Abstract

By studying the effect of spatially induced group velocity dispersion (SIGVD) during the propagation of ultrashort pulsed Bessel beams in free space, we numerically prove that third-order SIGVD can temporally cause Gaussian distribution of pulsed Bessel beams to gradually evolve as unsymmetrical trailing oscillatory structures. The pulse shape is confirmed to be temporal Airy distributions on the basis of the cross-correlation function. Therefore, it is demonstrated that the scheme of generating spatiotemporally nonspreading Airy–Bessel wave packets in free space is possible by using a precompensating second-order SIGVD. The results of numerical simulation show that the quasi-Airy pulses induced by third-order SIGVD are temporally nonspreading during propagation in dispersive media. The reasons for nonspreading of such Airy distribution pulses are phenomenologically analyzed by a time–frequency Wigner distribution function of the pulse.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (2)

K. Y. Kim, C. Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[CrossRef]

R. P. Chen, H. P. Zheng, and C. Q. Dai, “Wigner distribution function of an Airy beam,” J. Opt. Soc. Am. A 28, 1307–1311 (2011).
[CrossRef]

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

2009 (1)

2007 (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

2005 (1)

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

2002 (2)

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J Opt Soc Am. A 19, 49–53 (2002).
[CrossRef]

C. J. R. Sheppard, “Generalized Bessel pulse beams,” J. Opt. Soc. Am. A 19, 2218–2222 (2002).
[CrossRef]

2001 (2)

1999 (1)

G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
[CrossRef]

1997 (1)

1996 (1)

1989 (1)

1988 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

1978 (1)

M J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995), Chap. 3.

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Bastiaans, M J.

M J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Berriel-Valdos, L. R.

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Bescos, J.

Bowlan, P.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, R. P.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dai, C. Q.

Dholakia, K.

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Gonzalo, C.

Guo, H.

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J Opt Soc Am. A 19, 49–53 (2002).
[CrossRef]

Hu, W.

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J Opt Soc Am. A 19, 49–53 (2002).
[CrossRef]

Hwang, C. Y.

K. Y. Kim, C. Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[CrossRef]

Kim, K. Y.

K. Y. Kim, C. Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[CrossRef]

Lee, B.

K. Y. Kim, C. Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[CrossRef]

Lohmus, M.

Mcgloin, D.

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[CrossRef]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Piksarv, P.

Porras, M. A.

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Saari, P.

Santamaria, J.

Shaarawi, A. M.

Sheppard, C. J. R.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Sõnajalg, H.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Trebino, R.

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Valtna-Lukner, H.

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Zheng, H. P.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Appl. Opt. (1)

Contemp. Phys. (1)

D. Mcgloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J Opt Soc Am. A (1)

W. Hu and H. Guo, “Ultrashort pulsed Bessel beams and spatially induced group-velocity dispersion,” J Opt Soc Am. A 19, 49–53 (2002).
[CrossRef]

J. Opt. Soc. Am. A (4)

Nat. Photon. (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photon. 4, 103–106 (2010).
[CrossRef]

Opt. Commun. (2)

G. P. Agrawal, “Far-field diffraction of pulsed optical beams in dispersive media,” Opt. Commun. 167, 15–22 (1999).
[CrossRef]

M J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (3)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Slow non-dispersing wavepackets (1)

K. Y. Kim, C. Y. Hwang, and B. Lee, “Slow non-dispersing wavepackets,” Opt. Express 19, 2286–2293 (2011).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995), Chap. 3.

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Figures (7)

Fig. 1.
Fig. 1.

Broadening factor η of pulsed Bessel beams as a function of z / L 2 .

Fig. 2.
Fig. 2.

Temporal profile of pulsed Bessel beams after propagation through z  = 0 , L 3 , 5 L 3 in free space, being of a Gaussian profile at z = 0 .

Fig. 3.
Fig. 3.

Correlation coefficient of the pulse induced by third-order SIGVD and the IAP as a function of z / L 3 .

Fig. 4.
Fig. 4.

Evolution of the Gaussian pulse after dispersive propagation through z = 0 , L M 2 , 2 L M 2 , 3 L M 2 , 4 L M 2 , 5 L M 2 ; it denotes an initial input pulse at z = 0 .

Fig. 5.
Fig. 5.

Evolution of (a) IAP, (b) QAP, after dispersive propagation through z = 0 , L M 2 , 2 L M 2 , 3 L M 2 , 4 L M 2 , 5 L M 2 ; it denotes an initial input pulse at z = 0 .

Fig. 6.
Fig. 6.

Normalized time–frequency WDF in the plane z = 0 of media, (a) Gaussian pulse, (b), (c) QAP after free propagation through z = 5 L 3 , 50 L 3 , (d) IAP.

Fig. 7.
Fig. 7.

Normalized time–frequency WDF of pulse in the plane z = 5 L M 2 of media, (a) Gaussian pulse, (b), (c) QAP after free propagation through z = 5 L 3 , 50 L 3 , (d) IAP.

Equations (24)

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

2 E + k 2 E = 0 ,
F ( r ) = J 0 ( a r ) ,
E ( x , y , z ; ω ) = J 0 ( a r ) U ¯ ( z , ω ω 0 ) exp ( j β 0 z ) ,
Δ 2 J 0 ( a r ) = a 2 J 0 ( a r ) ,
2 j β U ¯ z + ( k 2 a 2 β 0 2 ) U ¯ = 0.
β 2 = k 2 a 2 ,
U ¯ z = j ( β β 0 ) U ¯ .
β ( ω ) = β 0 + m = 1 β m m ! ( ω ω 0 ) m .
sin φ = a / k 0 ,
β 0 = k 0 cos φ .
β 1 = 1 / ( c · cos φ ) .
β 2 = k 0 t g 2 φ / ω 0 2 cos φ .
β 3 = 3 k 0 t g 2 φ ω 0 3 cos 3 φ .
k z 2 = k 2 k 2 .
U ( z , t ) = 1 2 π U ¯ ( z , ω ω 0 ) exp [ i ( ω ω 0 ) t ] d ω .
i U z = β 2 2 2 U T 2 + i 6 β 3 3 U T 3 .
L 2 = 2 π λ 0 m 2 cos φ / t g 2 φ ,
L 3 = 4 3 π 2 λ 0 m 3 cos 3 φ / t g 2 φ ,
γ = f * ( a ) g ( a ) d a [ | f ( a ) | 2 d a | g ( a ) | 2 d a ] 1 / 2 ,
Δ β + + β _ L _ = 0.
W ( T , ω ; z ) = A ( T + T / 2 , z ) · A * ( T T / 2 , z ) · exp ( i ω T ) d T ,
W ( T , ω ) d T = | F ( ω ) | 2 .
W ( T , ω ) d ω = | F ( T ) | 2 .
W ( T T 0 , ω ) f ( T T 0 ) .

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