Optical constants
Refractive index of Al (Aluminium)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.0620–248 µm
- Data
- tabulated nk
- Range
- 0.06199–248 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.09717
- Extinction coefficient k
- 6.79423
- Permittivity ε1
- -44.9577
- Permittivity ε2
- 14.9088
- Absorption coefficient α
- 1.45301e+06 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 13.7645 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 3.50811 µm⁻¹
- Group index ng
- -0.964201
- 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
# Al (Aluminium): Rakić et al. 1998: Brendel-Bormann model; n,k 0.0620–248 µm
al = ls.fetch_refractiveindex("main", "Al", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(al.range_nm) # (61.992, 247970) nm
eps = al.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_76325c10970a/lightsmith"
al = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(al.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (al/rakic-1998-bb).
# ... load al as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=al)],
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 |
|---|---|---|
| 0.061992 | 0.66415 | 0.0092039 |
| 0.06463 | 0.62647 | 0.011074 |
| 0.067381 | 0.58276 | 0.013512 |
| 0.070249 | 0.53121 | 0.016828 |
| 0.073239 | 0.46884 | 0.021649 |
| 0.076355 | 0.39013 | 0.029549 |
| 0.079605 | 0.282 | 0.046438 |
| 0.082993 | 0.11588 | 0.12841 |
| 0.086525 | 0.055295 | 0.3059 |
| 0.090208 | 0.044408 | 0.43313 |
| 0.094047 | 0.040584 | 0.53919 |
| 0.098049 | 0.039232 | 0.63492 |
| 0.10222 | 0.039141 | 0.72492 |
| 0.10657 | 0.039857 | 0.81159 |
| 0.11111 | 0.041181 | 0.89644 |
| 0.11584 | 0.043024 | 0.98045 |
| 0.12077 | 0.04535 | 1.0643 |
| 0.12591 | 0.048158 | 1.1487 |
| 0.13127 | 0.051461 | 1.2338 |
| 0.13685 | 0.055281 | 1.3202 |
| 0.14268 | 0.05964 | 1.408 |
| 0.14875 | 0.064557 | 1.4975 |
| 0.15508 | 0.07004 | 1.589 |
| 0.16168 | 0.076091 | 1.6826 |
| 0.16856 | 0.082703 | 1.7786 |
| 0.17573 | 0.089866 | 1.8771 |
| 0.18321 | 0.097571 | 1.9783 |
| 0.19101 | 0.10582 | 2.0826 |
| 0.19914 | 0.11461 | 2.1901 |
| 0.20762 | 0.12398 | 2.3011 |
| 0.21645 | 0.13398 | 2.4159 |
| 0.22566 | 0.14468 | 2.5347 |
| 0.23527 | 0.15617 | 2.6578 |
| 0.24528 | 0.1686 | 2.7856 |
| 0.25572 | 0.1821 | 2.9182 |
| 0.2666 | 0.19687 | 3.056 |
| 0.27795 | 0.21312 | 3.1992 |
| 0.28978 | 0.23109 | 3.3482 |
