Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.50884
Extinction coefficient k: 0

Permittivity ε₁: 6.29426
Permittivity ε₂: 0

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

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.471711 µm⁻¹

Group index n_g: 2.78601
Group velocity dispersion: 984.914 fs²/mm

Dispersion parameter D: -5373.23 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

# TiO2 (Titanium dioxide): Bodurov et al. 2016: Nanoparticles; n 0.405–0.635 µm
tio2 = ls.fetch_refractiveindex("main", "TiO2", "Bodurov", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tio2.range_nm)  # (405, 635) nm
eps = tio2.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_1bf3a9a14bbe/lightsmith"
tio2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(tio2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (tio2/bodurov-2016).

# ... load tio2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=tio2)],
    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_1bf3a9a14bbe/lightsmith?model=drude_lorentz"
tio2_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{4.6796 λ^{2}}{λ^{2} - {0.2002148}^{2}}

Valid from 0.405 to 0.635 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	4.6796
C3	0.2002148

Comments and conditions

Titanium dioxide in anatase phase. <35 nm diameter nanoparticles dispersed in water. Concentration 5 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

TiO2 (Titanium dioxide), Bodurov et al. 2016: Nanoparticles; n 0.405–0.635 µm: n and k versus wavelength
λ (µm)	n
0.405	2.682002
0.405457	2.681162
0.405914	2.680324
0.406372	2.67949
0.40683	2.678658
0.407289	2.677829
0.407748	2.677002
0.408208	2.676179
0.408669	2.675358
0.409129	2.67454
0.409591	2.673725
0.410053	2.672913
0.410515	2.672103
0.410978	2.671296
0.411442	2.670492
0.411906	2.66969
0.41237	2.668891
0.412835	2.668095
0.413301	2.667301
0.413767	2.66651
0.414234	2.665722
0.414701	2.664936
0.415169	2.664153
0.415637	2.663372
0.416106	2.662595
0.416575	2.661819
0.417045	2.661046
0.417515	2.660276
0.417986	2.659509
0.418457	2.658743
0.418929	2.657981
0.419402	2.657221
0.419875	2.656463
0.420348	2.655708
0.420822	2.654956
0.421297	2.654205
0.421772	2.653458
0.422248	2.652712
0.422724	2.65197
0.423201	2.651229
0.423678	2.650491
0.424156	2.649756
0.424634	2.649023
0.425113	2.648292
0.425592	2.647564
0.426072	2.646838
0.426553	2.646114
0.427034	2.645393
0.427516	2.644674
0.427998	2.643957
0.42848	2.643243
0.428964	2.642531
0.429448	2.641822
0.429932	2.641114
0.430417	2.640409
0.430902	2.639706
0.431388	2.639006
0.431875	2.638308
0.432362	2.637612
0.432849	2.636918
0.433337	2.636226
0.433826	2.635537
0.434315	2.63485
0.434805	2.634165
0.435296	2.633482
0.435787	2.632802
0.436278	2.632123
0.43677	2.631447
0.437263	2.630773
0.437756	2.630101
0.43825	2.629431
0.438744	2.628764
0.439239	2.628098
0.439734	2.627435
0.44023	2.626774
0.440726	2.626115
0.441223	2.625457
0.441721	2.624802
0.442219	2.62415
0.442718	2.623499
0.443217	2.62285
0.443717	2.622203
0.444218	2.621558
0.444719	2.620916
0.44522	2.620275
0.445722	2.619636
0.446225	2.619
0.446728	2.618365
0.447232	2.617733
0.447736	2.617102
0.448241	2.616473
0.448747	2.615847
0.449253	2.615222
0.44976	2.614599
0.450267	2.613978
0.450775	2.613359
0.451283	2.612742
0.451792	2.612127
0.452302	2.611514
0.452812	2.610903
0.453322	2.610294
0.453834	2.609686
0.454345	2.609081
0.454858	2.608477
0.455371	2.607875
0.455884	2.607275
0.456398	2.606677
0.456913	2.606081
0.457429	2.605487
0.457944	2.604894
0.458461	2.604304
0.458978	2.603715
0.459496	2.603128
0.460014	2.602542
0.460533	2.601959
0.461052	2.601377
0.461572	2.600798
0.462093	2.600219
0.462614	2.599643
0.463135	2.599069
0.463658	2.598496
0.464181	2.597925
0.464704	2.597356
0.465228	2.596788
0.465753	2.596222
0.466278	2.595658
0.466804	2.595096
0.467331	2.594535
0.467858	2.593976
0.468385	2.593419
0.468913	2.592863
0.469442	2.59231
0.469972	2.591757
0.470502	2.591207
0.471032	2.590658
0.471564	2.590111
0.472095	2.589566
0.472628	2.589022
0.473161	2.58848
0.473695	2.587939
0.474229	2.5874
0.474764	2.586863
0.475299	2.586327
0.475835	2.585793
0.476372	2.585261
0.476909	2.58473
0.477447	2.584201
0.477985	2.583673
0.478524	2.583147
0.479064	2.582622
0.479604	2.582099
0.480145	2.581578
0.480687	2.581058
0.481229	2.58054
0.481772	2.580023
0.482315	2.579508
0.482859	2.578995
0.483403	2.578483
