Materials¶

from hyperbolic_optics.materials import list_materials

list_materials()   # the built-in catalogue

Built-in Materials¶

Uniaxial Materials¶

Materials with a single optical axis (extraordinary axis differs from ordinary axes).

Quartz¶

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": "Quartz",
    "rotationX": 0,
    "rotationY": 90,  # Optical axis orientation
    "rotationZ": 0
}

Frequency range: 410-600 cm⁻¹
Type: Uniaxial positive
Applications: Mid-infrared phonon polaritons

Calcite¶

Two variants available:

Upper Reststrahlen Band:

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": "Calcite",  # or "CalciteUpper"
    "rotationX": 0,
    "rotationY": 90,
    "rotationZ": 0
}

Frequency range: 1300-1600 cm⁻¹
Type: Uniaxial negative (hyperbolic)

Lower Reststrahlen Band:

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": "CalciteLower",
    "rotationX": 0,
    "rotationY": 90,
    "rotationZ": 0
}

Frequency range: 860-920 cm⁻¹
Type: Uniaxial positive

Sapphire¶

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": "Sapphire",
    "rotationX": 0,
    "rotationY": 90,
    "rotationZ": 0
}

Frequency range: 210-1000 cm⁻¹
Type: Uniaxial negative
Applications: Wide-band phonon polaritons

AlN and SiC¶

Polar uniaxial crystals used (with MoO₃) in the layer-resolved absorption example. Both are modeled c-cut; SiC is treated as effectively isotropic in its reststrahlen band.

{"type": "Semi Infinite Anisotropic Layer", "material": "SiC", "rotationY": 0}
{"type": "Crystal Layer", "material": "AlN", "thickness": 1.0, "rotationY": 0}

Type: Uniaxial (AlN), near-isotropic (SiC)
Note: phonon parameters in material_params.json are literature values flagged for verification.

Monoclinic Materials¶

Gallium Oxide (β-Ga₂O₃)¶

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": "GalliumOxide",
    "rotationX": 0,
    "rotationY": 90,
    "rotationZ": 0
}

Frequency range: 350-800 cm⁻¹
Type: Monoclinic (non-zero off-diagonal elements)
Special: Has xy coupling (ε_xy ≠ 0)

Biaxial Materials¶

α-MoO₃ (molybdenum trioxide)¶

{
    "type": "Crystal Layer",
    "material": "MoO3",
    "thickness": 1.2,
    "rotationY": 0,
    "rotationZ": 0  # azimuthal rotation exposes the in-plane anisotropy
}

Type: Orthorhombic biaxial — a diagonal tensor with three distinct principal permittivities (no off-diagonal coupling, unlike monoclinic Ga₂O₃).
Special: strong in-plane anisotropy supports azimuth-dependent hyperbolic phonon polaritons (see examples/layer_resolved_absorption.py).
Note: parameters in material_params.json are literature values flagged for verification.

Transparency-Window Crystals (Sellmeier)¶

Lossless Sellmeier fits for the transparency windows, where photonic chips work:

name	crystal	valid (µm)	source
`LiNbO3`	congruent lithium niobate, negative uniaxial	0.4–5.0	Zelmon et al., JOSA B 14, 3319 (1997)
`TiO2`	rutile, positive uniaxial	0.43–1.53	DeVore, JOSA 41, 416 (1951)
`QuartzSellmeier`	α-quartz	0.198–2.05	Ghosh, Opt. Commun. 163, 95 (1999)
`CalciteSellmeier`	calcite	0.204–2.172	Ghosh (1999)
`SapphireSellmeier`	α-Al₂O₃	0.2–5.5	Malitson & Dodge, JOSA 62, 1405 (1972)
`SiO2`	fused silica, isotropic	0.21–6.7	Malitson, JOSA 55, 1205 (1965)
`Si3N4`	LPCVD silicon nitride, isotropic	0.31–5.5	Luke et al., Opt. Lett. 40, 4823 (2015)
`Si`	crystalline silicon, isotropic	1.36–11	Salzberg & Villa, JOSA 47, 244 (1957)

The tensor is diag(nₒ², nₒ², nₑ²) (optic axis along z). Frequencies are in cm⁻¹ (1550 nm is 6451.6 cm⁻¹); outside a fit's range a warning fires.

An x-cut LiNbO₃ film, with the optic axis in the plane of the film at 30° to the plane of incidence:

{
    "type": "Crystal Layer",
    "material": "LiNbO3",
    "thickness": 0.6,      # µm
    "rotationY": 90,       # optic axis into the plane of the film
    "rotationZ": 30,       # and turned within it
}

Isotropic Materials¶

Air¶

Used for air gaps and isotropic layers:

{
    "type": "Isotropic Middle-Stack Layer",
    "thickness": 0.5,
    "permittivity": 1.0  # Air
}

Custom Isotropic¶

{
    "type": "Isotropic Middle-Stack Layer",
    "thickness": 0.5,
    "permittivity": {"real": 2.5, "imag": 0.1}
}

Arbitrary Materials¶

Define custom materials with full tensors:

{
    "type": "Semi Infinite Anisotropic Layer",
    "material": {
        "eps_xx": {"real": 2.27, "imag": 0.001},
        "eps_yy": {"real": -4.84, "imag": 0.755},
        "eps_zz": {"real": -4.84, "imag": 0.755},
        "eps_xy": {"real": 0.0, "imag": 0.0},
        "eps_xz": {"real": 0.0, "imag": 0.0},
        "eps_yz": {"real": 0.0, "imag": 0.0}
    },
    "rotationX": 0,
    "rotationY": 0,
    "rotationZ": 0
}

Material Rotations¶

Rotation Types¶

Materials can be rotated using Euler angles (in degrees):

rotationX: Rotation around x-axis (Not really used)
rotationY: Rotation around y-axis (typically optical axis tilt)
rotationZ: Rotation around z-axis (azimuthal)

Rotation Examples¶

Optical axis perpendicular to interface:

"rotationX": 0,
"rotationY": 0,
"rotationZ": 0

Optical axis in the plane (70° tilt):

"rotationX": 0,
"rotationY": 70,
"rotationZ": 0

45° azimuthal rotation:

"rotationX": 0,
"rotationY": 90,
"rotationZ": 45

Rotation Types for Z-rotation¶

"rotationZ": 45,
"rotationZType": "relative"  # Default: rotates with azimuthal angle

or

"rotationZ": 45,
"rotationZType": "static"  # Fixed: doesn't rotate with azimuthal angle

Plotting Material Properties¶

from hyperbolic_optics.materials import CalciteUpper
from hyperbolic_optics.plots import plot_permittivity

# Create material
calcite = CalciteUpper()

# Get permittivity
eps_ext, eps_ord = calcite.permittivity_fetch()

# Plot
plot_permittivity(calcite, eps_ext, eps_ord, save_name="calcite_permittivity")

Material Properties Summary¶

Material	Type	Frequency Range	Hyperbolic?
Quartz	Uniaxial	410-600 cm⁻¹	Yes
Calcite Upper	Uniaxial	1300-1600 cm⁻¹	Yes
Calcite Lower	Uniaxial	860-920 cm⁻¹	Yes
Sapphire	Uniaxial	210-1000 cm⁻¹	Yes
Gallium Oxide	Monoclinic	350-800 cm⁻¹	Yes
α-MoO₃	Biaxial	500-1050 cm⁻¹	Yes
AlN	Uniaxial	500-1050 cm⁻¹	Yes
SiC	Uniaxial (≈isotropic)	500-1050 cm⁻¹	Yes

Note: A material is "hyperbolic" when the real parts of permittivity components have opposite signs.