Abstract

Lippmann–Bragg broadband volume holographic mirrors, with chirp normal to the surface, represent an entirely new class of grating. These gratings are presented and analyzed theoretically by using a combination of the multiple-beam interference method and Kogelnik’s local solution for uniform gratings. Particularly noteworthy is the new grating’s combination of a very high Bragg diffraction efficiency (>99.5%) with a large tunable bandwidth (from 5 to >300 nm).

© 1991 Optical Society of America

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  1. T. Jannson, J. Jannson, “High-efficiency Bragg holograms in the IR, visible, UV, and XUV spectral region,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 84–93 (1988).
    [Crossref]
  2. J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
    [Crossref]
  3. B. Moslehi, P. Harvey, J. Ng, T. Jannson, “Fiber-optic wavelength-division multiplexing and demultiplexing using volume holographic gratings,” Opt. Lett. 14, 1088–1090 (1989).
    [Crossref] [PubMed]
  4. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  5. B. J. Chang, C. D. Leonard, “Dichromated gelatin for the fabrication of holographic optical elements,” Appl. Opt. 18, 2407–2417 (1979).
    [Crossref] [PubMed]
  6. J. R. Magarinos, D. J. Coleman, “Holographic mirrors,” Opt. Eng. 24, 769–780 (1985).
  7. R. T. Ingwall, M. Troll, “The mechanism of hologram formation in DMP-129 photopolymer,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 94–101 (1988).
    [Crossref]
  8. T. Jannson, G. Savant, Y. Qiao, “Bragg holographic structures for XUV applications: a new approach,” Opt. Lett. 14, 344–346 (1989).
    [Crossref] [PubMed]
  9. G. Savant, T. Jannson, Y. Qiao, “Super-high resolution holographic materials for UV and XUV applications,” in Practical Holography, III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 148–155 (1989).
    [Crossref]
  10. G. Savant, T. Jannson, “Super-high resolution holographic composite polymer grafts for XUV applications,” in Proceedings of the Workshop on X-ray Microimaging for the Life Sciences (Lawrence Berkeley Laboratory, Berkeley, Calif., 1989), pp. 197–202.
  11. T. Jannson, “Information capacity of Bragg holograms in planar optics,”J. Opt. Soc. Am. 71, 342–347 (1981).
    [Crossref]
  12. T. Jannson, J. Jannson, P. Yeung, “Holographic planar optical interconnect,” U.S. Patent4,838,630, June13, 1989.
  13. R. Chen, W. Phillips, T. Jannson, D. Pelka, “Integration of holographic optical elements with polymer gelatin waveguides on GaAs, LiNbO3, glass, and aluminum,” Opt. Lett. 14, 892–894 (1989); F. Lin, E. Strzelecki, T. Jannson, “Optical multi-planar VLSI interconnects based on multiplexed waveguide holograms,” Appl. Opt. 29, 1126–1133 (1990).
    [Crossref] [PubMed]
  14. R. Collier, C. Burckhardt, L. Lin, Optical Holography (Academic, New York, 1971).
  15. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 87.
  16. J. P. Golden, G. P. Summers, W. H. Carter, “Resistance of hologram made in Polaroid DMP128 photopolymer to ionizing radiation damage,” Opt. Lett. 13, 949–951 (1988).
    [Crossref] [PubMed]
  17. A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).
  18. K. Johnson, “Coupled scalar wave theory,” Appl. Phys. 24, 249–260 (1981).
    [Crossref]
  19. M. Moharam, T. Gaylord, “Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings,”J. Opt. Soc. Am. 72, 187–190 (1982).
    [Crossref]
  20. W. W. Rigrod, “Diffraction efficiency of nonsinusoidal Bragg reflection gratings,”J. Opt. Soc. Am. 64, 97–99 (1974); Erratum, J. Opt. Soc. Am. 64, 895 (1974).
    [Crossref]
  21. J. D. Masso, “Multilayer thin film simulation of volume holograms,” in Holographic Optics: Design and Applications, I. Cindrich, ed., roc. Soc. Photo-Opt. Instrum. Eng.883, 68–74 (1988).
    [Crossref]
  22. J. Lekner, M. C. Dorf, “Matrix methods for the calculation of reflection amplitudes,” J. Opt. Soc. Am. A 4, 2092–2095 (1987).
    [Crossref]
  23. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 8.
  24. S. D. Smith, “Design of multilayer filters by considering two effective interfaces,”J. Opt. Soc. Am. 48, 43–50 (1958).
    [Crossref]
  25. See, for example, Ref. 15, p. 62.
  26. See Ref. 21, p. 70.
  27. W. H. Southwell, “Using apodization functions to reduce side-lobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989).
    [Crossref] [PubMed]
  28. D. Kermisch, “Nonuniform sinusoidally modulated dielectric gratings,”J. Opt. Soc. Am. 59, 1409–1414 (1969).
    [Crossref]
  29. W. R. Klein, “Theoretical efficiency of Bragg devices,” Proc. IEEE 54, 803–804 (1966).
    [Crossref]
  30. R. Jacobsson, “Light reflection from films of continuously varying reflective index,” in Progress in Optics 5, E. Wolf, ed. (North-Holland, Amsterdam, 1966), pp. 249–286.

