Optical constants
Refractive index of Au (Gold)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–6.20 µm
- Data
- tabulated nk
- Range
- 0.248–6.199 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.270351
- Extinction coefficient k
- 2.77896
- Permittivity ε1
- -7.64953
- Permittivity ε2
- 1.50259
- Absorption coefficient α
- 594306 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 33.6527 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.52466 µm⁻¹
- Group index ng
- 1.75384
- 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: Brendel-Bormann model; n,k 0.248–6.20 µm
au = ls.fetch_refractiveindex("main", "Au", "Rakic-BB", 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_ab02da0042e2/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-bb).
# ... 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 | 1.4943 | 1.9575 |
| 0.25201 | 1.5158 | 1.9594 |
| 0.25612 | 1.5382 | 1.9605 |
| 0.2603 | 1.5611 | 1.9604 |
| 0.26454 | 1.5844 | 1.9587 |
| 0.26886 | 1.6078 | 1.9551 |
| 0.27324 | 1.6306 | 1.9494 |
| 0.2777 | 1.6527 | 1.9414 |
| 0.28222 | 1.6733 | 1.9312 |
| 0.28683 | 1.6921 | 1.9188 |
| 0.2915 | 1.7085 | 1.9042 |
| 0.29626 | 1.722 | 1.8879 |
| 0.30109 | 1.7322 | 1.87 |
| 0.306 | 1.7387 | 1.8512 |
| 0.31099 | 1.7411 | 1.8319 |
| 0.31606 | 1.7391 | 1.8128 |
| 0.32121 | 1.7327 | 1.7946 |
| 0.32645 | 1.7219 | 1.7784 |
| 0.33177 | 1.7071 | 1.7648 |
| 0.33718 | 1.6887 | 1.7548 |
| 0.34268 | 1.6677 | 1.749 |
| 0.34827 | 1.6452 | 1.7479 |
| 0.35395 | 1.6224 | 1.7516 |
| 0.35972 | 1.6006 | 1.7597 |
| 0.36559 | 1.581 | 1.7714 |
| 0.37155 | 1.5645 | 1.7856 |
| 0.37761 | 1.5515 | 1.8007 |
| 0.38377 | 1.5419 | 1.8152 |
| 0.39002 | 1.5351 | 1.8276 |
| 0.39638 | 1.5301 | 1.8366 |
| 0.40285 | 1.5255 | 1.8413 |
| 0.40942 | 1.5196 | 1.8411 |
| 0.41609 | 1.5107 | 1.8362 |
| 0.42288 | 1.4971 | 1.8268 |
| 0.42977 | 1.4771 | 1.814 |
| 0.43678 | 1.4493 | 1.7988 |
| 0.4439 | 1.4126 | 1.7829 |
| 0.45114 | 1.3661 | 1.7681 |
| 0.4585 | 1.3095 | 1.7567 |
| 0.46598 | 1.2427 | 1.7509 |
| 0.47358 | 1.1664 | 1.7532 |
| 0.4813 | 1.0821 | 1.7661 |
| 0.48915 | 0.99182 | 1.7916 |
| 0.49712 | 0.89849 | 1.8312 |
| 0.50523 | 0.80543 | 1.8852 |
| 0.51347 | 0.7159 | 1.953 |
| 0.52184 | 0.6326 | 2.0328 |
| 0.53035 | 0.55731 | 2.1222 |
| 0.539 | 0.49085 | 2.2188 |
