Materials and Geometry

rfx uses a two-step workflow: register a material by name, then attach it to a geometric shape.

---

Material library

MATERIAL_LIBRARY is a dict of pre-defined RF/microwave materials that ships with rfx.

from rfx import MATERIAL_LIBRARY
print(list(MATERIAL_LIBRARY.keys()))
# ['vacuum', 'air', 'fr4', 'rogers4003c', 'alumina', 'silicon',
#  'ptfe', 'copper', 'aluminum', 'pec', 'water_20c']

Name	εᵣ	σ (S/m)	Notes
vacuum	1.0	0	Lossless free space
air	1.0006	0	Standard atmosphere
fr4	4.4	0.025	PCB laminate, tan_δ ≈ 0.02 at 1 GHz
rogers4003c	3.55	~0.0027·ω·ε₀·εᵣ	Low-loss microwave substrate
alumina	9.8	0	Ceramic substrate
silicon	11.9	0.01	Lightly doped semiconductor
ptfe	2.1	0	PTFE / Teflon
copper	1.0	5.8×10⁷	Good conductor
aluminum	1.0	3.5×10⁷	Good conductor
pec	1.0	1×10¹⁰	Perfect electric conductor (mask-enforced)
water_20c	4.9 + Debye	0	Water at 20 °C with one Debye pole

Library materials are available directly by name; no add_material() call is needed:

from rfx import Simulation, Box

sim = Simulation(freq_max=10e9, domain=(0.05, 0.05, 0.02), boundary="cpml")
sim.add(Box((0, 0, 0), (0.05, 0.05, 0.0016)), material="fr4")
sim.add(Box((0, 0, 0), (0.05, 0.05, 0.0)), material="pec")

---

Custom material registration

Register a named material with add_material() before using it in add().

sim.add_material(
    "my_ceramic",
    eps_r=9.0,
    sigma=0.001,
    mu_r=1.0,               # optional, default 1.0
)
sim.add(Box((0.01, 0.01, 0.0), (0.04, 0.04, 0.002)), material="my_ceramic")

add_material() returns self, so calls can be chained:

(sim
 .add_material("sub", eps_r=3.55, sigma=0.0)
 .add_material("metal", eps_r=1.0, sigma=5.8e7)
 .add(Box((0, 0, 0), (0.05, 0.03, 0.001)), material="sub")
 .add(Box((0.005, 0.005, 0.001), (0.045, 0.025, 0.001)), material="metal"))

---

Dispersive materials

Debye poles

Debye dispersion models frequency-dependent permittivity caused by dipolar relaxation (e.g., water, biological tissue):

ε(ω) = ε_∞ + Δε / (1 + jωτ)

from rfx import DebyePole

sim.add_material(
    "water_body",
    eps_r=4.9,            # ε_∞ (high-frequency limit)
    debye_poles=[
        DebyePole(delta_eps=74.1, tau=8.3e-12),  # primary relaxation
    ],
)

DebyePole fields:

Field	Description
delta_eps	Relaxation strength Δε = εₛ − ε_∞
tau	Relaxation time (seconds)

Lorentz poles

Lorentz poles model phonon resonances and plasma-like media:

from rfx import LorentzPole, drude_pole, lorentz_pole

# Manual Lorentz pole
sim.add_material(
    "resonant_material",
    eps_r=1.0,
    lorentz_poles=[
        LorentzPole(delta_eps=2.0, omega_0=2*3.14159*10e9, delta=1e8),
    ],
)

# Helper: Drude (free-electron) model for metals
drude = drude_pole(omega_p=1.37e16, gamma=4.05e13)   # gold
sim.add_material("gold", eps_r=1.0, lorentz_poles=[drude])

LorentzPole fields:

Field	Description
delta_eps	Oscillator strength
omega_0	Resonance angular frequency (rad/s)
delta	Damping rate (rad/s)

---

Geometry: CSG shapes

rfx uses constructive solid geometry (CSG). Shapes are rasterised onto the Yee grid at simulation time.

Box

from rfx import Box

# Box(corner_lo, corner_hi)  — axis-aligned rectangular prism
slab  = Box((0.0,  0.0,  0.0),  (0.05, 0.05, 0.002))
patch = Box((0.01, 0.01, 0.002),(0.04, 0.04, 0.002))

Coordinates are in metres. corner_lo and corner_hi are (x, y, z) tuples.

Sphere

from rfx import Sphere

# Sphere(centre, radius)
ball = Sphere((0.025, 0.025, 0.010), radius=0.005)
sim.add(ball, material="alumina")

Cylinder

from rfx import Cylinder

# Cylinder(centre, radius, height, axis)
# axis: "x", "y", or "z"
via  = Cylinder((0.025, 0.015, 0.000), radius=0.0005, height=0.002, axis="z")
rod  = Cylinder((0.010, 0.025, 0.000), radius=0.001,  height=0.050, axis="x")
sim.add(via, material="copper")

Boolean operations

Combine shapes with set operations:

from rfx.geometry.csg import union, difference, intersection

# Hollow cylinder (tube)
outer = Cylinder((0.025, 0.025, 0.0), radius=0.010, height=0.020, axis="z")
inner = Cylinder((0.025, 0.025, 0.0), radius=0.007, height=0.020, axis="z")
tube  = difference(outer, inner)
sim.add(tube, material="copper")

# Lens-shaped dielectric
sphere1 = Sphere((0.025, 0.025, 0.005), radius=0.008)
sphere2 = Sphere((0.025, 0.025, 0.015), radius=0.008)
lens    = intersection(sphere1, sphere2)
sim.add(lens, material="alumina")

---

PEC mask enforcement

Materials with σ ≥ 10⁶ S/m (including library pec) are automatically enforced via a Boolean PEC mask rather than through the conductivity update. This is exact (E-field set to zero on every PEC cell at each time step) and avoids the numerical instability that arises from very large σ in the standard update equations.

!!! warning Do not set σ > 10⁸ S/m for non-PEC conductors such as copper. Use the library value sigma=5.8e7 for copper or define "pec" explicitly when a perfect conductor is intended.

---

Thin conductor correction

For printed traces and patches thinner than one cell, use the subcell thin-conductor model:

from rfx import Box

trace = Box((0.010, 0.014, 0.0016), (0.040, 0.016, 0.0016))
sim.add_thin_conductor(
    trace,
    sigma_bulk=5.8e7,     # copper
    thickness=35e-6,       # 1 oz copper = 35 µm
)

This applies an effective surface conductivity correction to the Yee cells intersected by the thin sheet, rather than fully filling them.