1989 (4)

1988 (1)

1987 (1)

1986 (1)

J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
[Crossref]

1985 (1)

J. R. Magarinos, D. J. Coleman, “Holographic mirrors,” Opt. Eng. 24, 769–780 (1985).

1982 (1)

1981 (2)

1980 (1)

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

1979 (1)

1974 (1)

1969 (2)

D. Kermisch, “Nonuniform sinusoidally modulated dielectric gratings,”J. Opt. Soc. Am. 59, 1409–1414 (1969).
[Crossref]

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1966 (1)

W. R. Klein, “Theoretical efficiency of Bragg devices,” Proc. IEEE 54, 803–804 (1966).
[Crossref]

1958 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 87.

Burckhardt, C.

R. Collier, C. Burckhardt, L. Lin, Optical Holography (Academic, New York, 1971).

Carter, W. H.

Chang, B. J.

Chen, R.

Coleman, D. J.

J. R. Magarinos, D. J. Coleman, “Holographic mirrors,” Opt. Eng. 24, 769–780 (1985).

Collier, R.

R. Collier, C. Burckhardt, L. Lin, Optical Holography (Academic, New York, 1971).

Dorf, M. C.

Gaylord, T.

Golden, J. P.

Harvey, P.

Ingwall, R. T.

R. T. Ingwall, M. Troll, “The mechanism of hologram formation in DMP-129 photopolymer,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 94–101 (1988).
[Crossref]

Jacobsson, R.

R. Jacobsson, “Light reflection from films of continuously varying reflective index,” in Progress in Optics 5, E. Wolf, ed. (North-Holland, Amsterdam, 1966), pp. 249–286.

Jannson, J.

J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
[Crossref]

T. Jannson, J. Jannson, “High-efficiency Bragg holograms in the IR, visible, UV, and XUV spectral region,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 84–93 (1988).
[Crossref]

T. Jannson, J. Jannson, P. Yeung, “Holographic planar optical interconnect,” U.S. Patent4,838,630, June13, 1989.

Jannson, T.

R. Chen, W. Phillips, T. Jannson, D. Pelka, “Integration of holographic optical elements with polymer gelatin waveguides on GaAs, LiNbO3, glass, and aluminum,” Opt. Lett. 14, 892–894 (1989); F. Lin, E. Strzelecki, T. Jannson, “Optical multi-planar VLSI interconnects based on multiplexed waveguide holograms,” Appl. Opt. 29, 1126–1133 (1990).
[Crossref] [PubMed]

B. Moslehi, P. Harvey, J. Ng, T. Jannson, “Fiber-optic wavelength-division multiplexing and demultiplexing using volume holographic gratings,” Opt. Lett. 14, 1088–1090 (1989).
[Crossref] [PubMed]

