Abstract

The results of an analytical and numerical investigation of TM polarized plane wave scattering from an infinite, fin-corrugated surface are presented. The surface was composed of infinitely thin, perfectly conducting fins of spacing λ/2 < a < λ. Specular reflection from this ideal surface can be completely converted to backscatter in a direction opposite to the incident wave when the fin period and height are properly chosen. A procedure is described for the design and performance prediction of a finite, fin-corrugated surface composed of finitely thick fins. Experiments performed on some optimum, nonideal surfaces under TM polarized non-plane-wave illumination indicate that they behave essentially as predicted.

© 1976 Optical Society of America

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References

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  1. D. Y. Tseng, “Equivalent Network Representation for High Efficiency Corrugated Blaze Grating,” Proc. G-AP Symposium, Boulder, Colo. pp. 101–104 (1973) (unpublished).
  2. D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).
  3. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 430.
  4. J. A. DeSanto, “Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries,” J. Math. Phys. 12, 1913–1923 (1971).
    [Crossref]
  5. J. A. DeSanto, “Scattering from a Periodic Corrugated Structure II: Thin Comb with Hard Boundaries,” J. Math. Phys. 13, 336–341 (1972).
    [Crossref]
  6. A. Hessel and H. Hochstadt, “Plane Wave Scattering From Modulated Corrugated Structures,” Radio Sci. 3, 1019–1030 (1968).
  7. E. V. Jull and G. R. Ebbeson, “The Reduction of Interference from Large Reflecting Surfaces,” IEEE Trans. Ant. Prop. (in Press).
  8. Reference 6, Eqs. (2)–(6).
  9. Reference 2, p. 84; Ref. 3, pp. 433–437; Ref. 6, pp. 1026–1028.
  10. Reference 6, pp. 1023–1024.
  11. K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TE Polarization,” IEEE Trans. Ant. Prop. AP-19, 208–214 (1971).
    [Crossref]
  12. K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TM Polarization,” IEEE Trans. Ant. Prop. AP-19, 747–751 (1971).
    [Crossref]
  13. A. Wirgin and R. Deleuil, “Theoretical and Experimental Investigation of a New Type of Blazed Grating,” J. Opt. Soc. Am. 59, 1348–1357 (1969).
    [Crossref]
  14. A. Hessel, J. Schmoys, and D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
    [Crossref]
  15. G. R. Ebbeson, “The Use of Fin-Corrugated Periodic Surfaces for the Reduction of Interference from Large Reflecting Surfaces,” M. A. Sc. thesis (University of British Columbia, 1974) (unpublished).

1975 (1)

1972 (1)

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure II: Thin Comb with Hard Boundaries,” J. Math. Phys. 13, 336–341 (1972).
[Crossref]

1971 (3)

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries,” J. Math. Phys. 12, 1913–1923 (1971).
[Crossref]

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TE Polarization,” IEEE Trans. Ant. Prop. AP-19, 208–214 (1971).
[Crossref]

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TM Polarization,” IEEE Trans. Ant. Prop. AP-19, 747–751 (1971).
[Crossref]

1969 (1)

1968 (2)

D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).

A. Hessel and H. Hochstadt, “Plane Wave Scattering From Modulated Corrugated Structures,” Radio Sci. 3, 1019–1030 (1968).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 430.

Deleuil, R.

DeSanto, J. A.

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure II: Thin Comb with Hard Boundaries,” J. Math. Phys. 13, 336–341 (1972).
[Crossref]

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries,” J. Math. Phys. 12, 1913–1923 (1971).
[Crossref]

Ebbeson, G. R.

E. V. Jull and G. R. Ebbeson, “The Reduction of Interference from Large Reflecting Surfaces,” IEEE Trans. Ant. Prop. (in Press).

G. R. Ebbeson, “The Use of Fin-Corrugated Periodic Surfaces for the Reduction of Interference from Large Reflecting Surfaces,” M. A. Sc. thesis (University of British Columbia, 1974) (unpublished).

Hessel, A.

A. Hessel, J. Schmoys, and D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
[Crossref]

A. Hessel and H. Hochstadt, “Plane Wave Scattering From Modulated Corrugated Structures,” Radio Sci. 3, 1019–1030 (1968).

D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).

Hochstadt, H.

A. Hessel and H. Hochstadt, “Plane Wave Scattering From Modulated Corrugated Structures,” Radio Sci. 3, 1019–1030 (1968).

Jull, E. V.

E. V. Jull and G. R. Ebbeson, “The Reduction of Interference from Large Reflecting Surfaces,” IEEE Trans. Ant. Prop. (in Press).

Neureuther, A. R.

