Abstract

Partial wave analysis is used to obtain analytical expressions for the diffraction efficiencies of evanescent-wave holograms for TM polarization. It is shown that the diffraction efficiency for the evanescent-wave hologram is relatively lower for TM than for TE polarized illumination. Furthermore, the curves of diffraction efficiency as a function of the reconstruction angles have dips that are not observed in the TE case.

© 1978 Optical Society of America

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References

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  1. W.-H. Lee and W. Streifer, “Diffraction efficiency of evanescent-wave holograms, Part I: TE polarization,” J. Opt. Soc. Am. 68, 795–801 (1978).
    [Crossref]
  2. H. Kogelnik, “Coupled wave theory for the thick hologram gratings,” Bell Syst. Tech. J. 48, 291 (1969).
    [Crossref]
  3. H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602 (1970).
    [Crossref]

1978 (1)

1970 (1)

H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602 (1970).
[Crossref]

1969 (1)

H. Kogelnik, “Coupled wave theory for the thick hologram gratings,” Bell Syst. Tech. J. 48, 291 (1969).
[Crossref]

Kogelnik, H.

H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602 (1970).
[Crossref]

H. Kogelnik, “Coupled wave theory for the thick hologram gratings,” Bell Syst. Tech. J. 48, 291 (1969).
[Crossref]

Lee, W.-H.

Sosnowski, T. P.

H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602 (1970).
[Crossref]

Streifer, W.

Bell Syst. Tech. J. (2)

H. Kogelnik, “Coupled wave theory for the thick hologram gratings,” Bell Syst. Tech. J. 48, 291 (1969).
[Crossref]

H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602 (1970).
[Crossref]

J. Opt. Soc. Am. (1)

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Figures (5)

FIG. 1
FIG. 1

Reconstructing the diffracted wave field from the evanescent-wave hologram. The hologram is confined to a layer less than 1 μm in thickness at the substrate-emission interface. The E field of the illumination is parallel to the plane of incidence of the hologram.

FIG. 2
FIG. 2

Creation of three different holograms. The change in refractive index is assumed to be 0.01 and K is equal to 1. (a) Object and reference beam both evanescent; (b) reference beam evanescent, object beam orthogonal; and (c) reference beam evanescent, nonorthogonal homogeneous object beam.

FIG. 3
FIG. 3

Diffraction efficiency η in percent vs. the reconstruction angle θi (degree). The hologram is recorded as shown in Fig. 3(a). Its thickness = 0.14 μm and spatial frequency = 124 lines/mm.

FIG. 4
FIG. 4

Diffraction efficiency η in percent vs. the reconstruction angle θi (degree). The hologram is recorded as shown in Fig. 2(b). Its thickness = 0.51 μm and spatial frequency = 2516 lines/mm. Because the object beam is incident perpendicular to the hologram, βm is near 0. This results in the low diffraction efficiency of the hologram.

FIG. 5
FIG. 5

Diffraction efficiency η in percent vs. the reconstruction angle θi (degree). The hologram is recorded as shown in Fig. 2(c). Its thickness = 0.51 μm and spatial frequency = 4274 lines/mm.

Equations (26)

