Optical constants

Refractive index of GeO₂ (Germanium dioxide, Germania)

Fleming 1984: Fused germania; n 0.36–4.3 µm

Data: formula 1
Range: 0.36–4.3 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.60846
Extinction coefficient k: 0

Permittivity ε₁: 2.58713
Permittivity ε₂: 0

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

Abbe number V_d: 41.729
Chromatic dispersion dn/dλ: -0.0744743 µm⁻¹

Group index n_g: 1.65222
Group velocity dispersion: 141.141 fs²/mm

Dispersion parameter D: -770.001 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

# GeO2 (Germanium dioxide, Germania): Fleming 1984: Fused germania; n 0.36–4.3 µm
geo2 = ls.fetch_refractiveindex("main", "GeO2", "Fleming", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(geo2.range_nm)  # (360, 4300) nm
eps = geo2.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_17616d424018/lightsmith"
geo2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(geo2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (geo2/fleming-1984).

# ... load geo2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=geo2)],
    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_17616d424018/lightsmith?model=drude_lorentz"
geo2_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{0.80686642 λ^{2}}{λ^{2} - {0.068972606}^{2}} + \frac{0.71815848 λ^{2}}{λ^{2} - {0.15396605}^{2}} + \frac{0.85416831 λ^{2}}{λ^{2} - {11.841931}^{2}}

Valid from 0.36 to 4.3 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.80686642
C3	0.068972606
C4	0.71815848
C5	0.15396605
C6	0.85416831
C7	11.841931

References

J. W. Fleming. Dispersion in GeO₂-SiO₂ glasses. Appl. Opt. 23, 4486-4493 (1984)

doi:10.1364/ao.23.004486 Dispersion in GeO_2–SiO_2 glasses, Applied Optics (1984)

Cite

James W. Fleming. Dispersion in GeO_2–SiO_2 glasses. Applied Optics, 23, 4486 (1984), doi:10.1364/ao.23.004486; 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

