Optical constants

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

Radhakrishnan 1951: α-Quartz; n(e) 0.18–3 µm

Data: formula 1
Range: 0.18–3 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: 1.55343
Extinction coefficient k: 0

Permittivity ε₁: 2.41313
Permittivity ε₂: 0

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

Abbe number V_d: 68.854
Chromatic dispersion dn/dλ: -0.0418655 µm⁻¹

Group index n_g: 1.57803
Group velocity dispersion: 68.4024 fs²/mm

Dispersion parameter D: -373.172 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): Radhakrishnan 1951: α-Quartz; n(e) 0.18–3 µm
sio2 = ls.fetch_refractiveindex("main", "SiO2", "Radhakrishnan-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(sio2.range_nm)  # (180, 3000) 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_964f8d83c5ff/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/radhakrishnan-1951-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_964f8d83c5ff/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{0.665721 λ^{2}}{λ^{2} - {0.06}^{2}} + \frac{0.503511 λ^{2}}{λ^{2} - {0.106}^{2}} + \frac{0.214792 λ^{2}}{λ^{2} - {0.119}^{2}} + \frac{0.539173 λ^{2}}{λ^{2} - {8.792}^{2}} + \frac{1.807613 λ^{2}}{λ^{2} - {19.7}^{2}}

Valid from 0.18 to 3.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.665721
C3	0.06
C4	0.503511
C5	0.106
C6	0.214792
C7	0.119
C8	0.539173
C9	8.792
C10	1.807613
C11	19.7

Comments and conditions

18 °C

References

1) T. Radhakrishnan. Further studies on the temperature variation of the refractive index of crystals. Proc. Indian Acad. Sci. 31, 22-34 (1951)
2) T. Radhakrishnan. The dispersion, briefringence and optical activity of quartz. Proc. Indian Acad. Sci. 25, 260-265 (1947)

doi:10.1007/bf03172255 Further studies on the temperature variation of the refractive index of crystals, Proceedings of the Indian Academy of Sciences - Section A (1951)
doi:10.1007/bf03171408 The dispersion, briefringence and optical activity of quartz, Proceedings of the Indian Academy of Sciences - Section A (1947)