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n 2 2 ( x , z ) = n 2 2 + Δ ( n 2 2 ) + 2 K Δ ( n 2 2 ) exp ( - q r x ) × cos [ 2 π ( z / z - x / x ) ] .
z ( ν ( x , z ) H y z ) + x ( ν ( x , z ) H y x ) + k o 2 H y = 0 ,
ν ( x , z ) = ν ( x ) - 2 K Δ ν ( x ) × exp ( - q r x ) cos ( 2 π z / z - 2 π x / x ) ,
ν ( x ) = { 1 / n 1 2 , x < 0 , [ 1 - Δ ( n 2 2 ) / n 2 2 ] / n 2 2 , x > 0 ,
Δ ν ( x ) = { 0 , x < 0 , Δ ( n 2 2 ) / n 2 4 , x > 0.
H y = H m exp ( i β m z ) ,
x ( ν ( x ) H m x ) + [ k o 2 - β m 2 ν ( x ) ] H m = - K Δ ν ( x ) β m β m - 1 exp ( - q r x - i 2 π x x ) H m - 1 + K x [ Δ ν ( x ) exp ( - q r x - i 2 π x x ) H m - 1 x ] - K Δ ν ( x ) β m β m + 1 exp ( - q r x + i 2 π x x ) H m + 1 + K x [ Δ ν ( x ) exp ( - q r x + i 2 π x x ) H m + 1 x ] .
2 H 0 x 2 + [ k o 2 n 2 ( x ) - β 0 2 ] H 0 = 0 ,
2 H m x 2 + [ k o 2 n 2 ( x ) - β m 2 ] H m = - K n 2 ( x ) Δ ν ( x ) exp ( - q r x - i 2 π m x x ) × [ β m β 0 H 0 - 2 H 0 x 2 + ( q r + i 2 π m x ) H 0 x ] , m = ± 1.
H 0 ( x ) = { A 1 h exp ( i p 1 x ) + A 2 h exp ( - i p 1 x ) , for x < 0 B 1 h exp ( i p 2 x ) , for x > 0 ,
p 1 = ( k o 2 n 1 2 - β 2 ) 1 / 2 ,
p 2 = ( k o 2 n ˆ 2 2 - β 2 ) 1 / 2 ,
A 2 h = ( p 1 - p 2 h ) A 1 h / ( p 1 + p 2 h ) ,
B 1 h = 2 p 1 A 1 h / ( p 1 + p 2 h ) ,
H m ( x ) = { A 1 h m exp ( - i q 1 m x ) , for x < 0 B 1 h m exp ( i q 2 m x ) + B 2 h m exp ( - i q 2 m x ) + T h m ( x ) , for x > 0 ,
T h m ( x ) = - k o 2 Δ ( n 2 2 ) K B 1 q 2 m 0 x e - q r u e - i 2 π m u / Λ x × H 0 ( u ) sin [ q 2 m ( u - x ) ] d u , K = - ( β m β 0 + p 2 2 + i p 2 q r - 2 π m p 2 / Λ x ) K / k o 2 n 2 2 ,
q 1 m = ( k o 2 n 1 2 - β m 2 ) 1 / 2 , q 2 m = ( k o 2 n 2 2 - β m 2 ) 1 / 2 .
B 2 h m = - k o 2 Δ ( n 2 2 ) K B 1 h 2 q 2 m ( i q r - 2 π m / Λ x + p 2 + q 2 m ) .
A 1 h m = 2 q 2 h B 2 h m / ( q 2 h + q 1 )
B 1 h m = ( q 2 h - q 1 ) B 2 h m / ( q 2 h + q 1 ) ,
A 1 h m = 2 p 1 k o 2 n 1 2 Δ ( n 2 2 ) K A 1 h n 2 2 ( p 1 + p 2 h ) ( q 2 h + q 1 ) ( i q r - 2 π m / Λ x + p 2 + q 2 ) ,
C 2 h m = B 1 h m - k o 2 Δ ( n 2 2 ) K B 1 h 2 q 2 m ( i q r - 2 π m / Λ x + p 2 - q 2 m ) .
C 2 h m = 2 p 1 k o 2 n 1 2 Δ ( n 2 2 ) K A 1 h [ i q r - 2 π m / Λ x + p 2 + q 1 ( n ˆ 2 2 / n 1 2 ) ] / n ˆ 2 2 ( p 1 + p 2 h ) ( q 2 h + q 1 ) × [ ( p 2 - 2 π m / Λ x ) 2 - q 2 m 2 - q r 2 + i 2 q r ( p 2 - 2 π m / Λ x ) ] . - 1
η 1 h = ( q 1 / p 1 ) A 1 h m 2 / A 1 h 2 ,
η 2 h = ( q 2 / p 1 ) C 2 h m 2 / A 1 h 2 .
K = β m K / k o n 2 ,