Abstract

Gouy wave modes are linear waves with finite energy that propagate without distortion at any phase and group velocity through a focal region in a dispersive medium. These features make them potentially useful for the onset and control of nonlinear interactions.

© 2007 Optical Society of America

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References

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    [CrossRef]

2007 (1)

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

2006 (2)

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M. A. Porras, A. Piskarkskas, and P. Di Trapani, Phys. Rev. E 74, 047603 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

2003 (4)

S. Longhi, Phys. Rev. E 68, 066612 (2003).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

M. A. Porras, I. Gonzalo, and A. Mondello, Phys. Rev. E 67, 066604 (2003).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

2002 (1)

1996 (1)

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

M. A. Porras, A. Parola, D. Faccio, A. Couairon, and P. Di Trapani, Phys. Rev. A 76, 011803 (2007).
[CrossRef]

Phys. Rev. E (5)

M. A. Porras, I. Gonzalo, and A. Mondello, Phys. Rev. E 67, 066604 (2003).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

S. Longhi, Phys. Rev. E 68, 066612 (2003).
[CrossRef]

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M. A. Porras, A. Piskarkskas, and P. Di Trapani, Phys. Rev. E 74, 047603 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, Phys. Rev. Lett. 90, 170406 (2003).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

White curve, average transverse wavenumber [Eq. (7)] as a function of frequency for the Gouy WM in fused silica with ω 0 = 3.57 fs 1 , α = 0 , β = 0 . The propagation constant is calculated from a Selmeier relation for the refraction index. Gray-scale plots, spectral density a ̂ ω ( k , 0 ) 2 in logarithmic scale (10 decades plotted) of the (a) Gaussian beams of amplitude a ω ( r , 0 ) = exp ( r 2 s ω 2 ) at the waist and the (b) Bessel–Gauss beams with a ω ( r , 0 ) = J 0 ( K ω r ) exp ( r 2 s ω ) . The widths s ω of the Gaussian beams and K ω and s ω of the Bessel–Gauss beams are chosen at each frequency so as to fulfill Eq. (7).

Fig. 2
Fig. 2

(a) Average transverse wavenumber [Eq. (7)] of three Gouy WMs in fused silica and (b) Rayleigh range as a function of frequency when the constituents are Gaussian beams. The reference frequency is ω 0 = 3.57 fs 1 . Solid curve, α = β = 0 ; dashed curve, α = 0 , β = 0.04 μ m 1 ; dotted curve, α = 0.08 μ m 1 fs , β = 0.06 μ m 1 . For the spectral bandwidth Δ Ω = 3.15 fs 1 shown, the WM lengths are 2 L f = 20.0 , 14.3, and 7.0 μ m for the respective cases.

Fig. 3
Fig. 3

Propagation in fused silica of three Gouy WMs (solid curves) with (a) α = β = 0 , (b) α = 0 , β = 0.04 μ m 1 , and (c) α = 0.08 μ m 1 fs , β = 0.06 μ m 1 in their respective WM lengths [ L f , + L f ] , compared with the propagation of a plane pulse (dotted curves). The pulse form at L f (dashed curves) for the WMs and the plane pulse correspond to a uniform spectrum in Δ Ω = 3.15 fs 1 , about ω 0 = 3.57 fs 1 . The averaged intensity E ( 0 , z , t ) 2 and/or the instantaneous intensity ( R { E ( 0 , z , t ) } ) 2 are shown when convenient.

Equations (7)

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E ( r , z , t ) = d ω E ̂ ω ( r , z ) exp ( i ω t ) ,
a ̂ ω ( k , z ) = 2 π 0 d r r a ω ( r , z ) J 0 ( k r ) ,
d ϕ ω ( z ) d z = k 2 ω ( z ) 2 k ω ,
k 2 ω ( z ) = 0 d k k 3 a ̂ ω ( k , z ) [ 0 d k k a ̂ ω ( k , z ) ] 1 .
k z , Ω ( 0 ) = k Ω k 2 Ω ( 0 ) 2 k Ω = ( k 0 β ) + ( k 0 α ) Ω ,
E ( 0 , z , t ) = d Ω a Ω ( 0 , z ) exp { i Ω [ t ( k 0 α ) z ] } × exp [ i ( k 0 β ) z ] exp ( i ω 0 t ) ,
k 2 Ω 1 2 ( 0 ) = { 2 k Ω [ k Ω ( k 0 β ) ( k 0 α ) Ω ] } 1 2 .

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