Optical constants
Refractive index of Cu (Copper)
Stahrenberg et al. 2001: n,k 0.128–0.496 µm
- Data
- tabulated nk
- Range
- 0.1378–0.4959 µm
- Points
- 326
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.61314
- Extinction coefficient k
- 1.90927
- Permittivity ε1
- -1.04308
- Permittivity ε2
- 6.15983
- Absorption coefficient α
- 919255 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 21.7567 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.509091 µm⁻¹
- Group index ng
- 1.48027
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 4.75035 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): Stahrenberg et al. 2001: n,k 0.128–0.496 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Stahrenberg", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (137.76, 495.94) nm
eps = cu.eps([261]) # 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_e07731b55825/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/stahrenberg-2001).
# ... 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=495, 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:10.1103/physrevb.64.115111 Optical properties of copper and silver in the energy range 2.5–9.0 eV, Physical Review B (2001)
Cite
K. Stahrenberg et al.. Optical properties of copper and silver in the energy range 2.5–9.0 eV. Physical Review B, 64, 115111 (2001), doi:10.1103/physrevb.64.115111; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
326 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.13776 | 1.02524 | 1.10807 |
| 0.13807 | 1.02508 | 1.11011 |
| 0.13838 | 1.02497 | 1.1123 |
| 0.13868 | 1.02495 | 1.11479 |
| 0.139 | 1.0251 | 1.11755 |
| 0.13931 | 1.02543 | 1.12037 |
| 0.13962 | 1.02591 | 1.12296 |
| 0.13994 | 1.0265 | 1.12506 |
| 0.14025 | 1.02715 | 1.1265 |
| 0.14057 | 1.02783 | 1.12737 |
| 0.14089 | 1.02849 | 1.12785 |
| 0.14121 | 1.0291 | 1.12817 |
| 0.14153 | 1.02968 | 1.12856 |
| 0.14186 | 1.0302 | 1.12913 |
| 0.14218 | 1.0307 | 1.12986 |
| 0.14251 | 1.03114 | 1.13069 |
| 0.14284 | 1.03157 | 1.13164 |
| 0.14317 | 1.03198 | 1.13262 |
| 0.1435 | 1.03239 | 1.13354 |
| 0.14383 | 1.03279 | 1.13446 |
| 0.14417 | 1.03316 | 1.13541 |
| 0.1445 | 1.03349 | 1.13647 |
| 0.14484 | 1.03378 | 1.13763 |
| 0.14518 | 1.03402 | 1.13886 |
| 0.14552 | 1.03422 | 1.14017 |
| 0.14586 | 1.0344 | 1.14161 |
| 0.14621 | 1.0346 | 1.14331 |
| 0.14655 | 1.03486 | 1.14529 |
