Optical constants
Refractive index of Cu (Copper)
Babar and Weaver 2015: n,k 0.2066–12.40 µm
- Data
- tabulated nk
- Range
- 0.2066–12.4 µm
- Points
- 69
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.167525
- Extinction coefficient k
- 2.86493
- Permittivity ε1
- -8.17973
- Permittivity ε2
- 0.959895
- Absorption coefficient α
- 612691 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 32.6429 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -14.5448 µm⁻¹
- Group index ng
- 8.71404
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 2.11001 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): Babar and Weaver 2015: n,k 0.2066–12.40 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Babar", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (206.6, 12400) nm
eps = cu.eps([633]) # 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_cb38c1a4164d/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/babar-weaver-2015).
# ... 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=400, stop_nm=1000, 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/ao.54.000477 Optical constants of Cu, Ag, and Au revisited, Applied Optics (2015)
Cite
Shaista Babar and J. H. Weaver. Optical constants of Cu, Ag, and Au revisited. Applied Optics, 54, 477 (2015), doi:10.1364/ao.54.000477; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
69 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.2066 | 1.02 | 1.597 |
| 0.2101 | 1.054 | 1.656 |
| 0.2138 | 1.09 | 1.697 |
| 0.2175 | 1.133 | 1.739 |
| 0.2214 | 1.181 | 1.77 |
| 0.2254 | 1.228 | 1.8 |
| 0.2296 | 1.276 | 1.822 |
| 0.2339 | 1.329 | 1.843 |
| 0.2384 | 1.388 | 1.851 |
| 0.2431 | 1.439 | 1.844 |
| 0.248 | 1.489 | 1.84 |
| 0.253 | 1.546 | 1.814 |
| 0.2583 | 1.573 | 1.77 |
| 0.2638 | 1.58 | 1.734 |
| 0.2695 | 1.577 | 1.705 |
| 0.2755 | 1.564 | 1.678 |
| 0.2818 | 1.54 | 1.662 |
| 0.2883 | 1.507 | 1.652 |
| 0.2952 | 1.458 | 1.66 |
| 0.3024 | 1.422 | 1.698 |
| 0.31 | 1.404 | 1.735 |
| 0.3179 | 1.387 | 1.773 |
| 0.3263 | 1.375 | 1.814 |
| 0.3351 | 1.377 | 1.851 |
| 0.3444 | 1.369 | 1.874 |
| 0.3542 | 1.349 | 1.905 |
| 0.3647 | 1.324 | 1.937 |
| 0.3757 | 1.292 | 1.985 |
| 0.3875 | 1.276 | 2.037 |
| 0.3999 | 1.239 | 2.078 |
| 0.4133 | 1.198 | 2.158 |
| 0.4275 | 1.186 | 2.238 |
| 0.4428 | 1.168 | 2.299 |
| 0.4592 | 1.147 | 2.372 |
| 0.4769 | 1.131 | 2.445 |
| 0.4959 | 1.121 | 2.485 |
| 0.5166 | 1.089 | 2.501 |
| 0.5391 | 0.9717 | 2.413 |
| 0.5636 | 0.5166 | 2.41 |
| 0.5904 | 0.1268 | 2.918 |
| 0.6199 | 0.09461 | 3.382 |
| 0.6525 | 0.0878 | 3.759 |
| 0.6888 | 0.07277 | 4.123 |
| 0.7293 | 0.06434 | 4.507 |
| 0.7749 | 0.06 | 4.917 |
| 0.8266 | 0.06248 | 5.361 |
| 0.8856 | 0.06666 | 5.85 |
| 0.9537 | 0.07343 | 6.4 |
| 1.033 | 0.08395 | 7.028 |
| 1.127 | 0.09798 | 7.757 |
| 1.24 | 0.1189 | 8.619 |
| 1.305 | 0.1317 | 9.114 |
| 1.378 | 0.1465 | 9.66 |
| 1.459 | 0.1646 | 10.27 |
| 1.55 | 0.1863 | 10.95 |
| 1.653 | 0.2125 | 11.72 |
| 1.771 | 0.2439 | 12.59 |
| 1.907 | 0.2836 | 13.59 |
| 2.066 | 0.3333 | 14.76 |
| 2.254 | 0.3975 | 16.14 |
| 2.48 | 0.4814 | 17.78 |
| 2.755 | 0.5934 | 19.78 |
| 3.1 | 0.7493 | 22.28 |
| 3.542 | 0.9782 | 25.48 |
| 4.133 | 1.334 | 29.73 |
| 4.959 | 1.924 | 35.62 |
| 6.199 | 2.973 | 44.34 |
| 8.266 | 5.134 | 58.62 |
| 12.4 | 11.18 | 85.47 |
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
- —