Abstract

Partial wave analysis is used to obtain analytical expressions for the diffraction efficiencies of evanescent-wave holograms. Among other results it is shown that the maximum diffraction efficiency occurs when the angle of the reconstruction beam or the angle of the diffracted beam is equal to the critical angle. In paper I the dependence of the diffraction efficiency on spatial frequencies in the hologram and on the angle of the reconstruction beam is presented for a reconstruction beam with TE polarization. The analysis and results for TM polarization are presented in paper II.

© 1978 Optical Society of America

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References

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  1. H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). I,” Optik 29, 597 (1969).
  2. H. Nassenstein, “Evanescent interference fringes,” Optik 29, 456 (1969).
  3. H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). II,” Optik 30, 44 (1969).
  4. O. Bryngdahl, “Holography with evanescent waves,” J. Opt. Soc. Am. 59, 1645 (1969).
    [Crossref]
  5. O. Bryngdahl, “Evanescent waves in optical imaging,” in Progress in Optics XI, edited by E. Wolf (North-Holland, Amsterdam, 1973), p. 169.
  6. K. A. Stetson, “Holography with total internal reflected light,” Optik 29, 520 (1969).
  7. L. H. Lin, “Edge illuminated hologram,” J. Opt. Soc. Am. 60, 714 (1970).
  8. T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
    [Crossref]
  9. T. Suhara, H. Nishihara, and J. Koyama, “Design of high-efficiency waveguide holograms” in Technical Digest of 1977 International Conference on Integrated Optics and Optical Fiber Communications, Tokyo, Japan, p. 235 (IOOC, Tokey, 1977).
  10. W. Lukosz and A. Wuthrich, “Hologram recording and readout with the evanescent field of guided waves,” Opt. Commun. 19, 232 (1976).
    [Crossref]
  11. W. Lukosz and A. Wuthrich, “Holography with evanescent waves I. Theory of diffraction efficiency for s-polarized light,” Optik 41, 191 (1974).
  12. W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
    [Crossref]
  13. A. Wuthrich and W. Lukosz, “Holography with evanescent waves II. Measurements of diffraction efficiency,” Optik 42, 315 (1974).
  14. H. Nassenstein, “Reconstruction of hologram with higher diffraction efficiency,” Optik 30, 201 (1969).
  15. W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
    [Crossref]
  16. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
    [Crossref]

1977 (1)

W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
[Crossref]

1976 (3)

T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
[Crossref]

W. Lukosz and A. Wuthrich, “Hologram recording and readout with the evanescent field of guided waves,” Opt. Commun. 19, 232 (1976).
[Crossref]

W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
[Crossref]

1974 (2)

A. Wuthrich and W. Lukosz, “Holography with evanescent waves II. Measurements of diffraction efficiency,” Optik 42, 315 (1974).

W. Lukosz and A. Wuthrich, “Holography with evanescent waves I. Theory of diffraction efficiency for s-polarized light,” Optik 41, 191 (1974).

1970 (1)

L. H. Lin, “Edge illuminated hologram,” J. Opt. Soc. Am. 60, 714 (1970).

1969 (7)

K. A. Stetson, “Holography with total internal reflected light,” Optik 29, 520 (1969).

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). I,” Optik 29, 597 (1969).

H. Nassenstein, “Evanescent interference fringes,” Optik 29, 456 (1969).

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). II,” Optik 30, 44 (1969).

O. Bryngdahl, “Holography with evanescent waves,” J. Opt. Soc. Am. 59, 1645 (1969).
[Crossref]

H. Nassenstein, “Reconstruction of hologram with higher diffraction efficiency,” Optik 30, 201 (1969).

Bryngdahl, O.

O. Bryngdahl, “Holography with evanescent waves,” J. Opt. Soc. Am. 59, 1645 (1969).
[Crossref]

O. Bryngdahl, “Evanescent waves in optical imaging,” in Progress in Optics XI, edited by E. Wolf (North-Holland, Amsterdam, 1973), p. 169.

Burham, R. D.

W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
[Crossref]

W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

Koyama, J.

T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
[Crossref]

T. Suhara, H. Nishihara, and J. Koyama, “Design of high-efficiency waveguide holograms” in Technical Digest of 1977 International Conference on Integrated Optics and Optical Fiber Communications, Tokyo, Japan, p. 235 (IOOC, Tokey, 1977).

Lin, L. H.

L. H. Lin, “Edge illuminated hologram,” J. Opt. Soc. Am. 60, 714 (1970).

Lukosz, W.

W. Lukosz and A. Wuthrich, “Hologram recording and readout with the evanescent field of guided waves,” Opt. Commun. 19, 232 (1976).
[Crossref]

W. Lukosz and A. Wuthrich, “Holography with evanescent waves I. Theory of diffraction efficiency for s-polarized light,” Optik 41, 191 (1974).

A. Wuthrich and W. Lukosz, “Holography with evanescent waves II. Measurements of diffraction efficiency,” Optik 42, 315 (1974).

Nassenstein, H.

H. Nassenstein, “Reconstruction of hologram with higher diffraction efficiency,” Optik 30, 201 (1969).

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). I,” Optik 29, 597 (1969).

