Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.19996
Extinction coefficient k: 0

Permittivity ε₁: 4.83985
Permittivity ε₂: 0

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

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.286709 µm⁻¹

Group index n_g: 2.36843
Group velocity dispersion: 595.717 fs²/mm

Dispersion parameter D: -3249.95 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

# MgO:LiNbO3 (Magnesium oxide doped lithium niobate): Gayer et al. 2008: SLN, 1 mol % MgO; n(e) 0.5–4.0 µm
mgo_linbo3 = ls.fetch_refractiveindex("other", "MgO-LiNbO3", "Gayer-1-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mgo_linbo3.range_nm)  # (500, 4000) nm
eps = mgo_linbo3.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_62b5d4602b3d/lightsmith"
mgo_linbo3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(mgo_linbo3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (mgo-linbo3/gayer-2008-1-e).

# ... load mgo_linbo3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=mgo_linbo3)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=500, 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} = 5.078 + \frac{0.0964 λ^{0.0}}{λ^{2} - {0.2065}^{2.0}} + \frac{61.16 λ^{0.0}}{λ^{2} - {10.55}^{2.0}} - 0.0159 λ^{2.0}

Valid from 0.5 to 4.0 µm.

Coefficients as stored

C_i	Value
C1	5.078
C2	0.0964
C3	0.0
C4	0.2065
C5	2.0
C6	61.16
C7	0.0
C8	10.55
C9	2.0
C10	-0.0159
C11	2.0

Comments and conditions

24.5 °C. Extraordinary ray (e). Congruently grown lithium niobate SLN) doped with 1 mol. % MgO. See the original publication for temperature-dependent refractive index equations.

Conditions

temperature: 297.65 K
direction: e

References

O. Gayer, Z. Sacks, E. Galun, A. Arie. Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO₃. Appl. Phys. B 91, 343-348 (2008). Also see Erratum.

doi:10.1007/s00340-008-2998-2 Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3, Applied Physics B (2008)
doi:10.1007/s00340-008-3316-8 Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3, Applied Physics B (2008)

Cite

O. Gayer, Z. Sacks, E. Galun and A. Arie. Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3. Applied Physics B, 91, 343-348 (2008), doi:10.1007/s00340-008-2998-2; 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

