Abstract

We propose and demonstrate a approach for Airy-like wave generation using one-dimensional arrayed waveguides instead of a cubic phase plate and a Fourier lens. We show that this Airy-like wave with quasi-Airy amplitude and quasi-cubic phase from arrayed waveguides end has abilities to remain quasi-nondiffracting and freely accelerating during propagation. We also study wave propagation in these waveguides based on supermode theory and beam propagation method. The numerical results are in good agreement with theoretical prediction.

© 2013 Optical Society of America

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2010 (2)

2009 (2)

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

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

2008 (2)

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

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

2007 (2)

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

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

2004 (1)

2002 (1)

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

1996 (1)

K. Unnikrishnan and A. Rau, Am. J. Phys. 64, 1034 (1996).
[CrossRef]

1993 (1)

W. Huang and C. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

1990 (1)

A. Tervonen, J. Appl. Phys. 67, 2746 (1990).
[CrossRef]

1987 (2)

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

J. Durnin, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1979 (1)

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

1973 (1)

Balazs, N.

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

Baumgartl, J.

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

Berry, M. V.

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

Broky, J.

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]

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.

Conti, G. N.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Dholakia, K.

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

Ding, J.

Dogariu, A.

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]

Durnin, J.

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

J. Durnin, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Efremidis, N. K.

Emmerson, G.

Friberg, A. T.

J. Turunen and A. T. Friberg, Prog. Opt. 54, 1 (2010).
[CrossRef]

Gawith, C.

Geraghty, D. F.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Guilhot, D.

Honkanen, S.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Hu, Y.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Huang, W.

W. Huang and C. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

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

Liu, Y.

Lu, C.

Madasamy, P.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Mazilu, M.

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

McIntyre, P. D.

Mills, M. S.

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

Moloney, J. V.

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

Morrell, M. M.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Peyghambarian, N.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Polynkin, P.

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

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

Poyhonen, P.

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Prakash, J.

Rau, A.

K. Unnikrishnan and A. Rau, Am. J. Phys. 64, 1034 (1996).
[CrossRef]

Salandrino, A.

Shepherd, D.

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.

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

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

Smith, P.

Snyder, A. W.

Tervonen, A.

A. Tervonen, J. Appl. Phys. 67, 2746 (1990).
[CrossRef]

Turunen, J.

J. Turunen and A. T. Friberg, Prog. Opt. 54, 1 (2010).
[CrossRef]

Unnikrishnan, K.

K. Unnikrishnan and A. Rau, Am. J. Phys. 64, 1034 (1996).
[CrossRef]

Wang, H. T.

Wang, S.

Watts, S.

Williams, R.

Xu, C.

W. Huang and C. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Yin, X.

Zhang, B. F.

Zhang, P.

Zhang, X.

Zhang, Z.

Zheng, Z.

Am. J. Phys. (2)

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

K. Unnikrishnan and A. Rau, Am. J. Phys. 64, 1034 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

W. Huang and C. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

J. Appl. Phys. (1)

A. Tervonen, J. Appl. Phys. 67, 2746 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Photonics (1)

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

Opt. Eng. (1)

P. Madasamy, G. N. Conti, P. Poyhonen, Y. Hu, M. M. Morrell, D. F. Geraghty, S. Honkanen, and N. Peyghambarian, Opt. Eng. 41, 1084 (2002).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. Lett. (3)

P. Polynkin, M. Kolesik, and J. Moloney, Phys. Rev. Lett. 103, 123902 (2009).
[CrossRef]

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

J. Durnin, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Prog. Opt. (1)

J. Turunen and A. T. Friberg, Prog. Opt. 54, 1 (2010).
[CrossRef]

Science (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

(a) Propagation dynamics of a finite-energy Airy packet in free space and (b) partial amplitude (red line) and phase curve (blue line) of propagation field at Z=160μm.

Fig. 2.
Fig. 2.

Schematic diagram of 3-waveguide arrays.

Fig. 3.
Fig. 3.

Simulated numerical results of wave propagation in 3-waveguide arrays using supermode theory: (a) coupling electric field distribution of array waveguides in XZ cross section; (b) amplitude (red line) and phase curve (blue line) of coupling electric field at Z1=0.78mm; (c) phase curve (circles) and its fitting cubic curve (solid line) in waveguide 2, the ideal cubic phase is shown in the inset.

Fig. 4.
Fig. 4.

Schematic diagram of 1D arrayed waveguides.

Fig. 5.
Fig. 5.

Simulation result of wave propagation in 1D arrayed waveguides using supermode theory: (a) coupling electric field distribution of array waveguides in XZ cross section and (b) amplitude (red line) and phase curve (blue line) of coupling electric field at Z=10.9mm.

Fig. 6.
Fig. 6.

Propagation dynamics of (a) finite-energy Airy packet and (b) truncated planar Airy-like beam generated by 1D arrayed 9-waveguide in free space.

Equations (9)

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

iϕξ+122ϕs2=0,
ϕ(s,ξ)=Ai[s(ξ/2)+iaξ]exp[as(aξ2/2)]×exp[i(ξ3/12)+i(a2ξ/2)+i(sξ/2)],
φ(s,ξ=0)=Ai(s)exp(as).
Φ0(k)=exp(ak2)exp[i3(k33a2kia3)].
ddzA=jM¯A,
A=[A1A2A3]T,M¯=(β0c12c13c21β0c23c31c32β0),
cpq=ω2Sq(εqε)ep·eqdS,
Am(x,y,z)=[pApmep(x,y)]ejβmz,
φ(x,y=0,z=Z1)=c1(xd)3+c2(xd)2+c3(xd)+c4,

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