Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.29612
Extinction coefficient k: 0

Permittivity ε₁: 5.27215
Permittivity ε₂: 0

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

Abbe number V_d: 18.9
Chromatic dispersion dn/dλ: -0.341795 µm⁻¹

Group index n_g: 2.49696
Group velocity dispersion: 720.714 fs²/mm

Dispersion parameter D: -3931.88 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): Zelmon et al. 1997: CLN, 5 mol % MgO; n(o) 0.4–5.0 µm
mgo_linbo3 = ls.fetch_refractiveindex("other", "MgO-LiNbO3", "Zelmon-o", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mgo_linbo3.range_nm)  # (400, 5000) 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_6bbd7d79a51d/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/zelmon-1997-o).

# ... 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=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_6bbd7d79a51d/lightsmith?model=drude_lorentz"
mgo_linbo3_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 = \frac{2.4272 λ^{2}}{λ^{2} - 0.01478} + \frac{1.4617 λ^{2}}{λ^{2} - 0.05612} + \frac{9.6536 λ^{2}}{λ^{2} - 371.216}

Valid from 0.4 to 5.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	2.4272
C3	0.01478
C4	1.4617
C5	0.05612
C6	9.6536
C7	371.216

Comments and conditions

21 °C. Ordinary ray (o). Congruently grown lithium niobate (CLN) doped with 5 mol. % MgO.
In the original publication, the ordinary and extraordinary Sellmeier coefficients appear to be interchanged. The coefficients are presented here with n_o and n_e swapped to match the measured dispersion and the known negative uniaxial behavior of MgO:LiNbO₃.

Conditions

temperature: 294 K
direction: o

References

D. E. Zelmon, D. L. Small, D. Jundt. Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide-doped lithium niobate. J. Opt. Soc. Am. B 14, 3319-3322 (1997)

doi:10.1364/josab.14.003319 Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide –doped lithium niobate, Journal of the Optical Society of America B (1997)

