Plot gold’s refractive index and extinction coefficient in Python#

Load measured gold optical constants and plot the real refractive index and extinction coefficient separately. Use these wavelength-dependent values as inputs to material, interface, or electromagnetic calculations.

Run the notebook with Runtime → Run all, or download the notebook or Python script to run locally.

Run locally#

python -m pip install PyOptik
python gold_optical_constants.py

The script downloads the RefractiveIndex.INFO snapshot on first use. This needs internet access; subsequent runs reuse the local cache.

Calculate and plot#

import matplotlib.pyplot as plt
import numpy as np
from TypedUnit import ureg
from PyOptik import material

# Use the documented default and keep the resolved identity visible.
gold = material("gold")  # main/Au/Johnson
print("Resolved source:", gold.catalog_id)
wavelengths = np.linspace(400, 1600, 300) * ureg.nanometer
index = gold.compute_refractive_index(wavelengths, out_of_range="raise")

figure, axes = plt.subplots(1, 2, figsize=(10, 4), layout="constrained")
axes[0].plot(wavelengths.magnitude, index.real, color="tab:orange")
axes[0].set(xlabel="Vacuum wavelength [nm]", ylabel="Refractive index n",
            title="Gold: real part of the optical index")
axes[1].plot(wavelengths.magnitude, index.imag, color="tab:purple")
axes[1].set(xlabel="Vacuum wavelength [nm]", ylabel="Extinction coefficient k",
            title="Gold: imaginary part of the optical index")
for axis in axes:
    axis.grid(alpha=0.25)

print("Dataset: main/Au/Johnson (Johnson and Christy)")
print("Optical index at 550 nm:", gold.compute_refractive_index(
    550 * ureg.nanometer, out_of_range="raise"))
plt.show()

Understand the result#

PyOptik uses the convention \(\tilde n = n + i k\). The real part \(n\) describes phase propagation, while the positive extinction coefficient \(k\) describes attenuation. The intensity absorption coefficient is \(\alpha = 4\pi k/\lambda\), with vacuum wavelength \(\lambda\).

The canonical identifier main/Au/Johnson selects the Johnson and Christy dataset explicitly. Tabulated values are interpolated between source points; out_of_range="raise" prevents extrapolation outside the published range. These are bulk optical constants; films can differ with fabrication and measurement conditions. Cite the original measurement when using this data.

Try another design#

Replace main/Au/Johnson with main/Ag/Johnson to compare gold and silver over the same wavelength range. Use gold.absorption_coefficient to express attenuation as an inverse length.

See Physical and numerical conventions for physical conventions and Materials and catalog for source selection and provenance.