Abstract

A transmission hologram with two volume gratings is considered in the regime of wave A diffracted into wave B via an intermediate weakly excited wave C. In analogy to the phenomenon of stimulated Raman adiabatic passage in nonlinear optics, this new scheme demonstrates diffraction efficiency with low sensitivity to the hologram’s strength. A theory of three-wave adiabatic coupling has been developed and explored analytically. Numerical results show an example of a coupling profile that preserves high diffraction efficiency with almost no dependence on the hologram’s strength, including the suppressed influence of polarization.

© 2006 Optical Society of America

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References

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  1. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  2. R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  3. B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995), p. 279.
  4. O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, Appl. Opt. 38, 619 (1999).
    [CrossRef]
  5. L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
    [CrossRef]
  6. L. B. Glebov, Glass Sci. Technol. (Amsterdam) 75-C1, 73 (2002).
  7. M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
    [CrossRef]

2002 (2)

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

L. B. Glebov, Glass Sci. Technol. (Amsterdam) 75-C1, 73 (2002).

1999 (1)

1987 (1)

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

1969 (1)

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

Becker, M.

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

Bergmann, K.

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

Burckhardt, Ch. B.

R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Ciapurin, I. V.

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

Collier, R. J.

R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Efimov, O. M.

Gaubatz, U.

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

Glebov, L. B.

L. B. Glebov, Glass Sci. Technol. (Amsterdam) 75-C1, 73 (2002).

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, Appl. Opt. 38, 619 (1999).
[CrossRef]

Glebova, L. N.

Jones, P. L.

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

Kogelnik, H.

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

Lin, L. H.

R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Mamaev, A. V.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995), p. 279.

Richardson, K. C.

Shkunov, V. V.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995), p. 279.

Smirnov, V. I.

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

O. M. Efimov, L. B. Glebov, L. N. Glebova, K. C. Richardson, and V. I. Smirnov, Appl. Opt. 38, 619 (1999).
[CrossRef]

Stickley, C. M.

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

Zeldovich, B. Ya.

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995), p. 279.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

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

Glass Sci. Technol. (Amsterdam) (1)

L. B. Glebov, Glass Sci. Technol. (Amsterdam) 75-C1, 73 (2002).

J. Chem. Phys. (1)

M. Becker, U. Gaubatz, K. Bergmann, and P. L. Jones, J. Chem. Phys. 87, 5064 (1987).
[CrossRef]

Proc. SPIE (1)

L. B. Glebov, V. I. Smirnov, C. M. Stickley, and I. V. Ciapurin, in Proc. SPIE 4724, 101 (2002).
[CrossRef]

Other (2)

R. J. Collier, Ch. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

B. Ya. Zeldovich, A. V. Mamaev, and V. V. Shkunov, Speckle-Wave Interactions in Application to Holography and Nonlinear Optics (CRC Press, 1995), p. 279.

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Figures (3)

Fig. 1
Fig. 1

Configuration of three-wave interaction inside a double-recorded volume hologram with modulation of coupling coefficients. The counterintuitive order in which these gratings are turned on and off should be emphasized: dotted lines, κ C B ( z ) ; dashed lines, κ C A ( z ) .

Fig. 2
Fig. 2

Diffraction efficiency of the diffracted wave as a function of two hologram strengths, η = η ( M C A , M C B ) .

Fig. 3
Fig. 3

Diffraction efficiency of the diffracted wave as a function of angular and spectral detuning values ( δ θ , in degrees, in air; δ ω ω , dimensionless) with relatively small hologram strengths M C A = M C B = 4 , thickness L = 5 mm , λ vac = 1.06 μ m , and θ A , air = 50 ° . Maximum diffraction efficiency η max of power transfer A B is η max = 0.615 . There are both spectral and angular selectivity, as in a single-grating A B hologram, but the compensation for wavelength detuning by angular detuning is no longer perfect.

Equations (20)

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δ n = n C A ( z ) cos ( Q C A R ) + n C B ( z ) cos ( Q C B R ) = 0.5 [ n C A ( z ) exp ( i Q C A R ) + n C B ( z ) exp ( i Q C B R ) ] + complex conjugate .
E real ( R , t ) = E ( R , t ) + [ E ( R , t ) ] ;
E ( R , t ) = e ̂ y 2 { a ( z ) [ cos ( θ A , med ) ] 1 2 exp ( i k A R ) + b ( z ) [ cos ( θ B , med ) ] 1 2 exp ( i k B R ) + c ( z ) [ cos ( θ C , med ) ] 1 2 exp ( i k C R ) } exp [ i δ k x x i ( ω + δ ω ) t ] .
k A , B , C = ( ω n 0 c ) [ e x sin ( θ A , B , C , med ) + e z cos ( θ A , B , C , med ) ] ,
θ B , med = θ A , med , θ C , med = 0 ,
Q C A = k C k A , Q C B = k C k B ,
δ k x = δ ω c sin ( θ A , air ) + ω c cos ( θ A , air ) δ θ A , air .
d a d z = i [ κ C A ( z ) ] * c ( z ) + i α a ( z ) ,
d b d z = i [ κ C B ( z ) ] * c ( z ) + i β b ( z ) ,
d c d z = i κ C A ( z ) a ( z ) + i κ C B ( z ) b ( z ) + i γ c ( z ) ,
α = [ ω c ( ξ μ ) δ ω ω v δ θ A , air ] , β = [ ω c ( ξ + μ ) δ ω ω + v δ θ A , air ] , γ = ω c ( n δ ω ω ) , μ = sin 2 θ A , air n cos θ A , med ,
v = sin θ A , air cos θ A , air n cos θ A , med , ξ = n cos θ A , med ,
κ C A = ω 2 c [ cos ( θ A , med ) ] 1 2 n C A ,
κ C B = ω 2 c [ cos ( θ A , med ) ] 1 2 n C B .
[ κ A C * ( κ A C 2 + κ B C 2 ) 1 2 , κ B C * ( κ A C 2 + κ B C 2 ) 1 2 , 1 ] ,
[ κ A C * ( κ A C 2 + κ B C 2 ) 1 2 , κ B C * ( κ A C 2 + κ B C 2 ) 1 2 , 1 ] ,
[ κ B C , κ A C , 0 ] const. [ ( 1 κ A C ) , ( 1 κ B C ) , 0 ] .
M C A = κ C A ( z ) d z , M C B = κ C B ( z ) d z .
κ C B ( z ) = M C B [ cos ( π z 2 L z ) ] 2 ( 2 L z ) ,
κ C A ( z ) = M C A [ sin ( π z 2 L z ) ] 2 ( 2 L z ) .

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