Workflow (2D)

Wave Types and Polarizations

PhoXonic.jl supports various wave types for photonic and phononic crystals.

2D Wave Types

For 3D wave types, see 3D Calculations.

Basic Workflow

1. Define Lattice (square_lattice, hexagonal_lattice, etc.)
2. Define Materials (Dielectric, IsotropicElastic)
3. Create Geometry with Shapes (Circle, Rectangle, Sphere, etc.)
4. Create Solver with Wave Types — see also Solver Methods
5. Compute Band Structure (compute_bands)
6. Analyze results — see Analysis and Post-Processing

2D Photonic Crystal

Triangular Lattice Rods (TM mode)

See also: examples/101_triangular_rods.jl

using PhoXonic

# 1. Lattice
lat = hexagonal_lattice(1.0)

# 2. Materials
air = Dielectric(1.0)
rod = Dielectric(12.0)  # High-ε like GaAs

# 3. Geometry: rods in air
geo = Geometry(lat, air, [(Circle([0.0, 0.0], 0.2), rod)])

# 4. Solver
solver = Solver(TMWave(), geo, (64, 64); cutoff=7)

# 5. Compute bands
kpath = simple_kpath_hexagonal(npoints=30)
bands = compute_bands(solver, kpath; bands=1:8)

# 6. Find gaps
gaps = find_all_gaps(bands)
for g in gaps
    println("Gap between bands $(g.bands): $(g.gap_ratio*100)%")
end

Square Lattice (TE/TM comparison)

See also: examples/103_square_rods.jl

lat = square_lattice(1.0)
geo = Geometry(lat, air, [(Circle([0.0, 0.0], 0.2), rod)])

# TE mode
solver_te = Solver(TEWave(), geo, (64, 64); cutoff=7)
bands_te = compute_bands(solver_te, kpath; bands=1:8)

# TM mode
solver_tm = Solver(TMWave(), geo, (64, 64); cutoff=7)
bands_tm = compute_bands(solver_tm, kpath; bands=1:8)

2D Phononic Crystal

Steel/Epoxy (SH mode)

See also: examples/201_phononic_steel_epoxy.jl

# Materials
epoxy = IsotropicElastic(ρ=1180.0, λ=4.43e9, μ=1.59e9)
steel = IsotropicElastic(ρ=7800.0, λ=1.15e11, μ=8.28e10)

# Geometry
lat = square_lattice(0.01)  # 1 cm period
geo = Geometry(lat, epoxy, [(Circle([0.0, 0.0], 0.004), steel)])

# SH solver
solver = Solver(SHWave(), geo, (64, 64); cutoff=7)
kpath = simple_kpath_square(a=0.01, npoints=30)
bands = compute_bands(solver, kpath; bands=1:8)

P-SV Mode (in-plane)

solver_psv = Solver(PSVWave(), geo, (64, 64); cutoff=7)
bands_psv = compute_bands(solver_psv, kpath; bands=1:12)

Subpixel Averaging

For smoother convergence at material boundaries:

solver = Solver(TMWave(), geo, (64, 64);
    cutoff=7,
    discretization=SubpixelAverage(4)  # 4×4 subsampling
)

For 3D photonic/phononic crystals (TransverseEM, FullVectorEM, FullElastic), see 3D Calculations.

For solver methods (DenseMethod, KrylovKitMethod, LOBPCGMethod), see Solver Methods.

For post-processing (convergence, group velocity, k-path, plotting, saving/loading), see Analysis and Post-Processing.

API Reference

• Core API - Lattice, Materials, Shapes, Geometry
• Solver API - Wave types, Solver, BandStructure