| 0.54779 | 0.43326 | 2.3201 |
| 0.55672 | 0.38405 | 2.4245 |
| 0.5658 | 0.34242 | 2.5305 |
| 0.57503 | 0.30751 | 2.637 |
| 0.5844 | 0.27843 | 2.7434 |
| 0.59393 | 0.25437 | 2.8493 |
| 0.60362 | 0.23457 | 2.9545 |
| 0.61346 | 0.21841 | 3.0587 |
| 0.62346 | 0.20533 | 3.1621 |
| 0.63363 | 0.19487 | 3.2645 |
| 0.64396 | 0.18664 | 3.3662 |
| 0.65446 | 0.1803 | 3.4671 |
| 0.66514 | 0.17558 | 3.5675 |
| 0.67598 | 0.17227 | 3.6674 |
| 0.68701 | 0.17016 | 3.7669 |
| 0.69821 | 0.16911 | 3.8661 |
| 0.70959 | 0.16897 | 3.9653 |
| 0.72117 | 0.16966 | 4.0644 |
| 0.73292 | 0.17107 | 4.1635 |
| 0.74488 | 0.17313 | 4.2629 |
| 0.75702 | 0.17577 | 4.3625 |
| 0.76937 | 0.17895 | 4.4624 |
| 0.78191 | 0.18262 | 4.5627 |
| 0.79466 | 0.18675 | 4.6635 |
| 0.80762 | 0.19129 | 4.7649 |
| 0.82079 | 0.19621 | 4.8669 |
| 0.83418 | 0.20151 | 4.9695 |
| 0.84778 | 0.20715 | 5.0729 |
| 0.8616 | 0.21311 | 5.177 |
| 0.87565 | 0.21938 | 5.282 |
| 0.88993 | 0.22594 | 5.3878 |
| 0.90445 | 0.23278 | 5.4946 |
| 0.91919 | 0.23989 | 5.6024 |
| 0.93418 | 0.24725 | 5.7111 |
| 0.94942 | 0.25486 | 5.821 |
| 0.9649 | 0.26271 | 5.9319 |
| 0.98063 | 0.27079 | 6.044 |
| 0.99662 | 0.27909 | 6.1573 |
| 1.0129 | 0.28761 | 6.2718 |
| 1.0294 | 0.29634 | 6.3875 |
| 1.0462 | 0.30528 | 6.5046 |
| 1.0632 | 0.31442 | 6.6231 |
| 1.0806 | 0.32376 | 6.7429 |
| 1.0982 | 0.33329 | 6.8642 |
| 1.1161 | 0.34302 | 6.9869 |
| 1.1343 | 0.35293 | 7.1112 |
| 1.1528 | 0.36304 | 7.237 |
| 1.1716 | 0.37334 | 7.3644 |
| 1.1907 | 0.38382 | 7.4935 |
| 1.2101 | 0.39449 | 7.6242 |
| 1.2299 | 0.40535 | 7.7566 |
| 1.2499 | 0.41641 | 7.8908 |
| 1.2703 | 0.42765 | 8.0268 |
| 1.291 | 0.43909 | 8.1646 |
| 1.3121 | 0.45072 | 8.3044 |
| 1.3335 | 0.46256 | 8.446 |
| 1.3552 | 0.47459 | 8.5896 |
| 1.3773 | 0.48684 | 8.7353 |
| 1.3998 | 0.4993 | 8.8829 |
| 1.4226 | 0.51198 | 9.0327 |
| 1.4458 | 0.52488 | 9.1847 |
| 1.4694 | 0.53801 | 9.3388 |
| 1.4933 | 0.55138 | 9.4951 |
| 1.5177 | 0.56499 | 9.6538 |
| 1.5424 | 0.57885 | 9.8147 |
| 1.5676 | 0.59297 | 9.978 |
| 1.5931 | 0.60736 | 10.144 |
| 1.6191 | 0.62203 | 10.312 |
| 1.6455 | 0.63699 | 10.483 |
| 1.6723 | 0.65224 | 10.656 |
| 1.6996 | 0.6678 | 10.832 |
| 1.7273 | 0.68368 | 11.01 |
| 1.7555 | 0.69989 | 11.192 |
| 1.7841 | 0.71645 | 11.376 |
| 1.8132 | 0.73336 | 11.563 |