| 0.30211 | 0.25107 | 3.503 |
| 0.31497 | 0.27336 | 3.664 |
| 0.32837 | 0.29832 | 3.8313 |
| 0.34235 | 0.32634 | 4.0052 |
| 0.35692 | 0.35785 | 4.1856 |
| 0.37211 | 0.3933 | 4.3726 |
| 0.38795 | 0.43317 | 4.5661 |
| 0.40446 | 0.4779 | 4.7659 |
| 0.42167 | 0.52788 | 4.9717 |
| 0.43962 | 0.58336 | 5.183 |
| 0.45833 | 0.64439 | 5.3994 |
| 0.47783 | 0.71074 | 5.6203 |
| 0.49817 | 0.78186 | 5.8455 |
| 0.51937 | 0.85697 | 6.075 |
| 0.54147 | 0.93525 | 6.3099 |
| 0.56452 | 1.0162 | 6.5519 |
| 0.58855 | 1.1005 | 6.8042 |
| 0.61359 | 1.1911 | 7.0711 |
| 0.63971 | 1.2952 | 7.3576 |
| 0.66693 | 1.4286 | 7.6672 |
| 0.69532 | 1.6203 | 7.9931 |
| 0.72491 | 1.9115 | 8.2933 |
| 0.75576 | 2.3052 | 8.4555 |
| 0.78793 | 2.6523 | 8.3611 |
| 0.82146 | 2.7061 | 8.1106 |
| 0.85642 | 2.4465 | 7.9982 |
| 0.89287 | 2.0948 | 8.1553 |
| 0.93087 | 1.8089 | 8.499 |
| 0.97049 | 1.612 | 8.9296 |
| 1.0118 | 1.4821 | 9.3982 |
| 1.0549 | 1.3974 | 9.8877 |
| 1.0997 | 1.344 | 10.393 |
| 1.1465 | 1.3136 | 10.915 |
| 1.1953 | 1.3012 | 11.452 |
| 1.2462 | 1.3039 | 12.007 |
| 1.2993 | 1.3197 | 12.581 |
| 1.3546 | 1.3476 | 13.173 |
| 1.4122 | 1.3868 | 13.786 |
| 1.4723 | 1.437 | 14.421 |
| 1.535 | 1.4979 | 15.077 |
| 1.6003 | 1.5694 | 15.757 |
| 1.6684 | 1.6518 | 16.46 |
| 1.7394 | 1.7451 | 17.188 |
| 1.8134 | 1.8497 | 17.942 |
| 1.8906 | 1.9659 | 18.723 |
| 1.9711 | 2.0942 | 19.531 |
| 2.055 | 2.2349 | 20.367 |
| 2.1424 | 2.3887 | 21.233 |
| 2.2336 | 2.5562 | 22.128 |
| 2.3287 | 2.7379 | 23.054 |
| 2.4278 | 2.9346 | 24.012 |
| 2.5311 | 3.1468 | 25.002 |
| 2.6388 | 3.3754 | 26.025 |
| 2.7511 | 3.6209 | 27.082 |
| 2.8682 | 3.8841 | 28.173 |
| 2.9903 | 4.1657 | 29.3 |
| 3.1175 | 4.4664 | 30.463 |
| 3.2502 | 4.7867 | 31.662 |
| 3.3885 | 5.1273 | 32.898 |
| 3.5328 | 5.4887 | 34.172 |
| 3.6831 | 5.8714 | 35.484 |
| 3.8399 | 6.2757 | 36.836 |
| 4.0033 | 6.7019 | 38.228 |
| 4.1737 | 7.1501 | 39.66 |
| 4.3513 | 7.6206 | 41.135 |
| 4.5365 | 8.1133 | 42.652 |
| 4.7296 | 8.6281 | 44.214 |
| 4.9308 | 9.1649 | 45.821 |
| 5.1407 | 9.7236 | 47.476 |
| 5.3595 | 10.304 | 49.18 |
| 5.5876 | 10.906 | 50.936 |
| 5.8254 | 11.53 | 52.747 |
| 6.0733 | 12.175 | 54.615 |
| 6.3318 | 12.843 | 56.545 |
| 6.6013 | 13.534 | 58.539 |
| 6.8822 | 14.25 | 60.601 |
| 7.1751 | 14.991 | 62.736 |
| 7.4805 | 15.76 | 64.948 |
| 7.7988 | 16.56 | 67.242 |
| 8.1307 | 17.394 | 69.62 |
| 8.4768 | 18.266 | 72.089 |
