Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.17502
Extinction coefficient k: 0

Permittivity ε₁: 4.73072
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.377308 µm⁻¹

Group index n_g: 2.39673
Group velocity dispersion: 787.844 fs²/mm

Dispersion parameter D: -4298.11 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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

# ZrO2 (Zirconium dioxide, Zirconia): Bodurov et al. 2016: Nanoparticles; n 0.405–0.635 µm
zro2 = ls.fetch_refractiveindex("main", "ZrO2", "Bodurov", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(zro2.range_nm)  # (405, 635) nm
eps = zro2.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_b9c60da495d3/lightsmith"
zro2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(zro2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (zro2/bodurov-2016).

# ... load zro2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=zro2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=405, stop_nm=635, 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_b9c60da495d3/lightsmith?model=drude_lorentz"
zro2_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

Materials guide Open a sphere of it in Studio Quick start Ask the community

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 µm

n^{2} - 1 = \frac{3.3037 λ^{2}}{λ^{2} - {0.1987971}^{2}}

Valid from 0.405 to 0.635 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	3.3037
C3	0.1987971

Comments and conditions

<100 nm diameter nanoparticles dispersed in water. Concentration 10 wt.%. 24 °C. Refractive index of nanoparticles calculated using Bruggeman's effective medium approximation.

Conditions

temperature: 297 K

References

I. Bodurov, I. Vlaeva, A. Viraneva, T. Yovcheva, S. Sainov. Modified design of a laser refractometer. Nanoscience & Nanotechnology 16, 31-33 (2016)

Cite

I. Bodurov, I. Vlaeva, A. Viraneva, T. Yovcheva, S. Sainov. Modified design of a laser refractometer. Nanoscience & Nanotechnology 16, 31-33 (2016); 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

