Abstract

We demonstrate that the diffraction efficiency of a grating photoinduced in an FA(II) KCl:Li crystal by two perpendicularly polarized light vibrations may be amplified, for a given wavelength, by coupling the directly transmitted and diffracted beams. The best results are obtained for the reading wavelength λD, corresponding to the isobestic point of the crystal and situated between the maxima of the FA2 and FA1 bands. For this wavelength, the transmittance of the crystal is approximately 12.5% (at 78 K). Using beam ca coupling, we obtain a diffraction efficiency approximately equal to 12%.

© 1988 Optical Society of America

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References

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  1. F. Lüty, “FA centers in alkali halide crystals,” in Physics of Color Centers, W. B. Fowler, ed. (Academic, New York, 1968).
  2. F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
    [CrossRef]
  3. U. Röder, “Storage properties of FA-centre holograms,” Opt. Commun. 6, 270–274 (1972).
    [CrossRef]
  4. M. Lehmann, “Investigation of a photodichroic material for holographic storage and recovery,” J. Opt. Soc. Am. 63, 505 (1973).
  5. H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
    [CrossRef]
  6. H. Blume, “Highly efficient dichroic phase holograms in KCl:Na,” Opt. Acta 21, 357–363 (1974).
    [CrossRef]
  7. M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
    [CrossRef]
  8. F. Rosenberger, F. Lüty, “Low temperature electro-optical effects from off axis Li+ in FA centers,” Solid State Commun. 7, 983–987 (1969).
    [CrossRef]
  9. F. Lüty, “Electromodulation spectroscopy of localized excitations in crystals,” Surf. Sci. 37, 120–138 (1973).
    [CrossRef]
  10. D. L. Dexter, “Refractive index and Faraday effect in solid solutions,” Phys. Rev. 111, 119–124 (1958).
    [CrossRef]
  11. D. L. Dexter, “Absorption of light by atoms in solids,” Phys. Rev. 101, 48–55 (1956).
    [CrossRef]
  12. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  13. M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
    [CrossRef]
  14. G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

1987

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

1974

H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
[CrossRef]

H. Blume, “Highly efficient dichroic phase holograms in KCl:Na,” Opt. Acta 21, 357–363 (1974).
[CrossRef]

1973

F. Lüty, “Electromodulation spectroscopy of localized excitations in crystals,” Surf. Sci. 37, 120–138 (1973).
[CrossRef]

M. Lehmann, “Investigation of a photodichroic material for holographic storage and recovery,” J. Opt. Soc. Am. 63, 505 (1973).

1972

U. Röder, “Storage properties of FA-centre holograms,” Opt. Commun. 6, 270–274 (1972).
[CrossRef]

1971

F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
[CrossRef]

1969

F. Rosenberger, F. Lüty, “Low temperature electro-optical effects from off axis Li+ in FA centers,” Solid State Commun. 7, 983–987 (1969).
[CrossRef]

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

1958

D. L. Dexter, “Refractive index and Faraday effect in solid solutions,” Phys. Rev. 111, 119–124 (1958).
[CrossRef]

1956

D. L. Dexter, “Absorption of light by atoms in solids,” Phys. Rev. 101, 48–55 (1956).
[CrossRef]

Bader, T.

H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
[CrossRef]

Baldacchini, G.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Blume, H.

H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
[CrossRef]

H. Blume, “Highly efficient dichroic phase holograms in KCl:Na,” Opt. Acta 21, 357–363 (1974).
[CrossRef]

Cellai, G.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Debrus, S.

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

Dexter, D. L.

D. L. Dexter, “Refractive index and Faraday effect in solid solutions,” Phys. Rev. 111, 119–124 (1958).
[CrossRef]

D. L. Dexter, “Absorption of light by atoms in solids,” Phys. Rev. 101, 48–55 (1956).
[CrossRef]

Grassano, U. M.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Hong, J. P.

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

Kogelnik, H.

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

Lanzl, F.

F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
[CrossRef]

Lehmann, M.

M. Lehmann, “Investigation of a photodichroic material for holographic storage and recovery,” J. Opt. Soc. Am. 63, 505 (1973).

Lüty, F.

