Optical constants
Refractive index of Cu (Copper)
McPeak et al. 2015: n,k 0.3–1.7 µm
- Data
- tabulated nk
- Range
- 0.3–1.7 µm
- Points
- 141
- Licence
- CC0-1.0
- Lightsmith
- bundled
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.230856
- Extinction coefficient k
- 2.91025
- Permittivity ε1
- -8.41624
- Permittivity ε2
- 1.34369
- Absorption coefficient α
- 622383 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 32.1345 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -10.1575 µm⁻¹
- Group index ng
- 6.1994
- 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): McPeak et al. 2015: n,k 0.3–1.7 µm
cu = ls.LibraryMaterial(name="Cu", dataset="McPeak")
print(cu.range_nm) # (300, 1700) nm
eps = cu.eps([633]) # complex permittivity
Ships with the library: works offline.
import lightsmith as ls
# Cu (Copper): McPeak et al. 2015: n,k 0.3–1.7 µm
cu = ls.fetch_refractiveindex("main", "Cu", "McPeak", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (300, 1700) 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_0b1a9750ad35/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/mcpeak-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.
Comments and conditions
References
- doi:10.1021/ph5004237 Plasmonic Films Can Easily Be Better: Rules and Recipes, ACS Photonics (2015)
Cite
Kevin M. McPeak et al.. Plasmonic Films Can Easily Be Better: Rules and Recipes. ACS Photonics, 2, 326-333 (2015), doi:10.1021/ph5004237; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
141 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.3 | 1.347459987 | 1.679419071 |
| 0.31 | 1.321473211 | 1.740141215 |
| 0.32 | 1.301896917 | 1.781554261 |
| 0.33 | 1.278815346 | 1.816251273 |
| 0.34 | 1.257856058 | 1.857525737 |
| 0.35 | 1.229714372 | 1.895968733 |
| 0.36 | 1.205793784 | 1.941169403 |
| 0.37 | 1.183134074 | 1.99326522 |
| 0.38 | 1.16577487 | 2.046321345 |
| 0.39 | 1.139929606 | 2.090129064 |
| 0.4 | 1.119339006 | 2.14224644 |
| 0.41 | 1.097661459 | 2.193481406 |
| 0.42 | 1.082884327 | 2.251163803 |
| 0.43 | 1.067185209 | 2.306769228 |
| 0.44 | 1.056310845 | 2.361946782 |
| 0.45 | 1.048210496 | 2.413637347 |
| 0.46 | 1.044058354 | 2.464134299 |
| 0.47 | 1.040826414 | 2.50896784 |
| 0.48 | 1.040383818 | 2.549587906 |
| 0.49 | 1.035622719 | 2.577676166 |
| 0.5 | 1.0292166 | 2.600958825 |
| 0.51 | 1.01596237 | 2.610628188 |
| 0.52 | 0.995463808 | 2.613856957 |
| 0.53 | 0.957525814 | 2.60358516 |
| 0.54 | 0.896412084 | 2.584135179 |
| 0.55 | 0.79745994 | 2.56420404 |
| 0.56 | 0.649913539 | 2.566649101 |
| 0.57 | 0.467667795 | 2.633707115 |
| 0.58 | 0.308052581 | 2.774526337 |
| 0.59 | 0.206477543 | 2.953105649 |
| 0.6 | 0.15342929 | 3.124794481 |
| 0.61 | 0.129738592 | 3.28082796 |
| 0.62 | 0.116677068 | 3.422223479 |
| 0.63 | 0.110069919 | 3.546563885 |
| 0.64 | 0.107194012 | 3.666809315 |
| 0.65 | 0.104232496 | 3.775693898 |
| 0.66 | 0.102539467 | 3.879628119 |
| 0.67 | 0.102449402 | 3.981770445 |
| 0.68 | 0.101216009 | 4.082308744 |
| 0.69 | 0.101603953 | 4.175083635 |
| 0.7 | 0.101236908 | 4.27062629 |
| 0.71 | 0.101557633 | 4.365353818 |
| 0.72 | 0.101132194 | 4.453675754 |
| 0.73 | 0.100848965 | 4.541494304 |
| 0.74 | 0.100919789 | 4.632837662 |
| 0.75 | 0.101173963 | 4.718605321 |
| 0.76 | 0.101837799 | 4.806908667 |
| 0.77 | 0.101672055 | 4.890330992 |
| 0.78 | 0.104166566 | 4.985764803 |
| 0.79 | 0.10154611 | 5.058785587 |
| 0.8 | 0.105089997 | 5.141307607 |
