Optical constants
Refractive index of Pd (Palladium)
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
- 1.72289
- Extinction coefficient k
- 3.97541
- Permittivity ε1
- -12.8355
- Permittivity ε2
- 13.6984
- Absorption coefficient α
- 850178 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 23.5245 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 2.22319 µm⁻¹
- Group index ng
- 0.416541
- 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
# Pd (Palladium): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–12.4 µm
pd = ls.fetch_refractiveindex("main", "Pd", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pd.range_nm) # (247.97, 12398) nm
eps = pd.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_f4f2a5e03d13/lightsmith"
pd = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pd.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (pd/rakic-1998-bb).
# ... load pd as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=pd)],
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 | 1.1567 | 2.0317 |
| 0.25289 | 1.1581 | 2.043 |
| 0.25791 | 1.1579 | 2.0572 |
| 0.26303 | 1.1566 | 2.0743 |
| 0.26825 | 1.1544 | 2.0944 |
| 0.27358 | 1.1519 | 2.1175 |
| 0.27901 | 1.1493 | 2.1434 |
| 0.28455 | 1.147 | 2.1721 |
| 0.2902 | 1.1452 | 2.2035 |
| 0.29596 | 1.1443 | 2.2373 |
| 0.30184 | 1.1443 | 2.2733 |
| 0.30783 | 1.1454 | 2.3114 |
| 0.31394 | 1.1479 | 2.3513 |
| 0.32017 | 1.1516 | 2.3929 |
| 0.32653 | 1.1567 | 2.4358 |
| 0.33301 | 1.1632 | 2.48 |
| 0.33962 | 1.1711 | 2.5253 |
| 0.34637 | 1.1802 | 2.5715 |
| 0.35324 | 1.1907 | 2.6185 |
| 0.36025 | 1.2024 | 2.6661 |
| 0.36741 | 1.2153 | 2.7144 |
| 0.3747 | 1.2293 | 2.7631 |
| 0.38214 | 1.2443 | 2.8123 |
| 0.38973 | 1.2602 | 2.8618 |
| 0.39746 | 1.2771 | 2.9117 |
| 0.40535 | 1.2948 | 2.962 |
| 0.4134 | 1.3132 | 3.0125 |
| 0.42161 | 1.3324 | 3.0633 |
| 0.42998 | 1.3522 | 3.1145 |
| 0.43852 | 1.3726 | 3.1659 |
| 0.44722 | 1.3935 | 3.2176 |
| 0.4561 | 1.4149 | 3.2696 |
| 0.46515 | 1.4368 | 3.3219 |
| 0.47439 | 1.4592 | 3.3746 |
| 0.48381 | 1.4819 | 3.4276 |
| 0.49341 | 1.505 | 3.481 |
| 0.50321 | 1.5285 | 3.5348 |
| 0.5132 | 1.5522 | 3.5891 |
| 0.52339 | 1.5763 | 3.6437 |
| 0.53378 | 1.6006 | 3.6988 |
| 0.54437 | 1.6252 | 3.7544 |
| 0.55518 | 1.65 | 3.8105 |
| 0.5662 | 1.6751 | 3.8671 |
