Optical constants
Refractive index of Au (Gold)
Rakić et al. 1998: Lorentz-Drude model; n,k 0.248–6.20 µm
- Data
- tabulated nk
- Range
- 0.248–6.199 µm
- Points
- 200
- Licence
- CC0-1.0
- Lightsmith
- bundled
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.38735
- Extinction coefficient k
- 2.73349
- Permittivity ε1
- -7.32191
- Permittivity ε2
- 2.11763
- Absorption coefficient α
- 584581 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 34.2125 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.16264 µm⁻¹
- Group index ng
- 1.65812
- 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
# Au (Gold): Rakić et al. 1998: Lorentz-Drude model; n,k 0.248–6.20 µm
au = ls.LibraryMaterial(name="Au", dataset="Rakic-LD")
print(au.range_nm) # (247.97, 6199.2) nm
eps = au.eps([633]) # complex permittivity
Ships with the library: works offline.
import lightsmith as ls
# Au (Gold): Rakić et al. 1998: Lorentz-Drude model; n,k 0.248–6.20 µm
au = ls.fetch_refractiveindex("main", "Au", "Rakic-LD", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(au.range_nm) # (247.97, 6199.2) nm
eps = au.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_b1fcd5c79f6c/lightsmith"
au = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(au.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (au/rakic-1998-ld).
# ... load au as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=au)],
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
[Calculation script (Python)]
- doi:10.1364/ao.37.005271 Optical properties of metallic films for vertical-cavity optoelectronic devices, Applied Optics (1998)
Cite
Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar and Marian L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics, 37, 5271 (1998), doi:10.1364/ao.37.005271; [Calculation script (Python)]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
200 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.24797 | 1.0941 | 1.5478 |
| 0.25201 | 1.1321 | 1.5836 |
| 0.25612 | 1.1718 | 1.6151 |
| 0.2603 | 1.2127 | 1.6421 |
| 0.26454 | 1.2543 | 1.6643 |
| 0.26886 | 1.2958 | 1.6816 |
| 0.27324 | 1.3366 | 1.6938 |
| 0.2777 | 1.3759 | 1.7011 |
| 0.28222 | 1.413 | 1.7037 |
| 0.28683 | 1.447 | 1.7019 |
| 0.2915 | 1.4774 | 1.6962 |
| 0.29626 | 1.5034 | 1.6872 |
| 0.30109 | 1.5247 | 1.6757 |
| 0.306 | 1.5407 | 1.6624 |
| 0.31099 | 1.5514 | 1.6483 |
| 0.31606 | 1.5567 | 1.6342 |
| 0.32121 | 1.5567 | 1.6211 |
| 0.32645 | 1.5517 | 1.6098 |
| 0.33177 | 1.5422 | 1.6012 |
| 0.33718 | 1.5288 | 1.596 |
| 0.34268 | 1.5123 | 1.5949 |
| 0.34827 | 1.4937 | 1.5983 |
| 0.35395 | 1.4741 | 1.6065 |
| 0.35972 | 1.4549 | 1.6193 |
| 0.36559 | 1.4373 | 1.6365 |
