Abstract
Since their first observation in metallic alloys, quasicrystals have remained highly intriguing ubiquitous physical structures, sharing properties of ordered and disordered media. They can be created in various ways, including optically induced or technologically fabricated structures in photonic and phononic systems. Understanding the wave propagation in such two-dimensional structures attracts considerable attention, with strikingly different localization properties observed in various quasicrystalline systems. Direct observation of localization in purely linear photonic quasicrystals remains elusive, and the impact of varying rotational symmetry on localization is yet to be understood. Here, using sets of interfering plane waves, we create photonic two-dimensional quasicrystals with different rotational symmetries. We demonstrate experimentally that linear localization of light does occur even in clean linear quasicrystals. We found that light localization occurs above a critical depth of optically induced potential and that this critical depth rapidly decreases with increasing order of the discrete rotational symmetry of the quasicrystal. These findings pave the way for achieving wave localization in a wide variety of aperiodic systems obeying discrete symmetries, with possible applications in photonics, atomic physics, acoustics and condensed matter.
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Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.
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The codes that support the findings of this study are available from the corresponding author on reasonable request.
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Acknowledgements
P.W., Q.F. and F.Y. acknowledge the support of “Shanghai Jiao Tong University Scientific and Technological Innovation Funds”, and Shanghai Outstanding Academic Leaders Plan (grant no. 20XD1402000). P.W. acknowledges funding from the National Natural Science Foundation (grant no. 12304366) and China Postdoctoral Science Foundation (grant no. BX20230217). Q.F. acknowledges the support of China Postdoctoral Science Foundation (grant no. BX20230218). V.V.K. acknowledges financial support from the Portuguese Foundation for Science and Technology (FCT) under Contracts PTDC/FIS-OUT/3882/2020 and UIDB/00618/2020. Y.V.K. acknowledges funding by the research project no. FFUU-2021-0003 of the Institute of Spectroscopy of the Russian Academy of Sciences. We would like to express our gratitude to the anonymous referees for their valuable suggestions regarding the filling fractions and structure factors used to elucidate the order of the quasicrystals in explaining the threshold LDT.
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Extended data
Extended Data Fig. 1 Numerically calculated symmetric quasicrystal patterns.
Numerically calculated N-fold symmetric quasicrystal patterns with N = 5, 7, 8., 12, as well as the periodic pattern with N = 6, for k = 2 and A2 = 2.24.
Extended Data Fig. 2 Experimentally intensity distributions below and above LDT point.
Experimentally observed delocalized output intensity distributions for probe beam observed below LDT point (at low values of the applied electric field) and localized distributions observed above LDT point (at sufficiently high values of the electric field), for N = 5, 7-12. At N = 6 the field is delocalized at all amplitudes of the electric field. The distributions are shown within the window of 400 µm × 400 µm.
Extended Data Fig. 3 Experimental setup.
SLM, spatial light modulator; BS, beam splitter; L, lens; FM, Fourier mask; AT,variable attenuator; SBN, strontium barium niobate crystal; CCD, charged-coupled device. Bottom-left, the phase diagram for N = 5; bottom-right, the structure of Fourier mask.
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Supplementary Figs. 1–5 and Discussion.
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Wang, P., Fu, Q., Konotop, V.V. et al. Observation of localization of light in linear photonic quasicrystals with diverse rotational symmetries. Nat. Photon. 18, 224–229 (2024). https://doi.org/10.1038/s41566-023-01350-6
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DOI: https://doi.org/10.1038/s41566-023-01350-6