Abstract

We introduce nonparaxial spatially accelerating waves whose two-dimensional transverse profiles propagate along semicircular trajectories while approximately preserving their shape. We derive these waves by considering imaginary displacements on spherical fields, leading to simple closed-form expressions. The structure of these waves also allows the closed-form description of pulses.

© 2012 Optical Society of America

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References

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  1. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. S. Vo, K. Fuerschbach, K. P. Thompson, M. A. Alonso, and J. P. Rolland, J. Opt. Soc. Am. A 27, 2574 (2010).
    [CrossRef]
  4. M. A. Bandres, Opt. Lett. 33, 1678 (2008).
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  5. M. A. Bandres, Opt. Lett. 34, 3791 (2009).
    [CrossRef]
  6. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
    [CrossRef]
  7. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
    [CrossRef]
  8. L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, Opt. Express 19, 16455 (2011).
    [CrossRef]
  9. F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
    [CrossRef]
  10. M. V. Berry, J. Phys. A 27, L391 (1994).
    [CrossRef]
  11. M. V. Berry, Sci. Prog. 57, 43 (1969).

2012 (3)

2011 (1)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

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

1994 (1)

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

1969 (1)

M. V. Berry, Sci. Prog. 57, 43 (1969).

Alonso, M. A.

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bandres, M. A.

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

M. V. Berry, Sci. Prog. 57, 43 (1969).

Broky, J.

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

Cannan, D.

Chen, Z.

Christodoulides, D. N.

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

Courvoisier, F.

Dogariu, A.

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

Dudley, J. M.

Froehly, L.

Fuerschbach, K.

Furfaro, L.

Giust, R.

Hu, Y.

Jacquot, M.

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Lacourt, P. A.

Li, T.

Mathis, A.

Morandotti, R.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Rolland, J. P.

Salandrino, A.

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Siviloglou, G. A.

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

Thompson, K. P.

Vo, S.

Zhang, P.

Zhang, X.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. A (1)

M. V. Berry, J. Phys. A 27, L391 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

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

Sci. Prog. (1)

M. V. Berry, Sci. Prog. 57, 43 (1969).

Supplementary Material (4)

» Media 1: MOV (1020 KB)     
» Media 2: MOV (1155 KB)     
» Media 3: MOV (1307 KB)     
» Media 4: MOV (1255 KB)     

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Figures (2)

Fig. 1.
Fig. 1.

Intensities over a 90×80 rectangle (in units of k1) of m=40 Bessel fields: (a) unapertured, apertured with (b) α=π and (c) α=π/2, and apodized with (d) q=1.88 and (e) q=3. The insets indicate the power angular spectrum.

Fig. 2.
Fig. 2.

Intensities over sections of size 180×156 (in units of k1) of the z=0 and x=0 planes for (a)–(h),(m) the waves in Eq. (5) [(f) Media 1, (g) Media 2, (h) Media 3], (i)–(l) truncated spherical waves with α=π, (n) the waves in Eq. (6), and (o)–(q) the pulses in Eq. (8) (Media 4). The caustic’s cross section is shown in (m) and (n).

Equations (8)

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ψm(x,z)=u0imJm[kx2+z2]exp[imarctan(z,x)],
ψm(x,z)=ππAm(ϕ)exp[ik(xsinϕ+zcosϕ)]dϕ,
ψm(x,z;q)=exp(q)ψm(x,ziq/k).
Λlm(r)=Ylm(θ,ϕ)exp(ikr·u)dΩ=4πiljl(kx2+y2+z2)×Ylm[arctan(y,x2+z2),arctan(z,x)],
Ψnm(r;q)=u0exp(q)Λm+nm(x,y,ziq/k)
Ψnmi2(Ψn+1mΨn1m).
jl(u)=p=0l(2lp)![(iu)pexp(iu)(iu)pexp(iu)]2lp+1iul+1p!(lp)!.
Pnm(r,t)=f˜(ω)ωm+n+1Λm+nm(r)exp(iωt)dω=4πYm+nm(θ,ϕ)(ic2r)m+n+1×p=0m+n(2m+2np)!p!(m+np)!(2rc)p×[(1)pf(p)(t+rc)f(p)(trc)],

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