Abstract

The finite dimension of the incident beam used to read out volume holographic gratings has interesting effects on their filtering properties. As the readout beam gets narrower, there is more deviation from the ideal response predicted for monochromatic plane waves. In this paper we experimentally explore beam-width-dependent phenomena such as wavelength selectivities, angular selectivities, and diffracted beam profiles. Volume gratings in both reflection and transmission geometries are investigated near 1550  nm. Numerical simulations utilizing the technique of Fourier decomposition provide a satisfactory explanation and confirm that the spread of spatial harmonics is the main contributing factor.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. B. Glebov, "Kinetics modeling in photosensitive glass," Opt. Mater. 25, 413-418 (2004).
    [CrossRef]
  2. G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
    [CrossRef]
  3. J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
    [CrossRef]
  4. H. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909-2947 (1969).
  5. J. W. Goodman, Fourier Optics (McGraw-Hill, 1996).
  6. P. Yeh, Optical Waves in Layered Media (Wiley, 1991).
  7. D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
    [CrossRef] [PubMed]
  8. M. Levene, G. J. Steckman, and D. Psaltis, "Method for controlling the shift invariance of optical correlators," Appl. Opt. 38, 394-398 (1999).
    [CrossRef]
  9. D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156-159(1969).
    [CrossRef]
  10. D. Psaltis and F. Mok, "Holographic memories," Sci. Am. 273, 70-76 (1995).
    [CrossRef]
  11. G. A. Rakuljic and V. Leyva, "Volume holographic narrow-band optical filter," Opt. Lett. 18, 459-461 (1993).
    [CrossRef] [PubMed]
  12. S. Breer and K. Buse, "Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate," Appl. Phys. B 66, 339-345 (1998).
    [CrossRef]
  13. V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
    [CrossRef]
  14. S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, "Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating," Opt. Lett. 29, 29-31 (2004).
    [CrossRef] [PubMed]
  15. G. A. Ball and W. W. Morey, "Compression-tuned single-frequency Bragg grating fiber laser," Opt. Lett. 19, 1979-1981 (1994).
    [CrossRef] [PubMed]
  16. H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
    [CrossRef]

2004 (3)

L. B. Glebov, "Kinetics modeling in photosensitive glass," Opt. Mater. 25, 413-418 (2004).
[CrossRef]

S. Y. Li, N. Q. Ngo, S. C. Tjin, P. Shum, and J. Zhang, "Thermally tunable narrow-bandpass filter based on a linearly chirped fiber Bragg grating," Opt. Lett. 29, 29-31 (2004).
[CrossRef] [PubMed]

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

2003 (1)

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

1999 (1)

1998 (1)

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

1997 (1)

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

1996 (1)

J. W. Goodman, Fourier Optics (McGraw-Hill, 1996).

1995 (1)

D. Psaltis and F. Mok, "Holographic memories," Sci. Am. 273, 70-76 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

P. Yeh, Optical Waves in Layered Media (Wiley, 1991).

1990 (1)

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

1988 (1)

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

1969 (2)

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

D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156-159(1969).
[CrossRef]

Ball, G. A.

Brady, D.

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

Breer, S.

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

Buse, K.

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

Corral, J. L.

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

Gabor, D.

D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156-159(1969).
[CrossRef]

Glebov, L. B.

L. B. Glebov, "Kinetics modeling in photosensitive glass," Opt. Mater. 25, 413-418 (2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Fourier Optics (McGraw-Hill, 1996).

Hsieh, H. T.

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Kogelnik, H.

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

Korzinin, Y. L.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Levene, M.

Leyva, V.

Li, S. Y.

Liger, M.

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

Lin, S.

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

Ludman, J. E.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Marti, J.

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

Mok, F.

D. Psaltis and F. Mok, "Holographic memories," Sci. Am. 273, 70-76 (1995).
[CrossRef]

Morey, W. W.

Mullen, R. A.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Ngo, N. Q.

Panotopoulos, G.

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

Polo, V.

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

Psaltis, D.

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

M. Levene, G. J. Steckman, and D. Psaltis, "Method for controlling the shift invariance of optical correlators," Appl. Opt. 38, 394-398 (1999).
[CrossRef]

D. Psaltis and F. Mok, "Holographic memories," Sci. Am. 273, 70-76 (1995).
[CrossRef]

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

Rakuljic, G. A.

Reinhard, N. O.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Riccobono, J. R.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Rytz, D.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Semenova, I. V.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Shahriar, S. M.

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Shum, P.

Steckman, G. J.

Tai, Y. C.

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

Tjin, S. C.

Valley, G. C.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Vidal, B.

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

Wechsler, B.

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Xu, X. G.

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1991).

Zhang, J.

