Abstract

The moth’s eye principle of optical-impedance matching by means of an array of tapered protuberances has been studied to determine the limit obtainable for reflection reduction. Analogous multilayer equivalents were optimized over a wide band, using a recently developed optimization method, in which one or more of the layers are specified inclusions. A limit of 30 dB reduction of reflectance was obtained over a bandwidth 1.4 times the short-wavelength limit of the band. These results are also related to corrugated conducting surfaces used in a new solar-absorber design that uses corrugations in a conductor and is required to be optimized for best absorption (a) and emissivity (e) values. The optimum corrugation geometry for two types of periodic surface is studied and results are discussed in view of further development in practical applications.

© 1975 Optical Society of America

Full Article  |  PDF Article

Corrections

B. S. Thornton, "Erratum: Limit of the moth’s eye principle and other impedance-matching corrugations for solar-absorber design," J. Opt. Soc. Am. 65, 748-748 (1975)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-65-6-748

References

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  1. C. G. Bernhard, Endeavour 26, 79 (1967).
  2. P. B. Clapman and M. C. Hutley, Nature 244, 281 (1973).
  3. H. G. Haddenhorst, Z. Angew. Phys. 7, 487 (1955).
  4. B. S. Thornton, Computer J. 15, 84 (1972).
    [Crossref]
  5. V. F. Wiekhorst, Z. Angew. Phys. 10, 173 (1957).
  6. C. M. Horwitz, Opt. Commun. 11, 210 (1974).
    [Crossref]
  7. J. R. Wait, IRE Trans. Antennas and Propagation,  AP-7, S154 (1959).
    [Crossref]
  8. J. R. Wait and A. M. Conda, J. Res. Natl. Bur. Stds. 59, 307 (1957).
    [Crossref]
  9. C. P. Wu and V. Galindo, IEEE Trans. AP-14, 163 (1966).
    [Crossref]
  10. A. G. Cha and J. K. Hsiao, IEEE Trans. AP-22106 (1974).
    [Crossref]
  11. B. S. Thornton, J. Opt. Soc. Am. 49, 476 (1959).
    [Crossref]
  12. L. O. Goldstone and A. A. Oliner, IRE Trans. AP-7, 274 (1959).
  13. H. Ikuno and K. Yasuura, IEEE Trans. AP-21, 657 (1973).
    [Crossref]
  14. K. H. Zaki and A. R. Neureuther, IEEE Trans AP-19(2), 208 (1971); IEEE Trans. AP-19(6), 747 (1971).
    [Crossref]
  15. Rayleigh, Proc. R. Soc., Ser. A 79, 399 (1907).
  16. R. Petit and M. Cadilhac, C. R. Acad. Sci. (Paris), Ser. B 262, 468 (1966).
  17. R. F. Millar, Proc. R. Soc. (Lond.) 69, 217 (1971).
  18. R. F. Millar, Radio Sci. 8, 607 (1973).
    [Crossref]
  19. M. C. Hutley, Opt. Acta 20, 8, 607 (1973).
  20. A. Roberts and B. Van Hippel, J. Appl. Phys. 17, 610 (1946).
    [Crossref]
  21. W. E. Desorbo and H. E. Kline, J. Appl. Phys. 41, 2099 (1970).
    [Crossref]
  22. S. Butterworth, Proc. R. Soc. (Lond.) 107, 693 (1925).
    [Crossref]
  23. P. J. Selgin, Electrical Transmission in Steady State (McGraw–Hill, New York, 1946).
  24. G. D. Holah and S. D. Smith, J. Phys. D 5, 496 (1972).
    [Crossref]

1974 (2)

C. M. Horwitz, Opt. Commun. 11, 210 (1974).
[Crossref]

A. G. Cha and J. K. Hsiao, IEEE Trans. AP-22106 (1974).
[Crossref]

1973 (4)

H. Ikuno and K. Yasuura, IEEE Trans. AP-21, 657 (1973).
[Crossref]

R. F. Millar, Radio Sci. 8, 607 (1973).
[Crossref]

M. C. Hutley, Opt. Acta 20, 8, 607 (1973).

P. B. Clapman and M. C. Hutley, Nature 244, 281 (1973).

1972 (2)

B. S. Thornton, Computer J. 15, 84 (1972).
[Crossref]

G. D. Holah and S. D. Smith, J. Phys. D 5, 496 (1972).
[Crossref]

1971 (2)

R. F. Millar, Proc. R. Soc. (Lond.) 69, 217 (1971).

K. H. Zaki and A. R. Neureuther, IEEE Trans AP-19(2), 208 (1971); IEEE Trans. AP-19(6), 747 (1971).
[Crossref]

1970 (1)

W. E. Desorbo and H. E. Kline, J. Appl. Phys. 41, 2099 (1970).
[Crossref]

1967 (1)

C. G. Bernhard, Endeavour 26, 79 (1967).

1966 (2)

