Abstract

We find accelerating beams in a general periodic optical system, such as photonic crystal slabs, honeycomb lattices, and various metamaterials. These beams retain a shape-preserving profile while bending to highly non-paraxial angles along a circular-like trajectory. The properties of such beams depend on the crystal lattice structure: on a small-scale, the fine features of the beams profile are uniquely derived from the exact structure of the crystalline cells, while on a large-scale the beam only depends on the periodicity of the lattice, asymptotically reaching the free-space analytic solutions when the wavelength is much larger than the cell size. We demonstrate such beams in a 2D Kronig-Penney separable model, but our methodology of finding such solutions is general, predicting accelerating beams in any periodic structure. This highlights how light can be guided through a general system by only tailoring the incoming field, without altering the structure itself.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2012 (9)

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett.37(10), 1736–1738 (2012).
[CrossRef] [PubMed]

I. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85(2), 023828 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37(15), 3201–3203 (2012).
[CrossRef] [PubMed]

I. D. Chremmos and N. K. Efremidis, “Band-specific phase engineering for curving and focusing light in waveguide arrays,” Phys. Rev. A85(6), 063830 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
[CrossRef] [PubMed]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys.8(12), 912–917 (2012).
[CrossRef]

2011 (9)

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
[CrossRef] [PubMed]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106(19), 193904 (2011).
[CrossRef] [PubMed]

B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, “Diverging rabi oscillations in subwavelength photonic lattices,” Phys. Rev. Lett.106(7), 073901 (2011).
[CrossRef] [PubMed]

R. E-, “Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
[CrossRef] [PubMed]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (3)

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
[CrossRef] [PubMed]

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

2008 (5)

2007 (3)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446(7131), 52–55 (2007).
[CrossRef] [PubMed]

2006 (2)

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440(7088), 1166–1169 (2006).
[CrossRef] [PubMed]

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

2005 (1)

2000 (1)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature404(6779), 740–743 (2000).
[CrossRef] [PubMed]

1999 (3)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60(8), 5751–5758 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett.83(23), 4756–4759 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83(23), 4752–4755 (1999).
[CrossRef]

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

1987 (1)

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett.83(23), 4756–4759 (1999).
[CrossRef]

Aleahmad, P.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
[CrossRef] [PubMed]

Alfassi, B.

B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, “Diverging rabi oscillations in subwavelength photonic lattices,” Phys. Rev. Lett.106(7), 073901 (2011).
[CrossRef] [PubMed]

Arie, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Bandres, M. A.

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446(7131), 52–55 (2007).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440(7088), 1166–1169 (2006).
[CrossRef] [PubMed]

Baumberg, J. J.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature404(6779), 740–743 (2000).
[CrossRef] [PubMed]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979).
[CrossRef]

Bongiovanni, D.

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83(23), 4752–4755 (1999).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett.33(3), 207–209 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007).
[CrossRef] [PubMed]

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80(5), 956–959 (1998).
[CrossRef]

Charlton, M. D. B.

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature404(6779), 740–743 (2000).
[CrossRef] [PubMed]

Chen, Z.

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37(15), 3201–3203 (2012).
[CrossRef] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

I. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85(2), 023828 (2012).
[CrossRef]

Chremmos, I.

I. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85(2), 023828 (2012).
[CrossRef]

Chremmos, I. D.

I. D. Chremmos and N. K. Efremidis, “Band-specific phase engineering for curving and focusing light in waveguide arrays,” Phys. Rev. A85(6), 063830 (2012).
[CrossRef]

Christodoulides, D. N.

I. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85(2), 023828 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett.35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16(14), 10309–10314 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett.33(3), 207–209 (2008).
[CrossRef] [PubMed]

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S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60(8), 5751–5758 (1999).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett.108(16), 163901 (2012).
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P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
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I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108(11), 113903 (2012).
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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106(19), 193904 (2011).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60(8), 5751–5758 (1999).
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L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys.8(12), 912–917 (2012).
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T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83(23), 4752–4755 (1999).
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L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys.8(12), 912–917 (2012).
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L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
[CrossRef] [PubMed]

