Core API

Dim1

One-dimensional structures (e.g., Bragg mirrors, superlattices).

Dim2

Two-dimensional structures (e.g., photonic crystal slabs, 2D phononic crystals).

Dim3

Three-dimensional structures (e.g., 3D photonic crystals, bulk phononic crystals).

Lattice{D<:Dimension}

Represents a periodic lattice in D dimensions.

Fields

• vectors: Primitive lattice vectors as a tuple of SVectors
• reciprocal: Reciprocal lattice vectors (computed automatically)

lattice_1d(a::Real=1.0)

Create a 1D periodic lattice with period a.

square_lattice(a::Real=1.0)

Create a 2D square lattice with lattice constant a.

hexagonal_lattice(a::Real=1.0)

Create a 2D hexagonal (triangular) lattice with lattice constant a.

cubic_lattice(a::Real=1.0)

Create a 3D simple cubic lattice with lattice constant a.

fcc_lattice(a::Real=1.0)

Create a 3D face-centered cubic lattice with conventional lattice constant a.

reciprocal_vectors(lattice::Lattice)

Return the reciprocal lattice vectors.

Dielectric(ε, μ=1.0)

Isotropic dielectric material with permittivity ε and permeability μ.

Examples

air = Dielectric(1.0)
silicon = Dielectric(11.7)

IsotropicElastic(ρ, C11, C12, C44)

Isotropic elastic material with density ρ and elastic constants.

For isotropic materials: C44 = (C11 - C12) / 2

Fields

• ρ: Mass density [kg/m³]
• C11: Elastic constant (λ + 2μ) [Pa]
• C12: Elastic constant (λ) [Pa]
• C44: Shear modulus (μ) [Pa]

Examples

# Steel
steel = IsotropicElastic(7800.0, 282e9, 113e9, 84.5e9)

# From Lamé parameters
epoxy = IsotropicElastic(ρ=1180.0, λ=4.43e9, μ=1.59e9)

from_E_ν(ρ, E, ν)

Create isotropic elastic material from Young's modulus E and Poisson's ratio ν.

Circle(center, radius)

A circle in 2D.

Examples

c = Circle(Vec2(0, 0), 0.2)
c = Circle([0.0, 0.0], 0.2)

Rectangle(center, size)

An axis-aligned rectangle in 2D.

Examples

r = Rectangle(Vec2(0, 0), Vec2(0.5, 0.3))

Polygon(vertices)

A polygon in 2D defined by its vertices (in order).

Sphere(center, radius)

A sphere in 3D.

Cylinder(center, radius, height, axis)

A cylinder in 3D with specified center, radius, height, and axis direction. Default axis is along z.

Segment(start, stop)

A line segment in 1D.

Geometry{D<:Dimension, M<:Material}

Represents the geometry of a periodic crystal structure.

Fields

• lattice: The periodic lattice
• background: Background material
• inclusions: List of (shape, material) pairs

Examples

lattice = square_lattice(1.0)
air = Dielectric(1.0)
rod = Dielectric(8.9)
geo = Geometry(lattice, air, [(Circle(Vec2(0,0), 0.2), rod)])

discretize(geo::Geometry{Dim2}, resolution, property, [method])

Discretize a 2D geometry onto a grid.

Arguments

• geo: The geometry to discretize
• resolution: Tuple (Nx, Ny) of grid points
• property: Property to extract (:ε, :μ, :ρ, :C11, :C12, :C44)
• method: Discretization method (default: SimpleGrid())

Returns

A matrix of property values on the grid.

discretize(geo::Geometry{Dim1}, resolution, property, [method])

Discretize a 1D geometry onto a grid.

discretize(geo::Geometry{Dim3}, resolution, property, [method])

Discretize a 3D geometry onto a grid.

Arguments

• geo: The 3D geometry to discretize
• resolution: Tuple (Nx, Ny, Nz) of grid points
• property: Property to extract (:ε, :μ, :ρ, :C11, :C12, :C44, etc.)
• method: Discretization method (default: SimpleGrid())

Returns

A 3D array of property values on the grid.

discretize(geometry, resolution, ...)

Discretize geometry on a grid.

See concrete method signatures for detailed documentation and keyword arguments.

DiscretizationMethod

Abstract type for material discretization methods.

SimpleGrid

Simple point-sampling discretization. Each grid point gets the material value at that exact location.

SubpixelAverage

Subpixel averaging for smoother material boundaries. Uses volume fractions to average material properties.

PlaneWaveBasis{D<:Dimension}

Plane wave basis for D-dimensional periodic structures.

Fields

• lattice: The underlying lattice
• cutoff: Maximum index for plane waves
• indices: List of (p, q, ...) indices for each plane wave
• G: Reciprocal lattice vectors for each plane wave
• num_pw: Total number of plane waves

convolution_matrix(f::AbstractMatrix, basis::PlaneWaveBasis{Dim2})

Compute the convolution matrix for a 2D function f(r).

The convolution matrix C has elements: C[i,j] = f̂(Gi - Gj) where f̂ is the Fourier transform of f.

Arguments

• f: Real-space function values on a grid (Nx × Ny)
• basis: Plane wave basis

Returns

A complex matrix of size (numpw × numpw).

convolution_matrix(f::AbstractVector, basis::PlaneWaveBasis{Dim1})

Compute the convolution matrix for a 1D function f(x).

convolution_matrix(f::AbstractArray{T,3}, basis::PlaneWaveBasis{Dim3}) where T

Compute the convolution matrix for a 3D function f(r).