Abstract

We model the grating-formation process in bacteriorhodopsin films for the interference of two plane waves. We simulate the temporal dependence of grating recording and readout, and we examine the behavior of the diffraction efficiency with respect to exposure, write and read wavelengths, and film parameters such as initial optical density and lifetime of the upper state. Gratings written in thick bacteriorhodopsin films are generally nonuniform and nonsinusoidal owing to the absorption and saturation properties of the material. The simulations also show that one can often obtain optimization of hologram recording and readout by writing and reading at wavelengths far off the peak of the ground-state absorbance spectrum, especially for films with high values of the peak optical density.

© 1998 Optical Society of America

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References

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  1. T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
    [CrossRef]
  2. N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant Asp96 → Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
    [CrossRef] [PubMed]
  3. J. D. Downie, “Real-time holographic image correction using bacteriorhodopsin,” Appl. Opt. 33, 4353–4357 (1994).
    [CrossRef] [PubMed]
  4. J. D. Downie, D. T. Smithey, “Measurements of holographic properties of bacteriorhodopsin films,” Appl. Opt. 35, 5780–5789 (1996).
    [CrossRef] [PubMed]
  5. N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
    [CrossRef]
  6. R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
    [CrossRef] [PubMed]
  7. Q. W. Song, C. Zhang, R. Blumer, R. B. Gross, Z. Chen, R. R. Birge, “Chemically enhanced bacteriorhodopsin thin-film spatial light modulator,” Opt. Lett. 18, 1373–1375 (1993).
    [CrossRef] [PubMed]
  8. D. Kermisch, “Efficiency of photochromic gratings,” J. Opt. Soc. Am. 61, 1202–1206 (1971).
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  9. W. J. Tomlinson, “Volume holograms in photochromic materials,” Appl. Opt. 14, 2456–2467 (1975).
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    [CrossRef]
  11. D. A. Timuçin, J. D. Downie, “Phenomenological theory of photochromic media: optical data storage and processing with bacteriorhodopsin films,” J. Opt. Soc. Am. A 14, 3285–3299 (1997).
    [CrossRef]
  12. R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
    [CrossRef]
  13. C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
    [CrossRef]
  14. A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
    [CrossRef]
  15. H. Kogelnik, “Coupled wave theory of thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  16. D. Kermisch, “Nonuniform sinusoidally modulated dielectric gratings,” J. Opt. Soc. Am. 59, 1409–1414 (1969).
    [CrossRef]
  17. N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
    [CrossRef] [PubMed]

1997 (1)

1996 (1)

1994 (1)

1993 (2)

1992 (2)

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant Asp96 → Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

1991 (2)

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

1990 (3)

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
[CrossRef]

N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
[CrossRef] [PubMed]

1975 (1)

1973 (1)

1971 (1)

1969 (2)

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

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

Birge, R. R.

Blumer, R.

Brauchle, C.

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
[CrossRef] [PubMed]

Bräuchle, C.

Chen, Z.

Downie, J. D.

Gross, R. B.

Hampp, N.

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant Asp96 → Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
[CrossRef] [PubMed]

Kermisch, D.

Kogelnik, H.

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

Miller, A.

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

Ninomiya, Y.

Oesterhelt, D.

N. Hampp, R. Thoma, D. Oesterhelt, C. Bräuchle, “Biological photochrome bacteriorhodopsin and its genetic variant Asp96 → Asn as media for optical pattern recognition,” Appl. Opt. 31, 1834–1841 (1992).
[CrossRef] [PubMed]

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

R. Thoma, N. Hampp, C. Bräuchle, D. Oesterhelt, “Bacteriorhodopsin films as spatial light modulators for nonlinear-optical filtering,” Opt. Lett. 16, 651–653 (1991).
[CrossRef] [PubMed]

N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
[CrossRef] [PubMed]

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

Popp, A.

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

Renner, T.

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

Smithey, D. T.

Song, Q. W.

Thoma, R.

Timuçin, D. A.

Tomlinson, W. J.

Zhang, C.

