Abstract

We study nondiffracting accelerating paraxial optical beams in periodic potentials, in both the linear and the nonlinear domains. In particular, we show that only a unique class of z-dependent lattices can support a true accelerating diffractionless beam. Accelerating lattice solitons, autofocusing beams and accelerating bullets in optical lattices are systematically examined.

© 2014 Optical Society of America

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  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
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  5. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  6. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  7. R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
    [CrossRef]
  8. X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, Opt. Lett. 39, 1065 (2014).
  9. N. K. Efremidis and I. D. Chremmos, Opt. Lett. 37, 1277 (2012).
    [CrossRef]
  10. I. D. Chremmos and N. K. Efremidis, Phys. Rev. A 85, 063830 (2012).
  11. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
    [CrossRef]
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  14. M. A. Bandres and B. M. Rodrıguez-Lara, New J. Phys. 15, 013054 (2013).
    [CrossRef]
  15. I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 8886 (2013).
    [CrossRef]
  16. I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
    [CrossRef]
  17. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  18. R. Iyer, J. S. Aitchison, J. Wan, M. C. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007).
  19. N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
    [CrossRef]
  20. D. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
    [CrossRef]

2014

2013

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 8886 (2013).
[CrossRef]

M. A. Bandres and B. M. Rodrıguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

2012

2011

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
[CrossRef]

D. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
[CrossRef]

2010

2007

2000

1999

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

1987

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

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

Aitchison, J. S.

Bai, J.

Bandres, M. A.

M. A. Bandres and B. M. Rodrıguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Bekenstein, R.

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

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Broky, J.

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

Cannan, D.

Chávez-Cerda, S.

Chen, Z.

Chremmos, I. D.

N. K. Efremidis and I. D. Chremmos, Opt. Lett. 37, 1277 (2012).
[CrossRef]

I. D. Chremmos and N. K. Efremidis, Phys. Rev. A 85, 063830 (2012).

Christodoulides, D. N.

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, Opt. Lett. 39, 1065 (2014).

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
[CrossRef]

D. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef]

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

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

Courvoisier, F.

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

de Sterke, C. M.

Dignam, M. C.

Dogariu, A.

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

Dudley, J. M.

Durnin, J.

J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
[CrossRef]

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

Eberly, J. H.

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

Efremidis, N. K.

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

El-Ganainy, R.

X. Qi, K. G. Makris, R. El-Ganainy, P. Zhang, J. Bai, D. N. Christodoulides, and Z. Chen, Opt. Lett. 39, 1065 (2014).

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
[CrossRef]

Froehly, L.

Furfaro, L.

Giust, R.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Gutiérrez-Vega, J. C.

Hu, Y.

Iturbe-Castillo, M. D.

Iyer, R.

Jacquot, M.

Kaminer, I.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 8886 (2013).
[CrossRef]

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

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Lacourt, P. A.

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Li, T.

Makris, K. G.

Mathis, A.

Miceli, J. J.

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

Miri, M. A.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
[CrossRef]

Morandotti, R.

Nemirovsky, J.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 8886 (2013).
[CrossRef]

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

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Papazoglou, D.

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Qi, X.

Rodriguez-Lara, B. M.

M. A. Bandres and B. M. Rodrıguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Salandrino, A.

Segev, M.

I. Kaminer, J. Nemirovsky, K. G. Makris, and M. Segev, Opt. Express 21, 8886 (2013).
[CrossRef]

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

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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]

Tzortzakis, S.

Wan, J.

Zhang, P.

Zhang, X.

J. Opt. Soc. Am. A

New J. Phys.

M. A. Bandres and B. M. Rodrıguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 491 (1987).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, Phys. Rev. A 84, 023842 (2011).
[CrossRef]

I. D. Chremmos and N. K. Efremidis, Phys. Rev. A 85, 063830 (2012).

Phys. Rev. Lett.

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

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

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

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Truncated WS beam (solid lines) of the lattice in the moving frame for a=1 at z=0 (the dotted lines represent the waveguide channels). (b) Linear propagation dynamics of the beam of (a) in a z-dependent linear potential. (c), (d) Same quantities as in (a), (b) but for a lattice with a=0.01. Both insets illustrate the z-dependent lattice in the lab frame (the vertical axis: propagation distance z, horizontal axis: transverse coordinate x).

Fig. 2.
Fig. 2.

(a) Highly confined accelerating lattice soliton for A=1, a=0.001 in a parabolically bended lattice and (b) dynamics of the same soliton in a lattice that follows the different trajectory x=(0.035z)1.5. In both cases the nonlinearity is self-focusing.

Fig. 3.
Fig. 3.

Diffraction dynamics of (a) a single WS mode and (b) an autofocusing beam (superposition of two WS modes) in a propagation-invariant lattice with A=1, a=0.01. In both cases the optical intensities of the propagating beams are depicted for various values of the propagation distance.

Fig. 4.
Fig. 4.

(a) Intensity profile of the accelerating optical bullet at z=0, and top view profiles for propagation distances (b) z=3, and (c) z=5.

Equations (9)

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

iUz+Uxx+V(x,z)U+γ|U|2U=0,
ϕx¯x¯+[F(z)θx¯θzθx¯2+V(x¯,z)]ϕ+γϕ3=0,
[2θx¯F(z)]ϕx¯+θx¯x¯ϕ=0.
F(z)θx¯θzθx¯2+V(x¯,z)=function ofx¯only,
θx¯=12F(z)=function ofzonly.
F2(z)4F(z)2x¯c1(z)+V(x¯,z)=function ofx¯.
V(x,z)=V0(x¯)λ,
U(x,z)=ϕ(x,z)exp[i(axz2a2z3/3)],
ϕx¯x¯+[V0(x¯)ax¯]ϕ+γϕ3=λϕ,

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