| 8.8376 | 19.179 | 74.651 |
| 9.2137 | 20.14 | 77.311 |
| 9.6058 | 21.153 | 80.072 |
| 10.015 | 22.224 | 82.936 |
| 10.441 | 23.359 | 85.906 |
| 10.885 | 24.565 | 88.985 |
| 11.348 | 25.849 | 92.173 |
| 11.831 | 27.217 | 95.47 |
| 12.335 | 28.677 | 98.878 |
| 12.86 | 30.235 | 102.39 |
| 13.407 | 31.898 | 106.02 |
| 13.978 | 33.672 | 109.75 |
| 14.573 | 35.565 | 113.59 |
| 15.193 | 37.582 | 117.52 |
| 15.84 | 39.728 | 121.56 |
| 16.514 | 42.01 | 125.68 |
| 17.216 | 44.432 | 129.9 |
| 17.949 | 46.998 | 134.2 |
| 18.713 | 49.712 | 138.58 |
| 19.51 | 52.578 | 143.04 |
| 20.34 | 55.597 | 147.57 |
| 21.206 | 58.773 | 152.16 |
| 22.108 | 62.105 | 156.81 |
| 23.049 | 65.596 | 161.51 |
| 24.03 | 69.244 | 166.26 |
| 25.053 | 73.05 | 171.06 |
| 26.119 | 77.013 | 175.89 |
| 27.23 | 81.13 | 180.76 |
| 28.389 | 85.4 | 185.65 |
| 29.598 | 89.82 | 190.58 |
| 30.857 | 94.387 | 195.53 |
| 32.17 | 99.098 | 200.5 |
| 33.54 | 103.95 | 205.49 |
| 34.967 | 108.94 | 210.5 |
| 36.455 | 114.06 | 215.53 |
| 38.007 | 119.31 | 220.57 |
| 39.624 | 124.69 | 225.63 |
| 41.311 | 130.18 | 230.71 |
| 43.069 | 135.8 | 235.82 |
| 44.902 | 141.53 | 240.94 |
| 46.813 | 147.37 | 246.09 |
| 48.805 | 153.32 | 251.27 |
| 50.882 | 159.38 | 256.48 |
| 53.048 | 165.54 | 261.73 |
| 55.305 | 171.8 | 267.01 |
| 57.659 | 178.17 | 272.34 |
| 60.113 | 184.63 | 277.72 |
| 62.671 | 191.19 | 283.15 |
| 65.339 | 197.85 | 288.63 |
| 68.119 | 204.61 | 294.18 |
| 71.019 | 211.47 | 299.8 |
| 74.041 | 218.42 | 305.49 |
| 77.192 | 225.47 | 311.26 |
| 80.478 | 232.63 | 317.11 |
| 83.903 | 239.88 | 323.05 |
| 87.473 | 247.24 | 329.08 |
| 91.196 | 254.71 | 335.21 |
| 95.078 | 262.28 | 341.45 |
| 99.124 | 269.96 | 347.79 |
| 103.34 | 277.76 | 354.25 |
| 107.74 | 285.67 | 360.82 |
| 112.33 | 293.7 | 367.52 |
| 117.11 | 301.85 | 374.34 |
| 122.09 | 310.12 | 381.3 |
| 127.29 | 318.52 | 388.4 |
| 132.7 | 327.05 | 395.64 |
| 138.35 | 335.72 | 403.03 |
| 144.24 | 344.53 | 410.57 |
| 150.38 | 353.48 | 418.26 |
| 156.78 | 362.57 | 426.12 |
| 163.45 | 371.82 | 434.15 |
| 170.41 | 381.22 | 442.34 |
| 177.66 | 390.78 | 450.71 |
| 185.22 | 400.5 | 459.26 |
| 193.1 | 410.39 | 468.0 |
| 201.32 | 420.45 | 476.93 |
| 209.89 | 430.68 | 486.05 |
| 218.82 | 441.1 | 495.37 |
| 228.14 | 451.71 | 504.9 |
| 237.85 | 462.5 | 514.63 |
| 247.97 | 473.49 | 524.58 |
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