| 0.1469 | 1.03515 | 1.14739 |
| 0.14725 | 1.03544 | 1.14935 |
| 0.1476 | 1.03572 | 1.15098 |
| 0.14795 | 1.03598 | 1.15226 |
| 0.14831 | 1.03623 | 1.15328 |
| 0.14866 | 1.03651 | 1.15421 |
| 0.14902 | 1.03682 | 1.15523 |
| 0.14938 | 1.03718 | 1.15643 |
| 0.14974 | 1.03756 | 1.15781 |
| 0.1501 | 1.03794 | 1.15929 |
| 0.15047 | 1.0383 | 1.16085 |
| 0.15083 | 1.03862 | 1.16248 |
| 0.1512 | 1.0389 | 1.1641 |
| 0.15157 | 1.03911 | 1.16564 |
| 0.15194 | 1.03923 | 1.167 |
| 0.15231 | 1.03926 | 1.16811 |
| 0.15269 | 1.03922 | 1.16901 |
| 0.15307 | 1.03911 | 1.16977 |
| 0.15345 | 1.03895 | 1.17048 |
| 0.15383 | 1.03873 | 1.1712 |
| 0.15421 | 1.03845 | 1.17204 |
| 0.15459 | 1.03811 | 1.17299 |
| 0.15498 | 1.03771 | 1.17406 |
| 0.15537 | 1.03725 | 1.17522 |
| 0.15576 | 1.03669 | 1.17637 |
| 0.15615 | 1.03602 | 1.17747 |
| 0.15655 | 1.03523 | 1.17853 |
| 0.15694 | 1.03431 | 1.17958 |
| 0.15734 | 1.03325 | 1.18063 |
| 0.15774 | 1.03204 | 1.1817 |
| 0.15814 | 1.03071 | 1.18283 |
| 0.15855 | 1.02925 | 1.18404 |
| 0.15895 | 1.02768 | 1.18532 |
| 0.15936 | 1.026 | 1.18668 |
| 0.15977 | 1.02423 | 1.18812 |
| 0.16019 | 1.02237 | 1.1897 |
| 0.1606 | 1.02042 | 1.19142 |
| 0.16102 | 1.0184 | 1.19328 |
| 0.16144 | 1.01631 | 1.19529 |
| 0.16186 | 1.01418 | 1.19747 |
| 0.16228 | 1.01202 | 1.19987 |
| 0.16271 | 1.00986 | 1.20252 |
| 0.16314 | 1.00771 | 1.20539 |
| 0.16357 | 1.00556 | 1.20845 |
| 0.164 | 1.0034 | 1.2116 |
| 0.16444 | 1.00123 | 1.2148 |
| 0.16487 | 0.99905 | 1.21802 |
| 0.16531 | 0.99686 | 1.22125 |
| 0.16575 | 0.99705 | 1.22352 |
| 0.1662 | 0.99482 | 1.22725 |
| 0.16665 | 0.9926 | 1.2311 |
| 0.16709 | 0.99039 | 1.23509 |
| 0.16755 | 0.98819 | 1.23922 |
| 0.168 | 0.98601 | 1.24348 |
| 0.16846 | 0.98385 | 1.24788 |
| 0.16892 | 0.98172 | 1.25239 |
| 0.16938 | 0.97959 | 1.25699 |
| 0.16984 | 0.97748 | 1.26168 |
| 0.17031 | 0.97537 | 1.26645 |
| 0.17078 | 0.97327 | 1.2713 |
| 0.17125 | 0.97117 | 1.27623 |
| 0.17172 | 0.96908 | 1.28124 |
| 0.1722 | 0.967 | 1.28634 |
| 0.17268 | 0.96494 | 1.29153 |
| 0.17316 | 0.96288 | 1.29681 |
| 0.17365 | 0.96085 | 1.30218 |
| 0.17413 | 0.95883 | 1.30765 |
| 0.17463 | 0.95683 | 1.3132 |
| 0.17512 | 0.95485 | 1.31886 |
| 0.17561 | 0.95289 | 1.32463 |
| 0.17611 | 0.95097 | 1.33051 |
| 0.17662 | 0.94908 | 1.33652 |
| 0.17712 | 0.94723 | 1.34265 |
| 0.17763 | 0.94544 | 1.34891 |
| 0.17814 | 0.9437 | 1.3553 |