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

ZrO2 (Zirconium dioxide, Zirconia), Bodurov et al. 2016: Nanoparticles; n 0.405–0.635 µm: n and k versus wavelength
λ (µm)	n
0.405	2.313517
0.405457	2.312845
0.405914	2.312175
0.406372	2.311508
0.40683	2.310843
0.407289	2.31018
0.407748	2.309519
0.408208	2.308861
0.408669	2.308204
0.409129	2.30755
0.409591	2.306899
0.410053	2.306249
0.410515	2.305602
0.410978	2.304956
0.411442	2.304313
0.411906	2.303672
0.41237	2.303033
0.412835	2.302397
0.413301	2.301762
0.413767	2.301129
0.414234	2.300499
0.414701	2.299871
0.415169	2.299245
0.415637	2.298621
0.416106	2.297998
0.416575	2.297379
0.417045	2.296761
0.417515	2.296145
0.417986	2.295531
0.418457	2.294919
0.418929	2.294309
0.419402	2.293701
0.419875	2.293096
0.420348	2.292492
0.420822	2.29189
0.421297	2.29129
0.421772	2.290692
0.422248	2.290096
0.422724	2.289502
0.423201	2.28891
0.423678	2.28832
0.424156	2.287732
0.424634	2.287146
0.425113	2.286561
0.425592	2.285979
0.426072	2.285398
0.426553	2.28482
0.427034	2.284243
0.427516	2.283668
0.427998	2.283095
0.42848	2.282524
0.428964	2.281955
0.429448	2.281387
0.429932	2.280821
0.430417	2.280258
0.430902	2.279695
0.431388	2.279135
0.431875	2.278577
0.432362	2.27802
0.432849	2.277465
0.433337	2.276912
0.433826	2.276361
0.434315	2.275812
0.434805	2.275264
0.435296	2.274718
0.435787	2.274174
0.436278	2.273631
0.43677	2.27309
0.437263	2.272551
0.437756	2.272014
0.43825	2.271478
0.438744	2.270944
0.439239	2.270412
0.439734	2.269882
0.44023	2.269353
0.440726	2.268826
0.441223	2.2683
0.441721	2.267776
0.442219	2.267254
0.442718	2.266734
0.443217	2.266215
0.443717	2.265698
0.444218	2.265182
0.444719	2.264668
0.44522	2.264156
0.445722	2.263645
0.446225	2.263136
0.446728	2.262628
0.447232	2.262122
0.447736	2.261618
0.448241	2.261115
0.448747	2.260614
0.449253	2.260114
0.44976	2.259616
0.450267	2.25912
0.450775	2.258625
0.451283	2.258131
0.451792	2.257639
0.452302	2.257149
0.452812	2.25666
0.453322	2.256173
0.453834	2.255687
0.454345	2.255203
0.454858	2.25472
0.455371	2.254239
0.455884	2.253759
0.456398	2.253281
0.456913	2.252804
0.457429	2.252328
0.457944	2.251854
0.458461	2.251382
0.458978	2.250911
0.459496	2.250442
0.460014	2.249973
0.460533	2.249507
0.461052	2.249042
0.461572	2.248578
0.462093	2.248116
0.462614	2.247655
0.463135	2.247195
0.463658	2.246737
0.464181	2.24628
0.464704	2.245825
0.465228	2.245371
0.465753	2.244918
0.466278	2.244467
0.466804	2.244018
0.467331	2.243569
0.467858	2.243122
0.468385	2.242676
0.468913	2.242232
0.469442	2.241789
0.469972	2.241348
0.470502	2.240907
0.471032	2.240468
0.471564	2.240031
0.472095	2.239594
0.472628	2.239159
0.473161	2.238726
0.473695	2.238293
0.474229	2.237862
0.474764	2.237433
0.475299	2.237004
0.475835	2.236577
0.476372	2.236151
0.476909	2.235727
0.477447	2.235303
0.477985	2.234881
0.478524	2.234461
0.479064	2.234041
0.479604	2.233623
0.480145	2.233206
0.480687	2.23279
0.481229	2.232376
0.481772	2.231962
0.482315	2.23155
0.482859	2.23114
0.483403	2.23073
0.483949	2.230322
0.484494	2.229915
0.485041	2.229509
0.485588	2.229104
0.486136	2.2287
0.486684	2.228298
0.487233	2.227897
0.487782	2.227497
0.488332	2.227098
0.488883	2.226701
0.489434	2.226305
0.489986	2.225909
0.490539	2.225515
0.491092	2.225122
0.491646	2.224731
0.492201	2.22434
0.492756	2.223951
0.493311	2.223563
0.493868	2.223176
0.494425	2.22279
0.494982	2.222405
0.495541	2.222021
0.496099	2.221639
0.496659	2.221257
0.497219	2.220877
0.49778	2.220498
0.498341	2.22012
0.498903	2.219743
0.499466	2.219367
0.500029	2.218992
0.500593	2.218619
0.501158	2.218246
0.501723	2.217875
0.502289	2.217504
0.502855	2.217135
0.503422	2.216767
0.50399	2.216399
0.504559	2.216033