Adv. Mater. (1)

C. Bräuchle, N. Hampp, D. Oesterhelt, “Optical applications of bacteriorhodopsin and its mutated variants,” Adv. Mater. 3, 420–428 (1991).
[CrossRef]

Ann. Rev. Phys. Chem. (1)

R. R. Birge, “Photophysics and molecular electronic applications of the rhodopsins,” Ann. Rev. Phys. Chem. 41, 683–733 (1990).
[CrossRef]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

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

Biochim. Biophys. Acta (1)

A. Miller, D. Oesterhelt, “Kinetic optimization of bacteriorhodopsin by aspartic acid 96 as an internal proton donor,” Biochim. Biophys. Acta 1020, 57–64 (1990).
[CrossRef]

Biophys. J. (1)

N. Hampp, C. Brauchle, D. Oesterhelt, “Bacteriorhodopsin wildtype and variant aspartate-96 → asparagine as reversible holographic media,” Biophys. J. 58, 83–93 (1990).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (3)

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

J. Phys. Chem. (1)

N. Hampp, A. Popp, C. Brauchle, D. Oesterhelt, “Diffraction efficiency of bacteriorhodopsin films for holography containing bacteriorhodopsin wildtype BRWT and its variants BRD85E and BRD96N,” J. Phys. Chem. 96, 4679–4685 (1992).
[CrossRef]

Opt. Commun. (1)

T. Renner, N. Hampp, “Bacteriorhodopsin-films for dynamic time average interferometry,” Opt. Commun. 96, 142–149 (1993).
[CrossRef]

Opt. Lett. (2)

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Figures (13)

Fig. 1
Fig. 1

Schematic of the BR photocycle. The numbers in parentheses indicate the peak wavelength of the absorption spectrum at the bR and intermediate states.

Fig. 2
Fig. 2

Simple two-state model of the BR photocycle. The solid arrows represent transitions induced by the absorption of a photon, and the dashed arrow represents a thermal transition from the M state back down to the bR state.

Fig. 3
Fig. 3

Schematic of the optical setup for simulated holography measurements of BR films.

Fig. 4
Fig. 4

Absorption spectra for the bR and M states of a D96N film.

Fig. 5
Fig. 5

Diffraction efficiency as a function of the exposure time for a D96N film. The wavelength of the write beams is 514 nm, the wavelength of the read beam is 633 nm, the average intensity of the write beams is 84 mW/cm2, and the contrast of the write beams is 1. The solid curve represents the simulation results, and the discrete data points are experimental values.

Fig. 6
Fig. 6

Time evolution of absorption coefficients α0 and α1 at two different depths (solid curves, 10 μm; dashed curves, 100 μm) within the BR film for the read wavelength of 633 nm. The total film thickness is 100 μm. The film and system parameters are the same as for Fig. 5.

Fig. 7
Fig. 7

Spatial profile in the x dimension of N B /N 0 for two different depths within the BR film at the time of peak diffraction efficiency (t ∼ 0.3 s) in Fig. 5.

Fig. 8
Fig. 8

Diffraction efficiency versus the exposure time for different write wavelengths. The average write intensity is 56 mW/cm2. The read wavelength is 633 nm.

Fig. 9
Fig. 9

Maximum diffraction efficiency versus the peak absorbance value (optical density) of the bR state. The read wavelength is 633 nm.

Fig. 10
Fig. 10

Maximum diffraction efficiency versus the read wavelength. The discrete points are the results of simulations by use of the grating-formation model. The write wavelength is 568 nm with an intensity of 100 mW/cm2. The solid curve represents an assumed uniform sinusoidal grating with α0 = 0.5*(α B + α M ) and α1 = 0.5*(α B - α M ).

Fig. 11
Fig. 11

Time evolution of absorption coefficients α0 and α1 for the read wavelength at two different depths (solid curves, 10 μm; dashed curves, 100 μm) within the BR film. The total film thickness is 100 μm. The write and read wavelengths are both 568 nm.

Fig. 12
Fig. 12

Dependence of the hologram decay behavior on the intensity of the read beam. The write beams at 568 nm are turned off at t = 0.5 s, and the read beam at 633 nm is turned on at t = 0.5 s. Strong read-beam intensities wash the grating out quickly.