Annu. Rev. Mater. Sci. (1)

G. C. Valley, M. B. Klein, R. A. Mullen, D. Rytz, and B. Wechsler, "Photorefractive materials," Annu. Rev. Mater. Sci. 18, 165-188 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

S. Breer and 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).

IBM J. Res. Dev. (1)

D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156-159(1969).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

V. Polo, B. Vidal, J. L. Corral, and J. Marti, "Novel tunable photonic microwave filter based on laser arrays and N × N AWG-based delay lines," IEEE Photon. Technol. Lett. 15, 584-586 (2003).
[CrossRef]

H. T. Hsieh, G. Panotopoulos, M. Liger, Y. C. Tai, and D. Psaltis, "Athermal holographic filters," IEEE Photon. Technol. Lett. 16, 177-179 (2004).
[CrossRef]

Nature (1)

D. Psaltis, D. Brady, X. G. Xu, and S. Lin, "Holography in artificial neural networks," Nature 343, 325-330 (1990).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. E. Ludman, J. R. Riccobono, N. O. Reinhard, I. V. Semenova, Y. L. Korzinin, and S. M. Shahriar, "Very thick holographic nonspatial filtering of laser beams," Opt. Eng. 36, 1700-1705 (1997).
[CrossRef]

Opt. Lett. (3)

Opt. Mater. (1)

L. B. Glebov, "Kinetics modeling in photosensitive glass," Opt. Mater. 25, 413-418 (2004).
[CrossRef]

Sci. Am. (1)

D. Psaltis and F. Mok, "Holographic memories," Sci. Am. 273, 70-76 (1995).
[CrossRef]

Other (2)

J. W. Goodman, Fourier Optics (McGraw-Hill, 1996).

P. Yeh, Optical Waves in Layered Media (Wiley, 1991).

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 (10)

Fig. 1
Fig. 1

Theoretical configuration. The volume holographic grating has a transfer function H ( k i ; k d ) . VHGR–T is a volume holographic grating in the reflection–transmission geometry.

Fig. 2
Fig. 2

Experimental setup: TL, tunable laser source (from 1520 to 1600 nm); EXP(5×); beam expander; VHGR–T, volume holographic grating in the reflection–transmission geometry; D diff, detector for the transmitted–diffracted beam; RS, rotational stage: RB, razor blade controlled by a translation stage for measurement of the diffracted beam profile.

Fig. 3
Fig. 3

Wavelength selectivity curves from normal to oblique incidence in the reflection geometry. The 20 measured curves in (a) and (b) correspond, from right to left, to incident angles 0°, 1°, 2°, … , 19° outside the glass sample (≈0°–13.3° inside the glass).

Fig. 4
Fig. 4

Summary of the wavelength selectivity measurements and the comparison with numerical simulations. The increasing transmission of the narrow beam at oblique incidence contrasts strongly with the transmission of the expanded beam, which does not increase much at oblique incidence.

Fig. 5
Fig. 5

Angular selectivity curves from normal to oblique incidence in the reflection geometry. The 20 solid curves in (a) and (b) correspond, from left to right, to incident angles 0°, 1°, 2°, … , 19° outside the glass sample (≈0°–13.3° inside the glass). The dashed curves in both plots are measured for an incident angle of 0.5° outside the glass.

Fig. 6
Fig. 6

Summary of the angular selectivity measurements. The 0.5 dB angular bandwidth, ΔθBW, is plotted against the angle of incidence θ. Numerical simulations are seen to agree well with the experimental data.

Fig. 7
Fig. 7

Diffracted beam intensity profiles for three incident angles from normal to oblique incidence in the reflection geometry.

Fig. 8
Fig. 8

Wavelength selectivity curves at θ ≈ 5.1° in the transmission geometry for beam widths W = 0.5 and 2.5 mm.

Fig. 9
Fig. 9

Angular selectivity curves in the transmission geometry around Bragg angle θ B ≈ 5°.

Fig. 10
Fig. 10

Normalized diffracted intensity beam profiles in the transmission geometry around Bragg angle θ B ≈ 5°; Δθ = θ − θ B. All beam profiles are measured 50 mm from the output face. The circles represent experimental measurements and the dashed lines are the numerical simulations.

Equations (12)

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

n ( r ) = n + Δ n cos K r ,
K = k i k d
E i ( x , y , z ) = F ( k i x , k i y ) exp [ j ( k i x x + k i y y + k i z z ) ] d k i x 2 π d k i y 2 π ,
x = x cos θ + z sin θ , z = x sin θ + z cos θ .
F ( k i x , k i y ) H ( k i ; k d ) e j k d r .
E d ( x , y , z ) = F ( k i x , k i y ) H ( k i ; k d ) e j k d r d k i x 2 π d k i y 2 π .
η = o | E d ( x , y , z ) | 2 d o | E i ( x , y , z = L ) | 2 d x d y + o | E d ( x , y , z ) | 2 d o .
λ B = 2 n Λ cos θ .
H = j κ sinh s L s cosh s L j Δ β 2 sinh s L ,
s = κ 2 ( Δ β 2 ) 2 .
H = j exp ( j Δ β 2 L ) π Δ n λ   cos   θ d sin s L s ,
s = κ 2 + ( Δ β 2 ) 2 .

Metrics