Abstract

We identify a virtual source for generating an Airy wave. A spectral integral expression is derived to describe the Airy wave, which, in the paraxial limit, yields the freely accelerating, nondiffracting, and finite energy Airy beam. From the spectral representation of the Airy wave, the first two orders of nonparaxial corrections to the paraxial Airy beam are determined. Also, a connection between the obtained Airy wave and the well-known complex source point spherical wave is given.

© 2012 Optical Society of America

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References

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2009 (1)

2008 (2)

M. A. Bandres, Opt. Lett. 33, 1678 (2008).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

2007 (3)

2004 (1)

2003 (1)

2002 (2)

2001 (1)

2000 (1)

1987 (1)

1977 (1)

1976 (1)

1971 (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Bandres, M. A.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chávez-Cerda, S.

Chen, Z.

Christodoulides, D. N.

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

Felsen, L. B.

Gutiérrez-Vega, J. C.

Iturbe-Castillo, M. D.

Ji, J. H.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
[CrossRef]

New, G. H. C.

Novitsky, A. V.

Novitsky, D. V.

Seshadri, S. R.

Shi, Z. X.

Shin, S. Y.

Siviloglou, G. A.

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Song, Y. J.

Zhang, Y. H.

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Equations (29)

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ϕ(u,s=0)=Ai(u)exp(au),
[2/u2+2/s2+(kx0)2]F(u,s)=Sextexp[D(u)]δ(u)δ(szext),
D(u)=13(3u33a2u).
F(u,s)=12πF¯(p,s)exp(ipu)dp,
F¯(p,s)=F(u,s)exp(ipu)du,
F(u,s)=12πdpexp(ipu)iSext2ζ×exp[i3(p33a2p)]exp[iζ(szext)]
ζ=[(kx0)2p2]1/2.
Fp(u,s)=12πexp(ikz)[iSext2kx0exp(ikx0zext)]dpexp(ipu)exp[i3(p33a2p)]exp[ip22kx0s+ip22kx0zext],
Fp(u,s)=12πexp(ikz)[iSext2kx0exp(2ak2x02)]dpexp(ipu)×exp[i3(p33a2p)]exp[ip22kx0sap2].
Ai(t)=12πdqexp(iqt)exp(iq3/3),
Fp(u,s)=iSext2kx0e(ikz+2ak2x02a3/3)Ai[u(s1/2)2+ias1]×exp[auas12/2is13/12+ia2s1/2+ius1/2]
Fp(u,0)=[iSext2kx0exp(2ak2x02a3/3)]Ai(u)exp(au).
zext=i2akx0ib,
Sext=i2kx0exp[a3/32a(kx0)2],
F(u,s)=kx02πexp[a3/32a(kx0)2]dpexp(ipu)/ζ×exp[i3(p33a2p)]exp[iζ(sib)].
[t2+2/s2+(kx0)2]F(u,v,s)=Sextexp[D(u,v)]×δ(u)δ(v)δ(szext)
t2=2/u2+2/v2,
D(u,v)=13[(3u3+3a2u)(3v3+3a2v)].
ϕ(u,v,s=0)=Ai(u)Ai(v)exp[a(u+v)],
F(u,s)=12πexp[a3/3+ikz]dpexp(ipu)×exp[i3(p33a2p)ap2ip2s/(2kx0)]G(p,s).
G(p,s)=1+f2[p22ap44q2(s)]
F(u,s)=Fp(u,s)+f2F2(u,s),
F2(u,s)=[A(u,s)+B(u,s)u]Fp(u,s).
A(u,s)=(ua2)22a24q4a(ua2)24q2a3(ua2)q6,
B(u,s)=3a2q2a2(ua2)q42a4q8.
[t2+2/s2+(kx0)2]G(x,xext)=δ(u)δ(v)δ(sib).
G(x,xext)=exp(ikx0R)/4πR,
R=[u2+v2+(sib)2]1/2.
F(u,v,s)=i2kx0exp[2a3/32a(kx0)2]×exp[D(u,v)]exp(ikR)4πR.

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