Abstract
Control over light propagation and localization in photonic crystals offers wide applications ranging from sensing and on-chip routing to lasing and quantum light–matter interfaces. Although in electronic crystals, magnetic fields can be used to induce a multitude of unique phenomena, the uncharged nature of photons necessitates alternative approaches to bring about similar control over photons at the nanoscale. Here we experimentally realize pseudomagnetic fields in two-dimensional photonic crystals through engineered strain of the lattice. Analogous to strained graphene, this induces flat-band Landau levels at discrete energies. We study the spatial and spectral properties of these states in silicon photonic crystals at telecom wavelengths with far-field spectroscopy. Moreover, taking advantage of the photonic crystal’s design freedom, we realize domains of opposite pseudomagnetic field and observe chiral edge states at their interface. We reveal that the strain-induced states can achieve remarkably high quality factors despite being phase matched to the radiation continuum. Together with the high density of states and high degeneracy associated with flat bands, this provides powerful prospects for enhancing light–matter interactions, and illustrates the broad potential of psdeudomagnetic fields in the nanophotonic domain. This work, thus, establishes a new design principle to govern both on-chip and radiating light fields.
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Data availability
The data in this study are available via Zenodo at https://doi.org/10.5281/zenodo.10125585.
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Acknowledgements
We thank S. Arora and D. Muis for fruitful discussions. This work is part of the research programme of the Netherlands Organisation for Scientific Research (NWO). We acknowledge support from the European Research Council (ERC) Starting Grant no. 759644-TOPP and Advanced Investigator grant no. 340438-CONSTANS.
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R.B. and E.V conceived the project. R.B. fabricated the devices, carried out the measurements, performed the data analysis and modelling, and drafted the paper. E.V. and L.K. supervised the project. All authors contributed extensively to the interpretation of the results and writing of the paper.
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Extended data
Extended Data Fig. 1 Far-field Fourier spectroscopy.
Schematic depiction of the experimental far-field Fourier spectropolarimetry setup used for angularly resolved measurement of the photonic crystals’ band dispersion. See Methods for details and abbreviations.
Extended Data Fig. 2 Symmetry breaking to control radiative coupling.
Measured (top) and simulated (bottom) bands of Landau levels in PhCs with varying unit cell shrinking factor ρ, all at κ = 0.125. The linewidth in the simulations is scaled by a factor two for enhanced visibility. The linewidth increases with decreasing ρ.
Extended Data Fig. 3 Tailoring Landau levels via strain.
Measured (top) and simulated (bottom) bands of Landau levels in PhCs with increasing strain magnitude κ, all at ρ = 0.98. The gap at small κ is due to the sub-lattice symmetry breaking.
Extended Data Fig. 4 Landau level localization and polarization.
Position- and polarization-dependent excitation of photonic Landau levels, where the displacement in x relative to the lattice center and the polarization state of the incident beam (linear horizontal (X), linear vertical (Y), right-handed circular (R) and left-handed circular (L)) are indicated (ρ = 0.98 and κ = 0.125 in these measurements).
Extended Data Fig. 5 Quality factors of pristine lattices.
a, Numerically retrieved bands of a pristine strained photonic crystal featuring Landau levels, with color-coded quality factors (ρ = 1.00, κ = 0.125). b, Same as a, for a photonic crystal featuring chiral edge states.
Extended Data Fig. 6 Landau level losses versus wavevector.
Numerically retrieved contributions of radiative and in-plane losses to the total linewidth of the zeroth Landau level (left), corresponding to the section of the band highlighted in red (right). For large ky, the in-plane losses exceed the radiative losses to the top and bottom of the PhC slab, which reduces the visibility of the bands in the experiment as they become under-coupled to the free-space radiation.
Extended Data Fig. 7 Tailoring chiral edge states via strain.
Measured (top) and simulated (bottom) bands of chiral edge states in PhCs with increasing strain magnitude κ, all at ρ = 0.98.
Extended Data Fig. 8 Polarization and position dependence of chiral edge states.
The incident polarization state is denoted as X (linear horizontal), R (right-hand circular), or L (left-hand circular) besides each row. The transverse position of the focus with respect to the interface between the domains is shown above each column. The strain magnitude is κ = 0.125 for all panels. For right- and left-handed circularly polarized light, we see signatures of spin-orbit coupling in the chiral edge states. At a fixed frequency, one can selectively couple into forward or backward propagating modes by changing the helicity (pseudospin) of the incident beam. However, we note that the same state can be launched with opposite helicity at the other side of the center. Moreover, the panels show that two different edge states can be excited at the same location with equal helicity, despite having opposite group velocity.
Extended Data Fig. 9 Sub-lattice symmetry breaking and edge state dispersion.
Measured (top) and simulated (bottom) bands of chiral edge states in PhCs with varying unit cell shrinking factor ρ, all at κ = 0.125. The linewidth is scaled by a factor two for enhanced visibility. The sub-lattice symmetry breaking leads to avoided crossings around the Γ point in the edge state dispersion.
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Supplementary Sections I and II and Figs. 1 and 2.
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Barczyk, R., Kuipers, L. & Verhagen, E. Observation of Landau levels and chiral edge states in photonic crystals through pseudomagnetic fields induced by synthetic strain. Nat. Photon. (2024). https://doi.org/10.1038/s41566-024-01412-3
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DOI: https://doi.org/10.1038/s41566-024-01412-3
