Optical constants
Refractive index of Ag (Silver)
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
- 0.150158
- Extinction coefficient k
- 3.47275
- Permittivity ε1
- -12.0374
- Permittivity ε2
- 1.04292
- Absorption coefficient α
- 742679 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 26.9295 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.138622 µm⁻¹
- Group index ng
- 0.0687038
- 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
# Ag (Silver): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm
ag = ls.fetch_refractiveindex("main", "Ag", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ag.range_nm) # (247.97, 12398) nm
eps = ag.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_48256444ccd7/lightsmith"
ag = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ag.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (ag/rakic-1998-bb).
# ... load ag as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ag)],
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 | 0.84863 | 1.192 |
| 0.25289 | 0.82493 | 1.2193 |
| 0.25791 | 0.79699 | 1.2844 |
| 0.26303 | 0.80009 | 1.3955 |
| 0.26825 | 0.87536 | 1.5246 |
| 0.27358 | 1.032 | 1.6142 |
| 0.27901 | 1.2351 | 1.6125 |
| 0.28455 | 1.4245 | 1.5017 |
| 0.2902 | 1.5424 | 1.3028 |
| 0.29596 | 1.5549 | 1.0631 |
| 0.30184 | 1.4594 | 0.83581 |
| 0.30783 | 1.2767 | 0.66203 |
| 0.31394 | 1.0361 | 0.56621 |
| 0.32017 | 0.76783 | 0.56549 |
| 0.32653 | 0.52213 | 0.67421 |
| 0.33301 | 0.36378 | 0.84735 |
| 0.33962 | 0.2796 | 1.0142 |
| 0.34637 | 0.23178 | 1.1589 |
| 0.35324 | 0.20172 | 1.286 |
| 0.36025 | 0.18151 | 1.4005 |
| 0.36741 | 0.16741 | 1.5059 |
| 0.3747 | 0.15739 | 1.6045 |
| 0.38214 | 0.15021 | 1.6979 |
| 0.38973 | 0.14506 | 1.7873 |
| 0.39746 | 0.14141 | 1.8736 |
| 0.40535 | 0.13887 | 1.9574 |
| 0.4134 | 0.13716 | 2.0394 |
| 0.42161 | 0.13609 | 2.12 |
| 0.42998 | 0.1355 | 2.1995 |
| 0.43852 | 0.13529 | 2.2782 |
| 0.44722 | 0.13537 | 2.3564 |
| 0.4561 | 0.13569 | 2.4344 |
| 0.46515 | 0.13621 | 2.5122 |
| 0.47439 | 0.13687 | 2.5901 |
| 0.48381 | 0.13767 | 2.6682 |
| 0.49341 | 0.13857 | 2.7466 |
| 0.50321 | 0.13958 | 2.8254 |
| 0.5132 | 0.14067 | 2.9048 |
| 0.52339 | 0.14184 | 2.9848 |
| 0.53378 | 0.14308 | 3.0656 |
| 0.54437 | 0.1444 | 3.1471 |
| 0.55518 | 0.14578 | 3.2295 |
| 0.5662 | 0.14723 | 3.3128 |
