Periodic structures

kind: "periodic", model lightsmith.problems.PeriodicProblem. A stack of patterned layers that is periodic in 1D or 2D, such as a grating, a metasurface or a photonic-crystal slab, illuminated by a plane wave.

Fields

Field	Meaning
lattice_a1_nm	First lattice vector (x, y)
lattice_a2_nm	Second lattice vector, or None for a 1D grating. A 1D grating is periodic along a1 and invariant perpendicular to it; its shapes are sampled along the line through the origin in the a1 direction.
superstrate, substrate	Semi-infinite materials
layers	PatternedLayer(thickness_nm, background, shapes), listed from the superstrate side. shapes are 2D structures in one unit cell.
wavelengths	Vacuum wavelengths in nm
incidence	Incidence(theta_deg, phi_deg, polarizations)
options	Per-method solver options

Result

SpectrumResult, with:

• total r, t and a;
• orders: a list of DiffractionOrder(order=(m, n), r, t) for the propagating orders;
• zeroth-order complex amplitudes.

Solvers

• RCWA is the default. It handles any lattice, conical incidence and metals, and is differentiable with respect to thicknesses and pixelated permittivity maps.
• FDTD handles normal incidence on rectangular lattices only.

Example

import lightsmith as ls
from lightsmith.problems import Circle, PatternedLayer, PeriodicProblem, Structure2D

holes = PeriodicProblem(
    lattice_a1_nm=(400, 0), lattice_a2_nm=(0, 400),
    superstrate=ls.ConstantIndex(n_real=1.0),
    layers=[PatternedLayer(thickness_nm=150, background=ls.ConstantIndex(n_real=2.0),
                           shapes=[Structure2D(profile=Circle(radius_nm=100),
                                               material=ls.ConstantIndex(n_real=1.0))])],
    substrate=ls.ConstantIndex(n_real=1.45),
    wavelengths=ls.WavelengthRange(start_nm=588, stop_nm=604, num=9),
    options={"rcwa": {"harmonics": 5}},
)
res = ls.solve(holes)