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TE Polarization,” IEEE Trans. Ant. Prop. AP-19, 208–214 (1971).
[Crossref]

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TM Polarization,” IEEE Trans. Ant. Prop. AP-19, 747–751 (1971).
[Crossref]

Oliner, A. A.

D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).

Schmoys, J.

Tseng, D. Y.

A. Hessel, J. Schmoys, and D. Y. Tseng, “Bragg-angle blazing of diffraction gratings,” J. Opt. Soc. Am. 65, 380–384 (1975).
[Crossref]

D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).

D. Y. Tseng, “Equivalent Network Representation for High Efficiency Corrugated Blaze Grating,” Proc. G-AP Symposium, Boulder, Colo. pp. 101–104 (1973) (unpublished).

Wirgin, A.

Zaki, K. A.

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TM Polarization,” IEEE Trans. Ant. Prop. AP-19, 747–751 (1971).
[Crossref]

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TE Polarization,” IEEE Trans. Ant. Prop. AP-19, 208–214 (1971).
[Crossref]

Alta Frequenza (1)

D. Y. Tseng, A. Hessel, and A. A. Oliner, “Scattering by a Multimode Corrugated Structure with Application to P type Wood Anomalies,” Alta Frequenza 38N, 82–88 (1968).

IEEE Trans. Ant. Prop. (2)

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TE Polarization,” IEEE Trans. Ant. Prop. AP-19, 208–214 (1971).
[Crossref]

K. A. Zaki and A. R. Neureuther, “Scattering from a Perfectly Conducting Surface with a Sinusoidal Height Profile: TM Polarization,” IEEE Trans. Ant. Prop. AP-19, 747–751 (1971).
[Crossref]

J. Math. Phys. (2)

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure: Thin Comb with Soft Boundaries,” J. Math. Phys. 12, 1913–1923 (1971).
[Crossref]

J. A. DeSanto, “Scattering from a Periodic Corrugated Structure II: Thin Comb with Hard Boundaries,” J. Math. Phys. 13, 336–341 (1972).
[Crossref]

J. Opt. Soc. Am. (2)

Radio Sci. (1)

A. Hessel and H. Hochstadt, “Plane Wave Scattering From Modulated Corrugated Structures,” Radio Sci. 3, 1019–1030 (1968).

Other (7)

E. V. Jull and G. R. Ebbeson, “The Reduction of Interference from Large Reflecting Surfaces,” IEEE Trans. Ant. Prop. (in Press).

Reference 6, Eqs. (2)–(6).

Reference 2, p. 84; Ref. 3, pp. 433–437; Ref. 6, pp. 1026–1028.

Reference 6, pp. 1023–1024.

G. R. Ebbeson, “The Use of Fin-Corrugated Periodic Surfaces for the Reduction of Interference from Large Reflecting Surfaces,” M. A. Sc. thesis (University of British Columbia, 1974) (unpublished).

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960), p. 430.

D. Y. Tseng, “Equivalent Network Representation for High Efficiency Corrugated Blaze Grating,” Proc. G-AP Symposium, Boulder, Colo. pp. 101–104 (1973) (unpublished).

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Figures (5)

FIG. 1
FIG. 1

Fin-corrugated structure with incident TM polarized plane wave.

FIG. 2
FIG. 2

Relative power of the n = 0 and n = −1 modes vs fin height, a = 0.578λ (θiop = 60°), 100% reduction at d = 0.559λ.

FIG. 3
FIG. 3

Relative power of the n = 0 and n = −1 modes vs angle of incidence, a = 0.578λ (θiop = 60°), d = 0.559λ, 100% reduction.

FIG. 4
FIG. 4

Optimum fin height vs fin period.

FIG. 5
FIG. 5

Relative power of the n = 0 mode vs angle of incidence; solid curve, experimental, a = 0.614λ, at = 0.581λ, d = 0.560λ, observed θiop = 55.5°; broken curve, predicted, a = 0.614λ (θiop = 54.5°), da = 0.595λ.

