Optical constants
Refractive index of W (Tungsten)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm
- Data
- tabulated nk
- Range
- 0.248–12.4 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.57762
- Extinction coefficient k
- 2.786
- Permittivity ε1
- 5.03752
- Permittivity ε2
- 19.9345
- Absorption coefficient α
- 595813 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 33.5676 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 1.74368 µm⁻¹
- Group index ng
- 2.55303
- 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
# W (Tungsten): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm
w = ls.fetch_refractiveindex("main", "W", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(w.range_nm) # (247.97, 12398) nm
eps = w.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_04908956a5ae/lightsmith"
w = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(w.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (w/rakic-1998-bb).
# ... load w as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=w)],
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 | 2.6972 | 2.6847 |
| 0.25289 | 2.7358 | 2.6738 |
| 0.25791 | 2.7728 | 2.6627 |
| 0.26303 | 2.8083 | 2.6514 |
| 0.26825 | 2.8422 | 2.64 |
| 0.27358 | 2.8745 | 2.6286 |
| 0.27901 | 2.9052 | 2.6173 |
| 0.28455 | 2.9345 | 2.6063 |
| 0.2902 | 2.9622 | 2.5955 |
| 0.29596 | 2.9884 | 2.5851 |
| 0.30184 | 3.0132 | 2.5752 |
| 0.30783 | 3.0365 | 2.5658 |
| 0.31394 | 3.0585 | 2.5571 |
| 0.32017 | 3.0791 | 2.5492 |
| 0.32653 | 3.0984 | 2.5421 |
| 0.33301 | 3.1165 | 2.536 |
| 0.33962 | 3.1334 | 2.5308 |
| 0.34637 | 3.1492 | 2.5268 |
| 0.35324 | 3.1641 | 2.5239 |
| 0.36025 | 3.178 | 2.5224 |
| 0.36741 | 3.1911 | 2.5221 |
| 0.3747 | 3.2035 | 2.5233 |
| 0.38214 | 3.2153 | 2.5259 |
| 0.38973 | 3.2267 | 2.5301 |
| 0.39746 | 3.2378 | 2.5357 |
| 0.40535 | 3.2489 | 2.5429 |
| 0.4134 | 3.26 | 2.5517 |
| 0.42161 | 3.2713 | 2.5619 |
| 0.42998 | 3.2831 | 2.5735 |
| 0.43852 | 3.2955 | 2.5864 |
| 0.44722 | 3.3086 | 2.6004 |
| 0.4561 | 3.3227 | 2.6154 |
| 0.46515 | 3.3377 | 2.6311 |
| 0.47439 | 3.3539 | 2.6474 |
| 0.48381 | 3.3713 | 2.6639 |
| 0.49341 | 3.3897 | 2.6804 |
| 0.50321 | 3.4092 | 2.6966 |
| 0.5132 | 3.4297 | 2.7121 |
| 0.52339 | 3.451 | 2.7269 |
| 0.53378 | 3.4728 | 2.7405 |
| 0.54437 | 3.4949 | 2.7528 |
