Photonic bands¶

kind: "bands", model lightsmith.problems.BandProblem. The band structure of a 2D or 3D photonic crystal along a path in k-space.

Fields¶

Field	Meaning
`dimension`	`2` (default) or `3`
`lattice_vectors_nm`	Two or three lattice vectors (x, y, z)
`background`	Material that fills the unit cell
`structures_2d`	Unit-cell inclusions for 2D crystals (profiles)
`structures`	Unit-cell inclusions for 3D crystals (geometries)
`k_path`	`KPoint(label, reduced)`: corners of the path, in units of the reciprocal lattice vectors
`points_per_segment`	Number of k-points between corners (default 16)
`num_bands`	Number of bands (default 8)
`polarization`	2D only. `te` (E in plane), `tm` (E along z) or `both`.
`options`	Per-method solver options

Result¶

BandResult contains:

k_reduced;
k_distance, for plotting;
k_labels;
frequencies[polarization][k][band], in normalised units a/λ, with a = |lattice_vectors_nm[0]|.

Solvers¶

PWE: plane-wave expansion, with dense or LOBPCG eigensolvers. lightsmith.backends.pwe also provides these helpers:

band_gaps;
density_of_states;
supercell, for line and point defects;
bands_from_permittivity, which is differentiable.

Example¶

import lightsmith as ls
from lightsmith.problems import BandProblem, Circle, KPoint, Structure2D

a = 500.0
rods = BandProblem(
    lattice_vectors_nm=[(a, 0, 0), (0, a, 0)],
    background=ls.ConstantIndex(n_real=1.0),
    structures_2d=[Structure2D(profile=Circle(radius_nm=0.2 * a), material=ls.ConstantPermittivity(eps_real=8.9))],
    k_path=[KPoint(label="Γ", reduced=(0, 0, 0)), KPoint(label="X", reduced=(0.5, 0, 0)),
            KPoint(label="M", reduced=(0.5, 0.5, 0)), KPoint(label="Γ", reduced=(0, 0, 0))],
    polarization="tm",
)
res = ls.solve(rods)