Abstract

Linear-optical solutions to the problem of temporal broadening of ultrashort light pulses propagating in air or in solid optical samples are proposed and tested by computer simulations. A special holographic-element setup is analyzed in detail.

© 1996 Optical Society of America

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References

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1995

1993

1992

J. Lu, J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[CrossRef]

1991

1989

1987

J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Besieris, I. M.

Boothroyd, S. A.

Chrostowski, J.

Churin, E. G.

Drolet, J.-J.

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Eliyahu, D.

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988), Chap. 4.

Gorokhovskii, A.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Greenleaf, J. F.

J. Lu, J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[CrossRef]

Herman, R. M.

Hidaka, T.

T. Hidaka, Jpn. J. Appl. Phys. 30, 1738 (1991).
[CrossRef]

Kaarli, R.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Kolner, B. H.

Koronkevich, V. P.

Liu, H.-K.

Lu, J.

J. Lu, J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[CrossRef]

MacDonald, R. P.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Mikhaltsova, I. A.

Nazarathy, M.

Palm, V.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Rätsep, M.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Rosen, J.

Saari, P.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

P. Saari, in Technical Digest of the IX International Symposium on Ultrafast Processes in Spectroscopy (International Centre for Theoretical Physics, Trieste, Italy, 1995), paper TuA-2.

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, C. C. Denardo, eds. (Plenum, New York) (to be published).

Salik, B.

Salvatore, R. A.

Shaarawi, A. M.

Sõnajalg, H.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Syrett, B. A.

Turunen, J.

Vasara, A.

Wiggins, T. A.

Yariv, A.

Yurlov, Yu. I.

Ziolkowski, R. W.

Appl. Opt.

IEEE Trans. Ultrasonics Ferroelectron. Freq. Control

J. Lu, J. F. Greenleaf, IEEE Trans. Ultrasonics Ferroelectron. Freq. Control 39, 19 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

T. Hidaka, Jpn. J. Appl. Phys. 30, 1738 (1991).
[CrossRef]

Opt. Commun.

H. Sõnajalg, A. Gorokhovskii, R. Kaarli, V. Palm, M. Rätsep, P. Saari, Opt. Commun. 71, 377 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef] [PubMed]

Other

P. Saari, in Technical Digest of the IX International Symposium on Ultrafast Processes in Spectroscopy (International Centre for Theoretical Physics, Trieste, Italy, 1995), paper TuA-2.

P. Saari, in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, C. C. Denardo, eds. (Plenum, New York) (to be published).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988), Chap. 4.

In Optics, Opto-Mechanics, Lasers, Instruments (Melles Griot, Irvine, Calif., 1995).

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Figures (3)

Fig. 1
Fig. 1

BBG for transforming light pulses focused to form a point source.

Fig. 2
Fig. 2

(a) Calculated axial intensity curve (solid curve) and (b), (c) nonaxial intensity distributions of the Bessel-X pulse formed with the scheme of Fig. 1 and (a) the corresponding plane-wave pulse (dashed curve), both propagating in the same sample medium. The propagation depth is (b) z = 12 mm and (c) 36 mm.

Fig. 3
Fig. 3

Second derivative of the spectral field amplitude of the Bessel-X pulse (solid curve) and the plane wave (dashed curve) both shown in Fig. 2.

Equations (9)

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E ( ρ , z , t ) = 0 d ω S ( ω ) J 0 ( k ρ ρ ) exp [ i ( k z z ω t ) ] , k ρ ( ω ) = ( ω / c ) n ( ω ) sin θ ( ω ) , k z ( ω ) = ( ω / c ) n ( ω ) cos θ ( ω ) .
( ω / c ) n ( ω ) cos θ ( ω ) = a + b ω ,
E 2 ( ρ , ω ) = i k l exp [ i k ( l + ρ 2 2 l ) ] d ρ ρ × exp ( i k ρ 2 2 l ) J 0 ( k ρ ρ l ) E 1 ( ρ , ω ) ,
E 1 ( ρ , ω ) = exp ( i k ρ 2 2 f ) exp ( i k 0 ρ sin Θ i k 0 ρ 2 2 f ) .
E ( ρ , z , ω ) = i kn ( ω ) z exp [ i k n ( ω ) ( z + ρ 2 2 z ) ] × d ρ ' ρ ' exp [ i k n ( ω ) ρ ' 2 2 z ] J 0 [ k n ( ω ) ρ ρ ' z ] E 2 ( M ρ ' , ω ) .
E ( 0 , z , ω ) = 2 k φ 2 k 0 2 sin 2 Θ n ( ω ) [ n ( ω ) l + M 2 z ] exp ( i φ 1 ) × ( 1 + π φ 2 exp ( i φ 2 i π 4 ) × { 1 + 2 exp ( i π 4 ) [ C ( φ 2 ) + i S ( φ 2 ) ] } ) ,
φ 1 ( z , ω ) = k [ l + n ( ω ) z ] ,
φ 2 ( z , ω ) = k 0 2 sin 2 Θ 2 k [ n ( ω ) n ( ω ) l + M 2 z + k k 0 k f ] 1 .
Θ M = [ 2 n 0 n 1 3 ( l / f ) 2 + 4 ( l / f ) + 1 ] 1 / 2 .

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