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

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B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440(7088), 1166–1169 (2006).
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Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
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K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16(14), 10309–10314 (2008).
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L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
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J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
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P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
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P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
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B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, “Diverging rabi oscillations in subwavelength photonic lattices,” Phys. Rev. Lett.106(7), 073901 (2011).
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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

Y. Hu, Z. Sun, D. Bongiovanni, D. Song, C. Lou, J. Xu, Z. Chen, and R. Morandotti, “Reshaping the trajectory and spectrum of nonlinear Airy beams,” Opt. Lett.37(15), 3201–3203 (2012).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett.83(23), 4756–4759 (1999).
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I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett.108(16), 163901 (2012).
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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106(19), 193904 (2011).
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A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
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A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
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M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature404(6779), 740–743 (2000).
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B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, “Diverging rabi oscillations in subwavelength photonic lattices,” Phys. Rev. Lett.106(7), 073901 (2011).
[CrossRef] [PubMed]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16(14), 10309–10314 (2008).
[CrossRef] [PubMed]

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A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83(23), 4752–4755 (1999).
[CrossRef]

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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett.83(23), 4756–4759 (1999).
[CrossRef]

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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
[CrossRef] [PubMed]

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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
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E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106(21), 213903 (2011).
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M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106(19), 193904 (2011).
[CrossRef] [PubMed]

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K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
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Schwartz, T.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446(7131), 52–55 (2007).
[CrossRef] [PubMed]

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P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
[CrossRef] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, “Hyper-transport of light and stochastic acceleration by evolving disorder,” Nat. Phys.8(12), 912–917 (2012).
[CrossRef]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett.108(16), 163901 (2012).
[CrossRef] [PubMed]

B. Alfassi, O. Peleg, N. Moiseyev, and M. Segev, “Diverging rabi oscillations in subwavelength photonic lattices,” Phys. Rev. Lett.106(7), 073901 (2011).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett.106(19), 193904 (2011).
[CrossRef] [PubMed]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
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P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater.5(2), 93–96 (2006).
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Nat. Photonics (1)

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Nature (3)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, “Complete photonic bandgaps in 12-fold symmetric quasicrystals,” Nature404(6779), 740–743 (2000).
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[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. A (4)

I. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A85(2), 023828 (2012).
[CrossRef]

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R. E-, “Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

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[CrossRef]

Phys. Rev. Lett. (14)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007).
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[CrossRef] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, and A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett.108(11), 113903 (2012).
[CrossRef] [PubMed]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

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I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett.109(19), 193901 (2012).
[CrossRef] [PubMed]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett.109(20), 203902 (2012).
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K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102(12), 123905 (2009).
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R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett.83(23), 4756–4759 (1999).
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Proc. Natl. Acad. Sci. U.S.A. (1)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large, complete photonic band gaps,” Proc. Natl. Acad. Sci. U.S.A.106(49), 20658–20663 (2009).
[CrossRef] [PubMed]

Science (2)

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, O. Manela, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science332(6037), 1541–1544 (2011).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Other (2)

X. Qi, R. El-Ganainy, P. Zang, K. G. Makris, D. N. Christodoulides, and Z. Chen, “Observation of accelerating Wannier-Stark beams in optically induced photonic lattices,” CLEO Technical Digest, Paper QM3E.2 (2012).

K. G. Makris, R. El-Ganainy, X. Qi, Z. Chen, and D. N. Christodoulides, “Accelerating and diffractionless beams in optical lattices,” CLEO Technical Digest, Paper JTu3K.6 (2012).

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Figures (3)

Fig. 1
Fig. 1

(a) A photonic crystal slab that is periodic in both x and z, but uniform along the y direction. The incoming beam is incident upon the structure in the xy plane, then bending in the xz plane. The cells' colors schematically illustrate the profile of an accelerating beam propagating through the sliced slab, with the black circles marking the air holes. (b) The band structure of the medium (first band in blue, second and third bands in yellow, forth band in red).A monochromatic curve is marked in green in the first band; superimposing the Bloch modes associated with such a curve, with appropriate phases, yields the accelerating solution. The self-accelerating beam is only composed of modes that propagate towards the positive z direction (“forward”), hence we cut the modes with negative z-element in their group velocity (“backward”). To illustrate this, the Bloch modes with negative group velocity (backward propagating waves) are marked in a dashed green line, while the Bloch modes with positive group velocity (forward propagating waves) are still marked by a continuous curve. (c) The structure of our 2D periodic system, schematically marking the trajectory of a self-accelerating beam. If backward propagating modes are included, we obtain a “whirlpool” beam that completes a full circle, turning back along the white arrow – see Figs. 2(a)-2(b) for an example.