T. Jannson, G. Savant, Y. Qiao, “Bragg holographic structures for XUV applications: a new approach,” Opt. Lett. 14, 344–346 (1989).
[Crossref] [PubMed]

J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
[Crossref]

T. Jannson, “Information capacity of Bragg holograms in planar optics,”J. Opt. Soc. Am. 71, 342–347 (1981).
[Crossref]

T. Jannson, J. Jannson, P. Yeung, “Holographic planar optical interconnect,” U.S. Patent4,838,630, June13, 1989.

G. Savant, T. Jannson, Y. Qiao, “Super-high resolution holographic materials for UV and XUV applications,” in Practical Holography, III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 148–155 (1989).
[Crossref]

G. Savant, T. Jannson, “Super-high resolution holographic composite polymer grafts for XUV applications,” in Proceedings of the Workshop on X-ray Microimaging for the Life Sciences (Lawrence Berkeley Laboratory, Berkeley, Calif., 1989), pp. 197–202.

T. Jannson, J. Jannson, “High-efficiency Bragg holograms in the IR, visible, UV, and XUV spectral region,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 84–93 (1988).
[Crossref]

Johnson, K.

K. Johnson, “Coupled scalar wave theory,” Appl. Phys. 24, 249–260 (1981).
[Crossref]

Kermisch, D.

Klein, W. R.

W. R. Klein, “Theoretical efficiency of Bragg devices,” Proc. IEEE 54, 803–804 (1966).
[Crossref]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lekner, J.

Leonard, C. D.

Lin, L.

R. Collier, C. Burckhardt, L. Lin, Optical Holography (Academic, New York, 1971).

Magarinos, J. R.

J. R. Magarinos, D. J. Coleman, “Holographic mirrors,” Opt. Eng. 24, 769–780 (1985).

Masso, J. D.

J. D. Masso, “Multilayer thin film simulation of volume holograms,” in Holographic Optics: Design and Applications, I. Cindrich, ed., roc. Soc. Photo-Opt. Instrum. Eng.883, 68–74 (1988).
[Crossref]

Moharam, M.

Moslehi, B.

Ng, J.

Pelka, D.

Phillips, W.

Qiao, Y.

T. Jannson, G. Savant, Y. Qiao, “Bragg holographic structures for XUV applications: a new approach,” Opt. Lett. 14, 344–346 (1989).
[Crossref] [PubMed]

G. Savant, T. Jannson, Y. Qiao, “Super-high resolution holographic materials for UV and XUV applications,” in Practical Holography, III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 148–155 (1989).
[Crossref]

Rigrod, W. W.

Savant, G.

T. Jannson, G. Savant, Y. Qiao, “Bragg holographic structures for XUV applications: a new approach,” Opt. Lett. 14, 344–346 (1989).
[Crossref] [PubMed]

G. Savant, T. Jannson, Y. Qiao, “Super-high resolution holographic materials for UV and XUV applications,” in Practical Holography, III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 148–155 (1989).
[Crossref]

G. Savant, T. Jannson, “Super-high resolution holographic composite polymer grafts for XUV applications,” in Proceedings of the Workshop on X-ray Microimaging for the Life Sciences (Lawrence Berkeley Laboratory, Berkeley, Calif., 1989), pp. 197–202.

Smith, S. D.

Southwell, W. H.

Summers, G. P.

Troll, M.

R. T. Ingwall, M. Troll, “The mechanism of hologram formation in DMP-129 photopolymer,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 94–101 (1988).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 87.

Yakimovich, A. P.

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 8.

Yeung, P.

T. Jannson, J. Jannson, P. Yeung, “Holographic planar optical interconnect,” U.S. Patent4,838,630, June13, 1989.

Yu, K.