C. P. Wu and V. Galindo, IEEE Trans. AP-14, 163 (1966).
[Crossref]

R. Petit and M. Cadilhac, C. R. Acad. Sci. (Paris), Ser. B 262, 468 (1966).

1959 (3)

L. O. Goldstone and A. A. Oliner, IRE Trans. AP-7, 274 (1959).

J. R. Wait, IRE Trans. Antennas and Propagation,  AP-7, S154 (1959).
[Crossref]

B. S. Thornton, J. Opt. Soc. Am. 49, 476 (1959).
[Crossref]

1957 (2)

J. R. Wait and A. M. Conda, J. Res. Natl. Bur. Stds. 59, 307 (1957).
[Crossref]

V. F. Wiekhorst, Z. Angew. Phys. 10, 173 (1957).

1955 (1)

H. G. Haddenhorst, Z. Angew. Phys. 7, 487 (1955).

1946 (1)

A. Roberts and B. Van Hippel, J. Appl. Phys. 17, 610 (1946).
[Crossref]

1925 (1)

S. Butterworth, Proc. R. Soc. (Lond.) 107, 693 (1925).
[Crossref]

1907 (1)

Rayleigh, Proc. R. Soc., Ser. A 79, 399 (1907).

Bernhard, C. G.

C. G. Bernhard, Endeavour 26, 79 (1967).

Butterworth, S.

S. Butterworth, Proc. R. Soc. (Lond.) 107, 693 (1925).
[Crossref]

Cadilhac, M.

R. Petit and M. Cadilhac, C. R. Acad. Sci. (Paris), Ser. B 262, 468 (1966).

Cha, A. G.

A. G. Cha and J. K. Hsiao, IEEE Trans. AP-22106 (1974).
[Crossref]

Clapman, P. B.

P. B. Clapman and M. C. Hutley, Nature 244, 281 (1973).

Conda, A. M.

J. R. Wait and A. M. Conda, J. Res. Natl. Bur. Stds. 59, 307 (1957).
[Crossref]

Desorbo, W. E.

W. E. Desorbo and H. E. Kline, J. Appl. Phys. 41, 2099 (1970).
[Crossref]

Galindo, V.

C. P. Wu and V. Galindo, IEEE Trans. AP-14, 163 (1966).
[Crossref]

Goldstone, L. O.

L. O. Goldstone and A. A. Oliner, IRE Trans. AP-7, 274 (1959).

Haddenhorst, H. G.

H. G. Haddenhorst, Z. Angew. Phys. 7, 487 (1955).

Holah, G. D.

G. D. Holah and S. D. Smith, J. Phys. D 5, 496 (1972).
[Crossref]

Horwitz, C. M.

C. M. Horwitz, Opt. Commun. 11, 210 (1974).
[Crossref]

Hsiao, J. K.

A. G. Cha and J. K. Hsiao, IEEE Trans. AP-22106 (1974).
[Crossref]

Hutley, M. C.

P. B. Clapman and M. C. Hutley, Nature 244, 281 (1973).

M. C. Hutley, Opt. Acta 20, 8, 607 (1973).

Ikuno, H.

H. Ikuno and K. Yasuura, IEEE Trans. AP-21, 657 (1973).
[Crossref]

Kline, H. E.

W. E. Desorbo and H. E. Kline, J. Appl. Phys. 41, 2099 (1970).
[Crossref]

Millar, R. F.

R. F. Millar, Radio Sci. 8, 607 (1973).
[Crossref]

R. F. Millar, Proc. R. Soc. (Lond.) 69, 217 (1971).

Neureuther, A. R.

K. H. Zaki and A. R. Neureuther, IEEE Trans AP-19(2), 208 (1971); IEEE Trans. AP-19(6), 747 (1971).
[Crossref]

Oliner, A. A.

L. O. Goldstone and A. A. Oliner, IRE Trans. AP-7, 274 (1959).

Petit, R.

R. Petit and M. Cadilhac, C. R. Acad. Sci. (Paris), Ser. B 262, 468 (1966).

Rayleigh,

Rayleigh, Proc. R. Soc., Ser. A 79, 399 (1907).

Roberts, A.

A. Roberts and B. Van Hippel, J. Appl. Phys. 17, 610 (1946).
[Crossref]

Selgin, P. J.

P. J. Selgin, Electrical Transmission in Steady State (McGraw–Hill, New York, 1946).

Smith, S. D.

G. D. Holah and S. D. Smith, J. Phys. D 5, 496 (1972).
[Crossref]

Thornton, B. S.

Van Hippel, B.

A. Roberts and B. Van Hippel, J. Appl. Phys. 17, 610 (1946).
[Crossref]

Wait, J. R.

J. R. Wait, IRE Trans. Antennas and Propagation,  AP-7, S154 (1959).
[Crossref]

J. R. Wait and A. M. Conda, J. Res. Natl. Bur. Stds. 59, 307 (1957).
[Crossref]

Wiekhorst, V. F.

V. F. Wiekhorst, Z. Angew. Phys. 10, 173 (1957).

Wu, C. P.

