Optical constants
Refractive index of Cu (Copper)
Werner et al. 2009: DFT calculations; n,k 0.01759–2.480 µm
- Data
- tabulated nk
- Range
- 0.01759–2.48 µm
- Points
- 150
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.24104
- Extinction coefficient k
- 3.25519
- Permittivity ε1
- -9.05605
- Permittivity ε2
- 8.07965
- Absorption coefficient α
- 696152 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 28.7294 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1.18322 µm⁻¹
- Group index ng
- 1.9363
- 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): Werner et al. 2009: DFT calculations; n,k 0.01759–2.480 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Werner-DFT", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (17.586, 2479.68) 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_f2d88814311a/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/werner-2009-dft).
# ... 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:10.1063/1.3243762 Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals, Journal of Physical and Chemical Reference Data (2009)
Cite
Wolfgang S. M. Werner, Kathrin Glantschnig and Claudia Ambrosch-Draxl. Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals. Journal of Physical and Chemical Reference Data, 38, 1013-1092 (2009), doi:10.1063/1.3243762; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
150 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.017586 | 0.9564 | 0.1291 |
| 0.017712 | 0.9926 | 0.0962 |
| 0.017839 | 0.9639 | 0.0716 |
| 0.017969 | 0.9502 | 0.07 |
| 0.0181 | 0.9437 | 0.0747 |
| 0.018233 | 0.9393 | 0.0724 |
| 0.018368 | 0.9341 | 0.0739 |
| 0.018505 | 0.9306 | 0.0774 |
| 0.018644 | 0.9317 | 0.0783 |
| 0.018785 | 0.9276 | 0.0798 |
| 0.018929 | 0.9271 | 0.0804 |
| 0.019074 | 0.9254 | 0.08 |
| 0.019222 | 0.9234 | 0.0818 |
| 0.019373 | 0.9212 | 0.0809 |
| 0.019525 | 0.9167 | 0.0802 |
| 0.01968 | 0.9092 | 0.0819 |
| 0.019837 | 0.9027 | 0.0892 |
| 0.019997 | 0.9027 | 0.0991 |
| 0.02016 | 0.9046 | 0.1067 |
| 0.020325 | 0.9103 | 0.1121 |
| 0.020493 | 0.9148 | 0.1137 |
| 0.020664 | 0.9184 | 0.1116 |
| 0.020838 | 0.9173 | 0.1112 |
| 0.021014 | 0.9163 | 0.1124 |
| 0.021194 | 0.9156 | 0.1158 |
| 0.021377 | 0.9189 | 0.1202 |
| 0.021562 | 0.9256 | 0.1215 |
| 0.021752 | 0.9332 | 0.1179 |
| 0.021944 | 0.932 | 0.103 |
| 0.02214 | 0.921 | 0.1015 |
| 0.022339 | 0.9118 | 0.102 |
| 0.022543 | 0.9073 | 0.1108 |
| 0.022749 | 0.9085 | 0.1156 |
| 0.02296 | 0.9092 | 0.1171 |
| 0.023175 | 0.9085 | 0.12 |
| 0.023393 | 0.9064 | 0.1164 |
| 0.023616 | 0.8994 | 0.1223 |
| 0.023843 | 0.8999 | 0.1295 |
| 0.024075 | 0.8995 | 0.1306 |
| 0.024311 | 0.9015 | 0.1331 |
| 0.024551 | 0.8984 | 0.1386 |
| 0.024797 | 0.9006 | 0.1382 |
| 0.025047 | 0.8975 | 0.1432 |
| 0.025303 | 0.897 | 0.1472 |
| 0.025564 | 0.895 | 0.1519 |
| 0.02583 | 0.8982 | 0.1603 |
| 0.026102 | 0.9011 | 0.1615 |
| 0.02638 | 0.9021 | 0.1668 |
| 0.026663 | 0.9098 | 0.1726 |
| 0.026953 | 0.9164 | 0.1669 |
| 0.027249 | 0.9151 | 0.1656 |
| 0.027552 | 0.9178 | 0.1656 |
| 0.027862 | 0.9188 | 0.1616 |
