Abstract

Experimental results at millimeter wavelengths on dielectric-coated gratings are reported that show sharp anomalous dips in the transmission intensity for both P and S polarizations (i.e., incident electric field parallel and perpendicular to the slits, respectively). These dips almost disappear when either the dielectric is removed or the slits are randomly spaced. Next, a theory is developed for the gratings of finite extent and nonuniform spacings. Theoretical results, although approximate, agree remarkably well with the experiment.

© 1972 Optical Society of America

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References

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  1. R. W. Wood, Proc. Phys. Soc. (London) 18, 396 (1902).
  2. For a comprehensive list of references and discussion, see A. A. Oliner, “Surface-Wave Effects and Blindness in Phased-Array Antennas,” Phased-Array Antenna Symposium (Polytechnic Institute of Brooklyn, Farmingdale, N. Y., 1970).
  3. E. V. Byron, J. Frank, IEEE Trans. Antennas Propagation AP-16, 496 (1968).
    [CrossRef]
  4. V. D. Agrawal, Y. T. Lo, IEEE Trans. Antennas Propagation AP-20, 288 (1972).
    [CrossRef]
  5. J. S. Yee, Proc. IEEE 49, 1837 (1961).
  6. R. A. Sigelmann, A. Ishimaru, IEEE Trans. Antennas Propagation AP-13, 354 (1965).
    [CrossRef]

1972 (1)

V. D. Agrawal, Y. T. Lo, IEEE Trans. Antennas Propagation AP-20, 288 (1972).
[CrossRef]

1968 (1)

E. V. Byron, J. Frank, IEEE Trans. Antennas Propagation AP-16, 496 (1968).
[CrossRef]

1965 (1)

R. A. Sigelmann, A. Ishimaru, IEEE Trans. Antennas Propagation AP-13, 354 (1965).
[CrossRef]

1961 (1)

J. S. Yee, Proc. IEEE 49, 1837 (1961).

1902 (1)

R. W. Wood, Proc. Phys. Soc. (London) 18, 396 (1902).

Agrawal, V. D.

V. D. Agrawal, Y. T. Lo, IEEE Trans. Antennas Propagation AP-20, 288 (1972).
[CrossRef]

Byron, E. V.

E. V. Byron, J. Frank, IEEE Trans. Antennas Propagation AP-16, 496 (1968).
[CrossRef]

Frank, J.

E. V. Byron, J. Frank, IEEE Trans. Antennas Propagation AP-16, 496 (1968).
[CrossRef]

Ishimaru, A.

R. A. Sigelmann, A. Ishimaru, IEEE Trans. Antennas Propagation AP-13, 354 (1965).
[CrossRef]

Lo, Y. T.

V. D. Agrawal, Y. T. Lo, IEEE Trans. Antennas Propagation AP-20, 288 (1972).
[CrossRef]

Oliner, A. A.

For a comprehensive list of references and discussion, see A. A. Oliner, “Surface-Wave Effects and Blindness in Phased-Array Antennas,” Phased-Array Antenna Symposium (Polytechnic Institute of Brooklyn, Farmingdale, N. Y., 1970).

Sigelmann, R. A.

R. A. Sigelmann, A. Ishimaru, IEEE Trans. Antennas Propagation AP-13, 354 (1965).
[CrossRef]

Wood, R. W.

R. W. Wood, Proc. Phys. Soc. (London) 18, 396 (1902).

Yee, J. S.

J. S. Yee, Proc. IEEE 49, 1837 (1961).

IEEE Trans. Antennas Propagation (3)

E. V. Byron, J. Frank, IEEE Trans. Antennas Propagation AP-16, 496 (1968).
[CrossRef]

V. D. Agrawal, Y. T. Lo, IEEE Trans. Antennas Propagation AP-20, 288 (1972).
[CrossRef]

R. A. Sigelmann, A. Ishimaru, IEEE Trans. Antennas Propagation AP-13, 354 (1965).
[CrossRef]

Proc. IEEE (1)

J. S. Yee, Proc. IEEE 49, 1837 (1961).

Proc. Phys. Soc. (London) (1)

R. W. Wood, Proc. Phys. Soc. (London) 18, 396 (1902).

Other (1)

For a comprehensive list of references and discussion, see A. A. Oliner, “Surface-Wave Effects and Blindness in Phased-Array Antennas,” Phased-Array Antenna Symposium (Polytechnic Institute of Brooklyn, Farmingdale, N. Y., 1970).

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Figures (10)

Fig. 1
Fig. 1

The experimental setup.

Fig. 2
Fig. 2

Measured transmitted power through uniform and random gratings vs incident angle α (P polarization).

Fig. 3
Fig. 3

Measured transmitted power through uniform and random gratings vs incidence angle α (S polarization).

Fig. 4
Fig. 4

Measured transmission through uniform gratings without dielectric (S polarization).

Fig. 5
Fig. 5

Measurements on the slit pattern in uniform grating with 0.6λ spacing (S polarization).

Fig. 6
Fig. 6

Dielectric-coated grating.

