Optical constants

Refractive index of SiO₂ (Silicon dioxide, Silica, Quartz)

Ghosh 1999: α-Quartz, n(e) 0.198–2.05 µm

Data: formula 2
Range: 0.198–2.053 µm
Optical axis: e
State: crystalline
Licence: CC0-1.0

Uniaxial crystal, axes: oe

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.55338
Extinction coefficient k: 0

Permittivity ε₁: 2.41298
Permittivity ε₂: 0

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

Abbe number V_d: 68.505
Chromatic dispersion dn/dλ: -0.0420792 µm⁻¹

Group index n_g: 1.5781
Group velocity dispersion: 68.7708 fs²/mm

Dispersion parameter D: -375.181 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): Ghosh 1999: α-Quartz, n(e) 0.198–2.05 µm
sio2 = ls.fetch_refractiveindex("main", "SiO2", "Ghosh-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(sio2.range_nm)  # (198, 2053.1) 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_00bb5d7c8bc3/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/ghosh-1999-e).

# ... 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_00bb5d7c8bc3/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 (C in µm²) (formula 2), λ in µm

n^{2} - 1 = 0.28851804 + \frac{1.09509924 λ^{2}}{λ^{2} - 0.0102101864} + \frac{1.15662475 λ^{2}}{λ^{2} - 100.0}

Valid from 0.198 to 2.0531 µm.

Coefficients as stored

C_i	Value
C1	0.28851804
C2	1.09509924
C3	0.0102101864
C4	1.15662475
C5	100.0

Comments and conditions

Extraordinary ray (e). Room temperature.

Conditions

direction: e

References

G. Ghosh. Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals. Opt. Commun. 163, 95-102 (1999)

doi:10.1016/s0030-4018(99)00091-7 Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals, Optics Communications (1999)

