Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.45846
Extinction coefficient k: 0

Permittivity ε₁: 2.12711
Permittivity ε₂: 0

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

Abbe number V_d: 67.821
Chromatic dispersion dn/dλ: -0.0352086 µm⁻¹

Group index n_g: 1.47915
Group velocity dispersion: 57.5406 fs²/mm

Dispersion parameter D: -313.914 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

# SiO2 (Silicon dioxide, Silica, Quartz): Malitson 1965: n 0.21–6.7 µm
sio2 = ls.LibraryMaterial(name="SiO2", dataset="Malitson")
print(sio2.range_nm)  # (210, 6700) nm
eps = sio2.eps([633])  # complex permittivity

Ships with the library: works offline and is the library's own default dataset choice.

import lightsmith as ls

# SiO2 (Silicon dioxide, Silica, Quartz): Malitson 1965: n 0.21–6.7 µm
sio2 = ls.fetch_refractiveindex("main", "SiO2", "Malitson", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(sio2.range_nm)  # (210, 6700) nm
eps = sio2.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_b28cb9317453/lightsmith"
sio2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(sio2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (sio2/malitson-1965).

# ... load sio2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=sio2)],
    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_b28cb9317453/lightsmith?model=drude_lorentz"
sio2_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{0.6961663 λ^{2}}{λ^{2} - {0.0684043}^{2}} + \frac{0.4079426 λ^{2}}{λ^{2} - {0.1162414}^{2}} + \frac{0.8974794 λ^{2}}{λ^{2} - {9.896161}^{2}}

Valid from 0.21 to 6.7 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.6961663
C3	0.0684043
C4	0.4079426
C5	0.1162414
C6	0.8974794
C7	9.896161

Comments and conditions

Fused silica, 20 °C

Conditions

temperature: 293 K

References

1) I. H. Malitson. Interspecimen comparison of the refractive index of fused silica. J. Opt. Soc. Am. 55, 1205-1208 (1965)
2) C. Z. Tan. Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy. J. Non-Cryst. Solids 223, 158-163 (1998)
* Sellmeier formula is reported in Ref. 1 for the 0.21–3.71 μm wavelength range. Ref. 2 verifies the validity of the formula up to 6.7 μm.

doi:10.1364/josa.55.001205 Interspecimen Comparison of the Refractive Index of Fused Silica*,†, Journal of the Optical Society of America (1965)
doi:10.1016/s0022-3093(97)00438-9 Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy, Journal of Non-Crystalline Solids (1998)

Cite

I. H. Malitson. Interspecimen Comparison of the Refractive Index of Fused Silica*,†. Journal of the Optical Society of America, 55, 1205 (1965), doi:10.1364/josa.55.001205; C.Z. Tan. Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy. Journal of Non-Crystalline Solids, 223, 158-163 (1998), doi:10.1016/s0022-3093(97)00438-9; 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