0.483949	2.577972
0.484494	2.577463
0.485041	2.576956
0.485588	2.57645
0.486136	2.575945
0.486684	2.575442
0.487233	2.574941
0.487782	2.574441
0.488332	2.573942
0.488883	2.573445
0.489434	2.57295
0.489986	2.572456
0.490539	2.571963
0.491092	2.571472
0.491646	2.570982
0.492201	2.570494
0.492756	2.570007
0.493311	2.569522
0.493868	2.569038
0.494425	2.568555
0.494982	2.568074
0.495541	2.567595
0.496099	2.567116
0.496659	2.566639
0.497219	2.566164
0.49778	2.56569
0.498341	2.565217
0.498903	2.564746
0.499466	2.564276
0.500029	2.563808
0.500593	2.56334
0.501158	2.562875
0.501723	2.56241
0.502289	2.561947
0.502855	2.561486
0.503422	2.561025
0.50399	2.560566
0.504559	2.560108
0.505128	2.559652
0.505697	2.559197
0.506268	2.558743
0.506839	2.558291
0.50741	2.55784
0.507982	2.55739
0.508555	2.556942
0.509129	2.556495
0.509703	2.556049
0.510278	2.555604
0.510853	2.555161
0.51143	2.554719
0.512006	2.554278
0.512584	2.553839
0.513162	2.553401
0.513741	2.552964
0.51432	2.552528
0.5149	2.552094
0.515481	2.551661
0.516062	2.551229
0.516644	2.550798
0.517227	2.550369
0.51781	2.549941
0.518394	2.549514
0.518979	2.549088
0.519564	2.548664
0.52015	2.54824
0.520737	2.547818
0.521324	2.547398
0.521912	2.546978
0.5225	2.546559
0.52309	2.546142
0.52368	2.545726
0.52427	2.545311
0.524862	2.544898
0.525453	2.544485
0.526046	2.544074
0.526639	2.543664
0.527233	2.543255
0.527828	2.542847
0.528423	2.54244
0.529019	2.542035
0.529616	2.541631
0.530213	2.541228
0.530811	2.540826
0.53141	2.540425
0.532009	2.540025
0.532609	2.539626
0.53321	2.539229
0.533811	2.538832
0.534413	2.538437
0.535016	2.538043
0.535619	2.53765
0.536223	2.537258
0.536828	2.536867
0.537433	2.536478
0.53804	2.536089
0.538646	2.535702
0.539254	2.535315
0.539862	2.53493
0.540471	2.534546
0.54108	2.534163
0.541691	2.533781
0.542302	2.5334
0.542913	2.53302
0.543525	2.532641
0.544138	2.532263
0.544752	2.531887
0.545366	2.531511
0.545982	2.531136
0.546597	2.530763
0.547214	2.53039
0.547831	2.530019
0.548449	2.529648
0.549067	2.529279
0.549687	2.528911
0.550306	2.528543
0.550927	2.528177
0.551548	2.527812
0.55217	2.527447
0.552793	2.527084
0.553417	2.526722
0.554041	2.526361
0.554666	2.526001
0.555291	2.525641
0.555917	2.525283
0.556544	2.524926
0.557172	2.52457
0.5578	2.524215
0.55843	2.52386
0.559059	2.523507
0.55969	2.523155
0.560321	2.522803
0.560953	2.522453
0.561586	2.522104
0.562219	2.521755
0.562853	2.521408
0.563488	2.521061
0.564123	2.520716
0.56476	2.520371
0.565396	2.520028
0.566034	2.519685
0.566673	2.519343
0.567312	2.519003
0.567951	2.518663
0.568592	2.518324
0.569233	2.517986
0.569875	2.517649
0.570518	2.517313
0.571161	2.516978
0.571805	2.516643
0.57245	2.51631
0.573096	2.515978
0.573742	2.515646
0.574389	2.515316
0.575037	2.514986
0.575686	2.514657
0.576335	2.514329
0.576985	2.514002
0.577636	2.513676
0.578287	2.513351
0.578939	2.513027
0.579592	2.512703
0.580246	2.512381
0.5809	2.512059
0.581555	2.511738
0.582211	2.511418
0.582868	2.511099
0.583525	2.510781
0.584183	2.510464
0.584842	2.510147
0.585502	2.509832
0.586162	2.509517
0.586823	2.509203
0.587485	2.50889
0.588148	2.508578
0.588811	2.508267
0.589475	2.507956
0.59014	2.507647
0.590805	2.507338
0.591472	2.50703
0.592139	2.506723
0.592807	2.506417
0.593475	2.506111
0.594144	2.505807
0.594814	2.505503
0.595485	2.5052
0.596157	2.504898
0.596829	2.504597
0.597502	2.504296
0.598176	2.503996
0.598851	2.503697
0.599526	2.503399
0.600202	2.503102
0.600879	2.502806
0.601557	2.50251
0.602235	2.502215
0.602915	2.501921
0.603595	2.501628
0.604275	2.501335
0.604957	2.501043
0.605639	2.500752
0.606322	2.500462
0.607006	2.500173
0.60769	2.499884
0.608376	2.499597
0.609062	2.499309
0.609749	2.499023
0.610437	2.498738
0.611125	2.498453
0.611814	2.498169
0.612504	2.497886
0.613195	2.497603
0.613887	2.497322
0.614579	2.497041
0.615272	2.49676
0.615966	2.496481
0.616661	2.496202
0.617356	2.495924
0.618052	2.495647
0.618749	2.495371
0.619447	2.495095
0.620146	2.49482
0.620845	2.494545
0.621545	2.494272
0.622246	2.493999
0.622948	2.493727
0.623651	2.493456
0.624354	2.493185
0.625058	2.492915
0.625763	2.492646
0.626469	2.492377
0.627175	2.49211
0.627883	2.491843
0.628591	2.491576
0.6293	2.491311
0.630009	2.491046
0.63072	2.490781
0.631431	2.490518
0.632143	2.490255
0.632856	2.489993
0.63357	2.489731
0.634285	2.489471
0.635	2.48921

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