Fig. 7
Fig. 7

Computed slit patterns in the 21-slit grating of 0.6λ spacing (r = 4.25, T = 0.5 mm, W = 1.25 mm, λ = 4.17 mm, S polarization).

Fig. 8
Fig. 8

Computed slit patterns in the 21-slit random grating of 0.6λ average spacing (r = 4.25, T = 0.5 mm, W = 1.25 mm, λ = 4.17 mm, S polarization).

Fig. 9
Fig. 9

Comparison of theoretical and measured transmission intensity of grating with 0.6λ spacing (S polarization).

Fig. 10
Fig. 10

Comparison of theoretical and measured transmission intensity of random grating with 0.6λ average spacing (S polarization).

Equations (30)

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( 2 H y i / x 2 ) + ( 2 H y i / z 2 ) + k i 2 H y i = 0 ,             i = 1 , 2 , 3 ,
ϕ i ( h , z ) = - H y i ( x , z ) exp ( - j h x ) d x ,             i = 1 , 2 , 3 ,
H y i ( x , z ) = 1 2 π - ϕ i ( h , z ) exp ( j h x ) d h ,             i = 1 , 2 , 3.
[ d 2 ϕ i ( h , z ) / d z 2 ] - ζ i 2 ϕ i ( h , z ) = 0 ,             i = 1 , 2 , 3 ,
H y 2 ( x , 0 ) = j ω 2 2 - 1 + Γ ( h ) exp ( - 2 ζ 2 T ) 1 - Γ ( h ) exp ( - 2 ζ 2 T ) ψ ( h , 0 ) exp ( j h x ) d h ζ 2 ,
Γ ( h ) = ( ζ 2 0 - ζ 1 2 ) / ( ζ 2 0 + ζ 1 2 )
E x ( x , 0 ) = n = 1 N E n ( x ) * δ ( x - x n ) ,
H y 2 ( x , 0 ) = 2 Y 2 ( x ) * n = 1 N E n ( x ) * δ ( x - x n ) = n = 1 N 2 Y 2 ( x - x n ) * E n ( x ) ,
Y 2 ( x ) = j ω 2 π - 1 + Γ ( h ) exp ( - 2 ζ 2 T ) 1 - Γ ( h ) exp ( - 2 ζ 2 T ) · exp ( j h x ) ζ 2 d h .
H y 3 ( x , 0 ) = - n = 1 N 0 Y 3 ( x - x n ) * E n ( x ) ,
Y 3 ( x ) = j ω 2 π - exp ( j h x ) ζ 1 d h .
H y 2 ( x , 0 ) = H y 3 ( x , 0 ) + H m ( x ) , x m - W / 2 x x m + W / 2 , m = 1 , 2 , , N .
n = 1 N Y ( x - x n ) * E n ( x ) = H m ( x ) , x m - W / 2 x x m + W / 2 , m = 1 , 2 , , N ,
Y ( x ) = 2 Y 2 ( x ) + 0 Y 3 ( x ) .
E x ( 0 ) ( x , 0 ) = E m ( 0 ) ( x ) * δ ( x - x m ) , x m - W / 2 x x m - W / 2 ,
Y ( x - x m ) * E m ( 0 ) ( x ) = H m ( x ) , x m - W / 2 x x m + W / 2.
n = 1 N Y ( x - x n ) * E n ( x ) = Y ( x - x m ) * E m ( 0 ) ( x ) , x m - W / 2 x x m + W / 2 , m = 1 , 2 , , N .
E n ( x ) = V n δ ( x )             and             E n ( 0 ) ( x ) = V n ( 0 ) δ ( x ) .
CV = V ( 0 ) ,
V = [ V 1 V N ] ,             V ( 0 ) = [ V 1 ( 0 ) V N ( 0 ) ] ,
C m n = Y ( x m - x n ) / Y ( x m - x m ) .
V m ( 0 ) = A exp ( - j k 0 x m sin α ) .
D = C - 1 ,
V n = m = 1 N D n m exp ( - j k 0 x m sin α ) .
F ( θ , α ) = 1 N n = 1 N m = 1 N D n m exp ( j k 0 x n sin θ - j k θ x m sin α ) ,
f ( α ) = F ( α , α ) = 1 N | n = 1 N D n n × { 1 + m = 1 m n N D n m D n n exp [ j k 0 ( x n - x m ) sin α ] } | .
Y 3 ( x ) = ( w / 2 ) H 0 ( 0 ) ( k 0 x ) .
1 - Γ ( h ) exp ( - 2 ζ 2 T ) = 0.
Y 2 ( x ) = j ω 2 π - exp ( j h x ) ζ 2 d h + j ω 2 π - 2 Γ ( h ) exp ( - 2 ζ 2 T ) 1 - Γ ( h ) exp ( - 2 ζ 2 T ) · exp ( j h x ) ζ 2 d h ( ω / 2 ) H 0 ( 2 ) ( k 2 x ) + Σ p Y p ( 0 ) exp ( j h p x ) ,
Y 3 ( 0 ) ( ω / 2 ) { 1 - ( 2 j / π ) [ ln ( γ k 0 W / 2 ) - 1.5 ] } ,

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