Abstract

In the optimization of multilayer stacks for various optical filtering purposes not only the thicknesses of the thin films are to be optimized, but also the sequence of materials. Materials with very different optical properties, such as metals and dielectrics, may be combined. A genetic algorithm is introduced to search for the optimal sequence of materials along with their optical thicknesses. This procedure is applied to a heat mirror in combination with a blackbody absorber for thermal solar energy applications at elevated temperatures (250 °C). The heat mirror is based on silver films with antireflective dielectric layers. Seven dielectrics have been considered. For a five-layer stack the sequence (TiO2/Ag/TiO2/Ag/Y2O3) is found to be optimal.

© 1993 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. M. Lazarov, T. Eisenhammer, R. Sizmann, “New absorber geometries for wavelength and angular solar selective absorber cover combinations,” in Solar World Congress, Proceedings of the Biennial Congress of the International Solar Energy Society, M. E. Arden, S. M. A. Burley, M. Coleman, eds. (Pergamon, Oxford, 1991), Vol. 2, Part II, pp. 2199–2204.
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    [CrossRef]
  16. E. Masetti, A. Piegari, A. Tirabassi, “Optical characterization of low-absorbing thin films in the visible and infrared spectrum,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 125–132 (1990).
  17. G. L. Harding, “Production and properties of high rate sputtered low index transparent dielectric materials based on aluminium-oxy-fluorine,” Sol. Energy Mater. 12, 169–186 (1985).
    [CrossRef]
  18. J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazarides, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium dioxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989). Highest reported values of the refractive index were used.
    [CrossRef] [PubMed]
  19. R. Raman, A. Thakur, “Emissivity of homogeneous thin films,” Thin Solid Films 87, 101–111 (1982).
    [CrossRef]
  20. H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–188.
  21. J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
    [CrossRef]
  22. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  23. E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
    [CrossRef]
  24. G. Woodard, T. Pass, “Role of suspended films in insulated glass units,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 213–222 (1992).

1992 (1)

1990 (1)

1989 (3)

1987 (1)

J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
[CrossRef]

1985 (3)

G. L. Harding, I. Hamberg, C. G. Granqvist, “Antireflection of sputtered heat mirror and transparent conduction coatings by metal-oxy-fluorine films,” Sol. Energy Mater. 12, 187–198 (1985).
[CrossRef]

M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12, 275–288 (1985).
[CrossRef]

G. L. Harding, “Production and properties of high rate sputtered low index transparent dielectric materials based on aluminium-oxy-fluorine,” Sol. Energy Mater. 12, 169–186 (1985).
[CrossRef]

1984 (1)

E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
[CrossRef]

1982 (1)

R. Raman, A. Thakur, “Emissivity of homogeneous thin films,” Thin Solid Films 87, 101–111 (1982).
[CrossRef]

1981 (1)

1976 (1)

Albrand, G.

Allen, T. H.

Bachner, F. J.

Bennett, H. E.

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–188.

Bennett, J. M.

J. M. Bennett, E. Pelletier, G. Albrand, J. P. Borgogno, B. Lazarides, C. K. Carniglia, R. A. Schmell, T. H. Allen, T. Tuttle-Hart, K. H. Guenther, A. Saxer, “Comparison of the properties of titanium dioxide films prepared by various techniques,” Appl. Opt. 28, 3303–3317 (1989). Highest reported values of the refractive index were used.
[CrossRef] [PubMed]

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–188.

Borgogno, J. P.

Carniglia, C. K.

Dietrich, A.

J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
[CrossRef]

Dobrowolski, J. A.

Eisenhammer, T.

M. Lazarov, T. Eisenhammer, R. Sizmann, “New absorber geometries for wavelength and angular solar selective absorber cover combinations,” in Solar World Congress, Proceedings of the Biennial Congress of the International Solar Energy Society, M. E. Arden, S. M. A. Burley, M. Coleman, eds. (Pergamon, Oxford, 1991), Vol. 2, Part II, pp. 2199–2204.

T. Eisenhammer, M. Lazarov, R. Sizmann, “Optimization of silver based heat mirrors using a genetic algorithm,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 194–202 (1992).

Fan, J. C. C.