0.505128	2.215668
0.505697	2.215304
0.506268	2.214942
0.506839	2.21458
0.50741	2.214219
0.507982	2.213859
0.508555	2.213501
0.509129	2.213143
0.509703	2.212786
0.510278	2.212431
0.510853	2.212076
0.51143	2.211723
0.512006	2.21137
0.512584	2.211019
0.513162	2.210668
0.513741	2.210319
0.51432	2.20997
0.5149	2.209623
0.515481	2.209276
0.516062	2.208931
0.516644	2.208587
0.517227	2.208243
0.51781	2.207901
0.518394	2.207559
0.518979	2.207219
0.519564	2.206879
0.52015	2.206541
0.520737	2.206203
0.521324	2.205866
0.521912	2.205531
0.5225	2.205196
0.52309	2.204862
0.52368	2.20453
0.52427	2.204198
0.524862	2.203867
0.525453	2.203537
0.526046	2.203208
0.526639	2.20288
0.527233	2.202553
0.527828	2.202227
0.528423	2.201901
0.529019	2.201577
0.529616	2.201254
0.530213	2.200931
0.530811	2.20061
0.53141	2.200289
0.532009	2.199969
0.532609	2.19965
0.53321	2.199332
0.533811	2.199015
0.534413	2.198699
0.535016	2.198384
0.535619	2.19807
0.536223	2.197756
0.536828	2.197444
0.537433	2.197132
0.53804	2.196821
0.538646	2.196511
0.539254	2.196202
0.539862	2.195894
0.540471	2.195587
0.54108	2.19528
0.541691	2.194975
0.542302	2.19467
0.542913	2.194366
0.543525	2.194063
0.544138	2.193761
0.544752	2.19346
0.545366	2.193159
0.545982	2.192859
0.546597	2.192561
0.547214	2.192263
0.547831	2.191966
0.548449	2.191669
0.549067	2.191374
0.549687	2.191079
0.550306	2.190785
0.550927	2.190492
0.551548	2.1902
0.55217	2.189909
0.552793	2.189618
0.553417	2.189329
0.554041	2.18904
0.554666	2.188752
0.555291	2.188464
0.555917	2.188178
0.556544	2.187892
0.557172	2.187607
0.5578	2.187323
0.55843	2.18704
0.559059	2.186757
0.55969	2.186475
0.560321	2.186194
0.560953	2.185914
0.561586	2.185635
0.562219	2.185356
0.562853	2.185078
0.563488	2.184801
0.564123	2.184524
0.56476	2.184249
0.565396	2.183974
0.566034	2.1837
0.566673	2.183427
0.567312	2.183154
0.567951	2.182882
0.568592	2.182611
0.569233	2.182341
0.569875	2.182071
0.570518	2.181802
0.571161	2.181534
0.571805	2.181267
0.57245	2.181
0.573096	2.180734
0.573742	2.180469
0.574389	2.180205
0.575037	2.179941
0.575686	2.179678
0.576335	2.179416
0.576985	2.179154
0.577636	2.178894
0.578287	2.178633
0.578939	2.178374
0.579592	2.178115
0.580246	2.177857
0.5809	2.1776
0.581555	2.177343
0.582211	2.177088
0.582868	2.176832
0.583525	2.176578
0.584183	2.176324
0.584842	2.176071
0.585502	2.175819
0.586162	2.175567
0.586823	2.175316
0.587485	2.175065
0.588148	2.174816
0.588811	2.174567
0.589475	2.174318
0.59014	2.174071
0.590805	2.173824
0.591472	2.173578
0.592139	2.173332
0.592807	2.173087
0.593475	2.172843
0.594144	2.172599
0.594814	2.172356
0.595485	2.172114
0.596157	2.171872
0.596829	2.171631
0.597502	2.171391
0.598176	2.171151
0.598851	2.170912
0.599526	2.170673
0.600202	2.170436
0.600879	2.170198
0.601557	2.169962
0.602235	2.169726
0.602915	2.169491
0.603595	2.169256
0.604275	2.169022
0.604957	2.168789
0.605639	2.168556
0.606322	2.168324
0.607006	2.168093
0.60769	2.167862
0.608376	2.167632
0.609062	2.167402
0.609749	2.167173
0.610437	2.166945
0.611125	2.166717
0.611814	2.16649
0.612504	2.166263
0.613195	2.166037
0.613887	2.165812
0.614579	2.165587
0.615272	2.165363
0.615966	2.16514
0.616661	2.164917
0.617356	2.164694
0.618052	2.164473
0.618749	2.164251
0.619447	2.164031
0.620146	2.163811
0.620845	2.163592
0.621545	2.163373
0.622246	2.163155
0.622948	2.162937
0.623651	2.16272
0.624354	2.162503
0.625058	2.162287
0.625763	2.162072
0.626469	2.161857
0.627175	2.161643
0.627883	2.16143
0.628591	2.161216
0.6293	2.161004
0.630009	2.160792
0.63072	2.160581
0.631431	2.16037
0.632143	2.16016
0.632856	2.15995
0.63357	2.159741
0.634285	2.159532
0.635	2.159324

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Plot