| 0.55518 | 3.517 | 2.7637 |
| 0.5662 | 3.5388 | 2.773 |
| 0.57744 | 3.5599 | 2.7806 |
| 0.58891 | 3.5799 | 2.7867 |
| 0.6006 | 3.5986 | 2.7911 |
| 0.61252 | 3.6154 | 2.794 |
| 0.62468 | 3.6301 | 2.7956 |
| 0.63709 | 3.6423 | 2.796 |
| 0.64973 | 3.6517 | 2.7955 |
| 0.66263 | 3.658 | 2.7944 |
| 0.67579 | 3.6611 | 2.7929 |
| 0.6892 | 3.6605 | 2.7915 |
| 0.70289 | 3.6563 | 2.7904 |
| 0.71684 | 3.6481 | 2.79 |
| 0.73107 | 3.6358 | 2.7908 |
| 0.74559 | 3.6195 | 2.7932 |
| 0.76039 | 3.5989 | 2.7977 |
| 0.77549 | 3.5741 | 2.8047 |
| 0.79088 | 3.5452 | 2.8148 |
| 0.80658 | 3.512 | 2.8285 |
| 0.8226 | 3.4748 | 2.8464 |
| 0.83893 | 3.4338 | 2.869 |
| 0.85558 | 3.3892 | 2.8971 |
| 0.87257 | 3.3414 | 2.9314 |
| 0.88989 | 3.2909 | 2.9726 |
| 0.90756 | 3.2385 | 3.0214 |
| 0.92557 | 3.1849 | 3.0785 |
| 0.94395 | 3.1314 | 3.1447 |
| 0.96269 | 3.0795 | 3.2205 |
| 0.9818 | 3.0309 | 3.3061 |
| 1.0013 | 2.9878 | 3.4015 |
| 1.0212 | 2.9528 | 3.5059 |
| 1.0414 | 2.9282 | 3.6177 |
| 1.0621 | 2.9166 | 3.7345 |
| 1.0832 | 2.9197 | 3.8526 |
| 1.1047 | 2.9381 | 3.9676 |
| 1.1266 | 2.9712 | 4.0743 |
| 1.149 | 3.0162 | 4.1678 |
| 1.1718 | 3.0687 | 4.244 |
| 1.1951 | 3.1229 | 4.3002 |
| 1.2188 | 3.1719 | 4.3358 |
| 1.243 | 3.209 | 4.3523 |
| 1.2677 | 3.2281 | 4.3534 |
| 1.2929 | 3.2247 | 4.3447 |
| 1.3185 | 3.1959 | 4.3327 |
| 1.3447 | 3.1411 | 4.3243 |
| 1.3714 | 3.0618 | 4.3264 |
| 1.3986 | 2.9612 | 4.3446 |
| 1.4264 | 2.844 | 4.3835 |
| 1.4547 | 2.7155 | 4.4457 |
| 1.4836 | 2.5814 | 4.5322 |
| 1.513 | 2.4469 | 4.6424 |
| 1.5431 | 2.3163 | 4.7743 |
| 1.5737 | 2.1928 | 4.9252 |
| 1.605 | 2.0784 | 5.092 |
| 1.6368 | 1.9743 | 5.2717 |
| 1.6693 | 1.8806 | 5.4617 |
| 1.7025 | 1.7969 | 5.6599 |
| 1.7363 | 1.7228 | 5.8644 |
| 1.7707 | 1.6573 | 6.074 |
| 1.8059 | 1.5998 | 6.2877 |
| 1.8417 | 1.5493 | 6.5049 |
| 1.8783 | 1.5052 | 6.7251 |
| 1.9156 | 1.4668 | 6.948 |
| 1.9536 | 1.4335 | 7.1734 |
| 1.9924 | 1.4048 | 7.4012 |
| 2.0319 | 1.3804 | 7.6315 |
| 2.0723 | 1.3597 | 7.8641 |
| 2.1134 | 1.3426 | 8.0993 |
| 2.1554 | 1.3288 | 8.337 |
| 2.1982 | 1.3179 | 8.5774 |
| 2.2418 | 1.3099 | 8.8204 |
| 2.2863 | 1.3045 | 9.0663 |
| 2.3317 | 1.3017 | 9.3152 |
| 2.378 | 1.3013 | 9.5671 |
| 2.4252 | 1.3032 | 9.8222 |
| 2.4734 | 1.3073 | 10.081 |
| 2.5225 | 1.3136 | 10.342 |
| 2.5725 | 1.3219 | 10.608 |
| 2.6236 | 1.3324 | 10.876 |