| 0.37155 | 1.4226 | 1.6571 |
| 0.37761 | 1.412 | 1.6797 |
| 0.38377 | 1.406 | 1.7025 |
| 0.39002 | 1.4047 | 1.7232 |
| 0.39638 | 1.4071 | 1.7394 |
| 0.40285 | 1.4112 | 1.749 |
| 0.40942 | 1.4141 | 1.7506 |
| 0.41609 | 1.4122 | 1.7441 |
| 0.42288 | 1.402 | 1.7311 |
| 0.42977 | 1.3808 | 1.7143 |
| 0.43678 | 1.3472 | 1.6973 |
| 0.4439 | 1.3011 | 1.684 |
| 0.45114 | 1.2439 | 1.6777 |
| 0.4585 | 1.1777 | 1.6812 |
| 0.46598 | 1.1054 | 1.6962 |
| 0.47358 | 1.0299 | 1.7233 |
| 0.4813 | 0.95396 | 1.7625 |
| 0.48915 | 0.88009 | 1.8129 |
| 0.49712 | 0.81015 | 1.873 |
| 0.50523 | 0.74535 | 1.941 |
| 0.51347 | 0.68631 | 2.0154 |
| 0.52184 | 0.63316 | 2.0945 |
| 0.53035 | 0.58568 | 2.177 |
| 0.539 | 0.54348 | 2.262 |
| 0.54779 | 0.50606 | 2.3486 |
| 0.55672 | 0.4729 | 2.4364 |
| 0.5658 | 0.44351 | 2.5249 |
| 0.57503 | 0.41743 | 2.614 |
| 0.5844 | 0.39427 | 2.7034 |
| 0.59393 | 0.37366 | 2.793 |
| 0.60362 | 0.3553 | 2.8828 |
| 0.61346 | 0.33893 | 2.9728 |
| 0.62346 | 0.32432 | 3.063 |
| 0.63363 | 0.31127 | 3.1534 |
| 0.64396 | 0.29962 | 3.2441 |
| 0.65446 | 0.28922 | 3.335 |
| 0.66514 | 0.27995 | 3.4263 |
| 0.67598 | 0.2717 | 3.518 |
| 0.68701 | 0.26438 | 3.6102 |
| 0.69821 | 0.25791 | 3.7028 |
| 0.70959 | 0.25222 | 3.796 |
| 0.72117 | 0.24725 | 3.8898 |
| 0.73292 | 0.24295 | 3.9843 |
| 0.74488 | 0.23927 | 4.0794 |
| 0.75702 | 0.23618 | 4.1753 |
| 0.76937 | 0.23364 | 4.272 |
| 0.78191 | 0.23162 | 4.3695 |
| 0.79466 | 0.2301 | 4.4679 |
| 0.80762 | 0.22906 | 4.5673 |
| 0.82079 | 0.22848 | 4.6676 |
| 0.83418 | 0.22834 | 4.7689 |
| 0.84778 | 0.22863 | 4.8713 |
| 0.8616 | 0.22935 | 4.9748 |
| 0.87565 | 0.23049 | 5.0795 |
| 0.88993 | 0.23204 | 5.1853 |
| 0.90445 | 0.23401 | 5.2923 |
| 0.91919 | 0.23639 | 5.4006 |
| 0.93418 | 0.23919 | 5.5102 |
| 0.94942 | 0.24241 | 5.6211 |
| 0.9649 | 0.24606 | 5.7334 |
| 0.98063 | 0.25015 | 5.8471 |
| 0.99662 | 0.25469 | 5.9622 |
| 1.0129 | 0.2597 | 6.0788 |
| 1.0294 | 0.2652 | 6.1969 |
| 1.0462 | 0.27121 | 6.3165 |
| 1.0632 | 0.27776 | 6.4377 |
| 1.0806 | 0.28486 | 6.5604 |
| 1.0982 | 0.29255 | 6.6848 |
| 1.1161 | 0.30086 | 6.8107 |
| 1.1343 | 0.30983 | 6.9383 |
| 1.1528 | 0.31949 | 7.0674 |
| 1.1716 | 0.32987 | 7.1981 |
| 1.1907 | 0.34102 | 7.3304 |
| 1.2101 | 0.35295 | 7.4642 |
| 1.2299 | 0.36569 | 7.5995 |
| 1.2499 | 0.37924 | 7.7361 |
| 1.2703 | 0.39359 | 7.8741 |
| 1.291 | 0.40869 | 8.0132 |
| 1.3121 | 0.42446 | 8.1534 |
| 1.3335 | 0.44076 | 8.2946 |
| 1.3552 | 0.45741 | 8.4367 |
| 1.3773 | 0.47419 | 8.5797 |
| 1.3998 | 0.49079 | 8.7235 |
| 1.4226 | 0.50692 | 8.8683 |
| 1.4458 | 0.52226 | 9.0142 |
| 1.4694 | 0.53655 | 9.1616 |
| 1.4933 | 0.5496 | 9.3109 |
| 1.5177 | 0.56135 | 9.4625 |