Cite

Gorachand Ghosh. Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals. Optics Communications, 163, 95-102 (1999), doi:10.1016/s0030-4018(99)00091-7; 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), Ghosh 1999: α-Quartz, n(e) 0.198–2.05 µm: n and k versus wavelength
λ (µm)	n
0.198	1.663972
0.199164	1.662151
0.200335	1.660363
0.201513	1.658609
0.202697	1.656886
0.203889	1.655196
0.205088	1.653535
0.206293	1.651905
0.207506	1.650304
0.208726	1.648732
0.209953	1.647187
0.211187	1.64567
0.212429	1.64418
0.213678	1.642715
0.214934	1.641276
0.216198	1.639862
0.217469	1.638472
0.218747	1.637107
0.220033	1.635764
0.221327	1.634444
0.222628	1.633147
0.223937	1.631871
0.225253	1.630617
0.226578	1.629384
0.22791	1.628171
0.229249	1.626978
0.230597	1.625805
0.231953	1.624651
0.233317	1.623516
0.234688	1.622399
0.236068	1.621301
0.237456	1.62022
0.238852	1.619156
0.240256	1.61811
0.241668	1.61708
0.243089	1.616066
0.244518	1.615069
0.245956	1.614087
0.247402	1.613121
0.248856	1.612169
0.250319	1.611233
0.251791	1.610311
0.253271	1.609403
0.25476	1.60851
0.256258	1.60763
0.257764	1.606763
0.25928	1.60591
0.260804	1.605069
0.262337	1.604242
0.26388	1.603426
0.265431	1.602623
0.266991	1.601832
0.268561	1.601053
0.27014	1.600286
0.271728	1.59953
0.273326	1.598785
0.274932	1.598051
0.276549	1.597328
0.278175	1.596615
0.27981	1.595913
0.281455	1.595221
0.28311	1.594539
0.284774	1.593867
0.286448	1.593205
0.288132	1.592552
0.289826	1.591909
0.29153	1.591275
0.293244	1.59065
0.294968	1.590033
0.296702	1.589426
0.298446	1.588827
0.300201	1.588237
0.301966	1.587654
0.303741	1.587081
0.305527	1.586515
0.307323	1.585957
0.309129	1.585406
0.310947	1.584864
0.312775	1.584329
0.314614	1.583801
0.316463	1.583281
0.318324	1.582767
0.320195	1.582261
0.322078	1.581762
0.323971	1.581269
0.325876	1.580784
0.327791	1.580304
0.329719	1.579832
0.331657	1.579365
0.333607	1.578905
0.335568	1.578451
0.337541	1.578004
0.339525	1.577562
0.341521	1.577126
0.343529	1.576696
0.345549	1.576272
0.34758	1.575853
0.349624	1.57544
0.351679	1.575032
0.353746	1.574629
0.355826	1.574232
0.357918	1.57384
0.360022	1.573454
0.362139	1.573072
0.364268	1.572695
0.366409	1.572323
0.368563	1.571956
0.37073	1.571594
0.37291	1.571236
0.375102	1.570883
0.377307	1.570534
0.379525	1.57019
0.381757	1.56985
0.384001	1.569515
0.386258	1.569184
0.388529	1.568857
0.390813	1.568534
0.393111	1.568215
0.395422	1.5679
0.397747	1.56759
0.400085	1.567283
0.402437	1.566979
0.404803	1.56668
0.407183	1.566385
0.409577	1.566093
0.411985	1.565804
0.414407	1.565519
0.416843	1.565238
0.419294	1.56496
0.421759	1.564686
0.424238	1.564415
0.426732	1.564147
0.429241	1.563882
0.431764	1.563621
0.434303	1.563363
0.436856	1.563108
0.439424	1.562856
0.442008	1.562607
0.444606	1.562361
0.44722	1.562117
0.449849	1.561877
0.452494	1.56164
0.455154	1.561405
0.45783	1.561173
0.460521	1.560944
0.463229	1.560718
0.465952	1.560494
0.468691	1.560273
0.471447	1.560054
0.474218	1.559838
0.477006	1.559625
0.479811	1.559413
0.482631	1.559205
0.485469	1.558998
0.488323	1.558794
0.491194	1.558592
0.494081	1.558393
0.496986	1.558196
0.499908	1.558001
0.502847	1.557808
0.505803	1.557617
0.508777	1.557429
0.511768	1.557242
0.514776	1.557058
0.517803	1.556875
0.520847	1.556695
0.523909	1.556516
0.526989	1.55634
0.530087	1.556165
0.533203	1.555992
0.536338	1.555821
0.539491	1.555652
0.542663	1.555485
0.545853	1.555319
0.549062	1.555156
0.55229	1.554993
0.555537	1.554833
0.558803	1.554674
0.562088	1.554517
0.565393	1.554361
0.568717	1.554207
0.57206	1.554055
0.575423	1.553904
0.578806	1.553755
0.582209	1.553607
0.585632	1.55346
0.589075	1.553315
0.592538	1.553172
0.596021	1.553029
0.599525	1.552888
0.60305	1.552749
0.606595	1.552611
0.610161	1.552474
0.613748	1.552338
0.617357	1.552204
0.620986	1.552071
0.624637	1.551939
0.628309	1.551808
0.632003	1.551679
0.635718	1.55155
0.639456	1.551423
0.643215	1.551297
0.646997	1.551172
0.6508	1.551048
0.654626	1.550925
0.658475	1.550803
0.662346	1.550682
0.66624	1.550562
0.670157	1.550443
0.674096	1.550326
0.678059	1.550209
0.682046	1.550093
0.686055	1.549977
0.690089	1.549863
0.694146	1.54975
0.698227	1.549637
0.702331	1.549526
0.70646	1.549415
0.710614	1.549305
0.714791	1.549196
0.718994	1.549087
0.723221	1.54898
0.727472	1.548873
0.731749	1.548767
0.736051	1.548661
0.740378	1.548556
0.744731	1.548452
0.749109	1.548349
0.753513	1.548246
0.757943	1.548144
0.762399	1.548042
0.766881	1.547942
0.77139	1.547841
0.775925	1.547741
0.780486	1.547642
0.785075	1.547544
0.78969	1.547445
0.794333	1.547348
0.799002	1.547251
0.8037	1.547154
0.808425	1.547058
0.813177	1.546962
0.817958	1.546867
0.822767	1.546772
0.827604	1.546678
0.832469	1.546584
0.837363	1.54649
0.842286	1.546397
0.847238	1.546304
0.852219	1.546212
0.857229	1.546119
0.862269	1.546028
0.867338	1.545936
0.872437	1.545845
0.877566	1.545754
0.882725	1.545663
0.887915	1.545573
0.893135	1.545482
0.898385	1.545392
0.903667	1.545303
0.90898	1.545213
0.914323	1.545124
0.919699	1.545034
0.925106	1.544945
0.930544	1.544856
0.936015	1.544768
0.941518	1.544679
0.947053	1.54459
0.95262	1.544502
0.958221	1.544414
0.963854	1.544325
0.969521	1.544237
0.975221	1.544149
0.980954	1.544061
0.986721	1.543973
0.992522	1.543884
0.998357	1.543796
1.00423	1.543708
1.01013	1.54362
1.01607	1.543532
1.02204	1.543443
1.02805	1.543355
1.03409	1.543267
1.04017	1.543178
1.04629	1.54309
1.05244	1.543001
1.05863	1.542912
1.06485	1.542823
1.07111	1.542734
1.07741	1.542644
1.08374	1.542555
1.09011	1.542465
1.09652	1.542375
1.10297	1.542285
1.10945	1.542194
1.11598	1.542103
1.12254	1.542013
1.12914	1.541921
1.13577	1.54183
1.14245	1.541738
1.14917	1.541646
1.15592	1.541553
1.16272	1.54146
1.16955	1.541367
1.17643	1.541274
1.18335	1.54118
1.1903	1.541085
1.1973	1.54099
1.20434	1.540895
1.21142	1.540799
1.21854	1.540703
1.22571	1.540607
1.23291	1.54051
1.24016	1.540412
1.24745	1.540314
1.25478	1.540215
1.26216	1.540116
1.26958	1.540016
1.27705	1.539916
1.28455	1.539815
1.2921	1.539713
1.2997	1.539611
1.30734	1.539509
1.31503	1.539405
1.32276	1.539301
1.33054	1.539196
1.33836	1.539091
1.34623	1.538984
1.35414	1.538877
1.3621	1.53877
1.37011	1.538661
1.37816	1.538552
1.38627	1.538442
1.39442	1.538331
1.40261	1.538219
1.41086	1.538107
1.41915	1.537994
1.4275	1.537879
1.43589	1.537764
1.44433	1.537648
1.45282	1.537531
1.46136	1.537413
1.46995	1.537294
1.4786	1.537174
1.48729	1.537053
1.49603	1.536931
1.50483	1.536808
1.51367	1.536684
1.52257	1.536559
1.53152	1.536432
1.54053	1.536305
1.54958	1.536176
1.55869	1.536046
1.56786	1.535915
1.57708	1.535783
1.58635	1.53565
1.59567	1.535515
1.60505	1.535379
1.61449	1.535242
1.62398	1.535104
1.63353	1.534964
1.64313	1.534823
1.65279	1.53468
1.66251	1.534536
1.67228	1.534391
1.68211	1.534244
1.692	1.534095
1.70195	1.533945
1.71196	1.533794
1.72202	1.533641
1.73214	1.533486
1.74233	1.53333
1.75257	1.533173
1.76287	1.533013
1.77324	1.532852
1.78366	1.532689
1.79415	1.532525
1.8047	1.532358
1.81531	1.53219
1.82598	1.53202
1.83671	1.531849
1.84751	1.531675
1.85837	1.5315
1.8693	1.531322
1.88029	1.531143
1.89134	1.530961
1.90246	1.530778
1.91365	1.530592
1.9249	1.530405
1.93621	1.530215
1.94759	1.530023
1.95904	1.529829
1.97056	1.529633
1.98215	1.529434
1.9938	1.529234
2.00552	1.52903
2.01731	1.528825
2.02917	1.528617
2.0411	1.528407
2.0531	1.528194