H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
[CrossRef]

F. Lüty, “Electromodulation spectroscopy of localized excitations in crystals,” Surf. Sci. 37, 120–138 (1973).
[CrossRef]

F. Rosenberger, F. Lüty, “Low temperature electro-optical effects from off axis Li+ in FA centers,” Solid State Commun. 7, 983–987 (1969).
[CrossRef]

F. Lüty, “FA centers in alkali halide crystals,” in Physics of Color Centers, W. B. Fowler, ed. (Academic, New York, 1968).

May, M.

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

Meucci, M.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Röder, U.

U. Röder, “Storage properties of FA-centre holograms,” Opt. Commun. 6, 270–274 (1972).
[CrossRef]

F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
[CrossRef]

Rosenberger, F.

F. Rosenberger, F. Lüty, “Low temperature electro-optical effects from off axis Li+ in FA centers,” Solid State Commun. 7, 983–987 (1969).
[CrossRef]

Rzepka, E.

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

Scacco, A.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Somaiah, K.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Somma, F.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Tonelli, M.

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

Waidelich, W.

F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
[CrossRef]

Appl. Phys. Lett.

F. Lanzl, U. Röder, W. Waidelich, “Hologram recording by aligning of anisotropic colors centers,” Appl. Phys. Lett. 18, 56–58 (1971).
[CrossRef]

Bell Syst. Tech. J.

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

J. Appl. Phys.

M. May, J. P. Hong, S. Debrus, E. Rzepka, “Diffraction efficiency of the gratings photoinduced in KCl:Li FA center crystals,” J. Appl. Phys. 61, 852–858 (1987).
[CrossRef]

J. Opt. Soc. Am.

M. Lehmann, “Investigation of a photodichroic material for holographic storage and recovery,” J. Opt. Soc. Am. 63, 505 (1973).

Opt. Acta

H. Blume, “Highly efficient dichroic phase holograms in KCl:Na,” Opt. Acta 21, 357–363 (1974).
[CrossRef]

Opt. Commun.

H. Blume, T. Bader, F. Lüty, “Bi-directional holographic information storage based on the optical reorientation of FA centers in KCl:Na,” Opt. Commun. 12, 147–151 (1974).
[CrossRef]

U. Röder, “Storage properties of FA-centre holograms,” Opt. Commun. 6, 270–274 (1972).
[CrossRef]

M. May, E. Rzepka, S. Debrus, J. P. Hong, “Reorientation of FA centers in lithium doped potassium chloride crystal,” Opt. Commun. 61, 325–331 (1987).
[CrossRef]

Phys. Rev.

D. L. Dexter, “Refractive index and Faraday effect in solid solutions,” Phys. Rev. 111, 119–124 (1958).
[CrossRef]

D. L. Dexter, “Absorption of light by atoms in solids,” Phys. Rev. 101, 48–55 (1956).
[CrossRef]

Solid State Commun.

F. Rosenberger, F. Lüty, “Low temperature electro-optical effects from off axis Li+ in FA centers,” Solid State Commun. 7, 983–987 (1969).
[CrossRef]

Surf. Sci.

F. Lüty, “Electromodulation spectroscopy of localized excitations in crystals,” Surf. Sci. 37, 120–138 (1973).
[CrossRef]

Other

F. Lüty, “FA centers in alkali halide crystals,” in Physics of Color Centers, W. B. Fowler, ed. (Academic, New York, 1968).

G. Baldacchini, G. Cellai, U. M. Grassano, M. Meucci, A. Scacco, K. Somaiah, F. Somma, M. Tonelli, “Optical studies on the reorientation process of FA(Li) centers in KCl,” Cryst. Latt. Def. Amorph. Mater. (to be published).

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Figures (8)

Fig. 1
Fig. 1

Off-center configuration of Li+ in an FA(II) KCl:Li crystal.

Fig. 2
Fig. 2

Grating recording geometry. The crystal at 78 K is cut parallel to the crystallographic axis.

Fig. 3
Fig. 3

Recorded grating, characterized by the wave vector K and illuminated by the R and S waves characterized, respectively, by the wave vectors ρ and σ.

Fig. 4
Fig. 4

Optical absorption of the FA(II) KCl:Li crystal (T = 78 K). The experimental curve is the sum of four elementary Gaussian curves: L1, K, FA2, and FA1.