| 0.57744 | 0.14875 | 3.3971 |
| 0.58891 | 0.15034 | 3.4825 |
| 0.6006 | 0.152 | 3.569 |
| 0.61252 | 0.15373 | 3.6567 |
| 0.62468 | 0.15554 | 3.7455 |
| 0.63709 | 0.15742 | 3.8357 |
| 0.64973 | 0.15939 | 3.9272 |
| 0.66263 | 0.16143 | 4.02 |
| 0.67579 | 0.16356 | 4.1143 |
| 0.6892 | 0.16579 | 4.21 |
| 0.70289 | 0.1681 | 4.3072 |
| 0.71684 | 0.17051 | 4.4061 |
| 0.73107 | 0.17303 | 4.5065 |
| 0.74559 | 0.17565 | 4.6085 |
| 0.76039 | 0.17838 | 4.7123 |
| 0.77549 | 0.18123 | 4.8178 |
| 0.79088 | 0.1842 | 4.9251 |
| 0.80658 | 0.18729 | 5.0343 |
| 0.8226 | 0.19051 | 5.1453 |
| 0.83893 | 0.19387 | 5.2583 |
| 0.85558 | 0.19737 | 5.3732 |
| 0.87257 | 0.20102 | 5.4902 |
| 0.88989 | 0.20482 | 5.6093 |
| 0.90756 | 0.20878 | 5.7304 |
| 0.92557 | 0.21291 | 5.8538 |
| 0.94395 | 0.21721 | 5.9793 |
| 0.96269 | 0.22169 | 6.1072 |
| 0.9818 | 0.22636 | 6.2373 |
| 1.0013 | 0.23122 | 6.3699 |
| 1.0212 | 0.23628 | 6.5048 |
| 1.0414 | 0.24155 | 6.6423 |
| 1.0621 | 0.24705 | 6.7823 |
| 1.0832 | 0.25277 | 6.9248 |
| 1.1047 | 0.25872 | 7.07 |
| 1.1266 | 0.26493 | 7.2179 |
| 1.149 | 0.27138 | 7.3686 |
| 1.1718 | 0.27811 | 7.5221 |
| 1.1951 | 0.28511 | 7.6785 |
| 1.2188 | 0.29239 | 7.8378 |
| 1.243 | 0.29998 | 8.0001 |
| 1.2677 | 0.30788 | 8.1654 |
| 1.2929 | 0.31609 | 8.3339 |
| 1.3185 | 0.32465 | 8.5056 |
| 1.3447 | 0.33355 | 8.6805 |
| 1.3714 | 0.34281 | 8.8587 |
| 1.3986 | 0.35245 | 9.0403 |
| 1.4264 | 0.36249 | 9.2254 |
| 1.4547 | 0.37292 | 9.414 |
| 1.4836 | 0.38379 | 9.6062 |
| 1.513 | 0.39509 | 9.8021 |
| 1.5431 | 0.40684 | 10.002 |
| 1.5737 | 0.41908 | 10.205 |
| 1.605 | 0.4318 | 10.412 |
| 1.6368 | 0.44504 | 10.624 |
| 1.6693 | 0.45882 | 10.839 |
| 1.7025 | 0.47314 | 11.059 |
| 1.7363 | 0.48805 | 11.282 |
| 1.7707 | 0.50355 | 11.51 |
| 1.8059 | 0.51967 | 11.743 |
| 1.8417 | 0.53644 | 11.979 |
| 1.8783 | 0.55389 | 12.221 |
| 1.9156 | 0.57203 | 12.467 |
| 1.9536 | 0.5909 | 12.718 |
| 1.9924 | 0.61053 | 12.973 |
| 2.0319 | 0.63094 | 13.234 |
| 2.0723 | 0.65216 | 13.499 |
| 2.1134 | 0.67424 | 13.77 |
| 2.1554 | 0.69719 | 14.046 |
| 2.1982 | 0.72106 | 14.327 |
| 2.2418 | 0.74588 | 14.614 |
| 2.2863 | 0.7717 | 14.906 |
| 2.3317 | 0.79854 | 15.203 |
| 2.378 | 0.82645 | 15.507 |
| 2.4252 | 0.85546 | 15.816 |
| 2.4734 | 0.88564 | 16.131 |
| 2.5225 | 0.91701 | 16.453 |
| 2.5725 | 0.94962 | 16.78 |
| 2.6236 | 0.98353 | 17.114 |
