Optical constants
Refractive index of AlN-Al2O3 (Aluminium oxynitride, ALON)
Hartnett et al. 1998: 6.69 at.% N; n 0.24–5.6 µm
- Data
- formula 1
- Range
- 0.24–5.6 µm
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.78891
- Extinction coefficient k
- 0
- Permittivity ε1
- 3.20022
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 58.205
- Chromatic dispersion dn/dλ
- -0.0701377 µm⁻¹
- Group index ng
- 1.83013
- Group velocity dispersion
- 122.359 fs²/mm
- Dispersion parameter D
- -667.534 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
# AlN-Al2O3 (Aluminium oxynitride, ALON): Hartnett et al. 1998: 6.69 at.% N; n 0.24–5.6 µm
aln_al2o3 = ls.fetch_refractiveindex("other", "AlN-Al2O3", "Hartnett-6.69", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(aln_al2o3.range_nm) # (240, 5600) nm
eps = aln_al2o3.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_51e565cd21ef/lightsmith"
aln_al2o3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(aln_al2o3.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (aln-al2o3/hartnett-1998-6-69).
# ... load aln_al2o3 as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=aln_al2o3)],
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"]).
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_51e565cd21ef/lightsmith?model=drude_lorentz"
aln_al2o3_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))
A dispersive Drude–Lorentz model for time-domain solvers.
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.
Dispersion formula
Sellmeier (formula 1), λ in µmValid from 0.24 to 5.6 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 2.1375 |
| C3 | 0.10256 |
| C4 | 4.5817 |
| C5 | 18.868 |
Comments and conditions
References
- doi:10.1016/s1350-4495(98)00007-3 Optical properties of ALON (aluminum oxynitride), Infrared Physics & Technology (1998)
Cite
T.M Hartnett, S.D Bernstein, E.A Maguire and R.W Tustison. Optical properties of ALON (aluminum oxynitride). Infrared Physics & Technology, 39, 203-211 (1998), doi:10.1016/s1350-4495(98)00007-3; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
Computed on 400 wavelengths, the same grid as the API and the library| λ (µm) | n |
|---|---|
| 0.24 | 1.901132 |
| 0.241902 | 1.898728 |
| 0.243819 | 1.896376 |
| 0.245752 | 1.894073 |
| 0.2477 | 1.891819 |
| 0.249663 | 1.889612 |
| 0.251642 | 1.88745 |
| 0.253636 | 1.885333 |
| 0.255646 | 1.88326 |
| 0.257672 | 1.881229 |
| 0.259715 | 1.879239 |
| 0.261773 | 1.87729 |
| 0.263848 | 1.875381 |
| 0.265939 | 1.873509 |
| 0.268047 | 1.871676 |
| 0.270171 | 1.869878 |
| 0.272312 | 1.868117 |
| 0.274471 | 1.86639 |
| 0.276646 | 1.864698 |
| 0.278839 | 1.863038 |
| 0.281049 | 1.861412 |
| 0.283276 | 1.859816 |
| 0.285521 | 1.858252 |
| 0.287784 | 1.856718 |
| 0.290065 | 1.855214 |
| 0.292364 | 1.853738 |
| 0.294681 | 1.852291 |
| 0.297017 | 1.850871 |
| 0.299371 | 1.849479 |
| 0.301744 | 1.848112 |
