Abstract

A new type of reflective hologram with both high angular and spectral selectivity is suggested. With novel design of crossed gratings inside the volume hologram, unusual angular selectivity is achieved via coupling of four waves. Analytic solution with spectral and angular detuning from Bragg regime is derived. The compensation between these two detuning forms an interesting figure of saddle shape.

© 2006 Optical Society of America

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References

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  1. O.M. Efimov, L.B. Glebov, L.N. Glebova, K.C. Richardson, and V.I. Smirnov, "High-Efficiency Bragg Gratings in Photothermorefractive Glass," Appl. Opt. 38, 619-627 (1999).
  2. L.B. Glebov, V.I. Smirnov, C.M. Stickley, I.V. Ciapurin, "New approach to robust optics for HEL systems", In Laser Weapons Technology III, W.E. Thompson and P.H. Merritt, eds., Proc. SPIE, 4724, 101-109 (2002).
  3. L.B. Glebov, "Volume hologram recording in inorganic glasses," Glass Science and Technology 75C1, 73-90 (2002).
  4. D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
    [CrossRef]
  5. C.-C. Tsai, L. B. Glebov, B. Ya. Zeldovich, "Adiabatic three-wave volume hologram: large efficiency independent on grating strength and polarization", Opt. Lett. 31, 718-720 (2006)
    [CrossRef] [PubMed]
  6. J. Zhao, Pochi Yeh, M. Khoshnevisan, and I. McMichael, "Diffraction properties of vector synthetic volume index gratings", J. Opt. Soc. Am. B 17, 898-903 (2000).
    [CrossRef]
  7. R. Alferness, S.K. Case, " Coupling in doubly exposed, thick holographic gratings", J. Opt. Soc. Am., 65, 730-739 (1975)
    [CrossRef]
  8. H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings", Bell Syst. Tech. J., 48, 2909 (1969)
  9. S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
    [CrossRef]
  10. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981)
    [CrossRef]

2006 (1)

2002 (1)

L.B. Glebov, "Volume hologram recording in inorganic glasses," Glass Science and Technology 75C1, 73-90 (2002).

2001 (1)

D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
[CrossRef]

2000 (1)

1981 (1)

1975 (2)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
[CrossRef]

R. Alferness, S.K. Case, " Coupling in doubly exposed, thick holographic gratings", J. Opt. Soc. Am., 65, 730-739 (1975)
[CrossRef]

1969 (1)

H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings", Bell Syst. Tech. J., 48, 2909 (1969)

Alferness, R.

Bertoni, H. L.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
[CrossRef]

Case, S.K.

Dunn, S.C.

D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
[CrossRef]

Gaylord, T. K.

Glebov, L. B.

Glebov, L.B.

L.B. Glebov, "Volume hologram recording in inorganic glasses," Glass Science and Technology 75C1, 73-90 (2002).

Jacob, D.K.

D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
[CrossRef]

Kogelnik, H.

H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings", Bell Syst. Tech. J., 48, 2909 (1969)

Moharam, M. G.

D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981)
[CrossRef]

Peng, S. T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
[CrossRef]

Pochi Yeh, J.

Tamir, T.

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
[CrossRef]

Tsai, C.-C.

Zeldovich, B. Ya.

Zhao, J.

Bell Syst. Tech. J. (1)

H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings", Bell Syst. Tech. J., 48, 2909 (1969)

Glass Science and Technology (1)

L.B. Glebov, "Volume hologram recording in inorganic glasses," Glass Science and Technology 75C1, 73-90 (2002).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

D.K. Jacob, S.C. Dunn, M. G. Moharam, "Normally incident resonant grating reflection filters for efficient narrow-band spectral filtering of finite beams", J. Opt. Soc. Am. B 18, 2109-2120 (2001).
[CrossRef]

J. Zhao, Pochi Yeh, M. Khoshnevisan, and I. McMichael, "Diffraction properties of vector synthetic volume index gratings", J. Opt. Soc. Am. B 17, 898-903 (2000).
[CrossRef]

MTT (1)

S. T. Peng, T. Tamir, and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., MTT- 23, 123-133 (1975).
[CrossRef]

Opt. Lett. (1)

Other (2)

O.M. Efimov, L.B. Glebov, L.N. Glebova, K.C. Richardson, and V.I. Smirnov, "High-Efficiency Bragg Gratings in Photothermorefractive Glass," Appl. Opt. 38, 619-627 (1999).