Fig. 2
Fig. 2

Examples of self-accelerating beams in a 2D photonic crystal slab. For each solution, we plot the amplitude (top row) and phase (bottom row). The black arrows schematically mark the Poynting vector hence the energy flow. (a) The full “whirlpool beam”, completing a full circle, is created from two counter-propagating input beams launched from top and bottom of the photonic crystal slab. (b) The self-accelerating beam initiated from the bottom of the slab, bending by close to 180°. (c) A periodically self-accelerating beam exhibiting breather-like propagation, created from non-uniform distribution of modes along the monochromatic curve. All subfigures present beams of order α = 40, accelerating in a circle of radius 1μm, in the same square shaped lattice from Fig. 1(c). Here, the width and the height of the cell are both 45nm. This causes the beams' amplitude to vary periodically as it propagates, exhibiting square features on a cell-scale. The width of the main lobe of the beams in (a)-(c) is 2-3 cells. εsilicon = 12.25; λ = 0.5μm.(d) 2D separable Kronig-Penney band structure with cross-sections of the monochromatic curves of (a)-(c) marked: Figs. 2(a)-2(c) correspond to the green continuous line, while Figs. 3(a)-3(d) correspond to the four red dashed lines. The horizontal axis is associated with the wavevector (normalized to [-π,π]), and the vertical axis reflects different scaling of the lattice - since it is proportional to the scaling of a unit cell (thus it is also inversely proportional to the wavelength and proportional to the frequency, as expected from band structure plots).

Fig. 3
Fig. 3

Families of self-accelerating beams in a 2D photonic crystal slab. A close-up subfigure is presented in the bottom row, highlighting the fine features of each solution from the top row. (a) An almost “free-space self-accelerating solution” found when the cells are much smaller than a single wavelength, leading to an “effective homogeneous medium” (occurring when the monochromatic curve is near the bottom of the 1st band). The main lobe is roughly 20 lattice cells in width.(b) A wide self-accelerating beam associated with the ninth band, presenting a main lobe with the width of 25 lattice cells (occurring when the monochromatic curve is near the bottom of the ninth band). (c) A thin self-accelerating beam associated with the ninth band, presenting a main lobe with the width of a single lattice cell (occurring when the monochromatic curve is near the top of the ninth band). (d) A super-thin self-accelerating beam with a main lobe slightly thinner than a single lattice cell. The smaller lobes become even thinner, reaching a width of less than 1/50 of the wavelength. The Poynting vector is marked by black arrows on the zoom-in subfigure, to stress how the lattice structure alters the power flow, and yet, does not prevent the overall flow from following a circular curve. All subfigures present beams of order α = 40, in the same square-shaped lattice from Fig. 1(c). The cells size is (a) 50nm, (b) 291nm, (c) 324nm, and (d) 78nm. Note that the overall profile of (a) and (b) is the same, occupying the same number of lattice cells, even though the cells themselves are of different sizes. Yet, the close-up subfigures show completely different small-scale features. When comparing (b) and (c), we find the close-ups to show the same single-cell profile, although the overall trajectory is completely different. The scales in both axes are in microns; εsilicon = 12.25; λ = 0.5μm.

Equations (5)

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E xx + E zz + k 0 2 ε( x,z )E=0.
u k 0 , k x , k z ( x,z )= u k 0 , k x , k z ( x+n L x ,z+m L z ), n,m.
E k 0 ( ( x,z )=r )= kCurve( k 0 ) w( k ) u k 0 ,k ( r ) e ikr dk ,
E k 0 ( ( x,z )=r )= η[ 0,2π ] w( η ) u k 0 ,k( η ) ( r ) e ik( η )r dη .
E k 0 + ( ( x,z )=r )= 0 π e iαk( η ) u k 0 ,k( η ) ( r ) e ik( η )r dη , k= k θ .

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