Abstract

The effects that quartic phase distortions produce in the beam-quality parameter of partially coherent symmetric-intensity beams are studied. An analytical expression for the beam-quality parameter at the output plane of a pure phase plate with quartic phase aberration has been derived. Explicit conditions to improve the beam quality are provided, and the corresponding optimized beam-quality value that can be attained for a given field has been determined.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1227 (1986).
    [Crossref]
  2. S. Lavi, R. Prochaska, E. Keren, Appl. Opt. 27, 3696 (1988).
    [Crossref] [PubMed]
  3. R. Simon, N. Mukunda, E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
    [Crossref]
  4. A. E. Siegman, Proc. Soc. Photo-Opt. Instrum. Eng. 1224, 2 (1990).
  5. P. A. Bélanger, Opt. Lett. 16, 196 (1991).
    [Crossref] [PubMed]
  6. A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
    [Crossref]
  7. J. Serna, R. Martínez-Herrero, P. M. Mejías, J. Opt. Soc. Am. A 8, 1094 (1991).
    [Crossref]
  8. R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 85, 162 (1991).
    [Crossref]
  9. J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
    [Crossref]
  10. A. E. Siegman, “Analysis of laser beam quality degradation cause by quartic phase aberrations,” submitted to Appl. Opt.

1992 (1)

J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
[Crossref]

1991 (4)

P. A. Bélanger, Opt. Lett. 16, 196 (1991).
[Crossref] [PubMed]

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[Crossref]

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

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 85, 162 (1991).
[Crossref]

1990 (1)

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

1988 (2)

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

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

1986 (1)

Bastiaans, M. J.

Bélanger, P. A.

Keren, E.

Lavi, S.

Martínez-Herrero, R.

J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
[Crossref]

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

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 85, 162 (1991).
[Crossref]

Mejías, P. M.

J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, Opt. Commun. 85, 162 (1991).
[Crossref]

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]

Prochaska, R.

Serna, J.

J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
[Crossref]

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

Siegman, A. E.

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[Crossref]

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

A. E. Siegman, “Analysis of laser beam quality degradation cause by quartic phase aberrations,” submitted to Appl. Opt.

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]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[Crossref]

J. Mod. Opt. (1)

J. Serna, P. M. Mejías, R. Martínez-Herrero, J. Mod. Opt. 39, 625 (1992).
[Crossref]

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. 85, 162 (1991).
[Crossref]

Opt. Lett. (1)

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

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

Other (1)

A. E. Siegman, “Analysis of laser beam quality degradation cause by quartic phase aberrations,” submitted to Appl. Opt.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (25)

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

G ( x 1 , x 2 ) , G ( x , x ) = G ( x , x ) = I ( x ) ,
G o ( x 1 , x 2 ) = G i ( x 1 , x 2 ) exp { i k [ f ( x 2 ) f ( x 1 ) ] } ,
h ( x , u , z ) = ( 1 / H ) G ( x + s / 2 , x s / 2 , z ) exp ( ikus ) d s ,
H = h d x d u
x m u n = x m u n h ( x , u , z ) d x d u .
x o = x i = 0 ,
x 2 o = x 2 i ,
u o = u i + ( 1 / P ) f ( x ) G i ( x , x ) d x ,
u o = x u i + ( 1 / P ) x f ( x ) G i ( x , x ) d x ,
u 2 o = u 2 i + ( i / k P ) f ( x ) { [ G i ( x 1 , x 2 ) / x 1 ] x 1 = x 2 = x [ G i ( x 1 , x 2 ) / x 2 ] x 1 = x 2 = x } d x + ( 1 / P ) [ f ( x ) ] 2 G i ( x , x ) d x ,
f ( x ) = a x 2 + b x 4 .
u o = 0 ,
( x u o ) 2 = ( x u i ) 2 + 4 a 2 ( x 2 i ) 2 + 16 b 2 ( x 4 i ) 2 + 4 a x u i x 2 i + 8 b x 4 i x u i + 16 a b x 4 i x 2 i ,
u 2 o = u 2 i + 4 a x u i + 8 b x 3 u i + 4 a 2 x 2 i + 16 b 2 x 6 i + 16 a b x 4 i ,
Q = x 2 u 2 x u 2 .
Q = ( M 2 ) 2 / 4 k 2 ,
Q o Q i = Δ Q = 16 b 2 S + 8 b T ,
S = x 6 i x 2 i ( x 4 i ) 2 ,
T = x 3 u i x 2 i x 4 i x u i .
( i ) sgn ( b ) sgn ( T ) ,
( ii ) | b | < | T | / 2 S .
| b | = | T | / 4 S .
2 ( Δ Q ) / b 2 > 0 ,
b = [ sgn ( T ) ] | T | / 4 S .
G ( x 1 , x 2 ) = A ( x 1 , x 2 ) exp [ ikd ( x 2 2 x 1 2 ) ] ,

Metrics