| 0.17865 | 0.94202 | 1.36181 |
| 0.17917 | 0.94041 | 1.36844 |
| 0.17969 | 0.93887 | 1.3752 |
| 0.18021 | 0.93743 | 1.38208 |
| 0.18073 | 0.93606 | 1.3891 |
| 0.18126 | 0.93479 | 1.39625 |
| 0.18179 | 0.93362 | 1.40354 |
| 0.18233 | 0.93254 | 1.41096 |
| 0.18287 | 0.93158 | 1.41852 |
| 0.18341 | 0.93073 | 1.42622 |
| 0.18395 | 0.93001 | 1.43407 |
| 0.1845 | 0.92942 | 1.44206 |
| 0.18505 | 0.92896 | 1.45019 |
| 0.1856 | 0.92865 | 1.45847 |
| 0.18616 | 0.92848 | 1.46687 |
| 0.18672 | 0.92845 | 1.47539 |
| 0.18729 | 0.92857 | 1.48405 |
| 0.18785 | 0.92885 | 1.49283 |
| 0.18843 | 0.92929 | 1.50173 |
| 0.189 | 0.92989 | 1.51077 |
| 0.18958 | 0.93065 | 1.51992 |
| 0.19016 | 0.9316 | 1.52919 |
| 0.19074 | 0.93272 | 1.53857 |
| 0.19133 | 0.93402 | 1.54805 |
| 0.19193 | 0.93551 | 1.55761 |
| 0.19252 | 0.93721 | 1.56726 |
| 0.19312 | 0.9391 | 1.57698 |
| 0.19373 | 0.9412 | 1.58678 |
| 0.19433 | 0.9435 | 1.59664 |
| 0.19494 | 0.94602 | 1.60654 |
| 0.19556 | 0.94875 | 1.61647 |
| 0.19618 | 0.9517 | 1.62642 |
| 0.1968 | 0.95486 | 1.63637 |
| 0.19743 | 0.95823 | 1.64631 |
| 0.19806 | 0.96183 | 1.65623 |
| 0.19869 | 0.96563 | 1.66611 |
| 0.19933 | 0.96964 | 1.67595 |
| 0.19997 | 0.97388 | 1.68574 |
| 0.20062 | 0.97831 | 1.69546 |
| 0.20127 | 0.98295 | 1.70512 |
| 0.20193 | 0.98779 | 1.71472 |
| 0.20259 | 0.99283 | 1.72426 |
| 0.20325 | 0.99806 | 1.73372 |
| 0.20392 | 1.00348 | 1.74311 |
| 0.20459 | 1.00909 | 1.75242 |
| 0.20527 | 1.01489 | 1.76166 |
| 0.20595 | 1.02089 | 1.77081 |
| 0.20664 | 1.02709 | 1.77989 |
| 0.20733 | 1.03348 | 1.7889 |
| 0.20803 | 1.04007 | 1.79784 |
| 0.20873 | 1.04686 | 1.80668 |
| 0.20943 | 1.05385 | 1.81545 |
| 0.21014 | 1.06104 | 1.82411 |
| 0.21086 | 1.06843 | 1.83268 |
| 0.21158 | 1.07601 | 1.84115 |
| 0.2123 | 1.08377 | 1.84953 |
| 0.21303 | 1.09172 | 1.8578 |
| 0.21377 | 1.09985 | 1.86596 |
| 0.21451 | 1.10817 | 1.874 |
| 0.21525 | 1.11666 | 1.88192 |
| 0.216 | 1.12534 | 1.8897 |
| 0.21676 | 1.1342 | 1.89734 |
| 0.21752 | 1.14324 | 1.90483 |
| 0.21828 | 1.15246 | 1.91214 |
| 0.21905 | 1.16186 | 1.91928 |
| 0.21983 | 1.17143 | 1.92623 |
| 0.22061 | 1.18119 | 1.93297 |
| 0.2214 | 1.19112 | 1.93949 |
| 0.22219 | 1.20123 | 1.94579 |
| 0.22299 | 1.21149 | 1.95186 |
| 0.2238 | 1.22192 | 1.95768 |
| 0.22461 | 1.2325 | 1.96325 |
| 0.22543 | 1.24323 | 1.96854 |
| 0.22625 | 1.2541 | 1.97357 |
| 0.22708 | 1.26509 | 1.9783 |
