Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.91031
Extinction coefficient k: 0

Permittivity ε₁: 8.46992
Permittivity ε₂: 0

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

Abbe number V_d: 9.2218
Chromatic dispersion dn/dλ: -0.9848 µm⁻¹

Group index n_g: 3.48898
Group velocity dispersion: 2464.67 fs²/mm

Dispersion parameter D: -13446.1 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): Devore 1951: n(e) 0.43–1.53 µm
tio2 = ls.fetch_refractiveindex("main", "TiO2", "Devore-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tio2.range_nm)  # (430, 1530) 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_490c8f735952/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/devore-1951-e).

# ... 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=430, 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"]).

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

RefractiveIndex.INFO (formula 4), λ in µm

n^{2} = 7.197 + \frac{0.3322 λ^{0.0}}{λ^{2} - {0.0843}^{1.0}}

Valid from 0.43 to 1.53 µm.

Coefficients as stored

C_i	Value
C1	7.197
C2	0.3322
C3	0.0
C4	0.0843
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	1.0

Comments and conditions

Extraordinary ray (e); Room temperature

Conditions

direction: e

References

J. R. Devore. Refractive indices of rutile and sphalerite. J. Opt. Soc. Am. 41, 416-419 (1951)

doi:10.1364/josa.41.000416 Refractive Indices of Rutile and Sphalerite, Journal of the Optical Society of America (1951)