Fig. 13
Fig. 13

Dependence of the hologram decay behavior on the wavelength of the read beam. The write beams at 568 nm are turned off at t = 0.5 s, and the read beam is turned on at t = 0.5 s. The intensity of the read beam equals 10 mW/cm2 for each read-beam wavelength.

Equations (27)

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d N B d t = - ρ B λ N B + ρ M λ N M + γ M N M ,
N B + N M = N 0 ,
d N B / N 0 d t = - ρ B λ + ρ M λ + γ M N B / N 0 + ρ M λ + γ m ,
ρ i = ln 10 i λ Φ i λ I t ,   λ N A c 0 h ,
Δ n λ = n M λ - n B λ = ln 10 2 π 2 D P . V . 0 A M λ - A B λ 1 - λ / λ 2 d λ ,
ψ λ = 2 π Δ n λ λ Δ α λ ,
Δ α λ = α M λ - α B λ = ln 10 D A M λ - A B λ .
E x ,   z ,   t = S z ,   t exp ik 0 n 0 x   sin θ w + z   cos θ w + R z ,   t exp ik 0 n 0 - x   sin θ w + z   cos θ w ,
α j x = α 0 j + α 1 j cos Kx + ϕ j , n j x = n 0 j + n 1 j cos Kx + ϕ j ,
S j R j = T j S j - 1 R j - 1 .
T 11 j = exp - α 0 j Δ z 2   cos θ w cos κ j Δ z cos θ w , T 22 j = T 11 j , T 12 j = - i   exp i ϕ j exp - α 0 j Δ z 2   cos θ w sin κ j Δ z cos θ w , T 21 j = - i   exp - i ϕ j exp - α 0 j Δ z 2   cos θ w sin κ j Δ z cos θ w ,
κ j = ψ λ w - i 2 α 1 j 2 ,
S refl z = D = r Fresnel S z = D , R refl z = D = r Fresnel R z = D ,
I x ,   z j ,   t m = | E total x ,   z j ,   t m | 2 n 0 2 η 0 ,
E x ,   z j ,   t m = S z j ,   t m exp ik 0 n 0 x   sin θ w + z   cos θ w + R z j ,   t m exp ik 0 n 0 - x   sin θ w + z   cos θ w + S refl z j ,   t m exp ik 0 n 0 x   sin θ w - z   cos θ w + R refl z j ,   t m exp ik 0 n 0 - x   sin θ w - z   cos θ w .  
ρ i x ,   z j ,   t m = ln 10 i λ w Φ i λ w I x ,   z j ,   t m N A c 0 h ,   i = B ,   M ,
N B N 0 x ,   z j ,   t m = N B N 0 x ,   z j ,   t m - 1 + Δ t - ρ B x ,   z j ,   t m + ρ M x ,   z j ,   t m + γ M N B N 0 x ,   z j ,   t m - 1 + ρ M x ,   z j ,   t m + γ M .
α x ,   z j ,   t m ,   λ w = ln 10 D N B N 0 x ,   z j ,   t m A B λ w - A M λ w + A M λ w .
α x ,   z j ,   t m ,   λ w = α 0 z j ,   t m ,   λ w + p = 1   α p z j ,   t m ,   λ w × cos pKx + ϕ p z j ,   t m .
α 0 z j ,   t m ,   λ w = K 2 π 0 2 π / K   α x ,   z j ,   t m ,   λ w d x
c 1 = K π 0 2 π / K   α x ,   z j ,   t m ,   λ w cos Kx d x ,
c 2 = K π 0 2 π / K   α x ,   z j ,   t m ,   λ w sin Kx d x ,
ϕ 1 z j ,   t m = tan - 1 - c 2 / c 1 ,
α 1 z j ,   t m ,   λ w = c 1 2 + c 2 2 1 / 2 .
n 1 λ w = ψ λ w λ w α 1 λ w 2 π .
η = exp - α 0 D cos   θ r sin 2 π n 1 D λ   cos   θ r + sinh 2 α 1 D 4   cos   θ r .
i λ = A i λ A B λ = 568   nm × 63 , 000   liters mole   ×   cm , i = B ,   M .

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