Optical constants
Refractive index of Cu (Copper)
Johnson and Christy 1972: n,k 0.188–1.937 µm
- Data
- tabulated nk
- Range
- 0.1879–1.937 µm
- Points
- 49
- Licence
- CC0-1.0
- Lightsmith
- bundled, default
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.636599
- Extinction coefficient k
- 2.78341
- Permittivity ε1
- -7.34211
- Permittivity ε2
- 3.54383
- Absorption coefficient α
- 595258 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 33.5989 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -11.5274 µm⁻¹
- Group index ng
- 7.41009
- 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): Johnson and Christy 1972: n,k 0.188–1.937 µm
cu = ls.LibraryMaterial(name="Cu", dataset="Johnson-Christy")
print(cu.range_nm) # (187.9, 1937) nm
eps = cu.eps([633]) # complex permittivity
Ships with the library: works offline and is the library's own default dataset choice.
import lightsmith as ls
# Cu (Copper): Johnson and Christy 1972: n,k 0.188–1.937 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Johnson", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (187.9, 1937) 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_3f1b7f932b27/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/johnson-christy-1972).
# ... 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.
Comments and conditions
References
- doi:10.1103/physrevb.6.4370 Optical Constants of the Noble Metals, Physical Review B (1972)
Cite
P. B. Johnson and R. W. Christy. Optical Constants of the Noble Metals. Physical Review B, 6, 4370-4379 (1972), doi:10.1103/physrevb.6.4370; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
49 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.1879 | 0.94 | 1.337 |
| 0.1916 | 0.95 | 1.388 |
| 0.1953 | 0.97 | 1.44 |
| 0.1993 | 0.98 | 1.493 |
| 0.2033 | 0.99 | 1.55 |
| 0.2073 | 1.01 | 1.599 |
| 0.2119 | 1.04 | 1.651 |
| 0.2164 | 1.08 | 1.699 |
| 0.2214 | 1.13 | 1.737 |
| 0.2262 | 1.18 | 1.768 |
| 0.2313 | 1.23 | 1.792 |
| 0.2371 | 1.28 | 1.802 |
| 0.2426 | 1.34 | 1.799 |
| 0.249 | 1.37 | 1.783 |
| 0.2551 | 1.41 | 1.741 |
| 0.2616 | 1.41 | 1.691 |
| 0.2689 | 1.45 | 1.668 |
| 0.2761 | 1.46 | 1.646 |
| 0.2844 | 1.45 | 1.633 |
| 0.2924 | 1.42 | 1.633 |
| 0.3009 | 1.4 | 1.679 |
| 0.3107 | 1.38 | 1.729 |
| 0.3204 | 1.38 | 1.783 |
| 0.3315 | 1.34 | 1.821 |
| 0.3425 | 1.36 | 1.864 |
| 0.3542 | 1.37 | 1.916 |
| 0.3679 | 1.36 | 1.975 |
| 0.3815 | 1.33 | 2.045 |
| 0.3974 | 1.32 | 2.116 |
| 0.4133 | 1.28 | 2.207 |
| 0.4305 | 1.25 | 2.305 |
| 0.4509 | 1.24 | 2.397 |
| 0.4714 | 1.25 | 2.483 |
| 0.4959 | 1.22 | 2.564 |
| 0.5209 | 1.18 | 2.608 |
| 0.5486 | 1.02 | 2.577 |
| 0.5821 | 0.7 | 2.704 |
| 0.6168 | 0.3 | 3.205 |
| 0.6595 | 0.22 | 3.747 |
| 0.7045 | 0.21 | 4.205 |
| 0.756 | 0.24 | 4.665 |
| 0.8211 | 0.26 | 5.18 |
| 0.892 | 0.3 | 5.768 |
| 0.984 | 0.32 | 6.421 |
| 1.088 | 0.36 | 7.217 |
| 1.216 | 0.48 | 8.245 |
| 1.393 | 0.6 | 9.439 |
| 1.61 | 0.76 | 11.12 |
| 1.937 | 1.09 | 13.43 |
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
- —
Room temperature