C. P. Wu and V. Galindo, IEEE Trans. AP-14, 163 (1966).
[Crossref]

Yasuura, K.

H. Ikuno and K. Yasuura, IEEE Trans. AP-21, 657 (1973).
[Crossref]

Zaki, K. H.

K. H. Zaki and A. R. Neureuther, IEEE Trans AP-19(2), 208 (1971); IEEE Trans. AP-19(6), 747 (1971).
[Crossref]

C. R. Acad. Sci. (Paris), Ser. B (1)

R. Petit and M. Cadilhac, C. R. Acad. Sci. (Paris), Ser. B 262, 468 (1966).

Computer J. (1)

B. S. Thornton, Computer J. 15, 84 (1972).
[Crossref]

Endeavour (1)

C. G. Bernhard, Endeavour 26, 79 (1967).

IEEE Trans (1)

K. H. Zaki and A. R. Neureuther, IEEE Trans AP-19(2), 208 (1971); IEEE Trans. AP-19(6), 747 (1971).
[Crossref]

IEEE Trans. (3)

H. Ikuno and K. Yasuura, IEEE Trans. AP-21, 657 (1973).
[Crossref]

C. P. Wu and V. Galindo, IEEE Trans. AP-14, 163 (1966).
[Crossref]

A. G. Cha and J. K. Hsiao, IEEE Trans. AP-22106 (1974).
[Crossref]

IRE Trans. (1)

L. O. Goldstone and A. A. Oliner, IRE Trans. AP-7, 274 (1959).

IRE Trans. Antennas and Propagation (1)

J. R. Wait, IRE Trans. Antennas and Propagation,  AP-7, S154 (1959).
[Crossref]

J. Appl. Phys. (2)

A. Roberts and B. Van Hippel, J. Appl. Phys. 17, 610 (1946).
[Crossref]

W. E. Desorbo and H. E. Kline, J. Appl. Phys. 41, 2099 (1970).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. D (1)

G. D. Holah and S. D. Smith, J. Phys. D 5, 496 (1972).
[Crossref]

J. Res. Natl. Bur. Stds. (1)

J. R. Wait and A. M. Conda, J. Res. Natl. Bur. Stds. 59, 307 (1957).
[Crossref]

Nature (1)

P. B. Clapman and M. C. Hutley, Nature 244, 281 (1973).

Opt. Acta (1)

M. C. Hutley, Opt. Acta 20, 8, 607 (1973).

Opt. Commun. (1)

C. M. Horwitz, Opt. Commun. 11, 210 (1974).
[Crossref]

Proc. R. Soc. (Lond.) (2)

R. F. Millar, Proc. R. Soc. (Lond.) 69, 217 (1971).

S. Butterworth, Proc. R. Soc. (Lond.) 107, 693 (1925).
[Crossref]

Proc. R. Soc., Ser. A (1)

Rayleigh, Proc. R. Soc., Ser. A 79, 399 (1907).

Radio Sci. (1)

R. F. Millar, Radio Sci. 8, 607 (1973).
[Crossref]

Z. Angew. Phys. (2)

H. G. Haddenhorst, Z. Angew. Phys. 7, 487 (1955).

V. F. Wiekhorst, Z. Angew. Phys. 10, 173 (1957).

Other (1)

P. J. Selgin, Electrical Transmission in Steady State (McGraw–Hill, New York, 1946).

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Figures (2)

FIG. 1
FIG. 1

Two types of periodic surface that can be fabricated.

FIG. 2
FIG. 2

Map of the function Ce = tanh(Te)/Te showing region A to B, as desirable for minimum change of effective surface impedance Z(∝Cf) as frequency (∝T) varies.

Tables (2)

Tables Icon

TABLE I Comparison of optimized multilayers and periodic (corrugated) surfaces as absorbers. Case (a) μ = 1, all layers; (b) μ, linearly increasing layer by layer towards base. Inner layer and outer layer specified. λ = 2.4 to 10 cm. (c) Case (b) with μ, exponentially increasing. λ = 2.4 to 10 cm. (d) Multilayer analogy for broadband moth’s eye, Cornea specified refractive index = 1.62. (e) Rectangular or cylindrical indentations with filler dielectric plus quarter-wave layer L.

Tables Icon

TABLE II Changes of Z/F = u + for Eq. (2) as p and q change with frequency f in the optimum-design region.

Equations (7)

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Z = R + i X = [ i ( w / d s ) tan s 2 π f h ] ,
Z = F ( w , d , s ) tan ( p i q ) ,
C e i ζ = tanh ( T e ± i τ ) / T e ± i τ .
C e i ζ = Z λ g / 2 π i , T e i ζ = α + i β ,
C e i ζ = tanh ( T e i τ ) / T e i τ ,
C e i ζ = Z d / 2 π f w h and T e i τ = p i q ; p , q h .
C e i ζ = Z λ g / 2 π h i , T e + i τ = ( α + i β ) h = p + i q ,