J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
[Crossref]

Appl. Opt. (2)

Appl. Phys. (1)

K. Johnson, “Coupled scalar wave theory,” Appl. Phys. 24, 249–260 (1981).
[Crossref]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

J. R. Magarinos, D. J. Coleman, “Holographic mirrors,” Opt. Eng. 24, 769–780 (1985).

Opt. Lett. (4)

Opt. Spectrosc. (USSR) (1)

A. P. Yakimovich, “Multilayer three-dimensional holographic gratings,” Opt. Spectrosc. (USSR) 49, 85–88 (1980).

Proc. IEEE (1)

W. R. Klein, “Theoretical efficiency of Bragg devices,” Proc. IEEE 54, 803–804 (1966).
[Crossref]

Sol. Energy Mat. (1)

J. Jannson, T. Jannson, K. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mat. 14, 289–299 (1986).
[Crossref]

Other (12)

T. Jannson, J. Jannson, “High-efficiency Bragg holograms in the IR, visible, UV, and XUV spectral region,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 84–93 (1988).
[Crossref]

G. Savant, T. Jannson, Y. Qiao, “Super-high resolution holographic materials for UV and XUV applications,” in Practical Holography, III, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1051, 148–155 (1989).
[Crossref]

G. Savant, T. Jannson, “Super-high resolution holographic composite polymer grafts for XUV applications,” in Proceedings of the Workshop on X-ray Microimaging for the Life Sciences (Lawrence Berkeley Laboratory, Berkeley, Calif., 1989), pp. 197–202.

R. T. Ingwall, M. Troll, “The mechanism of hologram formation in DMP-129 photopolymer,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. Soc. Photo-Opt. Instrum. Eng.883, 94–101 (1988).
[Crossref]

R. Collier, C. Burckhardt, L. Lin, Optical Holography (Academic, New York, 1971).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 87.

T. Jannson, J. Jannson, P. Yeung, “Holographic planar optical interconnect,” U.S. Patent4,838,630, June13, 1989.

J. D. Masso, “Multilayer thin film simulation of volume holograms,” in Holographic Optics: Design and Applications, I. Cindrich, ed., roc. Soc. Photo-Opt. Instrum. Eng.883, 68–74 (1988).
[Crossref]

R. Jacobsson, “Light reflection from films of continuously varying reflective index,” in Progress in Optics 5, E. Wolf, ed. (North-Holland, Amsterdam, 1966), pp. 249–286.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 8.

See, for example, Ref. 15, p. 62.

See Ref. 21, p. 70.

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Figures (12)

Fig. 1
Fig. 1

Experimental bandwidth tunability of nonuniform volume holograms.

Fig. 2
Fig. 2

Bragg plane distribution: (a) uniform case, (b) nonuniform case.

Fig. 3
Fig. 3

Typical refractive-index profile for nonuniform hologram with chirp normal to the surface.

Fig. 4
Fig. 4

Typical multilayer structure.

Fig. 5
Fig. 5

Comparison between simulations using our method (solid curves) and the matrix method (dashed curves) for 40 grating layers per sample in the matrix method; n = 1.56, Δn = 0.1. For the uniform cases (a), (b), and (c) M = 1, 2, and 10, respectively, and λB = 0.53 μm. For the nonuniform case (d), M = 10, with the λB range from 0.53 and 0.5462 μm and a linear increment of 0.0018 μm.

Fig. 6
Fig. 6

Bandwidth comparison between nonuniform and uniform holograms for Δn = 0.1 and n = 1.56, T = 18 μm: (a) Bragg wavelength distribution for nonuniform case. (b) Uniform case (dashed curve), where λB = 0.53 μm; nonuniform case (solid curve), where the Bragg wavelength range is 0.49–0.6682 μm and the linear increment is 0.0018 μm.

Fig. 7
Fig. 7

Bandwidth comparison between nonuniform and uniform holograms for smaller value of Δn = 0.025, n = 1.56: short-dashed curve, uniform hologram with λB = 0.53 μm; solid curve, nonuniform hologram with a Bragg wavelength range of 0.51–0.598 μm and a linear increment of 0.0018 μm, T = 8.8 μm, 50 grating layers; long-dashed curve, nonuniform hologram with a Bragg wavelength range of 0.51–0.598 μm and a linear increment of 0.00119 μm, T = 13.3 μm.

