Abstract

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
    [CrossRef]
  2. P. Günter, J.-P. Huignard, In Fundamental Phenomena, P. Gümer, J.-P. Huignard, eds.,Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, Heidelberg, Germany, 1988), pp. 7–70.
  3. P. Boffi, D. Piccinin, M. C. Ubaldi, and Infrared Holography for Optical Communications: Techniques, Materials, and Devices (Springer-Verlag, Heidelberg, Germany, 2003), pp. 13–16 and 157–176.
  4. S. Breer, K. Buse, “Wavelength demultiplexing with volume phase holograms in photorefractive lithium niobate,” Appl. Phys. B 66, 339–345 (1998).
    [CrossRef]
  5. B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
    [CrossRef]
  6. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation(Wiley, New York, 1983), pp. 84–88 and 220–238.
  7. J. Xie, Q. Wang, “Analysis and calculation on photorefractive property of Fe:LiNbO3 crystal,” Opt. Technol. 26, 268–269 (2000; in Chinese).
  8. Y. Taketomi, J. E. Ford, H. Saraki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  9. H. Yu Li, D. Psaltis, “Double grating formation in anisotropic photorefractive crystals,” J. Appl. Phys. 71, 1394–1400 (1992).
    [CrossRef]
  10. B. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2974 (1969).
    [CrossRef]

2003 (1)

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

2001 (1)

B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
[CrossRef]

2000 (1)

J. Xie, Q. Wang, “Analysis and calculation on photorefractive property of Fe:LiNbO3 crystal,” Opt. Technol. 26, 268–269 (2000; in Chinese).

1998 (1)

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

1992 (1)

H. Yu Li, D. Psaltis, “Double grating formation in anisotropic photorefractive crystals,” J. Appl. Phys. 71, 1394–1400 (1992).
[CrossRef]

1991 (1)

1969 (1)

B. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2974 (1969).
[CrossRef]

Boffi, P.

P. Boffi, D. Piccinin, M. C. Ubaldi, and Infrared Holography for Optical Communications: Techniques, Materials, and Devices (Springer-Verlag, Heidelberg, Germany, 2003), pp. 13–16 and 157–176.

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]

Cartwright, C. M.

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Fainman, Y.

Farries, M.

B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
[CrossRef]

Ford, J. E.

Fu, G.

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Günter, P.

P. Günter, J.-P. Huignard, In Fundamental Phenomena, P. Gümer, J.-P. Huignard, eds.,Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, Heidelberg, Germany, 1988), pp. 7–70.

Guo, Q.

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Huignard, J.-P.

P. Günter, J.-P. Huignard, In Fundamental Phenomena, P. Gümer, J.-P. Huignard, eds.,Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, Heidelberg, Germany, 1988), pp. 7–70.

Kogelnik, B. H.

B. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2974 (1969).
[CrossRef]

Lee, S. H.

Liang, B.

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Ma, J.

Nyman, B.

B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
[CrossRef]

Piccinin, D.

P. Boffi, D. Piccinin, M. C. Ubaldi, and Infrared Holography for Optical Communications: Techniques, Materials, and Devices (Springer-Verlag, Heidelberg, Germany, 2003), pp. 13–16 and 157–176.

Psaltis, D.

H. Yu Li, D. Psaltis, “Double grating formation in anisotropic photorefractive crystals,” J. Appl. Phys. 71, 1394–1400 (1992).
[CrossRef]

Saraki, H.

Si, C.

B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
[CrossRef]

Taketomi, Y.

Ubaldi, M. C.

P. Boffi, D. Piccinin, M. C. Ubaldi, and Infrared Holography for Optical Communications: Techniques, Materials, and Devices (Springer-Verlag, Heidelberg, Germany, 2003), pp. 13–16 and 157–176.

Wang, Q.

J. Xie, Q. Wang, “Analysis and calculation on photorefractive property of Fe:LiNbO3 crystal,” Opt. Technol. 26, 268–269 (2000; in Chinese).

Wang, Z.

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Xie, J.

J. Xie, Q. Wang, “Analysis and calculation on photorefractive property of Fe:LiNbO3 crystal,” Opt. Technol. 26, 268–269 (2000; in Chinese).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation(Wiley, New York, 1983), pp. 84–88 and 220–238.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation(Wiley, New York, 1983), pp. 84–88 and 220–238.

Yu Li, H.