| 0.028178 | 0.914 | 0.1592 |
| 0.028502 | 0.9117 | 0.1618 |
| 0.028834 | 0.909 | 0.1623 |
| 0.029173 | 0.9071 | 0.1637 |
| 0.02952 | 0.9062 | 0.165 |
| 0.029876 | 0.9012 | 0.1648 |
| 0.03024 | 0.8973 | 0.1705 |
| 0.030613 | 0.8964 | 0.1746 |
| 0.030996 | 0.8976 | 0.1782 |
| 0.031388 | 0.8982 | 0.1781 |
| 0.031791 | 0.8952 | 0.1771 |
| 0.032204 | 0.8903 | 0.178 |
| 0.032627 | 0.8845 | 0.1826 |
| 0.033062 | 0.881 | 0.1873 |
| 0.033509 | 0.8783 | 0.1935 |
| 0.033968 | 0.878 | 0.197 |
| 0.03444 | 0.8733 | 0.1992 |
| 0.034925 | 0.8686 | 0.2061 |
| 0.035424 | 0.8677 | 0.2144 |
| 0.035937 | 0.8677 | 0.2213 |
| 0.036466 | 0.8734 | 0.2255 |
| 0.03701 | 0.8698 | 0.2225 |
| 0.037571 | 0.871 | 0.2227 |
| 0.038149 | 0.8649 | 0.2191 |
| 0.038745 | 0.847 | 0.2202 |
| 0.03936 | 0.833 | 0.2323 |
| 0.039995 | 0.8306 | 0.2528 |
| 0.040651 | 0.8342 | 0.2625 |
| 0.041328 | 0.8417 | 0.2709 |
| 0.042029 | 0.8501 | 0.2423 |
| 0.042753 | 0.8118 | 0.226 |
| 0.043503 | 0.7535 | 0.2382 |
| 0.04428 | 0.7071 | 0.2899 |
| 0.045085 | 0.7047 | 0.3654 |
| 0.04592 | 0.7205 | 0.4039 |
| 0.046786 | 0.7294 | 0.4517 |
| 0.047686 | 0.755 | 0.498 |
| 0.048621 | 0.7987 | 0.544 |
| 0.049594 | 0.8657 | 0.566 |
| 0.050606 | 0.9202 | 0.5493 |
| 0.05166 | 0.9686 | 0.5369 |
| 0.052759 | 1.0215 | 0.4811 |
| 0.053906 | 0.9928 | 0.4094 |
| 0.055104 | 0.953 | 0.3888 |
| 0.056356 | 0.9181 | 0.3845 |
| 0.057667 | 0.8862 | 0.3904 |
| 0.05904 | 0.8542 | 0.4045 |
| 0.06048 | 0.8245 | 0.4287 |
| 0.061992 | 0.7988 | 0.4638 |
| 0.063582 | 0.7818 | 0.5072 |
| 0.065255 | 0.7763 | 0.5565 |
| 0.067018 | 0.7827 | 0.6063 |
| 0.06888 | 0.8014 | 0.6514 |
| 0.070848 | 0.8254 | 0.6857 |
| 0.072932 | 0.8397 | 0.717 |
| 0.075142 | 0.8606 | 0.7547 |
| 0.07749 | 0.8895 | 0.7926 |
| 0.07999 | 0.9285 | 0.8271 |
| 0.082656 | 0.9826 | 0.8518 |
| 0.085506 | 1.042 | 0.8311 |
| 0.08856 | 1.0441 | 0.8174 |
| 0.09184 | 1.0545 | 0.8241 |
| 0.095372 | 1.0686 | 0.83 |
| 0.099187 | 1.0885 | 0.8287 |
| 0.10332 | 1.0848 | 0.8029 |
| 0.107812 | 1.0354 | 0.8204 |
| 0.112713 | 1.023 | 0.8588 |
| 0.11808 | 1.0061 | 0.8861 |
| 0.123984 | 0.9482 | 0.9534 |
| 0.13051 | 0.9587 | 1.0593 |
| 0.13776 | 1.0052 | 1.146 |
| 0.145864 | 1.0168 | 1.1679 |
| 0.15498 | 1.0405 | 1.2902 |
| 0.165312 | 1.0915 | 1.3687 |
| 0.17712 | 1.146 | 1.421 |
| 0.190745 | 1.1124 | 1.5035 |
| 0.20664 | 1.134 | 1.687 |
| 0.225426 | 1.2621 | 1.9222 |
| 0.247968 | 1.6165 | 2.0372 |
| 0.261019 | 1.776 | 1.8818 |
| 0.27552 | 1.6302 | 1.7273 |
| 0.291728 | 1.5595 | 1.8202 |
| 0.30996 | 1.5304 | 1.8469 |
| 0.330625 | 1.4122 | 1.9484 |
| 0.354241 | 1.3896 | 2.1308 |
| 0.38149 | 1.405 | 2.2933 |
| 0.413281 | 1.4249 | 2.4387 |
| 0.450852 | 1.3862 | 2.5808 |
| 0.495937 | 1.3241 | 2.8166 |
| 0.551041 | 1.2843 | 3.1036 |
| 0.619921 | 1.2028 | 3.3892 |
| 0.708481 | 0.8602 | 3.7838 |
| 0.826561 | 0.377 | 4.8766 |
| 0.991874 | 0.3587 | 6.3943 |
| 1.239842 | 0.4912 | 8.3756 |
| 1.653123 | 0.8212 | 11.4688 |
| 2.479684 | 1.776 | 17.3882 |
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
- —
Theoretical density function theory (DFT) calculations.