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Materials System

The EMSIM FDTD simulator provides a unified materials system: built-in catalog, user libraries (CSV/JSON), and runtime custom materials. You can assign isotropic, dispersive (Drude, Lorentz, Debye), and anisotropic materials to regions of the grid.

Overview

  • Material: Isotropic, non-dispersive (ε_r, μ_r, σ).
  • DispersiveMaterial: Frequency-dependent permittivity (Drude for metals/plasmas, Lorentz for resonances, Debye for relaxation). The solver uses auxiliary differential equations (ADE) with polarization P and current J.
  • AnisotropicMaterial: Diagonal (or full) 3×3 permittivity tensor for uniaxial crystals, liquid crystals, etc.

Catalog and Manager

Use the global material manager to resolve materials by name and apply them to the grid:

from emsim.materials import get_material_manager

mgr = get_material_manager()
mat = mgr.get("rogers_ro4003c")   # by key (normalized name)
mat = mgr.get("Copper Drude")     # name is normalized to key

mgr.list_all()                    # all keys
mgr.list_by_category("dielectric")
mgr.search("rogers")

Built-in catalog keys include: vacuum, air, fr4, rogers_ro4003c, rt5880, alumina, ptfe, silicon, gaas, copper_dc, copper_drude, gold, aluminum, silver, water, muscle, skin_dry, lossy_test.

Loading Custom Libraries

CSV (header: name, eps_r, mu_r, sigma, category, description; optional columns for dispersive/anisotropic):

from emsim.materials import load_materials_from_csv, get_material_manager

materials = load_materials_from_csv("materials_library.csv")
mgr = get_material_manager()
mgr.load_csv("materials_library.csv")  # registers into manager

JSON: same keys as catalog entries; use load_materials_from_json(path) or mgr.load_json(path).

Applying Materials to the Grid

Isotropic (and fallback for dispersive/anisotropic if not yet implemented in grid):

mgr.apply_to_grid(
    grid,
    region={"i": (10, 40), "j": (10, 40), "k": (0, 5)},
    material_name="rogers_ro4003c",
)
grid.materials.compute_coefficients(grid.dt)

Dispersive (Drude): apply_to_grid with a material name that resolves to a DispersiveMaterial with model="drude" will call grid.materials.add_dispersive_region(...). The solver then uses the Drude ADE update in those cells.

Anisotropic: Pass an AnisotropicMaterial (or a name that resolves to one). The grid’s add_anisotropic_region is used; the solver applies a diagonal ε⁻¹ update in those cells.

YAML Configuration

In your simulation config you can define:

materials:
  library: "materials_library.csv"   # optional
  regions:
    - name: substrate
      material: rogers_ro4003c
      geometry:
        i_range: [10, 40]
        j_range: [10, 40]
        k_range: [0, 5]
    - name: ground
      material: copper_drude
      geometry:
        i_range: [10, 40]
        j_range: [10, 40]
        k_range: [5, 6]
    - name: anisotropic_layer
      material:
        type: anisotropic
        name: "Liquid Crystal"
        eps_r_xx: 3.0
        eps_r_yy: 3.0
        eps_r_zz: 2.0
      geometry:
        k_range: [10, 12]

After building the grid, the simulation loads the optional library and applies each region via the material manager; compute_coefficients(dt) is called after material changes.

Dispersive Models

  • Drude: ε(ω) = ε_∞ − ω_p²/(ω² + i γ ω). Parameters: eps_inf, omega_p, gamma (rad/s). Used for metals and plasmas.
  • Lorentz: Multi-pole resonance. Parameters: eps_inf, delta_eps, omega_0, delta (lists for multiple poles).
  • Debye: Relaxation. Parameters: eps_s, eps_inf, tau.

References: Taflove & Hagness, Computational Electrodynamics, 3rd ed., Ch. 9.