Abstract

The transmission of an optical beam through the compound cell of a differential refractometer with an absorbing sample is analyzed. Formulas for the lateral shift and the deflection angle of the transmitted optical beam for a complex refractive-index difference are obtained.

© 2009 Optical Society of America

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References

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  1. B. A. Brice and M. Halwer, J. Opt. Soc. Am. 41, 1033 (1951).
    [CrossRef]
  2. C. J. Penther and G. W. Noller, Rev. Sci. Instrum. 29, 43 (1958).
    [CrossRef]
  3. M. A. Karabegov, Meas. Tech. 50, 619 (2007).
    [CrossRef]
  4. H. F. Lam, J. Phys. Chem. B 111, 1531 (2007).
    [CrossRef] [PubMed]
  5. R. E. Collin, Antennas and Radiowave Propagation, McGraw Hill Series in Electrical Engineering (McGraw Hill, 1985), Chap. 4.
  6. W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
    [CrossRef]
  7. A. García-Valenzuela, E. G. Sandoval-Romero, and C. Sánchez-Pérez, Appl. Opt. 43, 4311 (2004).
    [CrossRef] [PubMed]

2007 (2)

M. A. Karabegov, Meas. Tech. 50, 619 (2007).
[CrossRef]

H. F. Lam, J. Phys. Chem. B 111, 1531 (2007).
[CrossRef] [PubMed]

2004 (1)

1996 (1)

W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
[CrossRef]

1958 (1)

C. J. Penther and G. W. Noller, Rev. Sci. Instrum. 29, 43 (1958).
[CrossRef]

1951 (1)

Brice, B. A.

Collin, R. E.

R. E. Collin, Antennas and Radiowave Propagation, McGraw Hill Series in Electrical Engineering (McGraw Hill, 1985), Chap. 4.

Gao, W.

W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
[CrossRef]

García-Valenzuela, A.

Halwer, M.

Karabegov, M. A.

M. A. Karabegov, Meas. Tech. 50, 619 (2007).
[CrossRef]

Kiyono, S.

W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
[CrossRef]

Lam, H. F.

H. F. Lam, J. Phys. Chem. B 111, 1531 (2007).
[CrossRef] [PubMed]

Noller, G. W.

C. J. Penther and G. W. Noller, Rev. Sci. Instrum. 29, 43 (1958).
[CrossRef]

Nomura, T.

W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
[CrossRef]

Penther, C. J.

C. J. Penther and G. W. Noller, Rev. Sci. Instrum. 29, 43 (1958).
[CrossRef]

Sánchez-Pérez, C.

Sandoval-Romero, E. G.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Phys. Chem. B (1)

H. F. Lam, J. Phys. Chem. B 111, 1531 (2007).
[CrossRef] [PubMed]

Meas. Tech. (1)

M. A. Karabegov, Meas. Tech. 50, 619 (2007).
[CrossRef]

Precis. Eng. (1)

W. Gao, S. Kiyono, and T. Nomura, Precis. Eng. 19, 37 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

C. J. Penther and G. W. Noller, Rev. Sci. Instrum. 29, 43 (1958).
[CrossRef]

Other (1)

R. E. Collin, Antennas and Radiowave Propagation, McGraw Hill Series in Electrical Engineering (McGraw Hill, 1985), Chap. 4.

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Figures (3)

Fig. 1
Fig. 1

Schematic of refraction and displacement of a light beam in a DR. In the drawing, it is assumed that n 2 = n m + δ n > n 1 = n m .

Fig. 2
Fig. 2

Schematic of the lateral displacement of the beam’s axis owing to attenuation in the second section of the cell.

Fig. 3
Fig. 3

Coordinate systems used. The distances along the incident-beam axis from the entrance plane to the partition slab ( z 1 = 0 ) and to the exit plane ( z 3 = 0 ) are L 1 and L 1 + L 2 , respectively.

Equations (17)

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Δ x = ± δ n [ L 2 n m + l ] tan ( χ ) ,
E ( x , y , z B ) = d k x d k y S ( k x , k y ) exp ( i k x x + i k y y + i k z z B ) ,
S t ( k x , k y ) = 1 4 π 2 d x d y E t ( x , y , z A ) exp ( i k x x i k y y ) ,
E ( x 3 , y 3 , 0 ) = t 1 t 2 t 3 d k x d k y S ( k x , k y ) exp ( i k z L 1 ) exp ( i k z 3 L 2 ) exp ( i k x 3 x 3 + i k y 3 y 3 ) ,
k x 3 = ( k x   cos   χ + k z   sin   χ ) cos   χ [ k 0 2 ( n 2 2 n 1 2 ) + ( k z   cos   χ k x   sin   χ ) 2 ] 1 / 2 sin   χ ,
k y 3 = k y ,
k z 3 = ( k x   cos   χ + k z   sin   χ ) sin   χ + [ k 0 2 ( n 2 2 n 1 2 ) + ( k z   cos   χ k x   sin   χ ) 2 ] 1 / 2 cos   χ ,
k z k 0 n m + k 0 δ n ( k x 2 + k y 2 ) / ( 2 n m k 0 ) ,
k x 3 k x + k 0 δ n   tan   χ + δ n k x tan 2 χ / n m ,
k z 3 k 0 n m δ n k x   tan   χ / n m ( k x 2 + k y 2 ) / ( 2 n m k 0 ) .
k z k 0 n m ( k x 2 + k y 2 ) / ( 2 n m k 0 ) ,
k x 3 k x k 0 δ n   tan   χ δ n k x tan 2 χ / n m ,
k z 3 k 0 n m + k 0 δ n + δ n k x   tan   χ / n m ( k x 2 + k y 2 ) / ( 2 n m k 0 ) .
( x 3 ) max ± ( δ n n m L 2 [ n m z R + L 1 ( L 1 + L 2 ) n m z R ] δ n n m ) tan   χ ,
I ( r , θ , ϕ ) = I 0 ( cos   θ / r ) 2 exp ( 2 k 0 δ n L q ) exp ( 1 2 w 2 η 2 ) exp ( 1 2 w 2 k 2 2 ) exp ( 1 2 w 2 [ k 1 η ] 2 ) ,
θ max ± ( δ n L 1 n m z R δ n ) tan   χ .
Δ x = ( x 3 ) max + θ max l .

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