Abstract

Following our recent approach in which the Jones matrix calculus was applied to a modulated double-refracted and partially interfering light beam propagating in a homogeneous electro-optic crystal [J. Opt. Soc. Am. A 21, 132 (2004) ], we generalize the method for any distribution of the light intensity. Special attention is paid to Gaussian, flat-topped Gaussian, and quasi-Gaussian beams for which the intensity of the light emerging from the optical system is found analytically. Application of the method to an optical system with an electro-optic crystal is described.

© 2006 Optical Society of America

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References

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  1. R. C. Jones, 'A new calculus for the treatment of optical systems. I. Description and discussion of the calculus,' J. Opt. Soc. Am. 31, 488-493 (1941).
    [CrossRef]
  2. R. C. Jones, 'A new calculus for the treatment of optical systems. IV,' J. Opt. Soc. Am. 32, 486-493 (1942).
    [CrossRef]
  3. R. C. Jones, 'A new calculus for the treatment of optical systems. V. A more general formulation, and description of another calculus,' J. Opt. Soc. Am. 37, 107-110 (1947).
    [CrossRef]
  4. M. Izdebski, W. Kucharczyk, and R. E. Raab, 'Application of the Jones calculus for a modulated double-refracted light beam propagating in a homogeneous and nondepolarizing electro-optic uniaxial crystal,' J. Opt. Soc. Am. A 21, 132-139 (2004).
    [CrossRef]
  5. I. Scierski and F. Ratajczyk, 'The Jones matrix of the real dichroic elliptic object,' Optik (Stuttgart) 68, 121-125 (1984).
  6. C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, 'Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations,' J. Opt. Soc. Am. A 19, 404-412 (2002).
    [CrossRef]
  7. A. Ciattoni, B. Crosignani, and P. Di Porto, 'Vectorial theory of propagation in uniaxially anisotropic media,' J. Opt. Soc. Am. A 18, 1656-1661 (2001).
    [CrossRef]
  8. J. J. Stamnes and V. Dhayalan, 'Transmission of a two-dimensional Gaussian beam into a uniaxial crystal,' J. Opt. Soc. Am. A 18, 1662-1669 (2001).
    [CrossRef]
  9. M. C. Simon, 'Ray tracing formulas for monoaxial optical components,' Appl. Opt. 22, 354-360 (1983).
    [CrossRef] [PubMed]
  10. M. C. Simon and R. M. Echarri, 'Ray tracing formulas for monoaxial optical components: vectorial formulation,' Appl. Opt. 25, 1935-1939 (1986).
    [CrossRef] [PubMed]
  11. F. Gori, 'Flattened Gaussian beams,' Opt. Commun. 107, 335-341 (1994).
    [CrossRef]
  12. Y. Li, 'New expressions for flat-topped light beams,' Opt. Commun. 206, 225-234 (2002).
    [CrossRef]
  13. Y. Li, H. Lee, and E. Wolf, 'New generalized Bessel-Gaussian beams,' J. Opt. Soc. Am. A 21, 640-646 (2004).
    [CrossRef]
  14. M. Izdebski, W. Kucharczyk, and R. E. Raab, 'Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence,' J. Opt. Soc. Am. A 18, 1393-1398 (2001).
    [CrossRef]
  15. M. Izdebski, W. Kucharczyk, and R. E. Raab, 'Analysis of accuracy of measurement of quadratic electro-optic coefficients in uniaxial crystals: a case study of KDP,' J. Opt. Soc. Am. A 19, 1417-1421 (2002).
    [CrossRef]
  16. R. Ledzion, K. Bondarczuk, and W. Kucharczyk, 'Temperature dependence of the quadratic electrooptic effect and estimation of antipolarization of ADP,' Cryst. Res. Technol. 39, 161-164 (2004).
    [CrossRef]
  17. T. A. Maldonaldo and T. K. Gaylord, 'Electrooptic effect calculations: simplified procedure for arbitrary cases,' Appl. Opt. 27, 5051-5066 (1988).
    [CrossRef]
  18. M. Izdebski and W. Kucharczyk, 'On the indirect electro-optic modulation in noncentrosymmetric uniaxial crystals,' J. Opt. A, Pure Appl. Opt. 7, 204-206 (2005).
    [CrossRef]

