Abstract

We propose and numerically analyze the transverse acceleration control for the Airy-like beams from incomplete Airy waveguide and Airy waveguide by rainbow effect. We show that the Airy-like beams have an obvious change in transverse acceleration with a slight variation (10 nm) in incident wavelength. The rainbow phenomenon is introduced to study the Airy-like beam propagation with a different wavelength. The equivalent initial launch angle is also considered to explain transverse acceleration of the Airy-like beams.

© 2014 Optical Society of America

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    [CrossRef]
  20. RSoft, http://optics.synopsys.com/rsoft/ (2013).

2013 (2)

2012 (1)

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

2011 (3)

2010 (2)

2009 (3)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

2008 (3)

2007 (2)

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

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

1977 (1)

H. M. Nussenzveig, Scientific American 236, 116 (1977).
[CrossRef]

Arie, A.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Baumgartl, J.

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

Broky, J.

Chen, H.

Chen, Z.

Christodoulides, D.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

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

Christodoulides, D. N.

Courvoisier, F.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Deng, H.

Dholakia, K.

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

Ding, J.

Dogariu, A.

Dolev, I.

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Dudley, J.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Ellenbogen, T.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Froehly, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Furfaro, L.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman and S. C. Gustafson, Introduction to Fourier Optics (McGraw-Hill, 1996), Vol. 10.

Gustafson, S. C.

J. W. Goodman and S. C. Gustafson, Introduction to Fourier Optics (McGraw-Hill, 1996), Vol. 10.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).

Hu, Y.

Huang, S.

Jacquot, M.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Lacourt, P.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Liu, S.

Liu, Y.

Lou, C.

Lu, C.

Mathis, A.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

Mazilu, M.

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

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).

Nussenzveig, H. M.

H. M. Nussenzveig, Scientific American 236, 116 (1977).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Salandrino, A.

Siviloglou, G.

G. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef]

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

Siviloglou, G. A.

Song, D.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

Wang, H. T.

Wang, S.

Xu, J.

Ye, Z.

Yin, X.

Yuan, L.

Zhang, B. F.

Zhang, P.

Zhang, X.

Zhao, J.

Zheng, Z.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

I. Dolev, T. Ellenbogen, N. Voloch-Bloch, and A. Arie, Appl. Phys. Lett. 95, 201112 (2009).
[CrossRef]

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. Lacourt, and J. Dudley, Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

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

Nat. Photonics (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photonics 3, 395 (2009).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

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

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef]

Scientific American (1)

H. M. Nussenzveig, Scientific American 236, 116 (1977).
[CrossRef]

Other (3)

RSoft, http://optics.synopsys.com/rsoft/ (2013).

J. W. Goodman and S. C. Gustafson, Introduction to Fourier Optics (McGraw-Hill, 1996), Vol. 10.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Ideal 2D truncated Airy beam. (b) Wave propagation. (c) Phase distributions of two truncated Airy beams with different initial launch angles θm=0 and θm=5mrad. The dotted line depicts the phase difference Δφ of the two beams. (d) Parabolic trajectories of main lobes of the truncated Airy beams with different wavelength.

Fig. 2.
Fig. 2.

(a) Scheme of the incomplete Airy waveguide. (b) Refractive index distribution in x axis (or in y axis).

Fig. 3.
Fig. 3.

Amplitude profiles of output beams from the incomplete Airy waveguide with a different incident wavelength: (a) λ=990nm, (b) λ=980nm and (c) λ=970nm. (d), (c), and (f) correspond to wave propagation of (a)–(c) along the 255° axis in free space, respectively.

Fig. 4.
Fig. 4.

Deflection of main lobes of output beams from the incomplete airy waveguide as a function of propagation distance in free space. Inset: scheme of primary rainbow.

Fig. 5.
Fig. 5.

(a) Phase distribution of output beams in Figs. 3(a)3(c). The dashed–dotted line depicts the phase profile of the ideal Airy beam. (b) Additional phase of three output beams compared to ideal truncated Airy beam. (c) Corresponds to the linear fitting curves of (b).

Fig. 6.
Fig. 6.

(a) Scheme of the Airy-waveguide. (b) Refractive index distribution in the x axis (or in y axis).

Fig. 7.
Fig. 7.

Amplitude profiles of output beams from the Airy waveguide with different wavelength input beams: (a) λ=990nm, (b) λ=980nm, and (c) λ=970nm. (d), (c) and (f) correspond to the wave propagation of (a), (b), and (c) along the 255° axis in free space, respectively.

Fig. 8.
Fig. 8.

(a) The phase distribution of output beams from the Airy waveguides of length 5.4 mm. (b) The additional phase of the three beams compared to ideal truncated Airy beam. (c) Linear fitting curves corresponding to (b).

Fig. 9.
Fig. 9.

Deflection of main lobes of output beams from the Airy waveguide as a function of propagation distance in free space. Inset: scheme of secondary rainbow.

Equations (7)

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

φ(x,y,z=0)=m=x,yAi(sm)exp(amsm)exp(ivmsm),
φ(x,y,z)=m=x,yum(sm,ξm),
u(sm,ξm)=Ai[smξm24vmξm+iamξm]exp[amsmamξm22amvmξm+i(ξm312+(am2vm2+sm)ξm2+vmsmvmξm22)].
θm=vmkm0,
{Δφx=vxsx=vx·(x/x0)=Kx·xΔφy=vysy=vy·(y/y0)=Ky·y,
θm=Km/k.
θy=θx=Kx/k=Kx/(2π/λ)=5mrad.

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