Abstract

Diffraction of monochromatic light on a grating leads to the attenuation of the transmitted beam of diffraction order zero. In the case of a thick grating the diffraction efficiency, and hence the effective attenuation coefficient, is a fast-varying function of the Bragg mismatch angle. According to Kramers–Kronig theory, the transmitted beam encounters a phase shift that also depends on the mismatch angle. This phase shift is measured for holographic gratings in a photoaddressable block copolymer and compared with analytical calculations.

© 2004 Optical Society of America

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References

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  1. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
    [CrossRef]
  2. G. Montemezzani and M. Zgonik, Phys. Rev. E 55, 1035 (1997).
    [CrossRef]
  3. H. I. Bjelkhagen and H. J. Caulfield, eds., Selected Papers on Fundamental Techniques in Holography, Vol. 171 of SPIE Milestone Series (SPIE, Bellingham, Wash., 2001).
  4. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  5. L. Kador, Appl. Phys. Lett. 66, 2938 (1995).
    [CrossRef]
  6. L. Kador, Mol. Cryst. Liq. Cryst. 283, 179 (1996).
    [CrossRef]
  7. C. Frenz, “Diblockcopolymere mit photoadressierbaren Chromophoren zur holographischen Datenspeicherung,” Ph.D. dissertation (University of Bayreuth, Bayreuth, Germany, 2003).
  8. T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
    [CrossRef]
  9. A. Natansohn, Azobenzene-Containing Materials, Vol. 137 of Macromolecular Symposia (Wiley, New York, 1999).

1997 (1)

G. Montemezzani and M. Zgonik, Phys. Rev. E 55, 1035 (1997).
[CrossRef]

1996 (1)

L. Kador, Mol. Cryst. Liq. Cryst. 283, 179 (1996).
[CrossRef]

1995 (2)

T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
[CrossRef]

L. Kador, Appl. Phys. Lett. 66, 2938 (1995).
[CrossRef]

1992 (1)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Bieringer, T.

T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
[CrossRef]

DeSalvo, R.

Frenz, C.

C. Frenz, “Diblockcopolymere mit photoadressierbaren Chromophoren zur holographischen Datenspeicherung,” Ph.D. dissertation (University of Bayreuth, Bayreuth, Germany, 2003).

Haarer, D.

T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
[CrossRef]

Hagan, D. J.

Kador, L.

L. Kador, Mol. Cryst. Liq. Cryst. 283, 179 (1996).
[CrossRef]

L. Kador, Appl. Phys. Lett. 66, 2938 (1995).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Montemezzani, G.

G. Montemezzani and M. Zgonik, Phys. Rev. E 55, 1035 (1997).
[CrossRef]

Natansohn, A.

A. Natansohn, Azobenzene-Containing Materials, Vol. 137 of Macromolecular Symposia (Wiley, New York, 1999).

Sheik-Bahae, M.

Stegeman, G.

Van Stryland, E. W.

Vanherzeele, H.

Wuttke, R.

T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
[CrossRef]

Zgonik, M.

G. Montemezzani and M. Zgonik, Phys. Rev. E 55, 1035 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

L. Kador, Appl. Phys. Lett. 66, 2938 (1995).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
[CrossRef]

Macromol. Chem. Phys. (1)

T. Bieringer, R. Wuttke, and D. Haarer, Macromol. Chem. Phys. 196, 1375 (1995).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

L. Kador, Mol. Cryst. Liq. Cryst. 283, 179 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

G. Montemezzani and M. Zgonik, Phys. Rev. E 55, 1035 (1997).
[CrossRef]

Other (3)

H. I. Bjelkhagen and H. J. Caulfield, eds., Selected Papers on Fundamental Techniques in Holography, Vol. 171 of SPIE Milestone Series (SPIE, Bellingham, Wash., 2001).

C. Frenz, “Diblockcopolymere mit photoadressierbaren Chromophoren zur holographischen Datenspeicherung,” Ph.D. dissertation (University of Bayreuth, Bayreuth, Germany, 2003).

A. Natansohn, Azobenzene-Containing Materials, Vol. 137 of Macromolecular Symposia (Wiley, New York, 1999).

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Figures (2)

Fig. 1
Fig. 1

Interferometer for measuring the phase shift of the zero-order beam.

Fig. 2
Fig. 2

(a) Phase shift of the transmitted light and (b) diffraction efficiency as a function of the Bragg mismatch angle outside the sample [arcsinn0 sin Δθ] for three different holographic gratings.

Equations (13)

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η=sinν2+ξ21/221+ξ2/ν2,
ν=πdn1λcS cosθ0+Δθ1/2,
ξ=πdΔθ sinψ-θ0ΛcS,
cS=cosθ0+Δθ-λ cos ψn0Λ.
η=ν2sin2 ξξ2.
Φ˜ξ=ϕξ-iδξ,
Et=E0texp-iΦ˜ξ.
δξ=-ln1-ηξ1/2,
δξ=12ηξ.
δξ=ν22sin2 ξξ2.
ϕξ=ν22ξsin2ξ2ξ-1,
Φ˜ξ=-iν22iξ2exp-2iξ+2iξ-1.
ϕmax=±ηmaxπ.

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