MgO:LiNbO3 (Magnesium oxide doped lithium niobate), Gayer et al. 2008: SLN, 1 mol % MgO; n(e) 0.5–4.0 µm: n and k versus wavelength
λ (µm)	n
0.5	2.233426
0.502613	2.232115
0.505239	2.230822
0.507879	2.229547
0.510533	2.228289
0.5132	2.227048
0.515882	2.225824
0.518578	2.224617
0.521287	2.223426
0.524011	2.22225
0.526749	2.221091
0.529502	2.219947
0.532268	2.218818
0.53505	2.217704
0.537845	2.216605
0.540656	2.21552
0.543481	2.214449
0.546321	2.213392
0.549175	2.212349
0.552045	2.21132
0.554929	2.210304
0.557829	2.2093
0.560744	2.20831
0.563674	2.207333
0.566619	2.206368
0.56958	2.205415
0.572556	2.204474
0.575548	2.203545
0.578555	2.202628
0.581578	2.201722
0.584617	2.200828
0.587672	2.199944
0.590743	2.199072
0.593829	2.198211
0.596932	2.19736
0.600051	2.196519
0.603187	2.195689
0.606339	2.194869
0.609507	2.194059
0.612692	2.193259
0.615893	2.192469
0.619111	2.191688
0.622346	2.190916
0.625598	2.190154
0.628867	2.189401
0.632153	2.188657
0.635456	2.187922
0.638777	2.187195
0.642114	2.186477
0.64547	2.185767
0.648842	2.185066
0.652233	2.184373
0.655641	2.183688
0.659067	2.183011
0.66251	2.182342
0.665972	2.18168
0.669452	2.181026
0.67295	2.18038
0.676466	2.179741
0.680001	2.179109
0.683554	2.178485
0.687126	2.177867
0.690716	2.177257
0.694326	2.176653
0.697954	2.176056
0.701601	2.175466
0.705267	2.174882
0.708952	2.174305
0.712656	2.173734
0.71638	2.173169
0.720123	2.172611
0.723886	2.172058
0.727669	2.171512
0.731471	2.170972
0.735293	2.170437
0.739135	2.169908
0.742997	2.169385
0.746879	2.168867
0.750782	2.168355
0.754705	2.167849
0.758649	2.167347
0.762613	2.166851
0.766598	2.16636
0.770603	2.165875
0.77463	2.165394
0.778677	2.164918
0.782746	2.164447
0.786836	2.163981
0.790948	2.16352
0.795081	2.163063
0.799235	2.162611
0.803411	2.162164
0.807609	2.161721
0.811829	2.161282
0.816071	2.160848
0.820335	2.160418
0.824622	2.159992
0.828931	2.159571
0.833262	2.159153
0.837616	2.15874
0.841993	2.15833
0.846392	2.157925
0.850815	2.157523
0.855261	2.157125
0.85973	2.156731
0.864222	2.156341
0.868738	2.155954
0.873277	2.155571
0.87784	2.155191
0.882427	2.154815
0.887038	2.154442
0.891673	2.154072
0.896332	2.153706
0.901016	2.153343
0.905724	2.152984
0.910456	2.152627
0.915214	2.152274
0.919996	2.151924
0.924803	2.151577
0.929635	2.151232
0.934493	2.150891
0.939376	2.150552
0.944284	2.150217
0.949218	2.149884
0.954178	2.149554
0.959164	2.149227
0.964176	2.148902
0.969214	2.14858
0.974278	2.14826
0.979369	2.147943
0.984487	2.147629
0.989631	2.147316
0.994802	2.147007
1	2.146699
1.00523	2.146394
1.01048	2.146092
1.01576	2.145791
1.02107	2.145493
1.0264	2.145197
1.03176	2.144903
1.03716	2.144611
1.04257	2.144321
1.04802	2.144033
1.0535	2.143748
1.059	2.143464
1.06454	2.143182
1.0701	2.142902
1.07569	2.142623
1.08131	2.142347
1.08696	2.142072
1.09264	2.141799
1.09835	2.141528
1.10409	2.141258
1.10986	2.14099
1.11566	2.140724
1.12149	2.140459
1.12735	2.140195
1.13324	2.139934
1.13916	2.139673
1.14511	2.139414
1.1511	2.139157
1.15711	2.1389
1.16316	2.138646
1.16923	2.138392
1.17534	2.13814
1.18149	2.137889
1.18766	2.137639
1.19386	2.13739
1.2001	2.137143
1.20637	2.136896
1.21268	2.136651
1.21901	2.136406
1.22538	2.136163
1.23179	2.135921
1.23822	2.13568
1.24469	2.135439
1.2512	2.1352
1.25773	2.134961
1.26431	2.134724
1.27091	2.134487
1.27755	2.134251
1.28423	2.134015
1.29094	2.133781
1.29768	2.133547
1.30447	2.133314
1.31128	2.133081
1.31813	2.132849
1.32502	2.132618
1.33194	2.132387
1.3389	2.132157
1.3459	2.131927
1.35293	2.131698
1.36	2.131469