GeO2 (Germanium dioxide, Germania), Fleming 1984: Fused germania; n 0.36–4.3 µm: n and k versus wavelength
λ (µm)	n
0.36	1.647953
0.362245	1.647094
0.364504	1.64625
0.366776	1.64542
0.369064	1.644603
0.371365	1.6438
0.373681	1.643009
0.376011	1.642232
0.378355	1.641467
0.380715	1.640714
0.383089	1.639973
0.385477	1.639245
0.387881	1.638527
0.3903	1.637821
0.392733	1.637127
0.395182	1.636443
0.397646	1.635769
0.400126	1.635107
0.402621	1.634454
0.405132	1.633812
0.407658	1.63318
0.4102	1.632557
0.412758	1.631944
0.415331	1.63134
0.417921	1.630746
0.420527	1.63016
0.423149	1.629583
0.425788	1.629015
0.428443	1.628456
0.431115	1.627905
0.433803	1.627362
0.436508	1.626827
0.43923	1.626301
0.441969	1.625782
0.444725	1.62527
0.447498	1.624767
0.450288	1.62427
0.453096	1.623781
0.455921	1.623299
0.458764	1.622824
0.461625	1.622356
0.464503	1.621894
0.4674	1.62144
0.470314	1.620992
0.473247	1.62055
0.476198	1.620114
0.479167	1.619685
0.482155	1.619262
0.485162	1.618845
0.488187	1.618434
0.491231	1.618028
0.494294	1.617628
0.497376	1.617234
0.500478	1.616846
0.503598	1.616462
0.506739	1.616085
0.509898	1.615712
0.513078	1.615344
0.516277	1.614982
0.519497	1.614625
0.522736	1.614272
0.525995	1.613924
0.529275	1.613581
0.532576	1.613243
0.535897	1.612909
0.539238	1.61258
0.542601	1.612255
0.545984	1.611935
0.549389	1.611619
0.552814	1.611307
0.556261	1.610999
0.55973	1.610696
0.56322	1.610396
0.566732	1.6101
0.570266	1.609809
0.573822	1.609521
0.5774	1.609237
0.581001	1.608956
0.584624	1.608679
0.588269	1.608406
0.591937	1.608137
0.595628	1.60787
0.599342	1.607608
0.60308	1.607348
0.60684	1.607092
0.610624	1.60684
0.614432	1.60659
0.618263	1.606344
0.622118	1.606101
0.625998	1.60586
0.629901	1.605623
0.633829	1.605389
0.637781	1.605158
0.641758	1.604929
0.64576	1.604704
0.649786	1.604481
0.653838	1.604261
0.657915	1.604044
0.662018	1.603829
0.666146	1.603617
0.6703	1.603407
0.674479	1.6032
0.678685	1.602996
0.682917	1.602794
0.687175	1.602594
0.69146	1.602397
0.695772	1.602202
0.70011	1.602009
0.704476	1.601819
0.708869	1.601631
0.713289	1.601445
0.717737	1.601261
0.722212	1.60108
0.726716	1.6009
0.731247	1.600723
0.735807	1.600547
0.740395	1.600374
0.745012	1.600202
0.749657	1.600032
0.754332	1.599865
0.759036	1.599699
0.763769	1.599535
0.768531	1.599372
0.773323	1.599212
0.778146	1.599053
0.782998	1.598896
0.78788	1.598741
0.792793	1.598587
0.797737	1.598435
0.802711	1.598285
0.807716	1.598136
0.812753	1.597988
0.817821	1.597843
0.82292	1.597698
0.828052	1.597555
0.833215	1.597414
0.838411	1.597274
0.843639	1.597135
0.848899	1.596998
0.854193	1.596862
0.859519	1.596727
0.864879	1.596594
0.870272	1.596462
0.875698	1.596331
0.881159	1.596202
0.886653	1.596073
0.892182	1.595946
0.897745	1.59582
0.903343	1.595695
0.908976	1.595571
0.914644	1.595449
0.920347	1.595327
0.926086	1.595207
0.931861	1.595087
0.937672	1.594968
0.943519	1.594851
0.949402	1.594734
0.955322	1.594619
0.961279	1.594504
0.967273	1.59439
0.973305	1.594277
0.979374	1.594165
0.985481	1.594054
0.991626	1.593944
0.997809	1.593834
1.00403	1.593725
1.01029	1.593617
1.01659	1.59351
1.02293	1.593404
1.02931	1.593298
1.03573	1.593193
1.04219	1.593088
1.04868	1.592985
1.05522	1.592882
1.0618	1.592779
1.06842	1.592677
1.07509	1.592576
1.08179	1.592475
1.08854	1.592375
1.09532	1.592276
1.10215	1.592177
1.10903	1.592078
1.11594	1.59198
1.1229	1.591883
1.1299	1.591786
1.13695	1.591689
1.14404	1.591593
1.15117	1.591497
1.15835	1.591402
1.16557	1.591307
1.17284	1.591212
1.18015	1.591118
1.18751	1.591024
1.19492	1.590931
1.20237	1.590837
1.20987	1.590744
1.21741	1.590652
1.225	1.590559
1.23264	1.590467
1.24033	1.590375
1.24806	1.590283
1.25584	1.590192
1.26367	1.5901
1.27155	1.590009
1.27948	1.589918
1.28746	1.589827
1.29549	1.589736
1.30357	1.589646
1.31169	1.589555
1.31987	1.589464
1.3281	1.589374
1.33639	1.589283
1.34472	1.589193
1.3531	1.589103
1.36154	1.589012
1.37003	1.588922
1.37857	1.588832
1.38717	1.588741
1.39582	1.588651