| 1.5424 | 0.57185 | 9.6168 |
| 1.5676 | 0.58129 | 9.7744 |
| 1.5931 | 0.58993 | 9.9355 |
| 1.6191 | 0.59813 | 10.1 |
| 1.6455 | 0.60622 | 10.269 |
| 1.6723 | 0.61455 | 10.442 |
| 1.6996 | 0.6234 | 10.619 |
| 1.7273 | 0.63304 | 10.799 |
| 1.7555 | 0.64366 | 10.984 |
| 1.7841 | 0.65541 | 11.172 |
| 1.8132 | 0.66839 | 11.363 |
| 1.8428 | 0.6827 | 11.558 |
| 1.8728 | 0.69839 | 11.757 |
| 1.9034 | 0.7155 | 11.959 |
| 1.9344 | 0.73408 | 12.164 |
| 1.966 | 0.75414 | 12.372 |
| 1.998 | 0.77573 | 12.584 |
| 2.0306 | 0.79886 | 12.798 |
| 2.0637 | 0.82356 | 13.016 |
| 2.0974 | 0.84987 | 13.237 |
| 2.1316 | 0.87781 | 13.46 |
| 2.1663 | 0.90742 | 13.687 |
| 2.2016 | 0.93872 | 13.917 |
| 2.2375 | 0.97174 | 14.149 |
| 2.274 | 1.0065 | 14.384 |
| 2.3111 | 1.043 | 14.622 |
| 2.3488 | 1.0812 | 14.863 |
| 2.3871 | 1.1211 | 15.106 |
| 2.426 | 1.1626 | 15.351 |
| 2.4656 | 1.2056 | 15.598 |
| 2.5058 | 1.2501 | 15.848 |
| 2.5467 | 1.2958 | 16.099 |
| 2.5882 | 1.3425 | 16.353 |
| 2.6304 | 1.3899 | 16.608 |
| 2.6733 | 1.4378 | 16.864 |
| 2.7169 | 1.4857 | 17.123 |
| 2.7612 | 1.5333 | 17.384 |
| 2.8062 | 1.5802 | 17.646 |
| 2.852 | 1.6261 | 17.911 |
| 2.8985 | 1.6705 | 18.179 |
| 2.9457 | 1.7133 | 18.45 |
| 2.9938 | 1.7542 | 18.725 |
| 3.0426 | 1.7932 | 19.004 |
| 3.0922 | 1.8304 | 19.288 |
| 3.1426 | 1.8658 | 19.578 |
| 3.1939 | 1.8999 | 19.874 |
| 3.246 | 1.9328 | 20.176 |
| 3.2989 | 1.965 | 20.486 |
| 3.3527 | 1.997 | 20.802 |
| 3.4074 | 2.0292 | 21.126 |
| 3.4629 | 2.062 | 21.457 |
| 3.5194 | 2.0958 | 21.796 |
| 3.5768 | 2.131 | 22.142 |
| 3.6351 | 2.168 | 22.496 |
| 3.6944 | 2.2069 | 22.857 |
| 3.7546 | 2.248 | 23.226 |
| 3.8159 | 2.2915 | 23.601 |
| 3.8781 | 2.3376 | 23.984 |
| 3.9413 | 2.3864 | 24.374 |
| 4.0056 | 2.438 | 24.77 |
| 4.0709 | 2.4925 | 25.174 |
| 4.1373 | 2.5499 | 25.584 |
| 4.2048 | 2.6103 | 26.001 |
| 4.2733 | 2.6738 | 26.425 |
| 4.343 | 2.7404 | 26.856 |
| 4.4138 | 2.8101 | 27.293 |
| 4.4858 | 2.883 | 27.737 |
| 4.5589 | 2.9592 | 28.188 |
| 4.6333 | 3.0386 | 28.646 |
| 4.7088 | 3.1214 | 29.111 |
| 4.7856 | 3.2075 | 29.582 |
| 4.8637 | 3.297 | 30.061 |
| 4.943 | 3.39 | 30.546 |
| 5.0236 | 3.4866 | 31.039 |
| 5.1055 | 3.5867 | 31.539 |
| 5.1888 | 3.6905 | 32.046 |
| 5.2734 | 3.7981 | 32.56 |
| 5.3594 | 3.9094 | 33.081 |
| 5.4468 | 4.0247 | 33.61 |
| 5.5356 | 4.1439 | 34.147 |
| 5.6258 | 4.2672 | 34.691 |
| 5.7176 | 4.3946 | 35.242 |
| 5.8108 | 4.5262 | 35.802 |
| 5.9056 | 4.6623 | 36.369 |
| 6.0019 | 4.8027 | 36.944 |
| 6.0997 | 4.9477 | 37.527 |
| 6.1992 | 5.0974 | 38.118 |
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
- —
Fit of experimental data from several sources to Lorentz-Drude (LD) model