Equations (31)

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( 2 + k 0 2 ) H y ( x , z ) = 0 ,
Γ n 2 = ( h + 2 n π / a ) 2 - k 0 2 ,             n = ± 0 , 1 , 2 , ,             z < 0 ,
γ n 2 = ( n π / a ) 2 - k 0 2 ,             n = + 0 , 1 , 2 , ,             0 < z < d ,
b 0 a 0 = B ¯ 0 A ¯ 0 + C 0 A 0 e - 2 γ 0 d Δ 1 + C ¯ ¯ 0 A ¯ ¯ 1 e - 2 γ 1 d Δ 2 ,
b - 1 a 0 = B ¯ - 1 A ¯ 0 + C - 1 A 0 e - 2 γ 0 d Δ 1 + C ¯ ¯ - 1 A ¯ ¯ 1 e - 2 γ 1 d Δ 2 ,
Δ 1 = [ C ¯ 0 A ¯ 0 ( 1 - B ¯ ¯ 1 A ¯ ¯ 1 e - 2 γ 1 d ) + B ¯ ¯ 0 A ¯ ¯ 1 · C ¯ 1 A ¯ 0 e - 2 γ 1 d ] × [ ( 1 - B 0 A 0 e - 2 γ 0 d ) · ( 1 - B ¯ ¯ 1 A ¯ ¯ 1 e - 2 γ 1 d ) - B 1 A 0 · B ¯ ¯ 0 A ¯ ¯ e - 2 ( γ 0 + γ 1 ) d ] - 1 ,
Δ 2 = [ C ¯ 1 A ¯ 0 ( 1 - B 0 A 0 e - 2 γ 0 d ) + B 1 A 0 · C ¯ 0 A ¯ 0 e - 2 γ 0 d ] × [ ( 1 - B 0 A 0 e - 2 γ 0 d ) · ( 1 - B ¯ ¯ 1 A ¯ ¯ 1 e - 2 γ 1 d ) - B 1 A 0 · B ¯ ¯ 0 A ¯ ¯ 1 e - 2 ( γ 0 + γ 1 ) d ] - 1 .
P 0 = b 0 / a 0 2 ,
P - 1 = ( Γ - 1 / Γ 0 ) b - 1 / a 0 2 ,
B ¯ 0 A ¯ 0 = ( Γ 0 - γ 0 ) ( Γ 0 + γ 0 ) Π ( - Γ 0 , Γ 0 , 1 ) ,
B ¯ - 1 A ¯ 0 = 2 Γ 0 ( Γ 0 - γ 0 ) ( γ 1 - Γ 0 ) ( Γ 1 + Γ 0 ) ( Γ 0 - Γ - 1 ) ( γ 0 + Γ - 1 ) ( γ 1 + Γ - 1 ) ( Γ 1 - Γ - 1 ) ) × Π ( - Γ 0 , Γ - 1 , 2 ) ,
C ¯ 0 A ¯ 0 = 2 j Γ 0 ( 1 - e - j h a ) ( γ 0 - Γ 0 ) h 2 sin ( h a ) Π ( - Γ 0 , - γ 0 , 1 ) ,
C ¯ 1 A ¯ 0 = 2 j Γ 0 ( 1 + e - j h a ) ( γ 0 - Γ 0 ) ( Γ 1 + Γ 0 ) ( Γ - 1 + Γ 0 ) sin ( h a ) ( Γ 0 + γ 1 ) ( γ 0 - γ 1 ) ( Γ 1 + γ 1 ) ( Γ - 1 + γ 1 ) × Π ( - Γ 0 , - γ 1 , 2 ) ,
B 0 A 0 = ( γ 0 - Γ 0 ) ( γ 0 + Γ 0 ) Π ( γ 0 , - γ 0 , 1 ) ,
B 1 A 0 = 2 γ 0 ( 1 + e - j h a ) ( Γ 0 - γ 0 ) ( Γ 1 - γ 0 ) ( Γ - 1 - γ 0 ) ( 1 - e - j h a ) ( γ 0 - γ 1 ) ( Γ 0 + γ 1 ) ( Γ 1 + γ 1 ) ( Γ - 1 + γ 1 ) × Π ( γ 0 , - γ 1 , 2 ) ,
C 0 A 0 = 2 j γ 0 sin ( h a ) ( Γ 0 - γ 0 ) h 2 ( 1 - e - j h a ) Π ( γ 0 , Γ 0 , 1 ) ,
C - 1 A 0 = 2 j γ 0 sin ( h a ) ( γ 1 + γ 0 ) ( Γ 0 - γ 0 ) ( Γ 1 - γ 0 ) ( 1 - e - j h a ) ( γ 0 + Γ - 1 ) ( γ 1 + Γ - 1 ) ( Γ 0 - Γ - 1 ) ( Γ 1 - Γ - 1 ) × Π ( γ 0 , Γ - 1 , 2 ) ,