SiO2 (Silicon dioxide, Silica, Quartz), Malitson 1965: n 0.21–6.7 µm: n and k versus wavelength
λ (µm)	n
0.21	1.538358
0.21183	1.536396
0.213677	1.534489
0.215539	1.532634
0.217418	1.530829
0.219313	1.529074
0.221225	1.527365
0.223153	1.525701
0.225098	1.52408
0.22706	1.522502
0.229039	1.520965
0.231036	1.519467
0.233049	1.518007
0.235081	1.516583
0.23713	1.515195
0.239197	1.513842
0.241282	1.512521
0.243385	1.511233
0.245506	1.509976
0.247646	1.50875
0.249805	1.507552
0.251982	1.506384
0.254178	1.505242
0.256394	1.504128
0.258629	1.503039
0.260883	1.501976
0.263157	1.500937
0.265451	1.499922
0.267765	1.49893
0.270098	1.49796
0.272453	1.497012
0.274828	1.496086
0.277223	1.49518
0.279639	1.494294
0.282077	1.493427
0.284535	1.49258
0.287016	1.49175
0.289517	1.490939
0.292041	1.490146
0.294586	1.489369
0.297154	1.488609
0.299744	1.487865
0.302357	1.487137
0.304992	1.486424
0.307651	1.485726
0.310332	1.485043
0.313037	1.484374
0.315766	1.483719
0.318518	1.483077
0.321295	1.482449
0.324095	1.481833
0.32692	1.48123
0.32977	1.480639
0.332644	1.48006
0.335543	1.479492
0.338468	1.478936
0.341418	1.478391
0.344394	1.477857
0.347396	1.477334
0.350424	1.47682
0.353478	1.476317
0.35656	1.475824
0.359667	1.47534
0.362802	1.474866
0.365965	1.474401
0.369155	1.473945
0.372372	1.473497
0.375618	1.473058
0.378892	1.472628
0.382195	1.472205
0.385526	1.471791
0.388886	1.471384
0.392276	1.470985
0.395695	1.470594
0.399144	1.47021
0.402623	1.469833
0.406133	1.469463
0.409673	1.469099
0.413244	1.468743
0.416846	1.468393
0.420479	1.468049
0.424144	1.467711
0.427841	1.46738
0.43157	1.467055
0.435332	1.466735
0.439126	1.466421
0.442954	1.466113
0.446815	1.46581
0.450709	1.465512
0.454638	1.46522
0.458601	1.464932
0.462598	1.46465
0.46663	1.464373
0.470698	1.4641
0.4748	1.463832
0.478939	1.463569
0.483114	1.46331
0.487325	1.463055
0.491572	1.462805
0.495857	1.462559
0.500179	1.462317
0.504539	1.462079
0.508936	1.461844
0.513373	1.461614
0.517847	1.461387
0.522361	1.461164
0.526914	1.460945
0.531507	1.460729
0.53614	1.460517
0.540813	1.460308
0.545527	1.460102
0.550282	1.459899
0.555078	1.459699
0.559916	1.459503
0.564797	1.459309
0.56972	1.459119
0.574686	1.458931
0.579695	1.458746
0.584748	1.458563
0.589845	1.458384
0.594986	1.458207
0.600172	1.458032
0.605403	1.45786
0.61068	1.45769
0.616003	1.457523
0.621372	1.457358
0.626789	1.457195
0.632252	1.457034
0.637763	1.456875
0.643322	1.456719
0.648929	1.456564
0.654585	1.456412
0.660291	1.456261
0.666046	1.456112
0.671852	1.455965
0.677708	1.45582
0.683615	1.455676
0.689574	1.455534
0.695584	1.455394
0.701647	1.455255
0.707763	1.455118
0.713932	1.454982
0.720155	1.454848
0.726432	1.454715
0.732764	1.454583
0.739151	1.454453
0.745594	1.454324
0.752093	1.454196
0.758648	1.454069
0.765261	1.453944
0.771931	1.453819
0.778659	1.453696
0.785447	1.453573
0.792293	1.453452
0.799199	1.453331
0.806165	1.453211
0.813192	1.453093
0.82028	1.452975
0.827429	1.452857
0.834642	1.452741
0.841917	1.452625
0.849255	1.45251
0.856658	1.452395
0.864124	1.452281
0.871656	1.452168
0.879254	1.452055
0.886918	1.451943
0.894649	1.451831
0.902447	1.451719
0.910313	1.451608
0.918247	1.451497
0.926251	1.451386
0.934325	1.451276
0.942469	1.451166
0.950684	1.451056
0.95897	1.450946
0.967329	1.450837
0.97576	1.450727
0.984265	1.450618
0.992845	1.450508
1.0015	1.450399
1.01023	1.450289
1.01903	1.450179
1.02792	1.450069
1.03688	1.449959
1.04591	1.449849
1.05503	1.449739
1.06423	1.449628
1.0735	1.449517
1.08286	1.449406
1.0923	1.449294
1.10182	1.449182
1.11142	1.44907