1.36711	2.131241
1.37425	2.131013
1.38143	2.130786
1.38865	2.130558
1.39591	2.130332
1.4032	2.130105
1.41053	2.129879
1.4179	2.129653
1.42531	2.129427
1.43276	2.129201
1.44025	2.128976
1.44777	2.128751
1.45534	2.128525
1.46294	2.1283
1.47059	2.128075
1.47827	2.12785
1.48599	2.127625
1.49376	2.1274
1.50156	2.127175
1.50941	2.12695
1.5173	2.126725
1.52523	2.1265
1.5332	2.126274
1.54121	2.126049
1.54926	2.125823
1.55735	2.125597
1.56549	2.12537
1.57367	2.125144
1.5819	2.124917
1.59016	2.124689
1.59847	2.124462
1.60682	2.124234
1.61522	2.124005
1.62366	2.123777
1.63214	2.123547
1.64067	2.123317
1.64924	2.123087
1.65786	2.122856
1.66652	2.122625
1.67523	2.122393
1.68399	2.12216
1.69278	2.121927
1.70163	2.121693
1.71052	2.121458
1.71946	2.121223
1.72844	2.120987
1.73748	2.12075
1.74655	2.120512
1.75568	2.120273
1.76485	2.120034
1.77408	2.119793
1.78335	2.119552
1.79266	2.119309
1.80203	2.119066
1.81145	2.118822
1.82091	2.118577
1.83043	2.11833
1.83999	2.118083
1.84961	2.117834
1.85927	2.117584
1.86899	2.117333
1.87875	2.117081
1.88857	2.116828
1.89844	2.116573
1.90836	2.116317
1.91833	2.11606
1.92835	2.115801
1.93843	2.115541
1.94856	2.115279
1.95874	2.115016
1.96897	2.114752
1.97926	2.114486
1.9896	2.114219
2	2.113949
2.01045	2.113679
2.02096	2.113406
2.03152	2.113132
2.04213	2.112857
2.0528	2.112579
2.06353	2.1123
2.07431	2.112019
2.08515	2.111736
2.09604	2.111451
2.107	2.111165
2.11801	2.110876
2.12907	2.110586
2.1402	2.110293
2.15138	2.109999
2.16262	2.109702
2.17392	2.109403
2.18528	2.109102
2.1967	2.108799
2.20818	2.108494
2.21972	2.108186
2.23132	2.107876
2.24297	2.107564
2.2547	2.10725
2.26648	2.106933
2.27832	2.106613
2.29022	2.106291
2.30219	2.105967
2.31422	2.10564
2.32631	2.10531
2.33847	2.104978
2.35069	2.104643
2.36297	2.104306
2.37532	2.103965
2.38773	2.103622
2.40021	2.103276
2.41275	2.102927
2.42535	2.102575
2.43803	2.102221
2.45077	2.101863
2.46357	2.101502
2.47645	2.101138
2.48939	2.100771
2.50239	2.100401
2.51547	2.100027
2.52861	2.09965
2.54182	2.09927
2.55511	2.098887
2.56846	2.0985
2.58188	2.098109
2.59537	2.097716
2.60893	2.097318
2.62256	2.096917
2.63627	2.096512
2.65004	2.096104
2.66389	2.095691
2.67781	2.095275
2.6918	2.094855
2.70587	2.094431
2.72	2.094003
2.73422	2.093572
2.7485	2.093136
2.76287	2.092695
2.7773	2.092251
2.79181	2.091802
2.8064	2.091349
2.82107	2.090892
2.83581	2.09043
2.85062	2.089964
2.86552	2.089493
2.88049	2.089018
2.89554	2.088538
2.91067	2.088053
2.92588	2.087563
2.94117	2.087069
2.95654	2.08657
2.97199	2.086065
2.98752	2.085556
3.00313	2.085041
3.01882	2.084521
3.03459	2.083996
3.05045	2.083466
3.06639	2.08293
3.08241	2.082389
3.09852	2.081842
3.11471	2.081289
3.13098	2.080731
3.14735	2.080167
3.16379	2.079598
3.18032	2.079022
3.19694	2.07844
3.21364	2.077852
3.23044	2.077259
3.24732	2.076658
3.26428	2.076052
3.28134	2.075439
3.29849	2.074819
3.31572	2.074193
3.33305	2.073561
3.35046	2.072921
3.36797	2.072275
3.38557	2.071622
3.40326	2.070962
3.42104	2.070294
3.43892	2.06962
3.45689	2.068938
3.47495	2.068248
3.49311	2.067552
3.51136	2.066847
3.52971	2.066135
3.54815	2.065415
3.56669	2.064687
3.58533	2.063951
3.60406	2.063207
3.62289	2.062455
3.64183	2.061694
3.66085	2.060925
3.67998	2.060147
3.69921	2.059361
3.71854	2.058565
3.73797	2.057761
3.7575	2.056948
3.77714	2.056126
3.79687	2.055294
3.81671	2.054453
3.83666	2.053602
3.8567	2.052741
3.87686	2.051871
3.89711	2.050991
3.91748	2.0501
3.93795	2.0492
3.95852	2.048289
3.97921	2.047367
4	2.046435

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