Cite

T. Radhakrishnan. Further studies on the temperature variation of the refractive index of crystals. Proceedings of the Indian Academy of Sciences - Section A, 33, 22 (1951), doi:10.1007/bf03172255; T. Radhakrishnan. The dispersion, briefringence and optical activity of quartz. Proceedings of the Indian Academy of Sciences - Section A, 25, 260 (1947), doi:10.1007/bf03171408; 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), Radhakrishnan 1951: α-Quartz; n(e) 0.18–3 µm: n and k versus wavelength
λ (µm)	n
0.18	1.703216
0.181274	1.699952
0.182556	1.696779
0.183848	1.693692
0.185149	1.690688
0.186459	1.687765
0.187779	1.684918
0.189107	1.682146
0.190446	1.679445
0.191793	1.676813
0.19315	1.674247
0.194517	1.671746
0.195893	1.669307
0.19728	1.666927
0.198676	1.664605
0.200081	1.662339
0.201497	1.660127
0.202923	1.657967
0.204359	1.655858
0.205805	1.653798
0.207261	1.651785
0.208728	1.649818
0.210205	1.647896
0.211692	1.646017
0.21319	1.64418
0.214699	1.642384
0.216218	1.640627
0.217748	1.638908
0.219289	1.637226
0.22084	1.635581
0.222403	1.633971
0.223977	1.632395
0.225562	1.630852
0.227158	1.629341
0.228765	1.627862
0.230384	1.626413
0.232014	1.624994
0.233656	1.623604
0.235309	1.622242
0.236974	1.620907
0.238651	1.6196
0.24034	1.618318
0.242041	1.617062
0.243753	1.61583
0.245478	1.614622
0.247215	1.613438
0.248964	1.612277
0.250726	1.611139
0.2525	1.610022
0.254287	1.608926
0.256086	1.607851
0.257898	1.606797
0.259723	1.605762
0.261561	1.604747
0.263412	1.60375
0.265276	1.602772
0.267153	1.601812
0.269043	1.60087
0.270947	1.599945
0.272864	1.599037
0.274795	1.598145
0.27674	1.597269
0.278698	1.596409
0.28067	1.595564
0.282656	1.594735
0.284656	1.59392
0.28667	1.593119
0.288699	1.592333
0.290742	1.59156
0.292799	1.590801
0.294871	1.590055
0.296957	1.589322
0.299059	1.588602
0.301175	1.587894
0.303306	1.587198
0.305452	1.586514
0.307614	1.585842
0.30979	1.585181
0.311982	1.584531
0.31419	1.583893
0.316413	1.583265
0.318652	1.582647
0.320907	1.58204
0.323178	1.581443
0.325465	1.580855
0.327768	1.580278
0.330087	1.57971
0.332423	1.579151
0.334775	1.578601
0.337144	1.578061
0.339529	1.577529
0.341932	1.577005
0.344352	1.57649
0.346788	1.575984
0.349242	1.575485
0.351713	1.574995
0.354202	1.574512
0.356708	1.574037
0.359233	1.57357
0.361775	1.57311
0.364334	1.572657
0.366913	1.572211
0.369509	1.571772
0.372123	1.57134
0.374757	1.570915
0.377408	1.570496
0.380079	1.570084
0.382769	1.569679
0.385477	1.569279
0.388205	1.568886
0.390952	1.568498
0.393718	1.568117
0.396504	1.567741
0.39931	1.567371
0.402135	1.567006
0.404981	1.566647
0.407846	1.566294
0.410732	1.565945
0.413639	1.565602
0.416566	1.565264
0.419513	1.564931
0.422482	1.564603
0.425471	1.56428
0.428482	1.563961
0.431514	1.563647
0.434567	1.563338
0.437642	1.563033
0.440739	1.562733
0.443858	1.562436
0.446999	1.562145
0.450162	1.561857
0.453347	1.561573
0.456555	1.561294
0.459786	1.561018
0.463039	1.560747
0.466316	1.560479
0.469615	1.560214
0.472938	1.559954
0.476285	1.559697
0.479655	1.559444
0.483049	1.559194
0.486467	1.558948
0.48991	1.558705
0.493376	1.558465
0.496867	1.558229
0.500383	1.557995
0.503924	1.557765
0.50749	1.557538
0.511081	1.557314
0.514697	1.557093
0.518339	1.556875
0.522007	1.556659
0.525701	1.556447
0.529421	1.556237
0.533167	1.55603
0.53694	1.555826
0.540739	1.555624
0.544565	1.555425
0.548419	1.555228
0.552299	1.555034
0.556208	1.554842
0.560143	1.554652
0.564107	1.554465
0.568099	1.55428
0.572119	1.554098
0.576167	1.553917
0.580244	1.553739
0.58435	1.553563
0.588485	1.553389
0.592649	1.553217
0.596842	1.553047
0.601066	1.552879
0.605319	1.552713
0.609602	1.552549
0.613916	1.552386
0.61826	1.552226
0.622635	1.552067
0.627041	1.55191
0.631478	1.551754
0.635946	1.5516
0.640446	1.551448
0.644978	1.551298
0.649542	1.551149
0.654138	1.551002
0.658767	1.550856