1.12111	1.448957
1.13088	1.448843
1.14074	1.448729
1.15068	1.448614
1.16071	1.448499
1.17083	1.448383
1.18103	1.448266
1.19133	1.448149
1.20171	1.448031
1.21219	1.447912
1.22275	1.447792
1.23341	1.447671
1.24416	1.447549
1.25501	1.447426
1.26595	1.447303
1.27698	1.447178
1.28811	1.447052
1.29934	1.446925
1.31066	1.446797
1.32209	1.446667
1.33361	1.446537
1.34524	1.446405
1.35696	1.446271
1.36879	1.446136
1.38072	1.446
1.39275	1.445863
1.40489	1.445723
1.41714	1.445582
1.42949	1.44544
1.44195	1.445296
1.45452	1.44515
1.4672	1.445002
1.47999	1.444853
1.49289	1.444701
1.5059	1.444548
1.51903	1.444393
1.53227	1.444235
1.54562	1.444076
1.55909	1.443914
1.57268	1.443751
1.58639	1.443585
1.60022	1.443416
1.61417	1.443246
1.62824	1.443072
1.64243	1.442897
1.65675	1.442719
1.67119	1.442538
1.68575	1.442354
1.70045	1.442168
1.71527	1.441979
1.73022	1.441787
1.7453	1.441592
1.76051	1.441394
1.77586	1.441193
1.79134	1.440988
1.80695	1.440781
1.8227	1.44057
1.83859	1.440356
1.85461	1.440138
1.87078	1.439917
1.88709	1.439692
1.90354	1.439463
1.92013	1.439231
1.93686	1.438994
1.95375	1.438754
1.97078	1.43851
1.98795	1.438261
2.00528	1.438008
2.02276	1.437751
2.04039	1.437489
2.05818	1.437223
2.07612	1.436952
2.09421	1.436676
2.11247	1.436395
2.13088	1.43611
2.14945	1.435819
2.16819	1.435523
2.18709	1.435221
2.20615	1.434914
2.22538	1.434602
2.24478	1.434284
2.26434	1.43396
2.28408	1.43363
2.30399	1.433293
2.32407	1.432951
2.34433	1.432602
2.36476	1.432246
2.38537	1.431884
2.40617	1.431515
2.42714	1.431139
2.44829	1.430756
2.46963	1.430365
2.49116	1.429967
2.51287	1.429561
2.53478	1.429147
2.55687	1.428725
2.57916	1.428295
2.60164	1.427856
2.62432	1.427409
2.64719	1.426953
2.67026	1.426487
2.69354	1.426013
2.71702	1.425529
2.7407	1.425035
2.76459	1.424531
2.78869	1.424017
2.81299	1.423492
2.83751	1.422957
2.86224	1.42241
2.88719	1.421852
2.91236	1.421283
2.93774	1.420702
2.96335	1.420108
2.98918	1.419503
3.01523	1.418884
3.04152	1.418252
3.06803	1.417607
3.09477	1.416948
3.12174	1.416275
3.14896	1.415587
3.1764	1.414884
3.20409	1.414166
3.23202	1.413433
3.26019	1.412683
3.28861	1.411916
3.31727	1.411133
3.34618	1.410332
3.37535	1.409513
3.40477	1.408676
3.43445	1.40782
3.46438	1.406944
3.49458	1.406048
3.52504	1.405132
3.55577	1.404194
3.58676	1.403234
3.61802	1.402253
3.64956	1.401248
3.68137	1.400219
3.71346	1.399165
3.74583	1.398087
3.77848	1.396983
3.81141	1.395851
3.84463	1.394692
3.87814	1.393505
3.91195	1.392289
3.94605	1.391042
3.98044	1.389764
4.01514	1.388454
4.05013	1.38711
4.08543	1.385733
4.12105	1.384319
4.15697	1.38287
4.1932	1.381382
4.22975	1.379855
4.26662	1.378288
4.30381	1.376679
4.34132	1.375027
4.37916	1.373329
4.41733	1.371586
4.45583	1.369794
4.49467	1.367952
4.53385	1.366059
4.57337	1.364112
4.61323	1.36211
4.65344	1.360049
4.694	1.357929
4.73492	1.355746
4.77619	1.353499
4.81782	1.351184
4.85981	1.3488
4.90217	1.346342
4.9449	1.343808
4.988	1.341195
5.03148	1.338499
5.07534	1.335718
5.11957	1.332846
5.1642	1.32988
5.20921	1.326816
5.25462	1.32365
5.30042	1.320375
5.34662	1.316989
5.39322	1.313484
5.44023	1.309855
5.48765	1.306097
5.53548	1.302201
5.58373	1.298163
5.6324	1.293973
5.6815	1.289624
5.73102	1.285108
5.78097	1.280414
5.83136	1.275534
5.88219	1.270456
5.93346	1.265168
5.98518	1.259659
6.03735	1.253914
6.08997	1.24792
6.14305	1.241659
6.1966	1.235115
6.25061	1.228269
6.30509	1.221099
6.36005	1.213584
6.41549	1.205699
6.4714	1.197416
6.52781	1.188704
6.58471	1.179532
6.64211	1.16986
6.7	1.159649

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