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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 7 — Apr. 8, 2013
  • pp: 8886–8896

Self-accelerating beams in photonic crystals

Ido Kaminer, Jonathan Nemirovsky, Konstantinos G. Makris, and Mordechai Segev  »View Author Affiliations

Optics Express, Vol. 21, Issue 7, pp. 8886-8896 (2013)

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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

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics
(260.2065) Physical optics : Effective medium theory
(160.5298) Materials : Photonic crystals
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Photonic Crystals

Original Manuscript: February 19, 2013
Revised Manuscript: March 24, 2013
Manuscript Accepted: March 25, 2013
Published: April 3, 2013

Ido Kaminer, Jonathan Nemirovsky, Konstantinos G. Makris, and Mordechai Segev, "Self-accelerating beams in photonic crystals," Opt. Express 21, 8886-8896 (2013)

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  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32(8), 979–981 (2007). [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett.33(15), 1678–1680 (2008). M. A. Bandres, “Accelerating beams,” Opt. Lett. 34(24), 3791–3793 (2009). [CrossRef] [PubMed]
  5. J. A. Davis, M. J. Mintry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express16(17), 12866–12871 (2008). [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008). [CrossRef]
  11. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett.35(12), 2082–2084 (2010). [CrossRef] [PubMed]
  12. 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]
  13. I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106(21), 213903 (2011). [CrossRef] [PubMed]
  14. 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]
  15. R. Bekenstein and M. Segev, “Self-accelerating optical beams in highly nonlocal nonlinear media,” Opt. Express19(24), 23706–23715 (2011). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. 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).
  19. 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).
  20. 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]
  21. 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).
  22. 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]
  23. 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]
  24. 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]
  25. 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]
  26. 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]
  27. 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]
  28. 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]
  29. 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]
  30. O. Manela, M. Segev, and D. N. Christodoulides, “Nondiffracting beams in periodic media,” Opt. Lett.30(19), 2611–2613 (2005). [CrossRef] [PubMed]
  31. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4(4), 651–654 (1987). [CrossRef]
  32. 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]
  33. 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]
  34. 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]
  35. 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]
  36. 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]
  37. 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]
  38. 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]
  39. 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]
  40. 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]
  41. 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]
  42. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys.47(3), 264–267 (1979). [CrossRef]

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