Abstract

It is shown that self-focusing can be taken into account in an optical paraxial system by simply defining a new generalized radius of curvature, namely,

1qNL=1RjσπW2λ,
where (σ − 1) is the ratio of the power of the beam to the critical power for self-focusing.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976).
  2. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  3. L. Ronchi, C. Garbarino, Opt. Acta 29, 1171 (1982).
    [CrossRef]
  4. F. T. Arecchi, E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972).

1982 (1)

L. Ronchi, C. Garbarino, Opt. Acta 29, 1171 (1982).
[CrossRef]

Arecchi, F. T.

F. T. Arecchi, E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972).

Arnaud, J. A.

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976).

Garbarino, C.

L. Ronchi, C. Garbarino, Opt. Acta 29, 1171 (1982).
[CrossRef]

Ronchi, L.

L. Ronchi, C. Garbarino, Opt. Acta 29, 1171 (1982).
[CrossRef]

Schulz-Dubois, E. O.

F. T. Arecchi, E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972).

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Opt. Acta (1)

L. Ronchi, C. Garbarino, Opt. Acta 29, 1171 (1982).
[CrossRef]

Other (3)

F. T. Arecchi, E. O. Schulz-Dubois, Laser Handbook (North-Holland, Amsterdam, 1972).

J. A. Arnaud, Beam and Fiber Optics (Academic, New York, 1976).

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

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 (28)

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

1 q N L = 1 R j σ π W 2 λ,
× × E ω 2 μ ε E = 0.
E = ψ ( x , y , z ) exp ( i k z ) ,
T 2 ψ 2 i k ψ z + ( ω 2 μ ε K 2 ) ψ = 0 , T 2 = 2 x 2 + 2 y 2 .
ω 2 μ ε = K 0 2 ( z ) K K 2 ( z ) r 2 , r 2 = x 2 + y 2 .
ψ = A ( z ) exp [ i K 2 r 2 q ( z ) ] ,
q ( z ) 1 q ( z ) 2 K 2 ( z ) K = 0 ,
A ( z ) A ( z ) + 1 q ( z ) [ K 0 2 ( z ) K 2 ] 2 i k = 0.
( | A ( z ) | 2 ) | A ( z ) | 2 + 2 R ( z ) = 0 ,
1 q ( z ) = 1 R ( z ) j λ π W ( z ) 2 .
1 R ( z ) = W ( z ) W ( z ) .
| A ( z ) | 2 = | A ( 0 ) | 2 W 0 2 W ( z ) 2 .
| A ( z ) | 2 = 4 η π 1 W ( z ) 2 P 0 ,
ε = ε 0 [ 1 + χ L + χ ( 3 ) | E | 2 ] .
ε ε 0 [ 1 + χ L + χ ( 3 ) | A | 2 2 χ ( 3 ) | A | 2 r 2 W 2 ] ,
K 2 ( z ) K = 2 χ ( 3 ) | A ( z ) | 2 ( 1 + χ L ) W ( z ) 2 .
K 2 ( z ) K = 8 η χ ( 3 ) π ( 1 + χ L ) P 0 W ( z ) 4 .
q 1 q 2 P 0 P c ( λ π W 2 ) 2 = 0 ,
P c = λ 2 ( 1 + χ L ) 8 π η χ ( 3 ) .
( 1 R ) + 1 R 2 σ ( λ π W 2 ) 2 = 0 ,
( λ π W 2 ) + 2 ( λ π W 2 ) 1 R = 0 ,
σ = 1 P 0 / P c .
( 1 R ) j σ ( λ π W 2 ) + 1 R 2 2 j σ R ( λ π W 2 ) σ ( λ π W 2 ) 2 = 0.
1 q N L = 1 R j σ λ π W 2 .
( q N L ) 1 = 0.
q N L = q 0 N L + Z .
W 2 ( z ) = W 0 2 [ ( 1 + Z R 0 ) 2 + σ z 2 z 0 2 ] ,
1 R = W 0 2 W 2 [ 1 R 0 + z R 0 2 + σ z z 0 2 ] ,

Metrics