Gamble, R.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Granqvist, C. G.

G. L. Harding, I. Hamberg, C. G. Granqvist, “Antireflection of sputtered heat mirror and transparent conduction coatings by metal-oxy-fluorine films,” Sol. Energy Mater. 12, 187–198 (1985).
[CrossRef]

Guenther, K. H.

Hamberg, I.

G. L. Harding, I. Hamberg, C. G. Granqvist, “Antireflection of sputtered heat mirror and transparent conduction coatings by metal-oxy-fluorine films,” Sol. Energy Mater. 12, 187–198 (1985).
[CrossRef]

Harding, G. L.

G. L. Harding, I. Hamberg, C. G. Granqvist, “Antireflection of sputtered heat mirror and transparent conduction coatings by metal-oxy-fluorine films,” Sol. Energy Mater. 12, 187–198 (1985).
[CrossRef]

G. L. Harding, “Production and properties of high rate sputtered low index transparent dielectric materials based on aluminium-oxy-fluorine,” Sol. Energy Mater. 12, 169–186 (1985).
[CrossRef]

Hartig, K.

J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Karlsson, B.

E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
[CrossRef]

Kasten, F.

Kemp, R. A.

Kunz, R. E.

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, H. K. Pulker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1989).

Lazarides, B.

Lazarov, M.

T. Eisenhammer, M. Lazarov, R. Sizmann, “Optimization of silver based heat mirrors using a genetic algorithm,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 194–202 (1992).

M. Lazarov, T. Eisenhammer, R. Sizmann, “New absorber geometries for wavelength and angular solar selective absorber cover combinations,” in Solar World Congress, Proceedings of the Biennial Congress of the International Solar Energy Society, M. E. Arden, S. M. A. Burley, M. Coleman, eds. (Pergamon, Oxford, 1991), Vol. 2, Part II, pp. 2199–2204.

Li, L.

Lissberger, P. H.

Masetti, E.

E. Masetti, A. Piegari, A. Tirabassi, “Optical characterization of low-absorbing thin films in the visible and infrared spectrum,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 125–132 (1990).

Morf, R.

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, H. K. Pulker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1989).

Pass, T.

G. Woodard, T. Pass, “Role of suspended films in insulated glass units,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 213–222 (1992).

Pelletier, E.

Piegari, A.

E. Masetti, A. Piegari, A. Tirabassi, “Optical characterization of low-absorbing thin films in the visible and infrared spectrum,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 125–132 (1990).

Pracchia, J. A.

Raman, R.

R. Raman, A. Thakur, “Emissivity of homogeneous thin films,” Thin Solid Films 87, 101–111 (1982).
[CrossRef]

Ribbing, C. G.

E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
[CrossRef]

Rubin, M.

M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12, 275–288 (1985).
[CrossRef]

Saxer, A.

Schmell, R. A.

Simon, J. M.

Sizmann, R.

M. Lazarov, T. Eisenhammer, R. Sizmann, “New absorber geometries for wavelength and angular solar selective absorber cover combinations,” in Solar World Congress, Proceedings of the Biennial Congress of the International Solar Energy Society, M. E. Arden, S. M. A. Burley, M. Coleman, eds. (Pergamon, Oxford, 1991), Vol. 2, Part II, pp. 2199–2204.

T. Eisenhammer, M. Lazarov, R. Sizmann, “Optimization of silver based heat mirrors using a genetic algorithm,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 194–202 (1992).

Strickberger, M. W.

M. W. Strickberger, Genetics (Macmillan, New York, 1985).

Szczyrbowski, J.

J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
[CrossRef]

Thakur, A.

R. Raman, A. Thakur, “Emissivity of homogeneous thin films,” Thin Solid Films 87, 101–111 (1982).
[CrossRef]

Tirabassi, A.

E. Masetti, A. Piegari, A. Tirabassi, “Optical characterization of low-absorbing thin films in the visible and infrared spectrum,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 125–132 (1990).

Tuttle-Hart, T.

Valkonen, E.

E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
[CrossRef]

Woodard, G.

G. Woodard, T. Pass, “Role of suspended films in insulated glass units,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 213–222 (1992).

Young, A. T.