| 0.304135 | 1.846772 |
| 0.306546 | 1.845456 |
| 0.308975 | 1.844165 |
| 0.311424 | 1.842899 |
| 0.313892 | 1.841656 |
| 0.31638 | 1.840436 |
| 0.318888 | 1.839239 |
| 0.321415 | 1.838063 |
| 0.323963 | 1.83691 |
| 0.32653 | 1.835777 |
| 0.329118 | 1.834665 |
| 0.331727 | 1.833574 |
| 0.334356 | 1.832502 |
| 0.337006 | 1.83145 |
| 0.339677 | 1.830417 |
| 0.342369 | 1.829402 |
| 0.345082 | 1.828405 |
| 0.347817 | 1.827427 |
| 0.350574 | 1.826466 |
| 0.353353 | 1.825522 |
| 0.356153 | 1.824595 |
| 0.358976 | 1.823684 |
| 0.361821 | 1.822789 |
| 0.364689 | 1.82191 |
| 0.367579 | 1.821047 |
| 0.370493 | 1.820198 |
| 0.373429 | 1.819365 |
| 0.376389 | 1.818546 |
| 0.379372 | 1.817741 |
| 0.382379 | 1.81695 |
| 0.385409 | 1.816173 |
| 0.388464 | 1.81541 |
| 0.391543 | 1.814659 |
| 0.394646 | 1.813921 |
| 0.397774 | 1.813196 |
| 0.400926 | 1.812484 |
| 0.404104 | 1.811783 |
| 0.407307 | 1.811094 |
| 0.410535 | 1.810418 |
| 0.413789 | 1.809752 |
| 0.417068 | 1.809098 |
| 0.420374 | 1.808454 |
| 0.423706 | 1.807822 |
| 0.427064 | 1.8072 |
| 0.430449 | 1.806588 |
| 0.43386 | 1.805987 |
| 0.437299 | 1.805396 |
| 0.440765 | 1.804814 |
| 0.444258 | 1.804242 |
| 0.447779 | 1.803679 |
| 0.451328 | 1.803126 |
| 0.454905 | 1.802582 |
| 0.458511 | 1.802046 |
| 0.462145 | 1.80152 |
| 0.465807 | 1.801002 |
| 0.469499 | 1.800492 |
| 0.47322 | 1.79999 |
| 0.476971 | 1.799497 |
| 0.480751 | 1.799011 |
| 0.484562 | 1.798533 |
| 0.488402 | 1.798063 |
| 0.492273 | 1.797601 |
| 0.496175 | 1.797145 |
| 0.500107 | 1.796697 |
| 0.504071 | 1.796256 |
| 0.508066 | 1.795822 |
| 0.512093 | 1.795395 |
| 0.516151 | 1.794974 |
| 0.520242 | 1.79456 |
| 0.524365 | 1.794152 |
| 0.528521 | 1.79375 |
| 0.53271 | 1.793355 |
| 0.536932 | 1.792966 |
| 0.541188 | 1.792583 |
| 0.545477 | 1.792205 |
| 0.549801 | 1.791833 |
| 0.554158 | 1.791467 |
| 0.55855 | 1.791107 |
| 0.562977 | 1.790751 |
| 0.567439 | 1.790401 |
| 0.571936 | 1.790057 |
| 0.576469 | 1.789717 |
| 0.581038 | 1.789382 |
| 0.585643 | 1.789053 |
| 0.590285 | 1.788728 |
| 0.594963 | 1.788407 |
| 0.599679 | 1.788092 |
| 0.604432 | 1.787781 |
| 0.609222 | 1.787474 |
| 0.614051 | 1.787171 |
| 0.618918 | 1.786873 |
| 0.623823 | 1.786579 |
| 0.628767 | 1.78629 |
| 0.633751 | 1.786004 |
| 0.638773 | 1.785722 |
| 0.643836 | 1.785444 |
| 0.648939 | 1.78517 |
| 0.654082 | 1.784899 |
| 0.659266 | 1.784632 |
| 0.664492 | 1.784369 |
| 0.669758 | 1.784109 |
| 0.675066 | 1.783853 |
| 0.680417 | 1.783599 |
| 0.68581 | 1.783349 |
| 0.691245 | 1.783103 |
| 0.696724 | 1.782859 |
| 0.702246 | 1.782619 |
| 0.707811 | 1.782381 |
| 0.713421 | 1.782147 |
| 0.719076 | 1.781915 |
| 0.724775 | 1.781686 |
| 0.730519 | 1.78146 |
| 0.736309 | 1.781236 |
| 0.742145 | 1.781016 |
| 0.748027 | 1.780797 |
| 0.753955 | 1.780581 |
| 0.759931 | 1.780368 |
| 0.765954 | 1.780157 |
| 0.772025 | 1.779948 |
| 0.778144 | 1.779742 |
| 0.784311 | 1.779538 |
