Abstract
Quasicrystals are unique structures with long-range order but no periodicity. Their properties have intrigued scientists ever since their discovery1 and initial theoretical analysis2,3. The lack of periodicity excludes the possibility of describing quasicrystal structures with well-established analytical tools, including common notions like Brillouin zones and Bloch's theorem. New and unique features such as fractal-like band structures4,5,6,7 and ‘phason’ degrees of freedom8 are introduced. In general, it is very difficult to directly observe the evolution of electronic waves in solid-state atomic quasicrystals, or the dynamics of the structure itself. Here we use optical induction9,10,11 to create two-dimensional photonic quasicrystals, whose macroscopic nature allows us to explore wave transport phenomena. We demonstrate that light launched at different quasicrystal sites travels through the lattice in a way equivalent to quantum tunnelling of electrons in a quasiperiodic potential. At high intensity, lattice solitons are formed. Finally, we directly observe dislocation dynamics when crystal sites are allowed to interact with each other. Our experimental results apply not only to photonics, but also to other quasiperiodic systems such as matter waves in quasiperiodic traps12, generic pattern-forming systems as in parametrically excited surface waves13, liquid quasicrystals14, and the more familiar atomic quasicrystals.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnature04722/MediaObjects/41586_2006_Article_BFnature04722_Fig1_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnature04722/MediaObjects/41586_2006_Article_BFnature04722_Fig2_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnature04722/MediaObjects/41586_2006_Article_BFnature04722_Fig3_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1038%2Fnature04722/MediaObjects/41586_2006_Article_BFnature04722_Fig4_HTML.jpg)
Similar content being viewed by others
References
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)
Levine, D., Lubensky, T. C., Ostlund, S., Ramaswamy, S. & Steinhardt, P. J. Elasticity and dislocations in pentagonal and icosahedral quasicrystals. Phys. Rev. Lett. 54, 1520–1523 (1985)
Socolar, J. E. S., Lubensky, T. C. & Steinhardt, P. J. Phonons, phasons, and dislocations in quasicrystals. Phys. Rev. B 34, 3345–3360 (1986)
Rotenberg, E., Theis, W., Horn, K. & Gille, P. Quasicrystalline valence bands in decagonal AlNiCo. Nature 406, 602–605 (2000)
Kaliteevski, M. A. et al. Two-dimensional Penrose-tiled photonic quasicrystals: from diffraction pattern to band structure. Nanotechnology 11, 274–280 (2000)
Dal Negro, L. et al. Light transport through the band-edge states of Fibonacci quasicrystals. Phys. Rev. Lett. 90, 055501 (2003)
Chan, Y. S., Chan, C. T. & Liu, Z. Y. Photonic band gaps in two dimensional photonic quasicrystals. Phys. Rev. Lett. 80, 956–959 (1998)
Edagawa, K. & Suzuki, K. High resolution transmission electron microscopy observation of thermally fluctuating phasons in decagonal Al-Cu-Co. Phys. Rev. Lett. 85, 1674–1677 (2000)
Efremidis, N. K., Sears, S., Christodoulides, D. N., Fleischer, J. W. & Segev, M. Discrete solitons in photorefractive optically induced photonic lattices. Phys. Rev. E 66, 046602 (2002)
Fleischer, J. W., Carmon, T., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of discrete solitons in optically induced real time waveguide arrays. Phys. Rev. Lett. 90, 023902 (2003)
Fleischer, J. W., Segev, M., Efremidis, N. K. & Christodoulides, D. N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422, 147–150 (2003)
Guidoni, L., Triché, C., Verkerk, P. & Grynberg, G. Quasiperiodic optical lattices. Phys. Rev. Lett. 79, 3363–3366 (1997)
Lifshitz, R. & Petrich, D. M. Theoretical model for Faraday waves with multiple-frequency forcing. Phys. Rev. Lett. 79, 1261–1264 (1997)
Zeng, X. et al. Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)
Clausen, C. B., Kivshar, Y. S., Bang, O. & Christiansen, P. L. Quasiperiodic envelope solitons. Phys. Rev. Lett. 83, 4740–4743 (1999)
Man, W., Megens, M., Steinhardt, P. J. & Chaikin, P. M. Experimental measurement of the photonic properties of icosahedral quasicrystals. Nature 436, 993–996 (2005)
Bratfalean, R. T., Peacock, A. C., Broderick, N. G. R. & Gallo, K. Harmonic generation in a two-dimensional nonlinear quasicrystal. Opt. Lett. 30, 424–426 (2005)
Lifshitz, R., Arie, A. & Bahabad, A. Photonic quasicrystals for nonlinear optical frequency conversion. Phys. Rev. Lett. 95, 133901 (2005)
Zoorob, M. E., Charlton, M. D. B., Parker, G. J., Baumberg, J. J. & Netti, M. C. Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature 404, 740–743 (2000)
Martin, H., Eugenieva, E. D., Chen, Z. & Christodoulides, D. N. Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices. Phys. Rev. Lett. 92, 123902 (2004)
Bartal, G. et al. Brillouin-zone spectroscopy of nonlinear photonic lattices. Phys. Rev. Lett. 94, 163902 (2005)
Russell, P. St J. Optics of Floquet-Bloch waves in dielectric gratings. Appl. Phys. B 39, 231–246 (1986)
Christodoulides, D. N. & Joseph, R. I. Discrete self-focusing in nonlinear arrays of coupled waveguides. Opt. Lett. 13, 794–796 (1988)
Christodoulides, D. N., Lederer, F. & Silberberg, Y. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature 424, 817–823 (2003)
Eisenberg, H. S., Silberberg, Y., Morandotti, R., Boyd, A. R. & Aitchison, J. S. Discrete spatial optical solitons in waveguide arrays. Phys. Rev. Lett. 81, 3383–3386 (1998)
Segev, M., Valley, G. C., Crosignani, B., DiPorto, P. & Yariv, A. Steady-state spatial screening solitons in photorefractive materials with external applied field. Phys. Rev. Lett. 73, 3211–3214 (1994)
Christodoulides, D. & Carvalho, M. Bright, dark, and gray spatial soliton states in photorefractive media. J. Opt. Soc. Am. B 12, 1628–1633 (1995)
Efremidis, N. K. et al. Two-dimensional optical lattice solitons. Phys. Rev. Lett. 91, 213906 (2003)
Barak, G. & Lifshitz, R. Dislocation dynamics in a dodecagonal quasiperiodic structure. Phil. Mag. 86, 1059–1064 (2006)
Joannopoulos, J. D., Meade, R. D. & Winn, J. N. Photonic Crystals: Molding the Flow of Light (Princeton, Princeton Univ. Press, 1995)
Acknowledgements
This work was supported by the Israeli Science Foundation, the Israel-USA Binational Science Foundation and the German-Israeli DIP Project.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
Rights and permissions
About this article
Cite this article
Freedman, B., Bartal, G., Segev, M. et al. Wave and defect dynamics in nonlinear photonic quasicrystals. Nature 440, 1166–1169 (2006). https://doi.org/10.1038/nature04722
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/nature04722
This article is cited by
-
Observation of localization of light in linear photonic quasicrystals with diverse rotational symmetries
Nature Photonics (2024)
-
A columnar liquid quasicrystal with a honeycomb structure that consists of triangular, square and trapezoidal cells
Nature Chemistry (2023)
-
Topological states in quasicrystals
Frontiers of Physics (2022)
-
Localization and delocalization of light in photonic moiré lattices
Nature (2020)
-
Engineered disorder in photonics
Nature Reviews Materials (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.