2005 (1)

M. Izdebski and W. Kucharczyk, 'On the indirect electro-optic modulation in noncentrosymmetric uniaxial crystals,' J. Opt. A, Pure Appl. Opt. 7, 204-206 (2005).
[CrossRef]

2004 (3)

2002 (3)

2001 (3)

1994 (1)

F. Gori, 'Flattened Gaussian beams,' Opt. Commun. 107, 335-341 (1994).
[CrossRef]

1988 (1)

1986 (1)

1984 (1)

I. Scierski and F. Ratajczyk, 'The Jones matrix of the real dichroic elliptic object,' Optik (Stuttgart) 68, 121-125 (1984).

1983 (1)

1947 (1)

1942 (1)

1941 (1)

Bondarczuk, K.

R. Ledzion, K. Bondarczuk, and W. Kucharczyk, 'Temperature dependence of the quadratic electrooptic effect and estimation of antipolarization of ADP,' Cryst. Res. Technol. 39, 161-164 (2004).
[CrossRef]

Chen, C. G.

Ciattoni, A.

Crosignani, B.

Dhayalan, V.

Di Porto, P.

Echarri, R. M.

Ferrera, J.

Gaylord, T. K.

Gori, F.

F. Gori, 'Flattened Gaussian beams,' Opt. Commun. 107, 335-341 (1994).
[CrossRef]

Heilmann, R. K.

Izdebski, M.

Jones, R. C.

Konkola, P. T.

Kucharczyk, W.

Ledzion, R.

R. Ledzion, K. Bondarczuk, and W. Kucharczyk, 'Temperature dependence of the quadratic electrooptic effect and estimation of antipolarization of ADP,' Cryst. Res. Technol. 39, 161-164 (2004).
[CrossRef]

Lee, H.

Li, Y.

Y. Li, H. Lee, and E. Wolf, 'New generalized Bessel-Gaussian beams,' J. Opt. Soc. Am. A 21, 640-646 (2004).
[CrossRef]

Y. Li, 'New expressions for flat-topped light beams,' Opt. Commun. 206, 225-234 (2002).
[CrossRef]

Maldonaldo, T. A.

Raab, R. E.

Ratajczyk, F.

I. Scierski and F. Ratajczyk, 'The Jones matrix of the real dichroic elliptic object,' Optik (Stuttgart) 68, 121-125 (1984).

Schattenburg, M. L.

Scierski, I.

I. Scierski and F. Ratajczyk, 'The Jones matrix of the real dichroic elliptic object,' Optik (Stuttgart) 68, 121-125 (1984).

Simon, M. C.

Stamnes, J. J.

Wolf, E.

Appl. Opt. (3)

Cryst. Res. Technol. (1)

R. Ledzion, K. Bondarczuk, and W. Kucharczyk, 'Temperature dependence of the quadratic electrooptic effect and estimation of antipolarization of ADP,' Cryst. Res. Technol. 39, 161-164 (2004).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Izdebski and W. Kucharczyk, 'On the indirect electro-optic modulation in noncentrosymmetric uniaxial crystals,' J. Opt. A, Pure Appl. Opt. 7, 204-206 (2005).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (7)

Opt. Commun. (2)

F. Gori, 'Flattened Gaussian beams,' Opt. Commun. 107, 335-341 (1994).
[CrossRef]

Y. Li, 'New expressions for flat-topped light beams,' Opt. Commun. 206, 225-234 (2002).
[CrossRef]

Optik (Stuttgart) (1)

I. Scierski and F. Ratajczyk, 'The Jones matrix of the real dichroic elliptic object,' Optik (Stuttgart) 68, 121-125 (1984).