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: —

SiO₂ (Silicon dioxide, Silica, Quartz): all datasets

Fused silica

Crystal

Thin film

About SiO2 (Silicon dioxide, Silica, Quartz)

Silicon dioxide (SiO₂), commonly known as silica, is found naturally in several crystalline forms, the most notable being quartz. Additionally, when silicon dioxide is manufactured without the crystalline structure, it forms what is known as fused silica. Fused silica is a non-crystalline (or amorphous) form of silicon dioxide and is produced by melting high purity silica at extremely high temperatures. It has superior optical clarity, especially in the ultraviolet (UV) range, and is resistant to thermal shock, making it valuable for many high-end optical applications, including lenses and windows in spacecraft and satellites. SiO₂ is extensively used in electronics as an insulator and serves as a primary ingredient in the production of glass. It's also used in thin-film optics, often as antireflection coatings on optical devices. Beyond its optical applications, silicon dioxide finds use in ceramics, construction, and even as a food additive. Polymorphs:

Alpha quartz (α-quartz, most common)
Beta quartz (β-quartz, only stable at temperatures above 573 °C)
Tridymite
Cristobalite
Coesite
Stishovite
Lechatelierite
Chalcedony

More about SiO2 (Silicon dioxide, Silica, Quartz) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/SiO2/nk/Ghosh-e.yml
ID: ds_00bb5d7c8bc3
API: /v1/datasets/ds_00bb5d7c8bc3

Plot