1.40452	1.58856
1.41328	1.588469
1.42209	1.588379
1.43096	1.588288
1.43988	1.588197
1.44886	1.588106
1.4579	1.588014
1.46699	1.587923
1.47614	1.587831
1.48534	1.587739
1.4946	1.587647
1.50392	1.587555
1.5133	1.587462
1.52274	1.587369
1.53223	1.587276
1.54179	1.587182
1.5514	1.587089
1.56107	1.586994
1.57081	1.5869
1.5806	1.586805
1.59046	1.58671
1.60038	1.586614
1.61035	1.586518
1.6204	1.586422
1.6305	1.586325
1.64067	1.586227
1.6509	1.586129
1.66119	1.586031
1.67155	1.585932
1.68197	1.585833
1.69246	1.585733
1.70302	1.585632
1.71363	1.585531
1.72432	1.58543
1.73507	1.585327
1.74589	1.585224
1.75678	1.585121
1.76773	1.585016
1.77876	1.584911
1.78985	1.584806
1.80101	1.584699
1.81224	1.584592
1.82354	1.584484
1.83491	1.584376
1.84635	1.584266
1.85786	1.584156
1.86945	1.584045
1.88111	1.583933
1.89284	1.58382
1.90464	1.583706
1.91651	1.583591
1.92847	1.583476
1.94049	1.583359
1.95259	1.583242
1.96477	1.583123
1.97702	1.583003
1.98935	1.582883
2.00175	1.582761
2.01423	1.582638
2.02679	1.582514
2.03943	1.582389
2.05215	1.582263
2.06494	1.582136
2.07782	1.582007
2.09078	1.581878
2.10381	1.581747
2.11693	1.581614
2.13013	1.581481
2.14341	1.581346
2.15678	1.581209
2.17023	1.581072
2.18376	1.580933
2.19738	1.580792
2.21108	1.58065
2.22487	1.580507
2.23874	1.580362
2.2527	1.580216
2.26675	1.580068
2.28088	1.579918
2.2951	1.579767
2.30942	1.579614
2.32382	1.57946
2.33831	1.579303
2.35289	1.579145
2.36756	1.578986
2.38232	1.578824
2.39718	1.578661
2.41212	1.578496
2.42717	1.578329
2.4423	1.57816
2.45753	1.577989
2.47285	1.577816
2.48827	1.577641
2.50379	1.577464
2.5194	1.577285
2.53511	1.577103
2.55092	1.57692
2.56683	1.576734
2.58283	1.576546
2.59894	1.576356
2.61514	1.576164
2.63145	1.575969
2.64786	1.575771
2.66437	1.575572
2.68098	1.57537
2.6977	1.575165
2.71452	1.574958
2.73145	1.574748
2.74848	1.574535
2.76562	1.57432
2.78286	1.574102
2.80022	1.573881
2.81768	1.573657
2.83525	1.573431
2.85293	1.573201
2.87072	1.572969
2.88862	1.572733
2.90663	1.572495
2.92475	1.572253
2.94299	1.572008
2.96134	1.57176
2.97981	1.571509
2.99839	1.571254
3.01709	1.570995
3.0359	1.570734
3.05483	1.570468
3.07388	1.570199
3.09305	1.569927
3.11233	1.56965
3.13174	1.56937
3.15127	1.569086
3.17092	1.568799
3.19069	1.568507
3.21059	1.568211
3.23061	1.567911
3.25075	1.567606
3.27102	1.567298
3.29142	1.566985
3.31194	1.566668
3.33259	1.566346
3.35337	1.566019
3.37428	1.565688
3.39532	1.565352
3.4165	1.565012
3.4378	1.564666
3.45924	1.564315
3.48081	1.56396
3.50251	1.563599
3.52435	1.563233
3.54633	1.562861
3.56844	1.562484
3.59069	1.562101
3.61308	1.561713
3.63561	1.561319
3.65828	1.560919
3.68109	1.560513
3.70405	1.560101
3.72714	1.559682
3.75038	1.559258
3.77377	1.558827
3.7973	1.558389
3.82098	1.557945
3.84481	1.557493
3.86878	1.557035
3.89291	1.55657
3.91718	1.556097
3.94161	1.555617
3.96618	1.55513
3.99092	1.554635
4.0158	1.554132
4.04084	1.553621
4.06604	1.553102
4.09139	1.552575
4.1169	1.552039
4.14258	1.551495
4.16841	1.550942
4.1944	1.55038
4.22055	1.549809
4.24687	1.549228
4.27335	1.548638
4.3	1.548039

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: —

GeO₂ (Germanium dioxide, Germania): all datasets

About GeO2 (Germanium dioxide, Germania)

Germanium dioxide (GeO₂) is often encountered in crystalline forms, which are transparent in the ultraviolet and infrared regions of the spectrum. This material is important in optical applications like fiber optic systems, where it is used as a dopant to adjust the refractive index of silica fibers. The compound can exist in multiple polymorphs, including hexagonal and tetragonal forms, each with their own set of optical and mechanical properties. It's also a precursor for producing high-purity germanium for use in semiconductors.

More about GeO2 (Germanium dioxide, Germania) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/GeO2/nk/Fleming.yml
ID: ds_17616d424018
API: /v1/datasets/ds_17616d424018

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