| 0.790527 | 1.779336 |
| 0.796793 | 1.779136 |
| 0.803108 | 1.778938 |
| 0.809473 | 1.778742 |
| 0.815888 | 1.778548 |
| 0.822355 | 1.778356 |
| 0.828873 | 1.778166 |
| 0.835442 | 1.777978 |
| 0.842064 | 1.777791 |
| 0.848737 | 1.777606 |
| 0.855464 | 1.777423 |
| 0.862244 | 1.777241 |
| 0.869078 | 1.777061 |
| 0.875966 | 1.776883 |
| 0.882909 | 1.776705 |
| 0.889907 | 1.77653 |
| 0.89696 | 1.776355 |
| 0.904069 | 1.776182 |
| 0.911234 | 1.77601 |
| 0.918456 | 1.77584 |
| 0.925736 | 1.77567 |
| 0.933073 | 1.775502 |
| 0.940468 | 1.775335 |
| 0.947922 | 1.775169 |
| 0.955435 | 1.775004 |
| 0.963007 | 1.77484 |
| 0.97064 | 1.774676 |
| 0.978333 | 1.774514 |
| 0.986087 | 1.774352 |
| 0.993902 | 1.774192 |
| 1.00178 | 1.774032 |
| 1.00972 | 1.773872 |
| 1.01772 | 1.773714 |
| 1.02579 | 1.773556 |
| 1.03392 | 1.773399 |
| 1.04211 | 1.773242 |
| 1.05037 | 1.773085 |
| 1.0587 | 1.772929 |
| 1.06709 | 1.772774 |
| 1.07555 | 1.772619 |
| 1.08407 | 1.772464 |
| 1.09266 | 1.77231 |
| 1.10132 | 1.772156 |
| 1.11005 | 1.772002 |
| 1.11885 | 1.771848 |
| 1.12772 | 1.771694 |
| 1.13665 | 1.771541 |
| 1.14566 | 1.771387 |
| 1.15474 | 1.771234 |
| 1.1639 | 1.771081 |
| 1.17312 | 1.770927 |
| 1.18242 | 1.770773 |
| 1.19179 | 1.77062 |
| 1.20123 | 1.770466 |
| 1.21076 | 1.770312 |
| 1.22035 | 1.770157 |
| 1.23002 | 1.770003 |
| 1.23977 | 1.769848 |
| 1.2496 | 1.769692 |
| 1.2595 | 1.769537 |
| 1.26948 | 1.769381 |
| 1.27955 | 1.769224 |
| 1.28969 | 1.769067 |
| 1.29991 | 1.768909 |
| 1.31021 | 1.76875 |
| 1.3206 | 1.768591 |
| 1.33106 | 1.768431 |
| 1.34161 | 1.768271 |
| 1.35225 | 1.76811 |
| 1.36296 | 1.767948 |
| 1.37377 | 1.767785 |
| 1.38465 | 1.767621 |
| 1.39563 | 1.767456 |
| 1.40669 | 1.76729 |
| 1.41784 | 1.767123 |
| 1.42908 | 1.766955 |
| 1.4404 | 1.766786 |
| 1.45182 | 1.766616 |
| 1.46332 | 1.766445 |
| 1.47492 | 1.766272 |
| 1.48661 | 1.766098 |
| 1.49839 | 1.765923 |
| 1.51027 | 1.765746 |
| 1.52224 | 1.765568 |
| 1.53431 | 1.765388 |
| 1.54647 | 1.765207 |
| 1.55872 | 1.765024 |
| 1.57108 | 1.76484 |
| 1.58353 | 1.764654 |
| 1.59608 | 1.764466 |
| 1.60873 | 1.764277 |
| 1.62148 | 1.764085 |
| 1.63433 | 1.763892 |
| 1.64728 | 1.763697 |
| 1.66034 | 1.7635 |
| 1.6735 | 1.763301 |
| 1.68676 | 1.763099 |
| 1.70013 | 1.762896 |
| 1.71361 | 1.762691 |
| 1.72719 | 1.762483 |
| 1.74088 | 1.762273 |
| 1.75467 | 1.76206 |
| 1.76858 | 1.761846 |
| 1.7826 | 1.761628 |
| 1.79673 | 1.761409 |
| 1.81097 | 1.761186 |
| 1.82532 | 1.760961 |
| 1.83979 | 1.760734 |
| 1.85437 | 1.760503 |
| 1.86907 | 1.76027 |
| 1.88388 | 1.760034 |
| 1.89881 | 1.759795 |
| 1.91386 | 1.759553 |
| 1.92903 | 1.759307 |
| 1.94432 | 1.759059 |
| 1.95973 | 1.758808 |
| 1.97526 | 1.758553 |
| 1.99092 | 1.758295 |
| 2.00669 | 1.758033 |
| 2.0226 | 1.757768 |
| 2.03863 | 1.757499 |
| 2.05479 | 1.757227 |
| 2.07107 | 1.756951 |
| 2.08749 | 1.756672 |
| 2.10403 | 1.756388 |
| 2.12071 | 1.756101 |
