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Observation of localization of light in linear photonic quasicrystals with diverse rotational symmetries

Nature Photonics volume 18, pages 224–229 (2024)Cite this article

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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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Fig. 1: Quasicrystals of different symmetries and cross-sections of corresponding optical potentials.
Fig. 2: Form factors and profiles of linear eigenmodes supported by quasicrystals.
Fig. 3: Propagation of input Gaussian beams and their form factors.
Fig. 4: Experimental observation of light localization in quasicrystals.
Fig. 5: Experimental results for different orders of the point rotational symmetry of the quasicrystals.

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Data availability

The data that support the findings of this study are available from the corresponding author on reasonable request.

Code availability

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.

Author information

Author notes

  1. These authors contributed equally: Peng Wang, Qidong Fu.

Authors and Affiliations

  1. School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China

    Peng Wang, Qidong Fu & Fangwei Ye

  2. Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Portugal

    Vladimir V. Konotop

  3. Institute of Spectroscopy, Russian Academy of Sciences, Moscow, Russia

    Yaroslav V. Kartashov

Authors
  1. Peng Wang
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  3. Vladimir V. Konotop
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  4. Yaroslav V. Kartashov
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Correspondence to Fangwei Ye.

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Nature Photonics thanks Gianluigi Zito and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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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.

Supplementary information

Supplementary Information

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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