Abstract

Femtosecond space–time coupling effects in dispersive nonlinear media are investigated by a simple approximate method. The applicability of the method is verified by comparison with earlier numerical simulations. New results are presented for astigmatic beams as well as for negative dispersion. The position of the beam waist in the material changes the collapse threshold. For astigmatic beams, collapse is prevented for pulse durations shorter than a critical value.

© 1996 Optical Society of America

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References

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1995

1994

1993

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

1992

1991

1990

Y. Silberberg, Opt. Lett. 15, 1282 (1990).
[CrossRef] [PubMed]

E. Cornolti, M. Lucchesi, B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

1989

S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Agrawal, G. P.

A. T. Ryan, G. P. Agrawal, Opt. Lett. 20, 506 (1995).
[CrossRef]

Anderson, D.

Cerullo, G.

Chernev, P.

Christov, I. P.

Cornolti, E.

E. Cornolti, M. Lucchesi, B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Crosignani, B.

B. Crosignani, P. Di Porto, M. Paizzola, Pure Appl. Opt. 1, 7 (1992).
[CrossRef]

De Silvestri, S.

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Desaix, M.

DeSilverstri, S.

Di Porto, P.

B. Crosignani, P. Di Porto, M. Paizzola, Pure Appl. Opt. 1, 7 (1992).
[CrossRef]

Huang, C.

Kapteyn, H. C.

Lisak, M.

Lucchesi, M.

E. Cornolti, M. Lucchesi, B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Luther, G. G.

Magni, V.

Moloney, J. V.

Monguzzi, A.

Murnane, M. M.

Newell, A. C.

Paizzola, M.

B. Crosignani, P. Di Porto, M. Paizzola, Pure Appl. Opt. 1, 7 (1992).
[CrossRef]

Petrov, V.

Piskunova, L. V.

S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Rothenberg, J. E.

Ryan, A. T.

A. T. Ryan, G. P. Agrawal, Opt. Lett. 20, 506 (1995).
[CrossRef]

Silberberg, Y.

Talanov, V. I.

S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Vlasov, S. N.

S. N. Vlasov, L. V. Piskunova, V. I. Talanov, Sov. Phys. JETP 68, 1125 (1989).

Wright, E. M.

Zambon, B.

E. Cornolti, M. Lucchesi, B. Zambon, Opt. Commun. 75, 129 (1990).
[CrossRef]

Zhou, J.

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Figures (2)

Fig. 1
Fig. 1

Collapse threshold versus normalized dispersion-pulse-width parameter γ for spatially symmetric beams. Solid curve, unfocused input beams; upper dashed curve, focused input beam α = −1.33; lower dashed curve, defocused input beam α = +1.33. Open and filled circles correspond to some of the points (collapsing and noncollapsing, respectively) numerically calculated in Ref. 4. The square is from Eq. (4) of Ref. 1, renormalized to our notation. The inset shows pulse evolution in the plane (wτ, wξ = wη) of one collapsing and one noncollapsing case for each positive (dashed curve) and negative (solid curve) GVD. The star marks the input wξ(0) = 200, wτ(0) = 150.

Fig. 2
Fig. 2

Collapse threshold for pulses with spatial (xy) astigmatism, positive GVD, and unfocused input beams. The dashed curve is the spatially symmetric case of Fig. 1.

Equations (6)

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4 j u ζ + ( 2 ξ 2 + 2 η 2 ± 2 τ 2 ) u + | u | 2 u = 0 ,
u = u 0 exp [ ξ 2 w ξ 2 η 2 w η 2 τ 2 w τ 2      j ( ξ 2 R ξ + η 2 R η + τ 2 R τ ) + j ϕ ] ,
| u | 2 3 4 [ 1 2 3 ( ξ 2 w ξ 2 + η 2 w η 2 + τ 2 w τ 2 ) ] ,
w i d 2 w i d ζ 2 = 1 w i 2 ± C w ξ w η w τ ,
1 R i = ± 1 w i d w 1 d ζ ,
α = w ξ 2 / R ξ = π w x 2 / λ R x , β = w τ 2 / R τ = w t 2 S , δ = w ξ 2 / w η 2 = w x 2 / w y 2 , γ = sgn ( k " ) w ξ 2 / w τ 2 = k " k w x 2 / w t 2 .

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