Appl. Opt. (7)

Sol. Energy (1)

E. Valkonen, B. Karlsson, C. G. Ribbing, “Solar optical properties of thin films of Cu, Ag, Au, Cr, Fe, Co, Ni and Al,” Sol. Energy 32, 211–222 (1984).
[CrossRef]

Sol. Energy Mater. (4)

G. L. Harding, “Production and properties of high rate sputtered low index transparent dielectric materials based on aluminium-oxy-fluorine,” Sol. Energy Mater. 12, 169–186 (1985).
[CrossRef]

J. Szczyrbowski, A. Dietrich, K. Hartig, “Evaluation and control of the properties of thin sputtered silver films for spectrally selective coatings,” Sol. Energy Mater. 16, 103–111 (1987).
[CrossRef]

G. L. Harding, I. Hamberg, C. G. Granqvist, “Antireflection of sputtered heat mirror and transparent conduction coatings by metal-oxy-fluorine films,” Sol. Energy Mater. 12, 187–198 (1985).
[CrossRef]

M. Rubin, “Optical properties of soda lime silica glasses,” Sol. Energy Mater. 12, 275–288 (1985).
[CrossRef]

Thin Solid Films (1)

R. Raman, A. Thakur, “Emissivity of homogeneous thin films,” Thin Solid Films 87, 101–111 (1982).
[CrossRef]

Other (11)

H. E. Bennett, J. M. Bennett, “Validity of the Drude theory for silver, gold and aluminum in the infrared,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abelès, ed. (North-Holland, Amsterdam, 1966), pp. 175–188.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

E. Masetti, A. Piegari, A. Tirabassi, “Optical characterization of low-absorbing thin films in the visible and infrared spectrum,” in Optical Thin Films and Applications, R. Herrmann, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1270, 125–132 (1990).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, H. K. Pulker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1989).

T. Eisenhammer, M. Lazarov, R. Sizmann, “Optimization of silver based heat mirrors using a genetic algorithm,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 194–202 (1992).

J. D. Schaffer, ed., Proceedings of the Third International Conference on Genetic Algorithms (Kaufmann, San Mateo, Calif., 1989).

M. W. Strickberger, Genetics (Macmillan, New York, 1985).

C.-J. Winter, R. L. Sizmann, L. L. Vant-Hull, eds., Solar Power Plants (Springer-Verlag, Berlin, 1991).
[CrossRef]

M. Lazarov, T. Eisenhammer, R. Sizmann, “New absorber geometries for wavelength and angular solar selective absorber cover combinations,” in Solar World Congress, Proceedings of the Biennial Congress of the International Solar Energy Society, M. E. Arden, S. M. A. Burley, M. Coleman, eds. (Pergamon, Oxford, 1991), Vol. 2, Part II, pp. 2199–2204.

G. Woodard, T. Pass, “Role of suspended films in insulated glass units,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XI: Selective Materials, Transparent Insulation, and Super Windows, C. G. Granqvist, A. Hugot-Le Goff, C. M. Lampert, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1727, 213–222 (1992).

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Figures (2)

Fig. 1
Fig. 1

Spectral transmittance and reflectance at normal incidence. Comparison between optimal five-layer sequences, 5, and three-layer stacks, 3.

Fig. 2
Fig. 2

Figure of merit η as a function of n (at 500 nm) of the third (dielectric) layer of design 1 in Table 1. Crosses, optical thickness fixed to the optimal value; triangles, geometrical thickness fixed to the optimal value.

Tables (1)

Tables Icon

Table 1 Optimal Sequences Found in Four Optimization Runs with Different Initial Bit-String Populations

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

τ n := 0 E λ ( λ ) τ ( λ ) d λ / 0 E λ ( λ ) d λ ,
ρ ¯ ( T ) := 0 0 π / 2 2 π L λ ( λ , T ) σ T 4 sin θ × cos θ [ 1 ρ ( θ , λ , T a ) ] d λ d θ,
η := τ n ρ ¯ ( T ) σ T 4 / E ,
η = η ( t 1 , m 1 ; ; t N , m N ) ,
t M ( nm ) := 1 N M ( X 20 + 3 ) ,

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