| 0.22791 | 1.27619 | 1.98273 |
| 0.22875 | 1.28739 | 1.98685 |
| 0.2296 | 1.29867 | 1.99065 |
| 0.23045 | 1.3193 | 2.00306 |
| 0.23131 | 1.33109 | 2.00604 |
| 0.23218 | 1.34278 | 2.00868 |
| 0.23305 | 1.35441 | 2.01099 |
| 0.23393 | 1.36597 | 2.01295 |
| 0.23482 | 1.37747 | 2.0145 |
| 0.23571 | 1.38889 | 2.01557 |
| 0.23661 | 1.40023 | 2.01621 |
| 0.23752 | 1.41147 | 2.01653 |
| 0.23843 | 1.42262 | 2.01664 |
| 0.23935 | 1.43368 | 2.01662 |
| 0.24028 | 1.44467 | 2.0165 |
| 0.24121 | 1.45555 | 2.01626 |
| 0.24216 | 1.46631 | 2.01585 |
| 0.24311 | 1.47695 | 2.01525 |
| 0.24406 | 1.48748 | 2.01438 |
| 0.24503 | 1.49795 | 2.01313 |
| 0.246 | 1.50842 | 2.01139 |
| 0.24698 | 1.51895 | 2.00903 |
| 0.24797 | 1.52948 | 2.00598 |
| 0.24896 | 1.53998 | 2.00217 |
| 0.24997 | 1.5503 | 1.99752 |
| 0.25098 | 1.56029 | 1.99194 |
| 0.252 | 1.56982 | 1.98541 |
| 0.25303 | 1.57875 | 1.97795 |
| 0.25407 | 1.5869 | 1.96969 |
| 0.25511 | 1.59411 | 1.9608 |
| 0.25617 | 1.60022 | 1.95146 |
| 0.25723 | 1.60512 | 1.94188 |
| 0.2583 | 1.60882 | 1.93227 |
| 0.25938 | 1.61138 | 1.92279 |
| 0.26047 | 1.61287 | 1.91357 |
| 0.26157 | 1.61343 | 1.90464 |
| 0.26268 | 1.6132 | 1.89614 |
| 0.2638 | 1.61237 | 1.88811 |
| 0.26492 | 1.61108 | 1.88062 |
| 0.26606 | 1.60945 | 1.87367 |
| 0.26721 | 1.60751 | 1.86724 |
| 0.26836 | 1.60533 | 1.86127 |
| 0.26953 | 1.603 | 1.85568 |
| 0.27071 | 1.60059 | 1.85038 |
| 0.27189 | 1.59814 | 1.84531 |
| 0.27309 | 1.59563 | 1.84042 |
| 0.2743 | 1.59298 | 1.83561 |
| 0.27552 | 1.59011 | 1.83077 |
| 0.27675 | 1.58695 | 1.82581 |
| 0.27799 | 1.58338 | 1.82063 |
| 0.27924 | 1.5792 | 1.81522 |
| 0.28051 | 1.57424 | 1.8096 |
| 0.28178 | 1.5683 | 1.80383 |
| 0.28307 | 1.56119 | 1.79804 |
| 0.28437 | 1.55281 | 1.79241 |
| 0.28568 | 1.54309 | 1.78719 |
| 0.287 | 1.53203 | 1.78274 |
| 0.28833 | 1.51972 | 1.77938 |
| 0.28968 | 1.5064 | 1.77739 |
| 0.29104 | 1.49238 | 1.77701 |
| 0.29242 | 1.47808 | 1.77842 |
| 0.2938 | 1.46387 | 1.78176 |
| 0.2952 | 1.45013 | 1.78705 |
| 0.29661 | 1.43719 | 1.7942 |
| 0.29804 | 1.42532 | 1.80301 |
| 0.29948 | 1.41473 | 1.81317 |
| 0.30093 | 1.40552 | 1.82432 |
| 0.3024 | 1.39773 | 1.83606 |
| 0.30388 | 1.39127 | 1.848 |
| 0.30538 | 1.38592 | 1.85984 |
| 0.30689 | 1.38149 | 1.87131 |
| 0.30842 | 1.37772 | 1.88222 |
| 0.30996 | 1.37827 | 1.8992 |
| 0.31152 | 1.37551 | 1.90606 |
| 0.31309 | 1.37361 | 1.9128 |
