A computer model of a triaxially strained photonic crystal links resonance frequency to radial position: the lowest-frequency mode has its intensity maximum at the center, while higher-index modes develop annular peaks that move outward from the device center. The result is a set of localized resonances ordered by both frequency and radius.
The study examines whether a graphene-like photonic crystal under triaxial strain can exhibit an intrinsic radial Landau rainbow—spectrally separated, radially ordered resonances. Its evidence comes from calculated eigenfrequencies, local band structures and electromagnetic field distributions in a finite model, so the result is a simulation finding rather than an experimental measurement.
Inside the modeled crystal
The researchers used COMSOL Multiphysics within a two-dimensional effective-index model. The calculation examined eigenfrequencies and field patterns rather than measurements from a fabricated structure.
The modeled crystal contained triangular air holes arranged on a honeycomb lattice. Its lattice constant was 500 nanometres, the triangular holes had sides measuring 300 nanometres, and the dielectric and air regions were assigned effective indices of 2.6 and 1. The finite structure extended for 40 lattice periods along each side of a hexagonal region.
The unstrained reference showed a gapless Dirac cone around 190 THz and provided the comparison state for the strained structures. The triaxial deformation was represented by a dimensionless strain-strength parameter C and a spatially uniform pseudomagnetic field in the effective description.
A separate scalar potential was given a quadratic radial form and interpreted as a pseudoelectric field. In the study’s effective description, that contribution was associated with splitting within each Landau level.
A frequency ladder with a spatial order
In simulations, increasing C was associated with reorganization of near-Dirac eigenfrequencies into well-separated branches. The separation between branches increased with strain strength, in qualitative agreement with the theoretical prediction.
The effective interpretation associates the pseudomagnetic field with the Landau-level-like branches, while the quadratic scalar potential is associated with splitting within each level. The reported levels split into equally spaced frequency ladders of localized resonances.
The radial pattern followed the same ordering. The lowest-frequency mode had a central intensity maximum; higher-index modes developed annular maxima, with each ring moving farther from the device center as frequency increased. The analysis did not report numerical peak radii or a frequency–radius slope.
Signatures within the calculated fields
The simulated zeroth-level modes showed strong sublattice polarization. Their fields were concentrated on the A sublattice of the honeycomb pattern, while modal weight on the B sublattice was strongly suppressed.
The researchers also separated the two valley components of the resonance field. They Fourier-filtered the complex field around K and K′ and removed the associated Bloch phases to obtain valley envelopes. The K and K′ components had opposite angular momenta, with magnitudes scaling approximately with the mode index, while the total angular momentum remained zero.
What the calculation does not establish
The findings are bounded by a finite, two-dimensional effective-index calculation of this photonic-crystal geometry. The supplied analysis reports no experimental fabrication or measurement, so it supports conclusions about simulated modes rather than a tested device.
The reported branch comparison comes without a quantitative fit metric or uncertainty interval. The equally spaced ladders are not accompanied by numerical spacing values, linewidths or error bars.
The idealized description also has a defined boundary: higher-order Landau levels gradually deviated from the ideal Dirac prediction as they moved outside the Dirac-cone region. The cleanest comparison therefore applies within the part of the spectrum where that description remains relevant.
The frequency–radius pattern points to a possible way of identifying modes by their calculated position and frequency, but selective coupling, lasing and device performance were not tested. The supplied text refers to Supplementary Information for additional discussion, but does not report a data- or code-availability statement.
The work is an arXiv preprint, and no journal is listed in the supplied metadata. Whether the predicted radial ladder can be fabricated and measured remains an open question beyond this computational result.
Paper data and sources
Original title: Intrinsic Radial Landau Rainbow in Triaxial Strained Photonic Crystal
Authors: Guangti Lu, Satoshi Iwamoto
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text