Abstract

The diffraction effects induced by a thick holographic grating on the propagation of a finite Gaussian beam are theoretically analyzed by means of the coupled-wave theory and the beam propagation method. Distortion of the transmitted and diffracted beams is simulated as a function of the grating parameters. Theoretical results are verified by experimentation realized by use of LiNbO3 volume gratings read out by a 1550-nm Gaussian beam, typical of optical fiber communications. This analysis can be implemented as a useful tool to aid with the design of volume grating-based devices employed in optical communications.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Rakuljic, V. Leyva, “Volume holographic narrow-band optical filter,” Opt. Lett. 18, 459–461 (1993).
    [CrossRef] [PubMed]
  2. S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
    [CrossRef]
  3. P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
    [CrossRef]
  4. H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  5. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Bragg diffraction of finite beams by thick gratings,” J. Opt. Soc. Am. 70, 300–304 (1980).
    [CrossRef]
  6. R. S. Chu, J. A. Kong, T. Tamir, “Diffraction of Gaussian beams by a periodically modulated layer,” J. Opt. Soc. Am. 67, 1555–1561 (1977).
    [CrossRef]
  7. R.-S. Chu, T. Tamir, “Bragg diffraction of Gaussian beams by periodically modulated media,” J. Opt. Soc. Am. 66, 220–226 (1976).
    [CrossRef]
  8. M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999).
    [CrossRef]
  9. M. R. Wang, “Analysis and observation of finite beam Bragg diffraction by a thick planar phase grating,” Appl. Opt. 35, 582–592 (1996).
    [CrossRef] [PubMed]
  10. D. Yevick, L. Thylén, “Analysis of gratings by the beam-propagation method,” J. Opt. Soc. Am. 72, 1084–1089 (1982).
    [CrossRef]
  11. A. E. Siegman, “Bragg diffraction of a Gaussian beam by a crossed-Gaussian volume grating,” J. Opt. Soc. Am. 67, 545–550 (1977).
    [CrossRef]
  12. I. Ilic, R. Scarmozzino, R. M. Osgood, “Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996).
    [CrossRef]
  13. S. Ahmed, E. N. Glytsis, “Comparison of beam propagation method and rigorous coupled-wave analysis for single and multiplexed volume gratings,” Appl. Opt. 35, 4426–4435 (1996).
    [CrossRef] [PubMed]
  14. M. R. B. Forshaw, “Diffraction of a narrow laser beam by a thick hologram: experimental results,” Opt. Commun. 12, 279–281 (1974).
    [CrossRef]

2000 (1)

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

1999 (1)

M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999).
[CrossRef]

1998 (1)

S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

1996 (3)

1993 (1)

1982 (1)

1980 (1)

1977 (2)

1976 (1)

1974 (1)

M. R. B. Forshaw, “Diffraction of a narrow laser beam by a thick hologram: experimental results,” Opt. Commun. 12, 279–281 (1974).
[CrossRef]

1969 (1)

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

Ahmed, S.

Boffi, P.

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

Breer, S.

S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

Buse, K.

S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

Chatterjee, M. R.

M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999).
[CrossRef]

Chu, R. S.

Chu, R.-S.

Forshaw, M. R. B.

M. R. B. Forshaw, “Diffraction of a narrow laser beam by a thick hologram: experimental results,” Opt. Commun. 12, 279–281 (1974).
[CrossRef]

Frascolla, C.

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Ilic, I.

I. Ilic, R. Scarmozzino, R. M. Osgood, “Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996).
[CrossRef]

Kogelnik, H.

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

Kong, J. A.

Leyva, V.

Magnusson, R.

Martinelli, M.

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

Moharam, M. G.

Osgood, R. M.

I. Ilic, R. Scarmozzino, R. M. Osgood, “Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996).
[CrossRef]

Piccinin, D.

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

Rakuljic, G. A.

Reagan, D. D.

M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999).
[CrossRef]

Scarmozzino, R.

I. Ilic, R. Scarmozzino, R. M. Osgood, “Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996).
[CrossRef]

Siegman, A. E.

Tamir, T.

Thylén, L.

Ubaldi, M. C.

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

Wang, M. R.

Yevick, D.

Appl. Opt. (2)

Appl. Phys. B (1)

S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
[CrossRef]

Bell Syst. Tech. J. (1)

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

IEEE Photon. Technol. Lett. (1)

P. Boffi, M. C. Ubaldi, D. Piccinin, C. Frascolla, M. Martinelli, “1550-nm volume holography for optical communication devices,” IEEE Photon. Technol. Lett. 12, 1355–1357 (2000).
[CrossRef]

J. Lightwave Technol. (1)

I. Ilic, R. Scarmozzino, R. M. Osgood, “Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits,” J. Lightwave Technol. 14, 2813–2822 (1996).
[CrossRef]

J. Opt. Soc. Am. (5)

Opt. Commun. (1)

M. R. B. Forshaw, “Diffraction of a narrow laser beam by a thick hologram: experimental results,” Opt. Commun. 12, 279–281 (1974).
[CrossRef]

Opt. Eng. (1)

M. R. Chatterjee, D. D. Reagan, “Examination of beam propagation in misaligned holographic gratings and comparison with the acousto-optic transfer function model for profiled beams,” Opt. Eng. 38, 1113–1121 (1999).
[CrossRef]

Opt. Lett. (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Model of a thick grating with unslanted fringes in the Bragg diffraction regime. θ B is the Bragg angle of incidence of the reading beam in the medium defined by 2Λ sin θ B = λ.