| 0.31468 | 1.37273 | 1.92096 |
| 0.31629 | 1.37197 | 1.92909 |
| 0.31791 | 1.37068 | 1.93624 |
| 0.31955 | 1.36872 | 1.94285 |
| 0.3212 | 1.36601 | 1.94912 |
| 0.32288 | 1.36308 | 1.95582 |
| 0.32457 | 1.35953 | 1.96179 |
| 0.32627 | 1.35586 | 1.9684 |
| 0.328 | 1.35257 | 1.9766 |
| 0.32974 | 1.34865 | 1.98368 |
| 0.33151 | 1.3441 | 1.99059 |
| 0.33329 | 1.33944 | 1.99869 |
| 0.33509 | 1.33471 | 2.00775 |
| 0.33691 | 1.33038 | 2.01873 |
| 0.33875 | 1.32543 | 2.02937 |
| 0.34062 | 1.31987 | 2.03931 |
| 0.3425 | 1.31377 | 2.04864 |
| 0.3444 | 1.30775 | 2.05823 |
| 0.34632 | 1.30227 | 2.06908 |
| 0.34827 | 1.29661 | 2.08045 |
| 0.35024 | 1.29061 | 2.09252 |
| 0.35223 | 1.28402 | 2.10295 |
| 0.35424 | 1.27768 | 2.11412 |
| 0.35628 | 1.27123 | 2.1258 |
| 0.35834 | 1.26494 | 2.13857 |
| 0.36042 | 1.25877 | 2.15184 |
| 0.36253 | 1.25281 | 2.16539 |
| 0.36466 | 1.24702 | 2.17909 |
| 0.36682 | 1.24219 | 2.19301 |
| 0.369 | 1.23815 | 2.20627 |
| 0.37121 | 1.2347 | 2.21962 |
| 0.37345 | 1.23165 | 2.23318 |
| 0.37571 | 1.22812 | 2.24604 |
| 0.378 | 1.2244 | 2.25862 |
| 0.38032 | 1.22107 | 2.27254 |
| 0.38267 | 1.21783 | 2.2859 |
| 0.38504 | 1.21456 | 2.29873 |
| 0.38745 | 1.2119 | 2.31109 |
| 0.38989 | 1.20919 | 2.32211 |
| 0.39235 | 1.20629 | 2.33412 |
| 0.39485 | 1.20332 | 2.34909 |
| 0.39738 | 1.1998 | 2.36397 |
| 0.39995 | 1.19592 | 2.37879 |
| 0.40255 | 1.1911 | 2.39276 |
| 0.40518 | 1.18543 | 2.40554 |
| 0.40784 | 1.18012 | 2.41917 |
| 0.41054 | 1.17561 | 2.43526 |
| 0.41328 | 1.17107 | 2.45136 |
| 0.41605 | 1.16672 | 2.4674 |
| 0.41886 | 1.1637 | 2.48347 |
| 0.42171 | 1.16216 | 2.49824 |
| 0.4246 | 1.16095 | 2.5133 |
| 0.42753 | 1.15905 | 2.52821 |
| 0.4305 | 1.15648 | 2.54316 |
| 0.43351 | 1.15283 | 2.55779 |
| 0.43656 | 1.14889 | 2.57283 |
| 0.43966 | 1.14608 | 2.59017 |
| 0.4428 | 1.14337 | 2.60791 |
| 0.44599 | 1.1403 | 2.62652 |
| 0.44922 | 1.13692 | 2.64222 |
| 0.4525 | 1.1346 | 2.65429 |
| 0.45582 | 1.13394 | 2.66567 |
| 0.4592 | 1.13478 | 2.68045 |
| 0.46263 | 1.13485 | 2.6937 |
| 0.46611 | 1.13475 | 2.70873 |
| 0.46964 | 1.13413 | 2.72335 |
| 0.47322 | 1.13347 | 2.73517 |
| 0.47686 | 1.13365 | 2.74462 |
| 0.48056 | 1.13378 | 2.75411 |
| 0.48431 | 1.1321 | 2.76248 |
| 0.48813 | 1.12863 | 2.77099 |
| 0.492 | 1.12523 | 2.78402 |
| 0.49594 | 1.12204 | 2.79501 |
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
- —