| 2.6757 | 1.0188 | 17.454 |
| 2.7288 | 1.0554 | 17.801 |
| 2.783 | 1.0935 | 18.154 |
| 2.8383 | 1.1332 | 18.514 |
| 2.8946 | 1.1743 | 18.881 |
| 2.9521 | 1.2171 | 19.255 |
| 3.0107 | 1.2616 | 19.636 |
| 3.0704 | 1.3079 | 20.025 |
| 3.1314 | 1.356 | 20.421 |
| 3.1936 | 1.406 | 20.824 |
| 3.257 | 1.4579 | 21.235 |
| 3.3216 | 1.5119 | 21.654 |
| 3.3876 | 1.568 | 22.081 |
| 3.4548 | 1.6263 | 22.516 |
| 3.5234 | 1.6869 | 22.959 |
| 3.5934 | 1.7499 | 23.41 |
| 3.6647 | 1.8153 | 23.87 |
| 3.7375 | 1.8833 | 24.339 |
| 3.8117 | 1.954 | 24.817 |
| 3.8873 | 2.0274 | 25.303 |
| 3.9645 | 2.1036 | 25.799 |
| 4.0432 | 2.1829 | 26.304 |
| 4.1235 | 2.2652 | 26.818 |
| 4.2053 | 2.3507 | 27.342 |
| 4.2888 | 2.4396 | 27.876 |
| 4.374 | 2.5319 | 28.419 |
| 4.4608 | 2.6277 | 28.973 |
| 4.5494 | 2.7273 | 29.537 |
| 4.6397 | 2.8307 | 30.111 |
| 4.7318 | 2.9381 | 30.696 |
| 4.8257 | 3.0496 | 31.291 |
| 4.9216 | 3.1654 | 31.898 |
| 5.0193 | 3.2856 | 32.515 |
| 5.1189 | 3.4104 | 33.143 |
| 5.2205 | 3.54 | 33.783 |
| 5.3242 | 3.6745 | 34.435 |
| 5.4299 | 3.8141 | 35.098 |
| 5.5377 | 3.9591 | 35.773 |
| 5.6476 | 4.1095 | 36.46 |
| 5.7597 | 4.2656 | 37.159 |
| 5.8741 | 4.4275 | 37.87 |
| 5.9907 | 4.5956 | 38.594 |
| 6.1096 | 4.7699 | 39.331 |
| 6.2309 | 4.9508 | 40.08 |
| 6.3546 | 5.1384 | 40.842 |
| 6.4808 | 5.3329 | 41.618 |
| 6.6094 | 5.5347 | 42.407 |
| 6.7407 | 5.7439 | 43.209 |
| 6.8745 | 5.9609 | 44.025 |
| 7.011 | 6.1857 | 44.854 |
| 7.1502 | 6.4188 | 45.697 |
| 7.2921 | 6.6604 | 46.555 |
| 7.4369 | 6.9107 | 47.426 |
| 7.5845 | 7.1701 | 48.312 |
| 7.7351 | 7.4389 | 49.212 |
| 7.8887 | 7.7172 | 50.126 |
| 8.0453 | 8.0055 | 51.055 |
| 8.205 | 8.304 | 51.999 |
| 8.3679 | 8.6131 | 52.958 |
| 8.534 | 8.933 | 53.931 |
| 8.7034 | 9.2642 | 54.92 |
| 8.8762 | 9.6068 | 55.923 |
| 9.0524 | 9.9614 | 56.942 |
| 9.2322 | 10.328 | 57.976 |
| 9.4154 | 10.707 | 59.025 |
| 9.6024 | 11.1 | 60.09 |
| 9.793 | 11.505 | 61.17 |
| 9.9874 | 11.924 | 62.265 |
| 10.186 | 12.357 | 63.376 |
| 10.388 | 12.805 | 64.502 |
| 10.594 | 13.267 | 65.643 |
| 10.804 | 13.744 | 66.8 |
| 11.019 | 14.237 | 67.973 |
| 11.238 | 14.746 | 69.16 |
| 11.461 | 15.27 | 70.363 |
| 11.688 | 15.812 | 71.581 |
| 11.92 | 16.37 | 72.814 |
| 12.157 | 16.946 | 74.063 |
| 12.398 | 17.54 | 75.326 |
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