Abstract

We show how the quantum process of splitting light may be modeled in classical optics. A second result is the possibility to engineer specific forms of a classical field.

© 2008 Optical Society of America

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References

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  1. M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
    [CrossRef]
  2. O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
    [CrossRef]
  3. F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
    [CrossRef]
  4. R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
    [CrossRef] [PubMed]
  5. M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
    [CrossRef]
  6. S. Scheel and D.-G. Welsch, Phys. Rev. A 64, 063811 (2001).
    [CrossRef]
  7. S. Chavez-Cerda, J. R. Moya-Cessa, and H. Moya-Cessa, J. Opt. Soc. Am. B 24, 404 (2007).
    [CrossRef]
  8. G. Arfken, Mathematical Methods for Physicists, (Academic, 1985), p. 720.
  9. H. Moya-Cessa, Phys. Rep. 432, 1 (2006).
    [CrossRef]
  10. S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
    [CrossRef] [PubMed]
  11. V. Buzek and T. Quang, J. Opt. Soc. Am. B 6, 2447 (1989).
    [CrossRef]
  12. K. Wodkiewicz and J. H. Eberly, J. Opt. Soc. Am. B 2, 458 (1985).
    [CrossRef]
  13. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
    [CrossRef]

2008 (1)

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

2007 (1)

2006 (1)

H. Moya-Cessa, Phys. Rep. 432, 1 (2006).
[CrossRef]

2004 (1)

O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
[CrossRef]

2002 (1)

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

2001 (2)

S. Scheel and D.-G. Welsch, Phys. Rev. A 64, 063811 (2001).
[CrossRef]

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
[CrossRef]

1993 (1)

S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
[CrossRef] [PubMed]

1989 (2)

V. Buzek and T. Quang, J. Opt. Soc. Am. B 6, 2447 (1989).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

1985 (1)

1963 (1)

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists, (Academic, 1985), p. 720.

Buzek, V.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

V. Buzek and T. Quang, J. Opt. Soc. Am. B 6, 2447 (1989).
[CrossRef]

Campos, R. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Chavez-Cerda, S.

Crasser, O.

O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
[CrossRef]

de Almeida, N. G.

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

Dutra, S. M.

S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
[CrossRef] [PubMed]

Eberly, J. H.

Glauber, R. J.

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Kim, M. S.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Knight, P. L.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
[CrossRef] [PubMed]

Mack, H.

O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
[CrossRef]

Man'ko, M. A.

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
[CrossRef]

Man'ko, V. I.

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
[CrossRef]

Moussa, M. H. Y.

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

Moya-Cessa, H.

S. Chavez-Cerda, J. R. Moya-Cessa, and H. Moya-Cessa, J. Opt. Soc. Am. B 24, 404 (2007).
[CrossRef]

H. Moya-Cessa, Phys. Rep. 432, 1 (2006).
[CrossRef]

S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
[CrossRef] [PubMed]

Moya-Cessa, J. R.

Prado, F. O.

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

Quang, T.

Saleh, B. E. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Scheel, S.

S. Scheel and D.-G. Welsch, Phys. Rev. A 64, 063811 (2001).
[CrossRef]

Schleich, W. P.

O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
[CrossRef]

Son, W.

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

Teich, M. C.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

Vilela Mendes, R.

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
[CrossRef]

Villas-Bôas, C. J.

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

Welsch, D.-G.

S. Scheel and D.-G. Welsch, Phys. Rev. A 64, 063811 (2001).
[CrossRef]

Wodkiewicz, K.

Fluct. Noise Lett. (1)

O. Crasser, H. Mack, and W. P. Schleich, Fluct. Noise Lett. 4, L43 (2004).
[CrossRef]

J. Opt. Soc. Am. B (3)

Phys. Lett. A (1)

M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, Phys. Lett. A 288, 132 (2001).
[CrossRef]

Phys. Rep. (1)

H. Moya-Cessa, Phys. Rep. 432, 1 (2006).
[CrossRef]

Phys. Rev. (1)

R. J. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Phys. Rev. A (5)

S. M. Dutra, P. L. Knight, and H. Moya-Cessa, Phys. Rev. A 48, 3168 (1993).
[CrossRef] [PubMed]

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, and C. J. Villas-Bôas, Phys. Rev. A 73, 043803 (2008).
[CrossRef]

R. A. Campos, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 40, 1371 (1989).
[CrossRef] [PubMed]

M. S. Kim, W. Son, V. Buzek, and P. L. Knight, Phys. Rev. A 65, 032323 (2002).
[CrossRef]

S. Scheel and D.-G. Welsch, Phys. Rev. A 64, 063811 (2001).
[CrossRef]

Other (1)

G. Arfken, Mathematical Methods for Physicists, (Academic, 1985), p. 720.

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Figures (1)

Fig. 1
Fig. 1

Configuration of the beam splitter (50:50) operation.