0.663428	1.550711
0.668123	1.550568
0.67285	1.550427
0.677611	1.550286
0.682406	1.550147
0.687235	1.55001
0.692098	1.549873
0.696995	1.549738
0.701927	1.549605
0.706894	1.549472
0.711896	1.54934
0.716934	1.54921
0.722007	1.549081
0.727116	1.548952
0.732261	1.548825
0.737442	1.548699
0.74266	1.548574
0.747916	1.54845
0.753208	1.548327
0.758538	1.548204
0.763905	1.548083
0.769311	1.547962
0.774754	1.547842
0.780236	1.547723
0.785757	1.547605
0.791318	1.547488
0.796917	1.547371
0.802556	1.547255
0.808235	1.54714
0.813954	1.547025
0.819714	1.546911
0.825514	1.546798
0.831355	1.546685
0.837238	1.546573
0.843163	1.546461
0.849129	1.54635
0.855137	1.546239
0.861188	1.546129
0.867282	1.546019
0.873419	1.545909
0.879599	1.5458
0.885824	1.545692
0.892092	1.545583
0.898404	1.545475
0.904761	1.545368
0.911164	1.54526
0.917611	1.545153
0.924104	1.545046
0.930643	1.54494
0.937228	1.544833
0.94386	1.544727
0.950539	1.544621
0.957265	1.544514
0.964039	1.544408
0.970861	1.544303
0.97773	1.544197
0.984649	1.544091
0.991616	1.543985
0.998633	1.543879
1.0057	1.543774
1.01282	1.543668
1.01998	1.543562
1.0272	1.543456
1.03447	1.543349
1.04179	1.543243
1.04916	1.543136
1.05658	1.54303
1.06406	1.542923
1.07159	1.542816
1.07917	1.542708
1.08681	1.542601
1.0945	1.542493
1.10224	1.542384
1.11004	1.542276
1.1179	1.542167
1.12581	1.542057
1.13378	1.541947
1.1418	1.541837
1.14988	1.541726
1.15801	1.541615
1.16621	1.541503
1.17446	1.541391
1.18277	1.541278
1.19114	1.541164
1.19957	1.54105
1.20806	1.540936
1.21661	1.54082
1.22521	1.540704
1.23388	1.540588
1.24261	1.54047
1.25141	1.540352
1.26026	1.540233
1.26918	1.540113
1.27816	1.539992
1.28721	1.539871
1.29631	1.539748
1.30549	1.539625
1.31472	1.539501
1.32403	1.539376
1.3334	1.539249
1.34283	1.539122
1.35233	1.538994
1.3619	1.538865
1.37154	1.538734
1.38125	1.538602
1.39102	1.53847
1.40086	1.538336
1.41077	1.538201
1.42076	1.538064
1.43081	1.537926
1.44093	1.537787
1.45113	1.537647
1.4614	1.537505
1.47174	1.537362
1.48215	1.537217
1.49264	1.537071
1.5032	1.536924
1.51384	1.536775
1.52455	1.536624
1.53534	1.536472
1.54621	1.536318
1.55715	1.536162
1.56816	1.536005
1.57926	1.535846
1.59044	1.535685
1.60169	1.535523
1.61302	1.535358
1.62444	1.535192
1.63593	1.535024
1.64751	1.534853
1.65917	1.534681
1.67091	1.534507
1.68273	1.53433
1.69464	1.534152
1.70663	1.533971
1.7187	1.533788
1.73087	1.533603
1.74311	1.533416
1.75545	1.533226
1.76787	1.533034
1.78038	1.532839
1.79298	1.532642
1.80567	1.532442
1.81844	1.53224
1.83131	1.532035
1.84427	1.531828
1.85732	1.531618
1.87046	1.531405
1.8837	1.531189
1.89703	1.53097
1.91045	1.530749
1.92397	1.530524
1.93758	1.530297
1.95129	1.530066
1.9651	1.529832
1.979	1.529595
1.99301	1.529355
2.00711	1.529111
2.02131	1.528864
2.03562	1.528614
2.05002	1.52836
2.06453	1.528102
2.07914	1.527841
2.09385	1.527576
2.10866	1.527307
2.12359	1.527035
2.13861	1.526758
2.15374	1.526478
2.16898	1.526193
2.18433	1.525905
2.19979	1.525612
2.21535	1.525315
2.23103	1.525013
2.24682	1.524707
2.26272	1.524397
2.27873	1.524081
2.29485	1.523762
2.31109	1.523437
2.32744	1.523108
2.34391	1.522773
2.3605	1.522434
2.3772	1.522089
2.39402	1.521739
2.41096	1.521384
2.42802	1.521023
2.4452	1.520657
2.46251	1.520285
2.47993	1.519908
2.49748	1.519524
2.51515	1.519135
2.53295	1.518739
2.55087	1.518338
2.56892	1.51793
2.5871	1.517515
2.60541	1.517094
2.62384	1.516666
2.64241	1.516232
2.66111	1.51579
2.67994	1.515342
2.6989	1.514886
2.718	1.514423
2.73723	1.513953
2.7566	1.513474
2.77611	1.512988
2.79575	1.512494
2.81553	1.511992
2.83546	1.511482
2.85552	1.510963
2.87573	1.510436
2.89608	1.5099
2.91657	1.509355
2.93721	1.508801
2.95799	1.508237
2.97892	1.507664
3	1.507082

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/Radhakrishnan-e.yml
ID: ds_964f8d83c5ff
API: /v1/datasets/ds_964f8d83c5ff

Plot