L.B. Glebov, V.I. Smirnov, C.M. Stickley, I.V. Ciapurin, "New approach to robust optics for HEL systems", In Laser Weapons Technology III, W.E. Thompson and P.H. Merritt, eds., Proc. SPIE, 4724, 101-109 (2002).

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Figures (2)

Fig. 1.
Fig. 1.

(a). Two crossed-gratings are to be recorded throughout the whole PTR glass. (b) Propagation of waves in two-crossed-grating hologram, where four waves arise and couple to each other. They are A +, A -, B +, B -, respectively, and A + is the incident wave.

Fig. 2.
Fig. 2.

The reflection efficiency η for conventional reflection hologram with thickness L=2.5·10-3 m and for our crossed hologram with thickness L=1·10-3 m, for wavelength λ vac=1.06·10-6 m, refraction index n 0=1.5, amplitude absorption β=10 m -1, and the grating amplitude κ varies from 0 to 1000 m -1 at normal incidence. (a) Conventional reflection hologram, thickness L=2.5·10-3 m, with no angular detuning, Δθ=0, Δλ from -3.58·10-10 m to 3.58·10-10 m, Δλ HWHM=1.48·10-10 m (b) Our crossed hologram, thickness L=10-3 m, with other parameters same as (a), Δλ HWHM=2.34·10-10 m; (c) Reflection hologram, thickness L=2.5·10-3 m, with no spectral detuning Δλ=0, the angular detuning Δθ air from -3° to 3°, ΔθHWHM=1.44° (d) Our crossed hologram, thickness L=2.5·10-3 m, the angular detuning Δθair from -0.03° to 0.03°, ΔθHWHM=0.0028°; (e) The compensation between spectral detuning and angular detuning for reflection hologram with thickness L=2·10-3 m, Δλ from -3.58·10-10 m to 3.58·10-10 m and Δθair from -3° to 3° (f) The compensation for our crossed hologram with parameters same as (e) except that Δθair is from -0.03° to 0.03°.

Equations (12)

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n ( r ) = n background + c [ I 1 ( r ) + I 2 ( r ) ] = n 0 + μ 1 cos ( Q 1 · r + φ 1 ) + μ 2 cos ( Q 2 · r + φ 2 )
2 E + ω 2 c 2 [ n 0 2 + n 0 ( μ 1 e i Q 1 · r + μ 1 * e i Q 1 · r + μ 2 e i Q 2 · r + μ 2 * e i Q 2 · r ) ] E = 0 .
E = A + exp [ i ω c n 0 k A · r ] + A exp [ i ω c n 0 k A · r ] + B + exp [ i ω c n 0 k B · r ] + B exp [ i ω c n 0 k B · r ]
A + z = i κ 1 B + + i κ 2 B + ( i γ β ) A + , A z = i κ 2 * B + i κ 1 * B ( i γ β ) A ,
B + x = i κ 1 * A + + i κ 2 A + ( i γ β ) B + , B x = i κ 2 * A + i κ 1 A ( i γ β ) B .
B + = i κ 1 * i q i γ + β A + + i κ 2 i q i γ + β A , B = i κ 2 * i q + i γ β A + i κ 1 i q + i γ β A
A + z = P A + + Q A , A z = Q A + P A
Q = i κ 2 [ ( 1 q γ i β ) ( 1 q + γ + i β ) ] , P = β + i γ + Q .
[ A + ( z ) A ( z ) ] = exp ( M ̂ z ) [ A + ( 0 ) A ( 0 ) ] .
exp ( M ̂ z ) = [ P sinh ( ρ z ) ρ + cosh ( ρ z ) Q sinh ( ρ z ) ρ Q sinh ( ρ z ) ρ P sinh ( ρ z ) ρ + cosh ( ρ z ) ]
η ref = A ( 0 ) A + ( 0 ) 2 = Q sinh ( ρ L ) P sinh ( ρ L ) + ρ cosh ( ρ L ) 2
η tran = A + ( L ) A + ( 0 ) 2 = P ρ sinh ( ρ L ) + cosh ( ρ L ) Q 2 sinh 2 ( ρ L ) ρ P sinh ( ρ L ) + ρ 2 cosh ( ρ L ) 2

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