Cite

J. R. DeVore. Refractive Indices of Rutile and Sphalerite. Journal of the Optical Society of America, 41, 416 (1951), doi:10.1364/josa.41.000416; 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), Devore 1951: n(e) 0.43–1.53 µm: n and k versus wavelength
λ (µm)	n
0.43	3.240245
0.43137	3.234331
0.432744	3.228506
0.434123	3.222768
0.435506	3.217115
0.436894	3.211544
0.438286	3.206055
0.439682	3.200645
0.441083	3.195314
0.442489	3.190059
0.443898	3.184879
0.445313	3.179772
0.446732	3.174737
0.448155	3.169772
0.449583	3.164877
0.451015	3.160049
0.452452	3.155288
0.453894	3.150591
0.45534	3.145959
0.456791	3.141389
0.458246	3.136881
0.459706	3.132433
0.461171	3.128045
0.46264	3.123714
0.464114	3.11944
0.465593	3.115223
0.467076	3.11106
0.468564	3.106951
0.470057	3.102895
0.471555	3.098892
0.473057	3.094939
0.474565	3.091037
0.476077	3.087184
0.477593	3.083379
0.479115	3.079622
0.480642	3.075912
0.482173	3.072248
0.483709	3.068629
0.48525	3.065054
0.486796	3.061523
0.488347	3.058035
0.489903	3.05459
0.491464	3.051185
0.49303	3.047822
0.494601	3.044499
0.496177	3.041216
0.497758	3.037971
0.499344	3.034765
0.500935	3.031596
0.502531	3.028464
0.504132	3.025369
0.505738	3.02231
0.507349	3.019286
0.508966	3.016296
0.510587	3.013341
0.512214	3.01042
0.513846	3.007532
0.515483	3.004676
0.517126	3.001853
0.518773	2.999061
0.520426	2.996301
0.522084	2.993571
0.523748	2.990872
0.525416	2.988202
0.52709	2.985562
0.52877	2.982951
0.530455	2.980368
0.532145	2.977813
0.53384	2.975286
0.535541	2.972787
0.537247	2.970314
0.538959	2.967868
0.540676	2.965448
0.542399	2.963053
0.544127	2.960684
0.545861	2.958341
0.5476	2.956021
0.549345	2.953727
0.551095	2.951456
0.552851	2.949209
0.554612	2.946985
0.556379	2.944784
0.558152	2.942606
0.55993	2.940451
0.561714	2.938317
0.563504	2.936206
0.565299	2.934116
0.5671	2.932047
0.568907	2.929999
0.57072	2.927972
0.572538	2.925965
0.574362	2.923978
0.576192	2.922012
0.578028	2.920064
0.57987	2.918137
0.581717	2.916228
0.583571	2.914338
0.58543	2.912467
0.587295	2.910614
0.589167	2.908779
0.591044	2.906962
0.592927	2.905163
0.594816	2.903382
0.596711	2.901617
0.598612	2.89987
0.60052	2.89814
0.602433	2.896426
0.604352	2.894728
0.606278	2.893047
0.608209	2.891382
0.610147	2.889732
0.612091	2.888099
0.614041	2.88648
0.615998	2.884877
0.617961	2.883289
0.619929	2.881716
0.621905	2.880158
0.623886	2.878614
0.625874	2.877084
0.627868	2.875569
0.629868	2.874068
0.631875	2.87258
0.633888	2.871106
0.635908	2.869646
0.637934	2.868199
0.639967	2.866766
0.642006	2.865345
0.644051	2.863937
0.646103	2.862543
0.648162	2.86116
0.650227	2.859791
0.652299	2.858433
0.654377	2.857088
0.656462	2.855755
0.658553	2.854434
0.660652	2.853125
0.662756	2.851827
0.664868	2.850541
0.666986	2.849266
0.669112	2.848003
0.671243	2.84675
0.673382	2.845509
0.675528	2.844279
0.67768	2.843059
0.679839	2.84185
0.682005	2.840652
0.684178	2.839464
0.686358	2.838287
0.688545	2.837119
0.690738	2.835962
0.692939	2.834815
0.695147	2.833678
0.697362	2.83255
0.699584	2.831432
0.701813	2.830324
0.704049	2.829226
0.706292	2.828136
0.708542	2.827056
0.7108	2.825985
0.713064	2.824924
0.715336	2.823871
0.717615	2.822827
0.719902	2.821792
0.722196	2.820766
0.724497	2.819748
0.726805	2.818739
0.729121	2.817739
0.731444	2.816746
0.733774	2.815762
0.736112	2.814787
0.738457	2.813819
0.74081	2.812859
0.74317	2.811908
0.745538	2.810964
0.747914	2.810028
0.750296	2.8091
0.752687	2.808179
0.755085	2.807266
0.757491	2.806361
0.759904	2.805463
0.762326	2.804572
0.764754	2.803689
0.767191	2.802813
0.769635	2.801943
0.772087	2.801081
0.774547	2.800226
0.777015	2.799378
0.779491	2.798537
0.781974	2.797703
0.784466	2.796875