Fig. 2
Fig. 2

Comparison of the (a) R-beam profiles and (b) S-beam profiles in the near field. The results were obtained by CWA and the BPM. The following parameters were used: n 1 = 5 × 10-3, ω0 = 9.21 μm, d = 71.45 μm, BPM distance of observation d obs = 120 μm, and BPM z axis computed step Δz = 0.04 μm. Hence, the geometry and grating strength parameters are g = 3.0 and γ = π/4.

Fig. 3
Fig. 3

Same as Fig. 2 except that the following parameters were used: n 1 = 6.7 × 10-5, ω0 = 50 μm, d = 581.5 μm, BPM distance of observation d obs = 1200 μm, and BPM z axis computed step Δz = 0.3 μm. The geometry and grating strength parameters are g = 4.5 and γ = 0.0858.

Fig. 4
Fig. 4

Same as Fig. 2 except that the following parameters were used: n 1 = 1 × 10-2, ω0 = 38.7 μm, d = 300 μm, BPM distance of observation d obs = 550 μm, and BPM z axis computed step Δz = 0.3 μm. The geometry and grating strength parameters are g = 3 and γ = 2, 1π.

Fig. 5
Fig. 5

Three-dimensional plot of the near-field diffracted S-beam profile for a Gaussian wave input as a function of gamma (0;5π) and s0 (-2;8) with a fixed g value of 3. The normalized intensity is plotted on the vertical axis.

Fig. 6
Fig. 6

Three-dimensional plot of the near-field diffracted S-beam profile for a Gaussian wave input as a function of g (0;6) and s0 (-2;12) with a fixed γ value of 9π/4. The normalized intensity is plotted on the vertical axis.

Fig. 8
Fig. 8

Three-dimensional plot of the near-field transmitted R-beam profile for a Gaussian wave input as a function of g (0,6) and r0 (-2,12) with a fixed γ value of 9π/4. The normalized intensity is plotted on the vertical axis.

Fig. 7
Fig. 7

Three-dimensional plot of the transmitted R-beam profile for a Gaussian wave input as a function of γ (0; 5π) and r0 (-2; 8) with a fixed g value of 3. The normalized intensity is plotted on the vertical axis.

Fig. 9
Fig. 9

Three-dimensional plot of the diffraction efficiency of a Gaussian wave as a function of g (0,6) and γ (0,5π).

Fig. 10
Fig. 10

Experimental setup of the grating recording.

Fig. 11
Fig. 11

Experimental setup for the grating analysis.

Fig. 12
Fig. 12

Comparison of the CWA simulated S-beam intensity profile with the experimental S-beam intensity profile for g ≅ 6 and γ ≅ 2.1π in (a) the near field and (b) the far field.

Fig. 13
Fig. 13

Comparison of the CWA simulated R-beam intensity profile with the experimental R-beam intensity profile for g ≅ 6 and γ ≅ 2.1π in (a) the near field and (b) the far field.

Fig. 14
Fig. 14

Comparison of the CWA simulated S-beam intensity profile with the experimental S-beam intensity profile for g ≅ 2 and γ ≅ π/2 in (a) the near field and (b) the far field.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

nx=n0+n1 cos2πxΛ=n0+n1fx,
Rr=R0r-1/2 γ -1+1 R0r-d1-usin θB×1+u1-u1/2 J1γ1-u2du,Ss=-i2 γ -1+1 R0s-d1-usin θB×J0γ1-u2du,
Rr=R0r-1/2 γE0-1+1exp-g1-u-r2×1+u1-u1/2J1γ1-u2du,Ss=-i 1/2 γE0-1+1exp-g1-u-s2×J0γ1-u21/2du,
SffΔθ=EΔθHSΔθ,RffΔθ=EΔθHRΔθ,
R=-expiξγ2+ξ21/2 cosγ2+ξ21/2-iξ sinγ2+ξ21/2γ2+ξ21/2,S=-iγ exp-iξsinγ2+ξ21/2γ2+ξ21/2.
ξ1=ΔθKd2=ΔθπdΛ.
η=sin2γ2+ξ21/21+ξ2γ2
d tan θB+2ω0=gcos θB+2ω0.
x=d tan θB+z-dtan θ for the R beam,
x=-d tan θB-z-dtan θ for the S beam,

Metrics