2.2) as the dielectric (the absorption of this mirror is large):

Fig. 12
Fig. 12

Thermal emissivity ɛ, collector efficiency, and combined efficiency (collector and carnot engine) as a function of the temperature for a black absorber covered with a selective mirror. The mirror is of La2O3, n = 1.95 (substance 4, Table I) and silver with thicknesses of 50, 5, and 50 nm. The solar radiation was assumed AM0 with concentration 10 and at normal incidence.

Fig. 13
Fig. 13

Optimum obtainable mechanical efficiency for each dielectric substance and each concentration plotted as a function of the refractive index. Encircled on the curve are the numbers of the substances of Table I. There are two groups of substances for dispersion and UV absorptance: substances 1, 2, and 3 with high dispersion and high UV absorptance and substances 4, 5, 6, and 8 with smaller dispersions and very small UV absorptance. Owing to this fact two different curves appear, one for n ≥ 2.2 and the other for n ≤ 2.2. Substance 7 has the dispersion of the low index group and the UV absorptance of the high index one.

Fig. 14
Fig. 14

Optimum collection efficiency that may be obtained with different temperatures of the absorber as a function of the refractive index. The jump at n = 2.2 is due to a change in the dispersion and UV absorptance (see Table I). We can see that for small temperatures smaller indices work better, while for higher temperatures higher indices are preferable. The optimum combined efficiency is obtained for the ideal case with collector temperatures between 480 and 510 K.

Tables (3)

Tables Icon

Table I Complex Refractive Index n + ik of the Dielectric Substances7,8 for Which Efficiencies and Spectral Responses of the Antireflected Metal Mirror were Calculated

Tables Icon

Table II Maximum Combined Efficiency (as Obtained from Fig. 12 and the Like) as a Function of the Thicknesses of the Films

Tables Icon

Table III Thickness Giving the Maximum Combined Efficiency for Various Dielectric Substances and Concentrations

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