Abstract

Second-order characteristic beam parameters, including beamwidth and far-field divergence, are generalized for hard-edge diffracted fields. On the basis of, the so-called moments formalism these parameters are shown to propagate through ABCD optical systems according to laws similar to those applied to systems with no hard-edge openings. The power–content ratio of any diffracted beam within a certain region is evaluated in terms of such generalized parameters. An alternative analytical expression of such generalized far-field divergence is also provided that is suitable for experimental measurements. Application to Gaussian beams diffracted by slits is included.

© 1993 Optical Society of America

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References

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1993 (1)

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 95, 18 (1993).
[CrossRef]

1992 (3)

H. Weber, Opt. Quantum Electron. 24, 1027 (1992).
[CrossRef]

J. Serna, P. M. Mejías, R. Martínez-Herrero, Opt. Quantum Electron. 24, 763 (1992).

R. Martínez-Herrero, P. M. Mejías, G. Piquero, Opt. Lett. 17, 1650 (1992).
[CrossRef] [PubMed]

1991 (2)

1990 (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

1988 (2)

R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

S. Lavi, R. Prochaska, E. Keren, Appl. Opt. 27, 3696 (1988).
[CrossRef] [PubMed]

1986 (1)

1970 (1)

Bastiaans, M. J.

Bélanger, P. A.

Collins, S. A.

Keren, E.

Lavi, S.

Martínez-Herrero, R.

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 95, 18 (1993).
[CrossRef]

J. Serna, P. M. Mejías, R. Martínez-Herrero, Opt. Quantum Electron. 24, 763 (1992).

R. Martínez-Herrero, P. M. Mejías, G. Piquero, Opt. Lett. 17, 1650 (1992).
[CrossRef] [PubMed]

J. Serna, R. Martínez-Herrero, P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
[CrossRef]

Mejías, P. M.

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 95, 18 (1993).
[CrossRef]

J. Serna, P. M. Mejías, R. Martínez-Herrero, Opt. Quantum Electron. 24, 763 (1992).

R. Martínez-Herrero, P. M. Mejías, G. Piquero, Opt. Lett. 17, 1650 (1992).
[CrossRef] [PubMed]

J. Serna, R. Martínez-Herrero, P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
[CrossRef]

Mukunda, N.

R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Piquero, G.

Prochaska, R.

Serna, J.

J. Serna, P. M. Mejías, R. Martínez-Herrero, Opt. Quantum Electron. 24, 763 (1992).

J. Serna, R. Martínez-Herrero, P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

Simon, R.

R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Sudarshan, E. C. G.

R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

Weber, H.

H. Weber, Opt. Quantum Electron. 24, 1027 (1992).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 95, 18 (1993).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (2)

H. Weber, Opt. Quantum Electron. 24, 1027 (1992).
[CrossRef]

J. Serna, P. M. Mejías, R. Martínez-Herrero, Opt. Quantum Electron. 24, 763 (1992).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).

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Equations (19)

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u 2 F = u 2 | F ( u ) | 2 d u / | F ( u ) | 2 d u ,
F ( u ) = D D f ( x ) exp ( ikxu ) d x ,
u 2 F = ( 4 / k 2 I D ) [ | f ( D ) | 2 + | f ( D ) | 2 ] + ( 1 / k 2 I ) D D | f ( x ) | 2 d x ,
u 2 F = ( 1 / J 0 ) u 2 | G ( u ) | 2 d u + 8 | f ( D ) | 2 λ / k 2 J 0 D ,
J ( u ) | F ( u ) | 2 2 | G ( u ) | 2 + 8 | f ( D | 2 sin 2 kDu / k 2 u 2 ,
( 1 / J 0 ) R Ω J ( u ) d u ( 2 / J 0 ) R Ω | G ( u ) | 2 d u + [ 8 | f ( D ) | 2 / J 0 ] R Ω d u sin 2 kDu / k 2 u 2 ,
( 1 / J 0 ) R Ω J ( u ) d u q ( 2 / W 2 J 0 ) u 2 | G ( u ) | 2 d u + 16 | f ( D ) | 2 / J 0 k 2 W .
q 2 u 2 F [ ( 1 / W 2 ) + ( D / W λ ) ] .
g ( y ) = ( i / λ B ) 1 / 2 × L L exp [ i ( k / 2 B ) ( A x 2 2 y x + D y 2 ) ] f ( x ) d x ,
| g ( y ) | 2 = | L L exp ( ikyx ) h ( x ) d x | 2 ,
y 2 g = [ 8 | h ( L ) | 2 / k 2 I L ] + ( 1 / k 2 I ) L L | h ( x ) | 2 d x ,
y 2 g = ( A 2 / I 0 ) L L x 2 | f ( x ) | 2 d x + ( B 2 / k 2 I 0 ) { [ 8 | f ( L ) | 2 / L + L L | f ( x ) | 2 d x } + ( 2 A B / 2 k I 0 i ) L L { x [ f ( x ) ] * f ( x ) x f ( x ) f * ( x ) } d x ,
[ 8 | f ( L ) | 2 / k 2 I 0 L ] + ( 1 / k 2 I 0 ) L L | f ( x ) | 2 d x = u 2 F ,
G ( v ) = exp ( ikyv ) g ( y ) d y .
G ( v ) = ( i / D ) 1 / 2 exp ( i π / 4 ) exp ( ikB v 2 / 2 D ) × L L exp ( ikC x 2 / 2 D ) exp ( ikxv / D ) f ( x ) d x .
g ( y ) = exp ( ikD y 2 / 2 B ) L L exp ( ikyx ) h ( x ) d x .
y v g = ( 1 / 2 ikI ) L L { x [ h ( x ) ] * h ( x ) x h * ( x ) h ( x ) } d x + ( D y 2 g / B ) ,
u 2 F = ( 1 / k 2 I ) { ( π 2 / 2 D 3 ) n n 2 J ( n λ / 2 D ) + [ 8 | f ( D ) | 2 / D } ,
q = L exp ( 2 p L 2 ) [ L L exp ( 2 p x 2 ) d x ] 1 .

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