| 0.57744 | 1.7003 | 3.9243 |
| 0.58891 | 1.7258 | 3.982 |
| 0.6006 | 1.7514 | 4.0404 |
| 0.61252 | 1.7772 | 4.0993 |
| 0.62468 | 1.8032 | 4.1589 |
| 0.63709 | 1.8292 | 4.2192 |
| 0.64973 | 1.8555 | 4.2802 |
| 0.66263 | 1.8818 | 4.3419 |
| 0.67579 | 1.9083 | 4.4044 |
| 0.6892 | 1.9348 | 4.4676 |
| 0.70289 | 1.9615 | 4.5316 |
| 0.71684 | 1.9882 | 4.5965 |
| 0.73107 | 2.015 | 4.6623 |
| 0.74559 | 2.0418 | 4.7289 |
| 0.76039 | 2.0687 | 4.7965 |
| 0.77549 | 2.0957 | 4.8651 |
| 0.79088 | 2.1227 | 4.9347 |
| 0.80658 | 2.1498 | 5.0053 |
| 0.8226 | 2.1768 | 5.077 |
| 0.83893 | 2.204 | 5.1498 |
| 0.85558 | 2.2311 | 5.2238 |
| 0.87257 | 2.2583 | 5.299 |
| 0.88989 | 2.2855 | 5.3755 |
| 0.90756 | 2.3128 | 5.4532 |
| 0.92557 | 2.3401 | 5.5323 |
| 0.94395 | 2.3675 | 5.6127 |
| 0.96269 | 2.395 | 5.6946 |
| 0.9818 | 2.4225 | 5.778 |
| 1.0013 | 2.4502 | 5.8628 |
| 1.0212 | 2.478 | 5.9492 |
| 1.0414 | 2.5059 | 6.0373 |
| 1.0621 | 2.534 | 6.1269 |
| 1.0832 | 2.5622 | 6.2183 |
| 1.1047 | 2.5908 | 6.3114 |
| 1.1266 | 2.6195 | 6.4063 |
| 1.149 | 2.6486 | 6.503 |
| 1.1718 | 2.678 | 6.6015 |
| 1.1951 | 2.7078 | 6.7019 |
| 1.2188 | 2.738 | 6.8042 |
| 1.243 | 2.7687 | 6.9084 |
| 1.2677 | 2.8 | 7.0146 |
| 1.2929 | 2.8318 | 7.1228 |
| 1.3185 | 2.8643 | 7.233 |
| 1.3447 | 2.8975 | 7.3451 |
| 1.3714 | 2.9314 | 7.4592 |
| 1.3986 | 2.9662 | 7.5752 |
| 1.4264 | 3.0019 | 7.6932 |
| 1.4547 | 3.0386 | 7.813 |
| 1.4836 | 3.0762 | 7.9348 |
| 1.513 | 3.115 | 8.0582 |
| 1.5431 | 3.1548 | 8.1835 |
| 1.5737 | 3.1958 | 8.3103 |
| 1.605 | 3.238 | 8.4387 |
| 1.6368 | 3.2814 | 8.5684 |
| 1.6693 | 3.326 | 8.6995 |
| 1.7025 | 3.3718 | 8.8317 |
| 1.7363 | 3.4187 | 8.9649 |
| 1.7707 | 3.4667 | 9.0989 |
| 1.8059 | 3.5157 | 9.2337 |
| 1.8417 | 3.5655 | 9.3689 |
| 1.8783 | 3.616 | 9.5044 |
| 1.9156 | 3.667 | 9.6401 |
| 1.9536 | 3.7182 | 9.7759 |
| 1.9924 | 3.7693 | 9.9115 |
| 2.0319 | 3.8201 | 10.047 |
| 2.0723 | 3.8701 | 10.182 |
| 2.1134 | 3.919 | 10.317 |
| 2.1554 | 3.9663 | 10.452 |
| 2.1982 | 4.0115 | 10.587 |
| 2.2418 | 4.0544 | 10.721 |
| 2.2863 | 4.0943 | 10.856 |
| 2.3317 | 4.1308 | 10.992 |
| 2.378 | 4.1636 | 11.128 |
| 2.4252 | 4.1923 | 11.266 |
| 2.4734 | 4.2164 | 11.406 |
| 2.5225 | 4.2359 | 11.548 |
| 2.5725 | 4.2503 | 11.694 |
| 2.6236 | 4.2597 | 11.843 |
| 2.6757 | 4.264 | 11.996 |
| 2.7288 | 4.2631 | 12.154 |
| 2.783 | 4.2571 | 12.317 |
| 2.8383 | 4.2463 | 12.487 |
| 2.8946 | 4.2309 | 12.664 |
| 2.9521 | 4.211 | 12.847 |
| 3.0107 | 4.1871 | 13.039 |
| 3.0704 | 4.1596 | 13.238 |
| 3.1314 | 4.1287 | 13.446 |
| 3.1936 | 4.095 | 13.663 |
| 3.257 | 4.0587 | 13.889 |
| 3.3216 | 4.0204 | 14.124 |
| 3.3876 | 3.9805 | 14.369 |
| 3.4548 | 3.9393 | 14.623 |
| 3.5234 | 3.8972 | 14.887 |
| 3.5934 | 3.8545 | 15.161 |
| 3.6647 | 3.8115 | 15.444 |
| 3.7375 | 3.7686 | 15.737 |
| 3.8117 | 3.726 | 16.04 |
| 3.8873 | 3.6839 | 16.352 |
| 3.9645 | 3.6425 | 16.674 |
| 4.0432 | 3.602 | 17.006 |
| 4.1235 | 3.5626 | 17.347 |
| 4.2053 | 3.5243 | 17.698 |
| 4.2888 | 3.4873 | 18.058 |
| 4.374 | 3.4517 | 18.428 |
| 4.4608 | 3.4175 | 18.807 |
| 4.5494 | 3.3848 | 19.196 |
| 4.6397 | 3.3537 | 19.594 |
| 4.7318 | 3.3242 | 20.002 |
| 4.8257 | 3.2962 | 20.419 |
| 4.9216 | 3.2699 | 20.846 |
| 5.0193 | 3.2452 | 21.282 |
| 5.1189 | 3.2222 | 21.728 |
| 5.2205 | 3.2009 | 22.184 |
| 5.3242 | 3.1813 | 22.65 |
| 5.4299 | 3.1633 | 23.126 |
| 5.5377 | 3.147 | 23.612 |
| 5.6476 | 3.1324 | 24.108 |
| 5.7597 | 3.1195 | 24.615 |
| 5.8741 | 3.1083 | 25.132 |
| 5.9907 | 3.0987 | 25.66 |
| 6.1096 | 3.0909 | 26.198 |
| 6.2309 | 3.0848 | 26.748 |
| 6.3546 | 3.0804 | 27.308 |
| 6.4808 | 3.0778 | 27.88 |
| 6.6094 | 3.0769 | 28.463 |
| 6.7407 | 3.0778 | 29.058 |
| 6.8745 | 3.0804 | 29.665 |
| 7.011 | 3.0849 | 30.284 |
| 7.1502 | 3.0911 | 30.916 |
| 7.2921 | 3.0993 | 31.559 |
| 7.4369 | 3.1093 | 32.216 |
| 7.5845 | 3.1212 | 32.885 |
| 7.7351 | 3.1351 | 33.568 |
| 7.8887 | 3.151 | 34.264 |
| 8.0453 | 3.1689 | 34.974 |
| 8.205 | 3.1889 | 35.697 |
| 8.3679 | 3.211 | 36.435 |
| 8.534 | 3.2353 | 37.187 |
| 8.7034 | 3.2618 | 37.955 |
| 8.8762 | 3.2906 | 38.737 |
| 9.0524 | 3.3217 | 39.534 |
| 9.2322 | 3.3553 | 40.347 |
| 9.4154 | 3.3914 | 41.176 |
| 9.6024 | 3.43 | 42.02 |
| 9.793 | 3.4712 | 42.882 |
| 9.9874 | 3.5151 | 43.76 |
| 10.186 | 3.5619 | 44.655 |
| 10.388 | 3.6115 | 45.568 |
| 10.594 | 3.6641 | 46.498 |
| 10.804 | 3.7198 | 47.447 |
| 11.019 | 3.7786 | 48.414 |
| 11.238 | 3.8408 | 49.4 |
| 11.461 | 3.9063 | 50.404 |
| 11.688 | 3.9754 | 51.429 |
| 11.92 | 4.048 | 52.473 |
| 12.157 | 4.1245 | 53.537 |
| 12.398 | 4.2048 | 54.622 |
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