Fig. 8
Fig. 8

Reflectance for a uniform hologram (ΔΛ/Λ = 0) for λB = 900 nm, n = 1.55, T =20 μm: (a) Δn = 0.01, (b) Δn = 0.05, (c) Δn = 0.1, (d) Δn = 0.2.

Fig. 9
Fig. 9

Reflectance for a nonuniform hologram (ΔΛ/Λ = 0.05) and remaining parameters as in Fig. 8.

Fig. 10
Fig. 10

Reflectance for a nonuniform hologram (ΔΛ/Λ = 0.1) and remaining parameters as in Fig. 8.

Fig. 11
Fig. 11

Reflectance for a nonuniform hologram (ΔΛ/Λ = 0.2) and remaining parameters as in Fig. 8.

Fig. 12
Fig. 12

(a) Multiple spectral windows for a sandwiched hologram with Bragg wavelength distribution as in (b): n = 1.56, Δn = 0.1, T = 88 μm, 369 grating layers.

Equations (20)

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M = 2 n ¯ T / λ B ,
Λ = Λ ( z ) .
n ( z ) = n ¯ + ( Δ n ) cos [ 2 π ( z - z p ) / Λ p ] ,             0 z p T ,             z p z z p + 1 = z p + Λ p ,             p = 1 , 2 , , m ,
r = - j ν 0 j ξ 0 + ( ν 0 2 - ξ 0 2 ) 1 / 2 coth ( ν 0 2 - ξ 0 2 ) 1 / 2 ,
t = [ ( ν 0 2 - ξ 0 2 ) 1 / 2 / sinh ( ν 0 2 - ξ 0 ) 1 / 2 ] exp ( j ξ 0 ) j ξ 0 + ( ν 0 2 - ξ 0 2 ) 1 / 2 coth ( ν 0 2 - ξ 0 2 ) 1 / 2 exp ( - j Ψ hol ) ,
ξ 0 = 2 π n ¯ h [ cos θ h λ - 1 λ B ( 0 ) ]
λ = λ B ( 0 ) cos θ h ,
ν 0 = π Δ n h λ cos θ h .
Q = 2 π h λ B ( 0 ) n ¯ Λ 2 ,
r L p = r p , p + 1 ,             t L p = t p , p + 1 ,
r L p - 1 = r p - 1 , p + [ t p - 1 , p exp ( - j ϕ p ) ] [ r p , p + 1 exp ( - j ϕ p ) ] t p , p - 1 1 - r p , p - 1 r p , p + 1 exp ( - 2 j ϕ p )
t L p - 1 = [ t p - 1 , p exp ( - j ϕ p ) ] t p , p + 1 1 - r p , p - 1 r p , p + 1 exp ( - 2 j ϕ p ) ,
ϕ p = 2 π n p d p cos θ p λ .
r L s = r s , s + 1 + [ t s , s + 1 exp ( - j ϕ s + 1 ) ] [ r L s + 1 exp ( - j ϕ s + 1 ) ] t s + 1 , s 1 - r s + 1 , s r L s + 1 exp ( - 2 j ϕ s + 1 )
t L s = [ t s , s + 1 exp ( - j ϕ s + 1 ) ] t L s + 1 1 - r s + 1 , s r L s + 1 exp ( - 2 j ϕ s + 1 ) ,             s = 1 , 2 , , ( p - 1 ) ,
ϕ s + 1 = 2 π n s + 1 d s + 1 cos ( θ s + 1 ) λ air ,             s = 1 , 2 , , ( p - 1 ) .
R total = reflectance = r L 1 2
T total = transmittance = n p + 1 cos ( θ p + 1 ) n 1 cos ( θ 1 ) t L 1 2 .
C = Δ Λ Λ ¯ = Δ λ B λ ¯ B
C M = Δ Λ M Λ ¯ = Δ λ B M λ ¯ B = Δ Λ T ,

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