Fig. 5
Fig. 5

Computed variations of (a) vl and of (b) ul versus λ.

Fig. 6
Fig. 6

Computed variations of (a) η0 and (b) ηmax versus λ.

Fig. 7
Fig. 7

Schematic diagram of the setup used to record and read the photoinduced grating.

Fig. 8
Fig. 8

Measured diffraction efficiency of the grating illuminated by the R and S waves dephased through π/2. The dashed curve represents the computed variations of ηmax(λ).

Equations (59)

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r 1 x = cos θ x + sin θ 2 y + sin θ 2 z
r 2 x = 1 2 y - 1 2 z
r 2 x = - sin θ x + cos θ 2 y + cos θ 2 z .
N x + N y + N z = N .
i = c + C i A 1 α A 1 + C i A 2 α A 2 ,
C i A 1 = N i ( i · r 1 i ) 2 + N j ( i · r 1 j ) 2 + N k ( i · r 1 k ) 2 ,
C i A 2 = N i [ ( i · r 2 ) 2 + ( i · r 2 i ) 2 ] + N j [ ( i · r 2 j ) 2 + ( i · r 2 j ) 2 ] + N k [ ( i · r 2 k ) 2 + ( i · r 2 k ) 2 ] ,
C i 0 A 2 = 2 C i 0 A 1 = 2 N 3
x = y = z = A = c + N 3 α A 1 + 2 N 3 α A 2 .
D 0 ( λ ) = K 0 A 1 ( λ ) + K 0 A 2 ( λ ) = 2 2 π λ l log 10 e Im [ ( A ) 1 / 2 ]
n 0 ( λ ) = n c + Δ n 0 A 1 ( λ ) + Δ n 0 A 2 ( λ ) = Re [ ( A ) 1 / 2 ] ,
n c = ( c ) 1 / 2
K 0 A j = j k l N 3 n c log 10 e Im ( α A j ) ,
Δ n 0 A j = j N 6 n c Re ( α A j ) ,
A = n 0 2 - i n c D 0 k l log 10 e ,
Δ n 0 A j = - N f e 2 m 0 ( n c 2 + 2 ) 2 9 n c 1 W j ( E j + E ) × exp [ - ( E - E j ) 2 / W j 2 ] 0 E - E j W j e t 2 d t ,
W j = 1 2 ( ln 2 ) 1 / 2 H j .
f j N = 18 m 0 e 2 c π n c ( n c 2 + 2 ) 2 W j π K 0 A j ( E j ) l log 10 e ,
Δ n 0 A j = - 2 c π log 10 e K 0 A j ( E j ) l ( E j + E ) × exp [ - ( E - E j ) 2 / W j 2 ] 0 E - E j W j e t 2 d t ,
Δ n 0 A j = - ( 5.127 × 10 - 5 ) K 0 A j ( E j ) l ( E j + E ) × exp [ - ( E - E j ) 2 / W j 2 ] 0 E - E j W j e t 2 d t ,
I x = I 0 ( 1 - cos ϕ ) , I y = I 0 ( 1 + cos ϕ ) ,
ϕ = 2 k 0 n 0 x sin α 0 ,
ν i = η 2 { I x [ ( x · r 2 i ) 2 + ( x · r 2 i ) 2 ] + I y [ ( y · r 2 i ) 2 + ( y · r 2 i ) 2 ] } ,
d N i = ν i N i d t .
d N x d t = - P η 2 I x sin 2 θ N x - P η 2 2 I y ( 1 + cos 2 θ ) N x + P η 2 I x 4 ( 1 + cos 2 θ ) ( N y + N z ) + P η 2 I y 2 sin 2 θ N y + P η 2 I y 4 ( 1 + cos 2 θ ) N z , d N y d t = - P η 2 2 I x ( 1 + cos 2 θ ) N y - P η 2 I y sin 2 θ N y + P η 2 I x 2 sin 2 θ N x + P η 2 4 I x ( 1 + cos 2 θ ) N z + P η 2 4 I y ( 1 + cos 2 θ ) ( N x + N z ) , d N z d t = - d N x d t - d N y d t .
