Optical constants
Refractive index of Cu (Copper)
Brimhall et al. 2009: n,k 0.0101–0.0421 µm
- Data
- tabulated nk
- Range
- 0.0101–0.0421 µm
- Points
- 31
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.969909
- Extinction coefficient k
- 0.0502727
- Permittivity ε1
- 0.938196
- Permittivity ε2
- 0.09752
- Absorption coefficient α
- 306673 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 65.2161 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.909091 µm⁻¹
- Group index ng
- 0.988636
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 60.1865 eV
ε = (n + ik)², α = 4πk/λ, ng = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.
Use it in Lightsmith
Load this data in Python, simulate in one more line
pip install lightsmith
import lightsmith as ls
# Cu (Copper): Brimhall et al. 2009: n,k 0.0101–0.0421 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Brimhall", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (10.1, 42.1) nm
eps = cu.eps([20.6]) # complex permittivity
Downloads the original record once (pinned to the imported snapshot) and caches it.
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_d4bdfb995eeb/lightsmith"
cu = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(cu.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (cu/brimhall-2009).
# ... load cu as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=cu)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=11, stop_nm=42, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelength
Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.
References
- doi:10.1364/oe.17.023873 Measured optical constants of copper from 10 nm to 35 nm, Optics Express (2009)
Cite
Nicole Brimhall et al.. Measured optical constants of copper from 10 nm to 35 nm. Optics Express, 17, 23873 (2009), doi:10.1364/oe.17.023873; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
34 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.0101 | 0.991 | 0.017 |
| 0.0104 | 0.985 | 0.025 |
| 0.0107 | 0.992 | 0.017 |
| 0.011 | 0.987 | 0.008 |
| 0.0113 | 0.982 | 0.016 |
| 0.0116 | 0.983 | 0.017 |
| 0.0119 | 0.985 | 0.01 |
| 0.0123 | 0.982 | 0.011 |
| 0.0127 | 0.978 | 0.022 |
| 0.0131 | 0.972 | 0.031 |
| 0.0136 | 0.971 | 0.039 |
| 0.0136 | 0.969 | 0.042 |
| 0.014 | 0.978 | 0.038 |
| 0.014 | 0.972 | 0.03 |
| 0.0145 | 0.976 | 0.044 |
| 0.0145 | 0.974 | 0.042 |
| 0.0151 | 0.974 | 0.051 |
| 0.0157 | 0.973 | 0.055 |
| 0.0163 | 0.976 | 0.047 |
| 0.017 | 0.975 | 0.041 |
| 0.0178 | 0.968 | 0.044 |
| 0.0186 | 0.967 | 0.044 |
| 0.0195 | 0.967 | 0.05 |
| 0.0205 | 0.97 | 0.05 |
| 0.0216 | 0.969 | 0.053 |
| 0.0229 | 0.961 | 0.063 |
| 0.0242 | 0.958 | 0.066 |
| 0.0258 | 0.949 | 0.068 |
| 0.0276 | 0.94 | 0.084 |
| 0.0296 | 0.927 | 0.093 |
| 0.032 | 0.912 | 0.107 |
| 0.0348 | 0.891 | 0.14 |
| 0.0381 | 0.88 | 0.184 |
| 0.0421 | 0.874 | 0.236 |
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —