Optical constants
Refractive index of Ag (Silver)
Rakić et al. 1998: Lorentz-Drude model; n,k 0.248–12.4 µm
- Data
- tabulated nk
- Range
- 0.248–12.4 µm
- Points
- 200
- Licence
- CC0-1.0
- Lightsmith
- bundled
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.137896
- Extinction coefficient k
- 3.4654
- Permittivity ε1
- -11.99
- Permittivity ε2
- 0.955731
- Absorption coefficient α
- 741109 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 26.9866 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.109852 µm⁻¹
- Group index ng
- 0.0733472
- 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: Lorentz-Drude model; n,k 0.248–12.4 µm
ag = ls.LibraryMaterial(name="Ag", dataset="Rakic-LD")
print(ag.range_nm) # (247.97, 12398) nm
eps = ag.eps([633]) # complex permittivity
Ships with the library: works offline.
import lightsmith as ls
# Ag (Silver): Rakić et al. 1998: Lorentz-Drude model; n,k 0.248–12.4 µm
ag = ls.fetch_refractiveindex("main", "Ag", "Rakic-LD", 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_c688aebb5282/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-ld).
# ... 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 | 0.44265 | 1.1737 |
| 0.25289 | 0.50049 | 1.3472 |
| 0.25791 | 0.60304 | 1.5244 |
| 0.26303 | 0.77353 | 1.6937 |
| 0.26825 | 1.0401 | 1.8121 |
| 0.27358 | 1.3888 | 1.7832 |
| 0.27901 | 1.6774 | 1.5367 |
| 0.28455 | 1.7549 | 1.1931 |
| 0.2902 | 1.6619 | 0.9143 |
| 0.29596 | 1.4987 | 0.7345 |
| 0.30184 | 1.3162 | 0.63073 |
| 0.30783 | 1.13 | 0.58101 |
| 0.31394 | 0.94332 | 0.57506 |
| 0.32017 | 0.7591 | 0.61282 |
| 0.32653 | 0.59002 | 0.69733 |
| 0.33301 | 0.45613 | 0.81835 |
| 0.33962 | 0.36329 | 0.95187 |
| 0.34637 | 0.30133 | 1.0817 |
| 0.35324 | 0.25903 | 1.203 |
| 0.36025 | 0.22908 | 1.3159 |
| 0.36741 | 0.20714 | 1.4217 |
| 0.3747 | 0.19062 | 1.5219 |
| 0.38214 | 0.17791 | 1.6176 |
| 0.38973 | 0.16796 | 1.7097 |
| 0.39746 | 0.16007 | 1.799 |
| 0.40535 | 0.15377 | 1.886 |
| 0.4134 | 0.14871 | 1.9714 |
| 0.42161 | 0.14463 | 2.0554 |
| 0.42998 | 0.14136 | 2.1384 |
| 0.43852 | 0.13874 | 2.2207 |
| 0.44722 | 0.13667 | 2.3025 |
| 0.4561 | 0.13507 | 2.384 |
| 0.46515 | 0.13386 | 2.4654 |
| 0.47439 | 0.133 | 2.5469 |
| 0.48381 | 0.13244 | 2.6285 |
| 0.49341 | 0.13214 | 2.7104 |
| 0.50321 | 0.13208 | 2.7927 |
| 0.5132 | 0.13224 | 2.8754 |
| 0.52339 | 0.13259 | 2.9588 |
| 0.53378 | 0.13311 | 3.0428 |
| 0.54437 | 0.13381 | 3.1276 |
| 0.55518 | 0.13465 | 3.2132 |
| 0.5662 | 0.13565 | 3.2996 |
| 0.57744 | 0.13678 | 3.3871 |
| 0.58891 | 0.13804 | 3.4755 |
| 0.6006 | 0.13943 | 3.565 |
| 0.61252 | 0.14094 | 3.6556 |
| 0.62468 | 0.14257 | 3.7474 |
| 0.63709 | 0.14432 | 3.8404 |
| 0.64973 | 0.14619 | 3.9347 |
| 0.66263 | 0.14817 | 4.0303 |
| 0.67579 | 0.15027 | 4.1273 |
| 0.6892 | 0.15249 | 4.2258 |
| 0.70289 | 0.15482 | 4.3257 |
| 0.71684 | 0.15727 | 4.4272 |
| 0.73107 | 0.15984 | 4.5303 |
| 0.74559 | 0.16253 | 4.6349 |
| 0.76039 | 0.16535 | 4.7413 |
| 0.77549 | 0.16829 | 4.8494 |
| 0.79088 | 0.17136 | 4.9593 |
| 0.80658 | 0.17457 | 5.071 |
| 0.8226 | 0.17791 | 5.1845 |
| 0.83893 | 0.1814 | 5.3 |
| 0.85558 | 0.18503 | 5.4175 |
| 0.87257 | 0.18881 | 5.5369 |
| 0.88989 | 0.19274 | 5.6585 |
| 0.90756 | 0.19684 | 5.7821 |
| 0.92557 | 0.2011 | 5.908 |
| 0.94395 | 0.20554 | 6.036 |
| 0.96269 | 0.21015 | 6.1664 |
| 0.9818 | 0.21495 | 6.299 |
| 1.0013 | 0.21994 | 6.4341 |
| 1.0212 | 0.22512 | 6.5716 |
| 1.0414 | 0.23052 | 6.7115 |
| 1.0621 | 0.23613 | 6.8541 |
| 1.0832 | 0.24196 | 6.9992 |
| 1.1047 | 0.24802 | 7.147 |
| 1.1266 | 0.25432 | 7.2975 |
| 1.149 | 0.26087 | 7.4507 |
| 1.1718 | 0.26769 | 7.6069 |
| 1.1951 | 0.27477 | 7.7659 |
| 1.2188 | 0.28213 | 7.9279 |
| 1.243 | 0.28978 | 8.0929 |
| 1.2677 | 0.29774 | 8.2609 |
| 1.2929 | 0.30601 | 8.4322 |
| 1.3185 | 0.3146 | 8.6066 |
| 1.3447 | 0.32354 | 8.7844 |
| 1.3714 | 0.33283 | 8.9655 |
| 1.3986 | 0.34249 | 9.15 |
| 1.4264 | 0.35254 | 9.338 |
| 1.4547 | 0.36298 | 9.5296 |
| 1.4836 | 0.37383 | 9.7248 |
| 1.513 | 0.38512 | 9.9237 |
| 1.5431 | 0.39685 | 10.126 |
| 1.5737 | 0.40905 | 10.333 |
| 1.605 | 0.42174 | 10.543 |
| 1.6368 | 0.43492 | 10.758 |
| 1.6693 | 0.44863 | 10.977 |
| 1.7025 | 0.46289 | 11.199 |
| 1.7363 | 0.47771 | 11.427 |
| 1.7707 | 0.49312 | 11.658 |
| 1.8059 | 0.50914 | 11.894 |
| 1.8417 | 0.5258 | 12.134 |
| 1.8783 | 0.54312 | 12.379 |
| 1.9156 | 0.56113 | 12.629 |
| 1.9536 | 0.57985 | 12.884 |
| 1.9924 | 0.59932 | 13.143 |
| 2.0319 | 0.61956 | 13.407 |
| 2.0723 | 0.64061 | 13.677 |
| 2.1134 | 0.66249 | 13.952 |
| 2.1554 | 0.68524 | 14.231 |
| 2.1982 | 0.7089 | 14.517 |
| 2.2418 | 0.7335 | 14.808 |
| 2.2863 | 0.75907 | 15.104 |
| 2.3317 | 0.78565 | 15.406 |
| 2.378 | 0.8133 | 15.714 |
| 2.4252 | 0.84204 | 16.028 |
| 2.4734 | 0.87192 | 16.348 |
| 2.5225 | 0.90298 | 16.674 |
| 2.5725 | 0.93528 | 17.006 |
| 2.6236 | 0.96885 | 17.345 |
| 2.6757 | 1.0038 | 17.69 |
| 2.7288 | 1.0401 | 18.042 |
| 2.783 | 1.0778 | 18.401 |
| 2.8383 | 1.117 | 18.766 |
| 2.8946 | 1.1578 | 19.139 |
| 2.9521 | 1.2002 | 19.518 |
| 3.0107 | 1.2442 | 19.905 |
| 3.0704 | 1.29 | 20.299 |
| 3.1314 | 1.3376 | 20.701 |
| 3.1936 | 1.3871 | 21.111 |
| 3.257 | 1.4385 | 21.528 |
| 3.3216 | 1.492 | 21.953 |
| 3.3876 | 1.5476 | 22.386 |
| 3.4548 | 1.6053 | 22.828 |
| 3.5234 | 1.6654 | 23.278 |
| 3.5934 | 1.7277 | 23.736 |
| 3.6647 | 1.7926 | 24.203 |
| 3.7375 | 1.86 | 24.679 |
| 3.8117 | 1.93 | 25.164 |
| 3.8873 | 2.0027 | 25.658 |
| 3.9645 | 2.0783 | 26.162 |
| 4.0432 | 2.1569 | 26.674 |
| 4.1235 | 2.2385 | 27.197 |
| 4.2053 | 2.3233 | 27.729 |
| 4.2888 | 2.4114 | 28.271 |
| 4.374 | 2.5029 | 28.823 |
| 4.4608 | 2.598 | 29.385 |
| 4.5494 | 2.6968 | 29.958 |
| 4.6397 | 2.7993 | 30.542 |
| 4.7318 | 2.9059 | 31.136 |
| 4.8257 | 3.0165 | 31.741 |
| 4.9216 | 3.1315 | 32.357 |
| 5.0193 | 3.2508 | 32.984 |
| 5.1189 | 3.3747 | 33.623 |
| 5.2205 | 3.5034 | 34.273 |
| 5.3242 | 3.637 | 34.935 |
| 5.4299 | 3.7757 | 35.609 |
| 5.5377 | 3.9197 | 36.295 |
| 5.6476 | 4.0692 | 36.994 |
| 5.7597 | 4.2243 | 37.705 |
| 5.8741 | 4.3853 | 38.428 |
| 5.9907 | 4.5523 | 39.164 |
| 6.1096 | 4.7257 | 39.914 |
| 6.2309 | 4.9056 | 40.676 |
| 6.3546 | 5.0922 | 41.451 |
| 6.4808 | 5.2858 | 42.24 |
| 6.6094 | 5.4865 | 43.043 |
| 6.7407 | 5.6948 | 43.859 |
| 6.8745 | 5.9107 | 44.689 |
| 7.011 | 6.1346 | 45.533 |
| 7.1502 | 6.3667 | 46.392 |
| 7.2921 | 6.6074 | 47.265 |
| 7.4369 | 6.8568 | 48.152 |
| 7.5845 | 7.1152 | 49.054 |
| 7.7351 | 7.3831 | 49.97 |
| 7.8887 | 7.6606 | 50.902 |
| 8.0453 | 7.948 | 51.849 |
| 8.205 | 8.2457 | 52.81 |
| 8.3679 | 8.5541 | 53.787 |
| 8.534 | 8.8733 | 54.779 |
| 8.7034 | 9.2038 | 55.787 |
| 8.8762 | 9.5459 | 56.81 |
| 9.0524 | 9.8999 | 57.849 |
| 9.2322 | 10.266 | 58.903 |
| 9.4154 | 10.645 | 59.974 |
| 9.6024 | 11.037 | 61.06 |
| 9.793 | 11.442 | 62.162 |
| 9.9874 | 11.861 | 63.28 |
| 10.186 | 12.294 | 64.413 |
| 10.388 | 12.742 | 65.563 |
| 10.594 | 13.204 | 66.729 |
| 10.804 | 13.682 | 67.91 |
| 11.019 | 14.175 | 69.108 |
| 11.238 | 14.685 | 70.321 |
| 11.461 | 15.21 | 71.551 |
| 11.688 | 15.753 | 72.796 |
| 11.92 | 16.313 | 74.057 |
| 12.157 | 16.89 | 75.334 |
| 12.398 | 17.485 | 76.626 |
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 Lorentz-Drude (LD) model