Abstract

The g44 grating is an electroholographic transmission grating in which the applied field is perpendicular to both the grating vector and the wave vector of the incident beam. It is argued that in this configuration the incident beam traverses through a periodically rotating index ellipsoid. It is shown that in the g44 configuration the Bragg condition is fulfilled for a specific value of the applied field and for a diffracting beam polarization that is perpendicular to that of the incident beam. Consequently, the g44 grating can be used as an electrically controlled filter. Tunability of 7nm is demonstrated in a 2mm thick grating.

© 2006 Optical Society of America

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References

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  1. A. J. Agranat, Infrared Holography for Optical Communications: Techniques, Materials and Devices, Vol. 86 of Topics in Applied Physics, P.Boffi, D.Piccinin, and M.C.Ubaldi, eds. (Springer-Verlag, 2002).
  2. A. J. Agranat, V. Leyva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
    [CrossRef] [PubMed]
  3. A. J. Agranat, R. Hofmeister, and A. Yariv, Opt. Lett. 17, 713 (1992).
    [CrossRef] [PubMed]
  4. J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
    [CrossRef]
  5. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  6. R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
    [CrossRef]

1993 (1)

R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
[CrossRef]

1992 (1)

1989 (1)

1969 (1)

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

1964 (1)

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Agranat, A. J.

R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
[CrossRef]

A. J. Agranat, R. Hofmeister, and A. Yariv, Opt. Lett. 17, 713 (1992).
[CrossRef] [PubMed]

A. J. Agranat, V. Leyva, and A. Yariv, Opt. Lett. 14, 1017 (1989).
[CrossRef] [PubMed]

A. J. Agranat, Infrared Holography for Optical Communications: Techniques, Materials and Devices, Vol. 86 of Topics in Applied Physics, P.Boffi, D.Piccinin, and M.C.Ubaldi, eds. (Springer-Verlag, 2002).

Geusic, J. E.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Hofmeister, R.

R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
[CrossRef]

A. J. Agranat, R. Hofmeister, and A. Yariv, Opt. Lett. 17, 713 (1992).
[CrossRef] [PubMed]

Kogelnik, H.

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

Kurtz, S. K.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Leyva, V.

Van Uitert, L. G.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Wemple, S. H.

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Yagi, S.

R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
[CrossRef]

Yariv, A.

Appl. Phys. Lett. (1)

J. E. Geusic, S. K. Kurtz, L. G. Van Uitert, and S. H. Wemple, Appl. Phys. Lett. 4, 141 (1964).
[CrossRef]

Bell Syst. Tech. J. (1)

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

J. Cryst. Growth (1)

R. Hofmeister, S. Yagi, A. Yariv, and A. J. Agranat, J. Cryst. Growth 131, 486 (1993).
[CrossRef]

Opt. Lett. (2)

Other (1)

A. J. Agranat, Infrared Holography for Optical Communications: Techniques, Materials and Devices, Vol. 86 of Topics in Applied Physics, P.Boffi, D.Piccinin, and M.C.Ubaldi, eds. (Springer-Verlag, 2002).

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Figures (3)

Fig. 1
Fig. 1

Transmission electrohologram in the g 44 configuration for the case of an incident beam ( I in ) in the TM polarization. The diffracting beam ( I d ) is TE polarized, and the direct output beam ( I out ) is TM polarized.

Fig. 2
Fig. 2

Measurement of the diffraction efficiency as a function of applied electric field for a TE-polarized incident beam.

Fig. 3
Fig. 3

Spectrum analyzer measurement of a grating illuminated by a TE-polarized broadband source incident at ϕ = 20 ° . (a) Applied field E = 5.48 kV cm . (b) Applied field E = 1.21 kV cm .

Equations (13)

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K = k d k in ,
θ in = θ d ,
2 n o Λ sin θ in = λ o .
Δ n = ( 1 2 ) n o 3 ε o 2 ε r 2 [ g 11 E sc 2 cos 2 ( K x ) + g 12 E o 2 2 g 44 E o E sc cos ( K x ) 0 2 g 44 E o E sc cos ( K x ) g 12 E sc 2 cos 2 ( K x ) + g 11 E o 2 0 0 0 g 12 E sc 2 cos 2 ( K x ) + g 12 E o 2 ] ,
0 = 2 π n TE λ o cos θ in 2 π n TM λ o cos θ d ,
2 π Λ = 2 π n TE λ o sin θ in + 2 π n TM λ o sin θ d ,
λ o = Λ { sin ϕ + [ n TM ( E B , TE , E sc ) ] 2 [ n TE ( E B , TE , E sc ) ] 2 + sin 2 ϕ } .
λ o = Λ { sin ϕ + [ n TE ( E B , TM , E sc ) ] 2 [ n TM ( E B , TM , E sc ) ] 2 + sin 2 ϕ } .
η = I d I in = L 2 κ 2 cos θ in cos θ d sinc 2 ( L Ω 2 ) ,
Ω = ( ν cos θ d ) 2 + 4 ( κ 2 cos θ d cos θ in ) .
κ = π δ ( Δ n ) λ o ,
ν = K ( k d k in ) .
[ n TE ( E B , TE ) ] 2 [ n TM ( E B , TE ) ] 2 = [ n TM ( E B , TM ) ] 2 [ n TE ( E B , TM ) ] 2 = 0.01946 ,

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