| 0.81 | 0.105640925 | 5.225721003 |
| 0.82 | 0.1047717 | 5.314412207 |
| 0.83 | 0.108065424 | 5.399044187 |
| 0.84 | 0.106329275 | 5.471682183 |
| 0.85 | 0.106803015 | 5.558363688 |
| 0.86 | 0.10806138 | 5.64355183 |
| 0.87 | 0.109423947 | 5.718126756 |
| 0.88 | 0.109226995 | 5.799390531 |
| 0.89 | 0.110739052 | 5.87326682 |
| 0.9 | 0.111474071 | 5.957887752 |
| 0.91 | 0.110565481 | 6.04212088 |
| 0.92 | 0.114354773 | 6.114742596 |
| 0.93 | 0.115741932 | 6.194384247 |
| 0.94 | 0.116243076 | 6.272201563 |
| 0.95 | 0.11651561 | 6.352367739 |
| 0.96 | 0.117227546 | 6.433641449 |
| 0.97 | 0.117612103 | 6.506983372 |
| 0.98 | 0.1200286 | 6.588429772 |
| 0.99 | 0.120693135 | 6.665250695 |
| 1.0 | 0.123314675 | 6.744939326 |
| 1.01 | 0.123500553 | 6.819402641 |
| 1.02 | 0.12589253 | 6.894769679 |
| 1.03 | 0.126656415 | 6.97753838 |
| 1.04 | 0.125456304 | 7.048669327 |
| 1.05 | 0.127879983 | 7.128558991 |
| 1.06 | 0.123044899 | 7.21443969 |
| 1.07 | 0.124058562 | 7.290911502 |
| 1.08 | 0.12724857 | 7.368255709 |
| 1.09 | 0.126108804 | 7.447140621 |
| 1.1 | 0.127049082 | 7.525831613 |
| 1.11 | 0.127924195 | 7.605285307 |
| 1.12 | 0.12687364 | 7.67574732 |
| 1.13 | 0.129233188 | 7.744914539 |
| 1.14 | 0.126930498 | 7.827905937 |
| 1.15 | 0.128135739 | 7.904898403 |
| 1.16 | 0.131236652 | 7.984812024 |
| 1.17 | 0.130534766 | 8.061453921 |
| 1.18 | 0.132958217 | 8.142031558 |
| 1.19 | 0.134086968 | 8.211088802 |
| 1.2 | 0.132204904 | 8.276924437 |
| 1.21 | 0.131954806 | 8.369911115 |
| 1.22 | 0.134536782 | 8.444530783 |
| 1.23 | 0.132059034 | 8.511723656 |
| 1.24 | 0.135380438 | 8.594668572 |
| 1.25 | 0.140947312 | 8.661747292 |
| 1.26 | 0.145305612 | 8.740887468 |
| 1.27 | 0.142654978 | 8.812170586 |
| 1.28 | 0.145808605 | 8.885620977 |
| 1.29 | 0.143636497 | 8.96290307 |
| 1.3 | 0.14357746 | 9.049122305 |
| 1.31 | 0.14815507 | 9.118823933 |
| 1.32 | 0.146774504 | 9.199486005 |
| 1.33 | 0.153662011 | 9.262861977 |
| 1.34 | 0.14795299 | 9.342156608 |
| 1.35 | 0.156618782 | 9.420006871 |
| 1.36 | 0.153286699 | 9.497236272 |
| 1.37 | 0.158020584 | 9.563627476 |
| 1.38 | 0.159435601 | 9.624262035 |
| 1.39 | 0.164929309 | 9.719012382 |
| 1.4 | 0.160903598 | 9.787537482 |
| 1.41 | 0.165878545 | 9.863240628 |
| 1.42 | 0.170083525 | 9.953638953 |
| 1.43 | 0.170430805 | 10.01843534 |
| 1.44 | 0.177719488 | 10.07430316 |
| 1.45 | 0.176808354 | 10.15732549 |
| 1.46 | 0.174975159 | 10.25088368 |
| 1.47 | 0.184898936 | 10.3234775 |
| 1.48 | 0.189874398 | 10.3863397 |
| 1.49 | 0.180372997 | 10.47246554 |
| 1.5 | 0.182478591 | 10.53438648 |
| 1.51 | 0.18486728 | 10.60679857 |
| 1.52 | 0.190872505 | 10.67597454 |
| 1.53 | 0.190985335 | 10.74925464 |
| 1.54 | 0.1989454 | 10.8263373 |
| 1.55 | 0.194332409 | 10.92097821 |
| 1.56 | 0.198165888 | 10.97767142 |
| 1.57 | 0.192594699 | 11.04885029 |
| 1.58 | 0.207420155 | 11.16839394 |
| 1.59 | 0.204793341 | 11.20544244 |
| 1.6 | 0.209186703 | 11.29087061 |
| 1.61 | 0.213365941 | 11.36334128 |
| 1.62 | 0.217596043 | 11.4432228 |
| 1.63 | 0.226803672 | 11.53045706 |
| 1.64 | 0.225634749 | 11.58753257 |
| 1.65 | 0.219982349 | 11.65025288 |
| 1.66 | 0.238848652 | 11.72164872 |
| 1.67 | 0.243445023 | 11.80081631 |
| 1.68 | 0.226005004 | 11.89332074 |
| 1.69 | 0.26002749 | 11.92047039 |
| 1.7 | 0.255894846 | 12.02603352 |
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
- —
Thermally evaporated Cu at 35 Å/s with base pressure of 3e-8 Torr, template stripped from Si wafer