Cite

David E. Zelmon, David L. Small and Dieter Jundt. Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide –doped lithium niobate. Journal of the Optical Society of America B, 14, 3319 (1997), doi:10.1364/josab.14.003319; 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), Zelmon et al. 1997: CLN, 5 mol % MgO; n(o) 0.4–5.0 µm: n and k versus wavelength
λ (µm)	n
0.4	2.4334
0.40254	2.429561
0.405096	2.425806
0.407669	2.422135
0.410258	2.418543
0.412863	2.415028
0.415485	2.411589
0.418123	2.408222
0.420778	2.404926
0.42345	2.4017
0.426139	2.398539
0.428845	2.395444
0.431569	2.392412
0.434309	2.389441
0.437067	2.38653
0.439843	2.383676
0.442636	2.380879
0.445446	2.378137
0.448275	2.375449
0.451122	2.372812
0.453987	2.370226
0.456869	2.367689
0.459771	2.365201
0.46269	2.362759
0.465628	2.360364
0.468585	2.358012
0.471561	2.355705
0.474555	2.353439
0.477569	2.351215
0.480602	2.349031
0.483654	2.346887
0.486725	2.344781
0.489816	2.342713
0.492926	2.340681
0.496056	2.338685
0.499206	2.336724
0.502376	2.334798
0.505567	2.332904
0.508777	2.331044
0.512008	2.329215
0.515259	2.327418
0.518531	2.325651
0.521824	2.323913
0.525138	2.322205
0.528473	2.320526
0.531829	2.318874
0.535206	2.31725
0.538604	2.315653
0.542025	2.314082
0.545467	2.312536
0.548931	2.311015
0.552416	2.309519
0.555924	2.308047
0.559455	2.306599
0.563007	2.305174
0.566582	2.303771
0.57018	2.302391
0.573801	2.301032
0.577445	2.299694
0.581112	2.298377
0.584802	2.297081
0.588516	2.295804
0.592253	2.294548
0.596014	2.29331
0.599799	2.292091
0.603607	2.290891
0.607441	2.289709
0.611298	2.288545
0.61518	2.287398
0.619086	2.286268
0.623018	2.285155
0.626974	2.284059
0.630955	2.282978
0.634962	2.281913
0.638994	2.280864
0.643052	2.27983
0.647136	2.278812
0.651245	2.277807
0.655381	2.276817
0.659542	2.275842
0.663731	2.27488
0.667945	2.273932
0.672187	2.272997
0.676456	2.272075
0.680751	2.271166
0.685074	2.27027
0.689424	2.269386
0.693802	2.268514
0.698208	2.267654
0.702642	2.266806
0.707104	2.26597
0.711594	2.265145
0.716113	2.264331
0.720661	2.263527
0.725237	2.262735
0.729842	2.261953
0.734477	2.261182
0.739141	2.26042
0.743835	2.259669
0.748558	2.258927
0.753312	2.258195
0.758096	2.257472
0.76291	2.256759
0.767754	2.256055
0.77263	2.255359
0.777536	2.254673
0.782474	2.253995
0.787442	2.253325
0.792443	2.252664
0.797475	2.252011
0.802539	2.251366
0.807636	2.250729
0.812764	2.250099
0.817925	2.249478
0.823119	2.248863
0.828346	2.248256
0.833607	2.247656
0.8389	2.247064
0.844227	2.246478
0.849588	2.245899
0.854984	2.245326
0.860413	2.24476
0.865877	2.244201
0.871375	2.243648
0.876909	2.243101
0.882477	2.24256
0.888081	2.242025
0.893721	2.241496
0.899396	2.240973
0.905107	2.240455
0.910855	2.239943
0.916639	2.239437
0.92246	2.238935
0.928318	2.238439
0.934213	2.237948
0.940145	2.237462
0.946115	2.236981
0.952123	2.236505
0.95817	2.236034
0.964254	2.235567
0.970377	2.235104
0.97654	2.234647
0.982741	2.234193
0.988981	2.233744
0.995262	2.233299
1.00158	2.232858
1.00794	2.232421
1.01434	2.231988
1.02078	2.231559
1.02727	2.231133
1.03379	2.230712
1.04035	2.230294
1.04696	2.229879
1.05361	2.229468
1.0603	2.22906
1.06703	2.228656
1.07381	2.228254
1.08063	2.227856
1.08749	2.227461
1.0944	2.227069
1.10135	2.22668
1.10834	2.226293
1.11538	2.22591
1.12246	2.225529
1.12959	2.22515
1.13676	2.224775
1.14398	2.224401
1.15124	2.224031
1.15856	2.223662
1.16591	2.223296
1.17332	2.222932
1.18077	2.22257
1.18827	2.22221
1.19581	2.221852
1.2034	2.221496
1.21105	2.221143
1.21874	2.22079
1.22648	2.22044
1.23426	2.220091
1.2421	2.219744
1.24999	2.219399
1.25793	2.219055
1.26592	2.218712
1.27395	2.218371
1.28204	2.218031
1.29019	2.217693