H. Nassenstein, “Evanescent interference fringes,” Optik 29, 456 (1969).

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). II,” Optik 30, 44 (1969).

Nishihara, H.

T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
[Crossref]

T. Suhara, H. Nishihara, and J. Koyama, “Design of high-efficiency waveguide holograms” in Technical Digest of 1977 International Conference on Integrated Optics and Optical Fiber Communications, Tokyo, Japan, p. 235 (IOOC, Tokey, 1977).

Scifres, D. R.

W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
[Crossref]

W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
[Crossref]

Stetson, K. A.

K. A. Stetson, “Holography with total internal reflected light,” Optik 29, 520 (1969).

Streifer, W.

W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
[Crossref]

W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
[Crossref]

Suhara, T.

T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
[Crossref]

T. Suhara, H. Nishihara, and J. Koyama, “Design of high-efficiency waveguide holograms” in Technical Digest of 1977 International Conference on Integrated Optics and Optical Fiber Communications, Tokyo, Japan, p. 235 (IOOC, Tokey, 1977).

Wuthrich, A.

W. Lukosz and A. Wuthrich, “Hologram recording and readout with the evanescent field of guided waves,” Opt. Commun. 19, 232 (1976).
[Crossref]

W. Lukosz and A. Wuthrich, “Holography with evanescent waves I. Theory of diffraction efficiency for s-polarized light,” Optik 41, 191 (1974).

A. Wuthrich and W. Lukosz, “Holography with evanescent waves II. Measurements of diffraction efficiency,” Optik 42, 315 (1974).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
[Crossref]

IEEE J. Quantum Electron. (2)

W. Streifer, D. R. Scifres, and R. D. Burham, “Analysis of grating coupled radiation in GaAs: GaAlAs lasers and waveguides,” IEEE J. Quantum Electron. QE-12, 422 (1976).
[Crossref]

W. Streifer, D. R. Scifres, and R. D. Burham, “Coupled wave analysis of DFB and DBR lasers,” IEEE J. Quantum Electron. QE-13, 134 (1977).
[Crossref]

J. Opt. Soc. Am. (2)

O. Bryngdahl, “Holography with evanescent waves,” J. Opt. Soc. Am. 59, 1645 (1969).
[Crossref]

L. H. Lin, “Edge illuminated hologram,” J. Opt. Soc. Am. 60, 714 (1970).

Opt. Commun. (2)

T. Suhara, H. Nishihara, and J. Koyama, “Waveguide holograms: a new approach to hologram integration,” Opt. Commun. 19, 353 (1976).
[Crossref]

W. Lukosz and A. Wuthrich, “Hologram recording and readout with the evanescent field of guided waves,” Opt. Commun. 19, 232 (1976).
[Crossref]

Optik (7)

W. Lukosz and A. Wuthrich, “Holography with evanescent waves I. Theory of diffraction efficiency for s-polarized light,” Optik 41, 191 (1974).

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). I,” Optik 29, 597 (1969).

H. Nassenstein, “Evanescent interference fringes,” Optik 29, 456 (1969).

H. Nassenstein, “Interference, diffraction and holography with surface waves (“subwaves”). II,” Optik 30, 44 (1969).

K. A. Stetson, “Holography with total internal reflected light,” Optik 29, 520 (1969).

A. Wuthrich and W. Lukosz, “Holography with evanescent waves II. Measurements of diffraction efficiency,” Optik 42, 315 (1974).

H. Nassenstein, “Reconstruction of hologram with higher diffraction efficiency,” Optik 30, 201 (1969).

Other (2)

O. Bryngdahl, “Evanescent waves in optical imaging,” in Progress in Optics XI, edited by E. Wolf (North-Holland, Amsterdam, 1973), p. 169.

T. Suhara, H. Nishihara, and J. Koyama, “Design of high-efficiency waveguide holograms” in Technical Digest of 1977 International Conference on Integrated Optics and Optical Fiber Communications, Tokyo, Japan, p. 235 (IOOC, Tokey, 1977).

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Figures (6)

FIG. 1
FIG. 1

Recording of evanescent-wave holograms. θo and θr are, respectively, the angles of the object beam and the reference beam. The substrate has a refractive index n1 which is higher than the refractive index n2 of the emulsion; n3 is the refractive index of the immersing liquid or air.

FIG. 2
FIG. 2

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-emulsion interface.

FIG. 3
FIG. 3

Creation of three different holograms. The change in refractive index is assumed to be 0.01 and K1. (a) Object and reference beam both evanescent; (b) reference beam evanescent, object beam orthogonal; and (c) reference beam evanescent nonorthogonal homogeneous object beam.

FIG. 4
FIG. 4

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. The maximum efficiencies of the two diffracted orders are equal.

FIG. 5
FIG. 5

Diffraction efficiency η in percent vs. the reconstruction angle θi (degree). The hologram is recorded as shown in Fig. 3(b). Its thickness = 0.51 μm and spatial frequency = 2516 lines/mm.

FIG. 6
FIG. 6

Diffraction efficiency η in percent vs. the reconstruction angle θi (degree). The hologram is recorded as shown in Fig. 3(c). Its thickness = 0.51 μm and spatial frequency = 4274 lines/mm.

Equations (34)

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