| 2.13752 | 1.755809 |
| 2.15446 | 1.755513 |
| 2.17153 | 1.755214 |
| 2.18874 | 1.75491 |
| 2.20609 | 1.754601 |
| 2.22358 | 1.754289 |
| 2.2412 | 1.753971 |
| 2.25896 | 1.753649 |
| 2.27687 | 1.753323 |
| 2.29491 | 1.752991 |
| 2.3131 | 1.752655 |
| 2.33143 | 1.752314 |
| 2.34991 | 1.751968 |
| 2.36854 | 1.751616 |
| 2.38731 | 1.75126 |
| 2.40623 | 1.750898 |
| 2.4253 | 1.75053 |
| 2.44452 | 1.750157 |
| 2.4639 | 1.749778 |
| 2.48343 | 1.749394 |
| 2.50311 | 1.749003 |
| 2.52295 | 1.748607 |
| 2.54294 | 1.748204 |
| 2.5631 | 1.747796 |
| 2.58341 | 1.747381 |
| 2.60389 | 1.746959 |
| 2.62453 | 1.746531 |
| 2.64533 | 1.746096 |
| 2.66629 | 1.745654 |
| 2.68742 | 1.745206 |
| 2.70872 | 1.74475 |
| 2.73019 | 1.744287 |
| 2.75183 | 1.743817 |
| 2.77364 | 1.743339 |
| 2.79562 | 1.742853 |
| 2.81778 | 1.74236 |
| 2.84011 | 1.741859 |
| 2.86262 | 1.74135 |
| 2.88531 | 1.740832 |
| 2.90818 | 1.740306 |
| 2.93123 | 1.739772 |
| 2.95446 | 1.739229 |
| 2.97788 | 1.738676 |
| 3.00148 | 1.738115 |
| 3.02527 | 1.737545 |
| 3.04925 | 1.736965 |
| 3.07341 | 1.736376 |
| 3.09777 | 1.735777 |
| 3.12232 | 1.735168 |
| 3.14707 | 1.734549 |
| 3.17201 | 1.73392 |
| 3.19715 | 1.73328 |
| 3.22249 | 1.732629 |
| 3.24803 | 1.731968 |
| 3.27378 | 1.731295 |
| 3.29972 | 1.730612 |
| 3.32588 | 1.729916 |
| 3.35224 | 1.729209 |
| 3.37881 | 1.72849 |
| 3.40558 | 1.727758 |
| 3.43258 | 1.727014 |
| 3.45978 | 1.726258 |
| 3.4872 | 1.725488 |
| 3.51484 | 1.724706 |
| 3.5427 | 1.723909 |
| 3.57078 | 1.7231 |
| 3.59908 | 1.722276 |
| 3.6276 | 1.721438 |
| 3.65635 | 1.720585 |
| 3.68533 | 1.719718 |
| 3.71454 | 1.718835 |
| 3.74398 | 1.717937 |
| 3.77366 | 1.717024 |
| 3.80357 | 1.716094 |
| 3.83371 | 1.715148 |
| 3.8641 | 1.714185 |
| 3.89472 | 1.713206 |
| 3.92559 | 1.712209 |
| 3.9567 | 1.711194 |
| 3.98806 | 1.710161 |
| 4.01967 | 1.70911 |
| 4.05153 | 1.70804 |
| 4.08364 | 1.706951 |
| 4.11601 | 1.705842 |
| 4.14863 | 1.704714 |
| 4.18151 | 1.703565 |
| 4.21465 | 1.702395 |
| 4.24805 | 1.701204 |
| 4.28172 | 1.699991 |
| 4.31566 | 1.698757 |
| 4.34986 | 1.697499 |
| 4.38434 | 1.696219 |
| 4.41909 | 1.694915 |
| 4.45411 | 1.693587 |
| 4.48941 | 1.692235 |
| 4.525 | 1.690857 |
| 4.56086 | 1.689454 |
| 4.59701 | 1.688025 |
| 4.63344 | 1.686569 |
| 4.67016 | 1.685086 |
| 4.70718 | 1.683575 |
| 4.74449 | 1.682035 |
| 4.78209 | 1.680466 |
| 4.81999 | 1.678868 |
| 4.85819 | 1.677239 |
| 4.8967 | 1.675578 |
| 4.93551 | 1.673886 |
| 4.97462 | 1.672162 |
| 5.01405 | 1.670404 |
| 5.05379 | 1.668613 |
| 5.09385 | 1.666786 |
| 5.13422 | 1.664924 |
| 5.17491 | 1.663025 |
| 5.21593 | 1.661089 |
| 5.25727 | 1.659115 |
| 5.29893 | 1.657102 |
| 5.34093 | 1.65505 |
| 5.38326 | 1.652956 |
| 5.42593 | 1.65082 |
| 5.46893 | 1.648641 |
| 5.51228 | 1.646419 |
| 5.55597 | 1.644151 |
| 5.6 | 1.641837 |
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
- —
Nitrogen content: 6.69 at.%