0.786965	2.796054
0.789473	2.79524
0.791988	2.794432
0.794511	2.79363
0.797043	2.792835
0.799582	2.792047
0.80213	2.791264
0.804685	2.790488
0.807249	2.789718
0.809821	2.788954
0.812401	2.788197
0.81499	2.787445
0.817587	2.786699
0.820191	2.785959
0.822805	2.785225
0.825426	2.784497
0.828056	2.783774
0.830694	2.783057
0.833341	2.782346
0.835996	2.78164
0.83866	2.78094
0.841332	2.780246
0.844012	2.779556
0.846702	2.778872
0.849399	2.778194
0.852105	2.77752
0.85482	2.776852
0.857544	2.776189
0.860276	2.775532
0.863017	2.774879
0.865767	2.774231
0.868525	2.773589
0.871292	2.772951
0.874068	2.772318
0.876853	2.77169
0.879647	2.771067
0.88245	2.770449
0.885261	2.769835
0.888082	2.769226
0.890911	2.768622
0.89375	2.768022
0.896598	2.767427
0.899454	2.766837
0.90232	2.766251
0.905195	2.765669
0.908079	2.765092
0.910972	2.764519
0.913875	2.76395
0.916786	2.763386
0.919707	2.762826
0.922638	2.762271
0.925577	2.761719
0.928526	2.761172
0.931485	2.760628
0.934452	2.760089
0.93743	2.759554
0.940416	2.759023
0.943413	2.758496
0.946419	2.757972
0.949434	2.757453
0.952459	2.756938
0.955494	2.756426
0.958538	2.755918
0.961592	2.755414
0.964656	2.754914
0.967729	2.754417
0.970812	2.753924
0.973906	2.753435
0.977009	2.75295
0.980121	2.752468
0.983244	2.751989
0.986377	2.751514
0.98952	2.751043
0.992672	2.750575
0.995835	2.75011
0.999008	2.749649
1.00219	2.749191
1.00538	2.748737
1.00859	2.748286
1.0118	2.747838
1.01502	2.747394
1.01826	2.746953
1.0215	2.746515
1.02476	2.74608
1.02802	2.745648
1.0313	2.74522
1.03458	2.744794
1.03788	2.744372
1.04119	2.743953
1.0445	2.743537
1.04783	2.743123
1.05117	2.742713
1.05452	2.742306
1.05788	2.741902
1.06125	2.7415
1.06463	2.741102
1.06802	2.740707
1.07143	2.740314
1.07484	2.739924
1.07826	2.739537
1.0817	2.739153
1.08515	2.738771
1.0886	2.738392
1.09207	2.738016
1.09555	2.737643
1.09904	2.737272
1.10254	2.736904
1.10606	2.736539
1.10958	2.736176
1.11312	2.735816
1.11666	2.735458
1.12022	2.735103
1.12379	2.73475
1.12737	2.7344
1.13096	2.734053
1.13456	2.733708
1.13818	2.733365
1.14181	2.733025
1.14544	2.732687
1.14909	2.732352
1.15275	2.732019
1.15643	2.731688
1.16011	2.73136
1.16381	2.731033
1.16752	2.73071
1.17124	2.730388
1.17497	2.730069
1.17871	2.729752
1.18247	2.729438
1.18623	2.729125
1.19001	2.728815
1.19381	2.728507
1.19761	2.728201
1.20142	2.727897
1.20525	2.727595
1.20909	2.727296
1.21295	2.726999
1.21681	2.726703
1.22069	2.72641
1.22458	2.726119
1.22848	2.725829
1.23239	2.725542
1.23632	2.725257
1.24026	2.724974
1.24421	2.724693
1.24817	2.724413
1.25215	2.724136
1.25614	2.723861
1.26014	2.723587
1.26416	2.723316
1.26818	2.723046
1.27222	2.722778
1.27628	2.722512
1.28034	2.722248
1.28442	2.721986
1.28852	2.721726
1.29262	2.721467
1.29674	2.72121
1.30087	2.720955
1.30502	2.720702
1.30917	2.72045
1.31335	2.7202
1.31753	2.719952
1.32173	2.719706
1.32594	2.719461
1.33016	2.719218
1.3344	2.718977
1.33865	2.718737
1.34292	2.718499
1.3472	2.718263
1.35149	2.718028
1.35579	2.717795
1.36011	2.717563
1.36445	2.717333
1.3688	2.717105
1.37316	2.716878
1.37753	2.716653
1.38192	2.716429
1.38632	2.716207
1.39074	2.715986
1.39517	2.715767
1.39962	2.715549
1.40408	2.715333
1.40855	2.715119
1.41304	2.714905
1.41754	2.714694
1.42206	2.714483
1.42659	2.714274
1.43113	2.714067
1.43569	2.713861
1.44027	2.713656
1.44485	2.713453
1.44946	2.713251
1.45408	2.71305
1.45871	2.712851
1.46336	2.712653
1.46802	2.712457
1.4727	2.712262
1.47739	2.712068
1.4821	2.711875
1.48682	2.711684
1.49156	2.711494
1.49631	2.711306
1.50107	2.711118
1.50586	2.710932
1.51066	2.710748
1.51547	2.710564
1.5203	2.710382
1.52514	2.710201
1.53	2.710021

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