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Figures (2)

Fig. 1
Fig. 1

Effective overlap S ef of the fast and slow beams emerging from a birefringent crystal versus the ratio of their lateral displacement u to their radius r for the following light profiles: uniform (solid curve), Gaussian (dotted curve), flat-topped Gaussian for M = 25 (dashed–dotted curve), and quasi-Gaussian (dashed curve).

Fig. 2
Fig. 2

Effect of the partial interference of the divergent fast and slow beams on the modulation index A ω : the case of Li Nb O 3 crystal in the configuration σ = ( 1 , 0 , 1 ) 2 and E = ( E , 0 , 0 ) . The results are plotted as a function of the ratio of the crystal length L to the radius r of the incident beam for the following light profiles: uniform (solid curve), Gaussian (dotted curve), flat-topped Gaussian for M = 25 (dashed–dotted curve), and quasi-Gaussian (dashed curve). The modulation parameters used are λ = 630 nm and the amplitude of the modulating electric field E 0 = 10 3 V m 1 .

Equations (26)

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J f = T f [ cos 2 β f sin β f cos β f e i δ sin β f cos β f e i δ sin 2 β f ] ,
J s = T s [ sin 2 β f e i Γ sin β f cos β f e i Γ e i δ sin β f cos β f e i Γ e i δ cos 2 β f e i Γ ] .
Γ = 2 π λ ( n s l s n f l f ) .
E f = J n J f J 1 E 0 ,
E s = J n J s J 1 E 0 ,
E m = J n ( J f + J s ) J 1 E 0 = E f + E s .
E ( x , y ) = J n [ ρ f ( x , y ) J f + ρ s ( x , y ) J s ] J 1 E 0 = ρ f ( x , y ) E f + ρ s ( x , y ) E s .
ρ f ( x , y ) = ρ ( x x f 0 , y y f 0 ) ,
ρ s ( x , y ) = ρ ( x x s 0 , y y s 0 ) ,
I ( x , y ) = ρ f 2 ( x , y ) I f + ρ s 2 ( x , y ) I s + ρ f ( x , y ) ρ s ( x , y ) ( I m I f I s ) .
Φ = I f + + ρ f 2 ( x , y ) d x d y + I s + + ρ s 2 ( x , y ) d x d y + ( I m I f I s ) + + ρ f ( x , y ) ρ s ( x , y ) d x d y .
I ¯ = I f + I s + ( I m I f I s ) S ef .
S ef = + + ρ f ( x , y ) ρ s ( x , y ) d x d y + + ρ 2 ( x , y ) d x d y .
u = [ ( x f 0 x s 0 ) 2 + ( y f 0 y s 0 ) 2 ] 1 2 .
I ¯ = I f + I s + 2 Re [ ( E f x E ̃ s x + E ̃ f y E s y ) S ef ] ,
S ef = + + ρ f ( x , y ) ρ ̃ s ( x , y ) d x d y + + ρ 2 ( x , y ) d x d y .
ρ ( x , y ) = 1 [ 1 exp ( γ x 2 + y 2 r 2 ) ] M ,
γ = m = 1 M 1 m .
ρ ( x , y ) = m = 1 M g m exp ( m γ x 2 + y 2 r 2 ) ,
g m = ( 1 ) m + 1 ( M m ) .
ρ ( x , y ) = ( x 2 + y 2 r 2 1 ) exp ( x 2 + y 2 r 2 ) ,
S ef = m = 1 M n = 1 M g m g n n + m exp ( γ m n m + n u 2 r 2 ) m = 1 M n = 1 M g m g n n + m .
S ef = 1 u π r 1 u 2 4 r 2 2 π sin 1 u 2 r .
S ef = exp ( u 2 2 r 2 ) ( 1 u 2 r 2 + u 4 8 r 4 ) .
σ = ( 1 , 0 , 1 ) 2 and E = ( E , 0 , 0 ) .
A ω = 2 2 π L E 0 n o 3 n e 3 r 232 λ ( n o 2 + n e 2 ) 3 2 .

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