| 2.6757 | 1.3449 | 11.149 |
| 2.7288 | 1.3594 | 11.426 |
| 2.783 | 1.3758 | 11.706 |
| 2.8383 | 1.3943 | 11.991 |
| 2.8946 | 1.4148 | 12.279 |
| 2.9521 | 1.4372 | 12.572 |
| 3.0107 | 1.4617 | 12.87 |
| 3.0704 | 1.4881 | 13.172 |
| 3.1314 | 1.5166 | 13.479 |
| 3.1936 | 1.5472 | 13.79 |
| 3.257 | 1.5798 | 14.106 |
| 3.3216 | 1.6146 | 14.428 |
| 3.3876 | 1.6516 | 14.754 |
| 3.4548 | 1.6908 | 15.086 |
| 3.5234 | 1.7322 | 15.422 |
| 3.5934 | 1.7759 | 15.765 |
| 3.6647 | 1.822 | 16.112 |
| 3.7375 | 1.8706 | 16.466 |
| 3.8117 | 1.9216 | 16.825 |
| 3.8873 | 1.9752 | 17.19 |
| 3.9645 | 2.0314 | 17.561 |
| 4.0432 | 2.0903 | 17.938 |
| 4.1235 | 2.1519 | 18.322 |
| 4.2053 | 2.2164 | 18.712 |
| 4.2888 | 2.2839 | 19.108 |
| 4.374 | 2.3544 | 19.51 |
| 4.4608 | 2.428 | 19.92 |
| 4.5494 | 2.5049 | 20.336 |
| 4.6397 | 2.585 | 20.758 |
| 4.7318 | 2.6686 | 21.188 |
| 4.8257 | 2.7557 | 21.625 |
| 4.9216 | 2.8464 | 22.069 |
| 5.0193 | 2.941 | 22.521 |
| 5.1189 | 3.0393 | 22.98 |
| 5.2205 | 3.1417 | 23.446 |
| 5.3242 | 3.2482 | 23.92 |
| 5.4299 | 3.359 | 24.402 |
| 5.5377 | 3.4741 | 24.891 |
| 5.6476 | 3.5938 | 25.389 |
| 5.7597 | 3.7182 | 25.894 |
| 5.8741 | 3.8474 | 26.408 |
| 5.9907 | 3.9816 | 26.929 |
| 6.1096 | 4.1209 | 27.459 |
| 6.2309 | 4.2655 | 27.998 |
| 6.3546 | 4.4156 | 28.545 |
| 6.4808 | 4.5713 | 29.1 |
| 6.6094 | 4.7328 | 29.664 |
| 6.7407 | 4.9003 | 30.237 |
| 6.8745 | 5.074 | 30.819 |
| 7.011 | 5.254 | 31.409 |
| 7.1502 | 5.4406 | 32.009 |
| 7.2921 | 5.6338 | 32.617 |
| 7.4369 | 5.8341 | 33.235 |
| 7.5845 | 6.0414 | 33.861 |
| 7.7351 | 6.2561 | 34.497 |
| 7.8887 | 6.4784 | 35.142 |
| 8.0453 | 6.7083 | 35.796 |
| 8.205 | 6.9463 | 36.46 |
| 8.3679 | 7.1925 | 37.132 |
| 8.534 | 7.447 | 37.815 |
| 8.7034 | 7.7102 | 38.506 |
| 8.8762 | 7.9823 | 39.207 |
| 9.0524 | 8.2634 | 39.917 |
| 9.2322 | 8.5538 | 40.637 |
| 9.4154 | 8.8538 | 41.366 |
| 9.6024 | 9.1635 | 42.104 |
| 9.793 | 9.4833 | 42.851 |
| 9.9874 | 9.8133 | 43.608 |
| 10.186 | 10.154 | 44.374 |
| 10.388 | 10.505 | 45.15 |
| 10.594 | 10.867 | 45.934 |
| 10.804 | 11.24 | 46.728 |
| 11.019 | 11.625 | 47.53 |
| 11.238 | 12.021 | 48.341 |
| 11.461 | 12.429 | 49.161 |
| 11.688 | 12.849 | 49.99 |
| 11.92 | 13.282 | 50.828 |
| 12.157 | 13.726 | 51.674 |
| 12.398 | 14.184 | 52.528 |
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