1.29838	2.217355
1.30662	2.217019
1.31492	2.216684
1.32327	2.21635
1.33167	2.216017
1.34013	2.215685
1.34864	2.215353
1.35721	2.215023
1.36582	2.214693
1.3745	2.214363
1.38323	2.214035
1.39201	2.213707
1.40085	2.213379
1.40974	2.213052
1.4187	2.212726
1.42771	2.212399
1.43677	2.212073
1.4459	2.211747
1.45508	2.211422
1.46432	2.211096
1.47362	2.210771
1.48297	2.210445
1.49239	2.210119
1.50187	2.209794
1.51141	2.209468
1.521	2.209142
1.53066	2.208815
1.54038	2.208488
1.55016	2.208161
1.56001	2.207834
1.56991	2.207505
1.57988	2.207177
1.58992	2.206847
1.60001	2.206517
1.61017	2.206186
1.6204	2.205855
1.63069	2.205522
1.64104	2.205189
1.65146	2.204855
1.66195	2.204519
1.6725	2.204183
1.68313	2.203845
1.69381	2.203506
1.70457	2.203166
1.71539	2.202825
1.72629	2.202482
1.73725	2.202138
1.74828	2.201792
1.75938	2.201445
1.77056	2.201096
1.7818	2.200746
1.79311	2.200393
1.8045	2.200039
1.81596	2.199683
1.82749	2.199325
1.8391	2.198965
1.85078	2.198604
1.86253	2.19824
1.87436	2.197873
1.88626	2.197505
1.89824	2.197134
1.91029	2.196761
1.92242	2.196386
1.93463	2.196008
1.94691	2.195627
1.95928	2.195244
1.97172	2.194858
1.98424	2.194469
1.99684	2.194078
2.00952	2.193683
2.02228	2.193286
2.03512	2.192886
2.04805	2.192482
2.06105	2.192076
2.07414	2.191666
2.08731	2.191253
2.10057	2.190836
2.11391	2.190416
2.12733	2.189992
2.14084	2.189565
2.15443	2.189134
2.16812	2.188699
2.18188	2.188261
2.19574	2.187818
2.20968	2.187372
2.22371	2.186922
2.23784	2.186467
2.25205	2.186008
2.26635	2.185545
2.28074	2.185077
2.29522	2.184605
2.3098	2.184128
2.32447	2.183647
2.33923	2.183161
2.35408	2.18267
2.36903	2.182174
2.38407	2.181673
2.39921	2.181167
2.41445	2.180656
2.42978	2.180139
2.44521	2.179617
2.46074	2.17909
2.47636	2.178557
2.49209	2.178018
2.50792	2.177474
2.52384	2.176924
2.53987	2.176368
2.556	2.175805
2.57223	2.175237
2.58856	2.174662
2.605	2.174081
2.62154	2.173493
2.63819	2.172899
2.65494	2.172298
2.6718	2.17169
2.68877	2.171075
2.70584	2.170454
2.72303	2.169825
2.74032	2.169188
2.75772	2.168545
2.77523	2.167893
2.79286	2.167234
2.81059	2.166568
2.82844	2.165893
2.8464	2.16521
2.86447	2.164519
2.88266	2.16382
2.90097	2.163112
2.91939	2.162396
2.93793	2.161671
2.95659	2.160937
2.97536	2.160194
2.99426	2.159442
3.01327	2.158681
3.03241	2.15791
3.05166	2.15713
3.07104	2.15634
3.09054	2.15554
3.11017	2.15473
3.12992	2.153909
3.14979	2.153079
3.1698	2.152237
3.18993	2.151385
3.21018	2.150522
3.23057	2.149648
3.25108	2.148763
3.27173	2.147866
3.2925	2.146958
3.31341	2.146037
3.33445	2.145105
3.35563	2.144161
3.37694	2.143204
3.39838	2.142234
3.41996	2.141252
3.44168	2.140257
3.46353	2.139249
3.48553	2.138227
3.50766	2.137191
3.52994	2.136142
3.55235	2.135079
3.57491	2.134001
3.59761	2.132909
3.62046	2.131802
3.64345	2.130679
3.66658	2.129542
3.68987	2.128389
3.7133	2.127221
3.73688	2.126036
3.76061	2.124835
3.78449	2.123618
3.80852	2.122383
3.83271	2.121132
3.85705	2.119863
3.88154	2.118577
3.90619	2.117272
3.93099	2.11595
3.95596	2.114609
3.98108	2.113249
4.00636	2.111869
4.0318	2.110471
4.0574	2.109052
4.08317	2.107613
4.1091	2.106154
4.13519	2.104674
4.16145	2.103173
4.18788	2.10165
4.21447	2.100105
4.24123	2.098538
4.26817	2.096949
4.29527	2.095336
4.32255	2.0937
4.34999	2.09204
4.37762	2.090355
4.40542	2.088646
4.43339	2.086912
4.46155	2.085152
4.48988	2.083366
4.51839	2.081554
4.54708	2.079715
4.57596	2.077849
4.60502	2.075954
4.63426	2.074031
4.66369	2.07208
4.6933	2.070098
4.72311	2.068087
4.7531	2.066046
4.78328	2.063973
4.81366	2.061869
4.84422	2.059733
4.87499	2.057563
4.90594	2.055361
4.9371	2.053125
4.96845	2.050853
5	2.048547

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