| 1.8428 | 0.75065 | 11.752 |
| 1.8728 | 0.76831 | 11.945 |
| 1.9034 | 0.78638 | 12.14 |
| 1.9344 | 0.80486 | 12.339 |
| 1.966 | 0.82377 | 12.541 |
| 1.998 | 0.84313 | 12.745 |
| 2.0306 | 0.86294 | 12.953 |
| 2.0637 | 0.88324 | 13.164 |
| 2.0974 | 0.90404 | 13.379 |
| 2.1316 | 0.92535 | 13.597 |
| 2.1663 | 0.9472 | 13.818 |
| 2.2016 | 0.96961 | 14.042 |
| 2.2375 | 0.99259 | 14.271 |
| 2.274 | 1.0162 | 14.502 |
| 2.3111 | 1.0404 | 14.738 |
| 2.3488 | 1.0652 | 14.977 |
| 2.3871 | 1.0907 | 15.219 |
| 2.426 | 1.1169 | 15.466 |
| 2.4656 | 1.1438 | 15.717 |
| 2.5058 | 1.1715 | 15.971 |
| 2.5467 | 1.1999 | 16.229 |
| 2.5882 | 1.2291 | 16.492 |
| 2.6304 | 1.2592 | 16.758 |
| 2.6733 | 1.2901 | 17.029 |
| 2.7169 | 1.3219 | 17.304 |
| 2.7612 | 1.3545 | 17.584 |
| 2.8062 | 1.3882 | 17.867 |
| 2.852 | 1.4228 | 18.156 |
| 2.8985 | 1.4584 | 18.448 |
| 2.9457 | 1.4951 | 18.746 |
| 2.9938 | 1.5328 | 19.048 |
| 3.0426 | 1.5717 | 19.354 |
| 3.0922 | 1.6117 | 19.666 |
| 3.1426 | 1.6529 | 19.982 |
| 3.1939 | 1.6954 | 20.304 |
| 3.246 | 1.7391 | 20.63 |
| 3.2989 | 1.7842 | 20.962 |
| 3.3527 | 1.8306 | 21.299 |
| 3.4074 | 1.8784 | 21.64 |
| 3.4629 | 1.9277 | 21.988 |
| 3.5194 | 1.9785 | 22.34 |
| 3.5768 | 2.0308 | 22.699 |
| 3.6351 | 2.0847 | 23.062 |
| 3.6944 | 2.1403 | 23.432 |
| 3.7546 | 2.1976 | 23.807 |
| 3.8159 | 2.2566 | 24.188 |
| 3.8781 | 2.3175 | 24.575 |
| 3.9413 | 2.3802 | 24.967 |
| 4.0056 | 2.4449 | 25.366 |
| 4.0709 | 2.5116 | 25.771 |
| 4.1373 | 2.5803 | 26.182 |
| 4.2048 | 2.6511 | 26.6 |
| 4.2733 | 2.7242 | 27.023 |
| 4.343 | 2.7995 | 27.454 |
| 4.4138 | 2.8771 | 27.89 |
| 4.4858 | 2.9572 | 28.334 |
| 4.5589 | 3.0397 | 28.784 |
| 4.6333 | 3.1247 | 29.241 |
| 4.7088 | 3.2124 | 29.705 |
| 4.7856 | 3.3028 | 30.176 |
| 4.8637 | 3.396 | 30.653 |
| 4.943 | 3.4921 | 31.139 |
| 5.0236 | 3.5911 | 31.631 |
| 5.1055 | 3.6932 | 32.13 |
| 5.1888 | 3.7985 | 32.637 |
| 5.2734 | 3.9069 | 33.152 |
| 5.3594 | 4.0187 | 33.674 |
| 5.4468 | 4.134 | 34.204 |
| 5.5356 | 4.2528 | 34.741 |
| 5.6258 | 4.3752 | 35.287 |
| 5.7176 | 4.5013 | 35.84 |
| 5.8108 | 4.6314 | 36.401 |
| 5.9056 | 4.7653 | 36.971 |
| 6.0019 | 4.9034 | 37.548 |
| 6.0997 | 5.0456 | 38.134 |
| 6.1992 | 5.1922 | 38.728 |
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 Brendel-Bormann (BB) model.