B ¯ ¯ 0 A ¯ ¯ 1 = ( 1 - e - j h a ) ( Γ 0 - γ 1 ) ( 1 + e - j h a ) ( Γ 0 + γ 0 ) Π ( γ 1 , - γ 0 , 1 ) ,
B ¯ ¯ 1 A ¯ ¯ 1 = ( γ 0 + γ 1 ) ( γ 1 - Γ 0 ) ( Γ 1 - γ 1 ) ( Γ - 1 - γ 1 ) ( γ 0 - γ 1 ) ( γ 1 + Γ 0 ) ( Γ 1 + γ 1 ) ( Γ - 1 + γ 1 ) × Π ( γ 1 , - γ 1 , 2 ) ,
C ¯ ¯ 0 A ¯ ¯ 1 = - j sin ( h a ) ( γ 0 + γ 1 ) ( 1 + e - j h a ) ( γ 0 + Γ 0 ) Π ( γ 1 , Γ 0 , 1 ) ,
C ¯ ¯ - 1 A ¯ ¯ 1 = 2 j γ 1 sin ( h a ) ( γ 0 + γ 1 ) ( γ 1 - Γ 0 ) ( Γ 1 - γ 1 ) ( 1 + e - j h a ) ( γ 1 + Γ - 1 ) ( γ 0 + Γ - 1 ) ( Γ 0 - Γ - 1 ) ( Γ 1 - Γ - 1 ) × Π ( γ 1 , Γ - 1 , 2 ) ,
Π ( x , y , z ) = e ( x - y ) ( a / π ) ln 2 n = z ( γ n + x ) ( Γ n - x ) ( Γ - n - x ) ( γ n + y ) ( Γ n - y ) ( Γ - n - y ) .
B ¯ 0 A ¯ 0 = ( Γ 0 - γ 0 ) ( Γ 1 + Γ 0 ) ( Γ - 1 + Γ 0 ) 2 ( Γ 0 + γ 0 ) ( γ 1 + Γ 0 ) ( Γ 1 - Γ 0 ) Π ( - Γ 0 , Γ 0 , 2 ) ,
B ¯ - 1 A ¯ 0 = Γ 0 ( γ 0 - Γ 0 ) ( Γ 1 + Γ 0 ) ( γ 0 + Γ - 1 ) ( γ 1 + Γ - 1 ) ( Γ 1 - Γ - 1 ) Π ( - Γ 0 , Γ - 1 , 2 ) ,
C ¯ 0 A ¯ 0 = 4 j Γ 0 ( γ 0 - Γ 0 ) ( Γ 1 + Γ 0 ) ( Γ - 1 + Γ 0 ) π γ 1 ( γ 1 - γ 0 ) ( Γ 1 + γ 0 ) ( Γ - 1 + γ 0 ) Π ( - Γ 0 , - γ 0 , 2 ) ,
C ¯ 1 A ¯ 0 = 2 Γ 0 ( γ 0 - Γ 0 ) ( Γ 1 + Γ 0 ) ( Γ - 1 + Γ 0 ) ( Γ 0 + γ 1 ) ( γ 0 - γ 1 ) ( Γ 1 + γ 1 ) ( Γ - 1 + γ 1 ) Π ( - Γ 0 , - γ 1 , 2 ) ,
C 0 A 0 = j a 4 γ 0 γ 1 ( γ 1 + γ 0 ) ( Γ 0 - γ 0 ) ( Γ 1 - γ 0 ) ( Γ - 1 - γ 0 ) 2 π 3 ( γ 1 + Γ 0 ) ( Γ 1 - Γ 0 ) × Π ( γ 0 , Γ 0 , 2 ) ,
C - 1 A 0 = j a 2 γ 0 γ 1 ( γ 1 + γ 0 ) ( γ 0 - Γ 0 ) ( Γ 1 - γ 0 ) 2 π ( γ 0 + Γ - 1 ) ( γ 1 + Γ - 1 ) ( Γ - 1 - Γ - 1 ) Π ( γ 0 , Γ - 1 , 2 ) ,
C ¯ ¯ 0 A ¯ ¯ 1 = γ 1 ( γ 0 + γ 1 ) ( Γ 1 - γ 1 ) ( γ 1 + Γ 0 ) ( γ 0 + Γ 0 ) ( Γ 1 - Γ 0 ) Π ( γ 1 , Γ 0 , 2 ) ,
C ¯ ¯ - 1 A ¯ ¯ 1 = γ 1 ( γ 0 + γ 1 ) ( Γ 1 - γ 1 ) ( γ 1 + Γ - 1 ) ( γ 0 + Γ - 1 ) ( Γ 1 - Γ - 1 ) Π ( γ 1 , Γ - 1 , 2 ) ,
b 0 a 0 = B ¯ 0 A ¯ 0 + C ¯ 0 A 0 · C ¯ 0 A ¯ 0 e - 2 γ 0 d 1 - ( B 0 / A 0 ) e - 2 γ 0 d + C ¯ ¯ 0 A ¯ ¯ 1 · C ¯ 1 A ¯ 0 e - 2 γ 1 d ,