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

H = ω x a x a x + ω y a y a y + χ ( a y a x + a x a y ) ,
B = e i θ ( a y a x + a x a y )
B a x B = cos ( θ ) a x + i sin ( θ ) a y ,
B a y B = cos ( θ ) a y + i sin ( θ ) a x
ψ F = i 2 ( 2 x 0 y + 0 x 2 y ) .
2 i k 0 E z = 2 E + k 2 ( x , y ) E ,
i E z = 2 2 k 0 E + [ k 0 2 1 2 ( k 0 α ̃ x 2 x 2 + k 0 α ̃ y 2 y 2 ) + χ x y ] E ,
a q = k 0 α ̃ q 2 q + 1 2 k 0 α ̃ q d d q ,
a q = k 0 α ̃ q 2 q 1 2 k 0 α ̃ q d d q ,
u m ( x ) = ( k 0 α ̃ x π ) 1 4 1 2 m m ! H m ( k 0 α ̃ x x ) e k 0 α ̃ x x 2 2 ,
a x u m ( x ) = m u m 1 ( x ) ,
a x u m ( x ) = m + 1 u m + 1 ( x ) .
i E z = [ α ̃ x ( n x + 1 2 ) + α ̃ y ( n y + 1 2 ) + χ x y + k 0 2 ] E ,
i ψ z = [ α ̃ x n x + α ̃ y n y + χ ̃ ( a x a y + a x a y ) ] ψ ,
i φ z = [ Δ n y + χ ̃ ( a x a y + a x a y ) ] φ H φ ,
A 1 = δ a x + γ a y , A 2 = γ a x δ a y ,
δ = 2 χ ̃ 2 Ω ( Ω Δ ) , γ = Ω Δ 2 Ω , δ 2 + γ 2 = 1
[ A 1 , A 1 ] = [ A 2 , A 2 ] = 1.
[ A 1 , A 2 ] = [ A 1 , A 2 ] = 0 .
H = μ 1 A 1 A 1 + μ 2 A 2 A 2 ,
A m u 0 ( x ) u 0 ( y ) = 0 , m = 1 , 2 ;
u 0 ( x ) u 0 ( y ) = U 0 1 ( x , y ) U 0 2 ( x , y ) .
φ ( z = 0 ; x , y ) = u 1 ( x ) u 1 ( y ) ,
φ ( z ; x , y ) = e i z ( μ 1 A 1 A 1 + μ 2 A 2 A 2 ) a x a y u 0 ( x ) u 0 ( y ) .
φ ( z ; x , y ) = e i z μ 1 A 1 A 1 e i z μ 2 A 2 A 2 ( δ A 1 + γ A 2 ) ( γ A 1 δ A 2 ) U 0 1 ( x , y ) U 0 2 ( x , y ) .
φ ( z ; x , y ) = ( δ A 1 e i z μ 1 + γ A 2 e i z μ 2 ) ( γ A 1 e i z μ 1 δ A 2 e i z μ 2 ) U 0 1 ( x , y ) U 0 2 ( x , y ) ,
φ ( z ; x , y ) = [ η ( z ) β ( z ) a x 2 + ε ( z ) β ( z ) a y 2 + ( β 2 ( z ) + ε ( z ) η ( z ) ) a x a y ] u 0 ( x ) u 0 ( y ) ,
φ ( z 0 ; x , y ) = η ( z 0 ) β ( z 0 ) u 2 ( x ) u 0 ( y ) + ε ( z 0 ) β ( z 0 ) u 0 ( x ) u 2 ( y ) .
φ ( z = 0 ; x , y ) = u m ( x ) u 0 ( y ) = a x m m ! u 0 ( x ) u 0 ( y ) ,
φ ( z ; x , y ) = ( η ( z ) a x + β ( z ) a y ) m m ! u 0 ( x ) u 0 ( y ) ,
φ ( z ; x , y ) = n = 0 m ( m n ) 1 2 η m n ( z ) n β ( z ) u m n ( x ) u n ( y ) .
φ ( z = 0 ; x , y ) = ( k 0 α ̃ x π ) 1 4 e ( α x k 0 α ̃ x 2 ) 2 u 0 ( y ) e α 2 2 n α n n ! u n ( x ) u 0 ( y ) .
φ ( z = 0 ; x , y ) = D a x ( α ) u 0 ( x ) u 0 ( y ) ,
φ ( z ; x , y ) = D a x [ α η ( z ) ] u 0 ( x ) D a y [ α β ( z ) ] u 0 ( y ) .

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