N x = N 3 ( A - B cos ϕ ) , N y = N 3 ( A + B cos ϕ ) , N z = N ( 1 - 2 A 3 ) ,
A = 12 ( 4 - sin 4 θ ) 3 ( 2 - sin 2 θ ) ( 6 + 5 sin 2 θ ) + 8 sin 2 θ ,
B = 12 ( 2 - sin 2 θ ) ( 2 - 3 sin 2 θ ) 3 ( 2 - sin 2 θ ) ( 6 + 5 sin 2 θ ) + 8 sin 2 θ .
1 = A + Δ 1 i + Δ 2 i cos ϕ .
Δ 1 x = Δ 1 y = - Δ 1 z 2 = - n c 4 k l ( A - 1 ) ( 2 - 3 sin 2 θ ) × [ 2 b - i log 10 e d ] ,
Δ 2 x = - Δ 2 y = B n c 4 k l ( 2 - 3 sin 2 θ ) ( 2 b - i log 10 e d ) ,
Δ 2 z = 0 ,
b = k l ( Δ n 0 A 2 - 2 Δ n 0 A 1 ) ,
d = K 0 A 2 - 2 K 0 A 1 .
K = k 0 2 n 0 sin α 0 x .
ρ = k n 0 .
σ = ρ - K .
sin α λ = sin α 0 λ 0 .
E = R ( z ) exp ( - ρ · r ) + S ( z ) exp ( - σ · r )
2 E - ( · E ) + k 2 E = 0.
R ( l ) = exp ( γ 1 + γ 2 2 l ) [ E R cosh ( γ 1 - γ 2 2 l ) - E s sinh ( γ 1 - γ 2 2 l ) ] , S ( l ) = exp ( γ 1 + γ 2 2 l ) [ - E R sinh ( γ 1 - γ 2 2 l ) + E s cosh ( γ 1 + γ 2 2 l ) ] ,
γ 1 + γ 2 2 = - i 2 ρ z [ k 2 ( A + Δ 1 y ) - ρ 2 ] ,
γ 1 + γ 2 2 = i 4 ρ z k 2 Δ 2 y .
γ 1 + γ 2 2 = - 1 2 l log 10 e [ D 0 - ( A - 1 ) ( 2 - 3 ) sin 2 θ 4 d ] + i ( A - 1 ) ( 2 - 3 sin 2 θ ) 4 b ,
γ 1 - γ 2 2 = - i B ( 2 - 3 sin 2 θ ) 16 l ( 2 b - i d log 10 e ) = - i ( u - i v ) .
E s ( 0 ) = E R ( 0 ) exp ( i ϕ s ) .
I R ( l ) = I e - δ l [ U c 2 + U s 2 + 2 U c U s cos ( ψ s + ϕ s - ψ c ) ] ,
I s ( l ) = I e - δ l [ U c 2 + U s 2 + 2 U c U s cos ( ψ c + ϕ s - ψ s ) ] ,
U c = cosh ( γ 1 - γ 2 ) l = ( cos 2 u l + sinh 2 v l ) 1 / 2 ,
U s = sinh ( γ 1 - γ 2 ) l = ( sin 2 u l + sinh 2 v l ) 1 / 2 ,
ψ c = Arg [ cosh ( γ 1 - γ 2 ) l ] = tan - 1 ( tan u l tanh v l ) ,
ψ s = Arg [ sinh ( γ 1 - γ 2 ) l ] = tan - 1 ( tan u l tanh v l ) ,
δ = Re ( γ 1 + γ 2 ) .
η = I s ( l ) 2 I = 1 2 e - δ l [ U c 2 + U s 2 + 2 U c U s cos ( ψ c + ϕ s - ψ s ) ] .
η 0 = e - δ l U s 2 .
u l = B ( 2 - 3 sin 2 θ ) 16 2 k l ( Δ n 0 A 2 - 2 Δ n 0 A 1 )
v l = B ( 2 - 3 sin 2 θ 16 K 0 A 2 - 2 K 0 A 1 ) log 10 e ,
K 0 A 2 ( λ D ) = 2 K 0 A 1 ( λ D ) .
η max ( λ ) = ½ e - δ l ( U c + U s ) 2 .

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