H. Yu Li, D. Psaltis, “Double grating formation in anisotropic photorefractive crystals,” J. Appl. Phys. 71, 1394–1400 (1992).
[CrossRef]

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)

B. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2974 (1969).
[CrossRef]

J. Appl. Phys. (1)

H. Yu Li, D. Psaltis, “Double grating formation in anisotropic photorefractive crystals,” J. Appl. Phys. 71, 1394–1400 (1992).
[CrossRef]

Opt. Commun. (1)

B. Liang, Z. Wang, Q. Guo, G. Fu, C. M. Cartwright, “Optical switching property of a Ce:KNSBN photorefractive volume grating controlled by the readout beam polarization,” Opt. Commun. 217, 111–115 (2003).
[CrossRef]

Opt. Fiber Technol. (1)

B. Nyman, M. Farries, C. Si, “Technology trends in dense WDM demultiplexers,” Opt. Fiber Technol. 7: 255–274 (2001).
[CrossRef]

Opt. Lett. (1)

Opt. Technol. (1)

J. Xie, Q. Wang, “Analysis and calculation on photorefractive property of Fe:LiNbO3 crystal,” Opt. Technol. 26, 268–269 (2000; in Chinese).

Other (3)

P. Günter, J.-P. Huignard, In Fundamental Phenomena, P. Gümer, J.-P. Huignard, eds.,Vol. 1 of Photorefractive Materials and Their Applications (Springer-Verlag, Heidelberg, Germany, 1988), pp. 7–70.

P. Boffi, D. Piccinin, M. C. Ubaldi, and Infrared Holography for Optical Communications: Techniques, Materials, and Devices (Springer-Verlag, Heidelberg, Germany, 2003), pp. 13–16 and 157–176.

A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation(Wiley, New York, 1983), pp. 84–88 and 220–238.

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 (9)

Fig. 1
Fig. 1

Refractive index of a light wave in a uniaxial crystal.

Fig. 2
Fig. 2

Wave vectors of a symmetrically recorded volume grating.

Fig. 3
Fig. 3

Wave vectors of an asymmetrically recorded volume grating.

Fig. 4
Fig. 4

Wave vectors of recorded double gratings.

Fig. 5
Fig. 5

Experimental setup for recording photorefractive volume gratings.

Fig. 6
Fig. 6

Relationship between diffraction efficiency and polarization direction of the readout beam.

Fig. 7
Fig. 7

Angular selectivity of double gratings at different polarization states of the readout beam.

Fig. 8
Fig. 8

Measured diffraction efficiency of double gratings as a function of angular deviation at a 45° polarization direction of the readout beam.

Fig. 9
Fig. 9

Measured diffraction efficiency of double gratings read by o and e waves as a function of angular deviation.

Equations (13)

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

x 2 n o 2 + y 2 n o 2 + z 2 n e 2 = 1 .
n 1 = n o ,
n 2 ( ψ ) = n o n e [ n o 2 sin 2 ( π 2 ψ ) + n e 2 cos 2 ( π 2 ψ ) ] 1 / 2 ,
ψ = arcsin [ 1 n 2 ( ψ ) sin ( θ 0 ) ] .
( 1 n o 2 + γ 13 E sc ) x 2 + ( 1 n o 2 + γ 13 E sc ) y 2 + ( 1 n e 2 + γ 33 E sc ) z 2 = 1 .
x = x cos ψ z sin ψ , y = y , z = x sin ψ + z cos ψ .
( 1 n o 2 + γ 13 E sc ) y 2 + ( sin 2 ψ n o 2 + cos 2 ψ n e 2 + γ 13 E sc sin 2 ψ + γ 33 E sc cos 2 ψ ) z 2 = 1 .
n o = n o ½ n o 3 γ 13 E sc = n o ( 1 ½ n o 2 γ 13 E sc ) , n e = n o n e ( n o 2 cos 2 ψ + n e 2 sin 2 ψ ) 1 / 2 × [ 1 ½ n o 2 n e 2 n o 2 cos 2 ψ + n e 2 sin 2 ψ × ( γ 13 sin 2 ψ + γ 33 cos 2 ψ ) E sc ] .
Δ n o = ½ n o 3 γ 13 E sc , Δ n e = ½ n o 3 n e 3 ( n o 2 cos 2 ψ + n e 2 sin 2 ψ ) 3 / 2 ( γ 13 sin 2 ψ + γ 33 cos 2 ψ ) E sc .
E sc = ( E sc sin ϕ , 0 , E sc cos ϕ ) .
( 1 n o 2 + γ 13 E sc cos ϕ ) x 2 + ( 1 n o 2 + γ 13 E sc cos ϕ ) y 2 + ( 1 n e 2 + γ 33 E sc cos ϕ ) z 2 2 γ 51 x z E sc sin ϕ + 2 γ 22 x y E sc sin ϕ = 1 .
( 1 n o 2 + γ 13 E sc cos ϕ ) y 2 + ( 1 n e 2 + γ 33 E sc cos ϕ ) z 2 = 1 .
Δ n o = ½ n o 3 γ 13 E sc cos ϕ , Δ n e = ½ n e 3 γ 33 E sc cos ϕ .

Metrics