Optical constants

Refractive index of LiNbO₃ (Lithium niobate)

Zelmon et al. 1997: n(e) 0.4–5.0 µm

Data: formula 2
Range: 0.4–5 µm
Temperature: 294 K
Optical axis: e
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: 2.21401
Extinction coefficient k: 0

Permittivity ε₁: 4.90184
Permittivity ε₂: 0

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

Abbe number V_d: 20.526
Chromatic dispersion dn/dλ: -0.295333 µm⁻¹

Group index n_g: 2.38755
Group velocity dispersion: 616.788 fs²/mm

Dispersion parameter D: -3364.9 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

# LiNbO3 (Lithium niobate): Zelmon et al. 1997: n(e) 0.4–5.0 µm
linbo3 = ls.fetch_refractiveindex("main", "LiNbO3", "Zelmon-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(linbo3.range_nm)  # (400, 5000) nm
eps = 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_621368c769f8/lightsmith"
linbo3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(linbo3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (linbo3/zelmon-1997-e).

# ... load linbo3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=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_621368c769f8/lightsmith?model=drude_lorentz"
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{2.9804 λ^{2}}{λ^{2} - 0.02047} + \frac{0.5981 λ^{2}}{λ^{2} - 0.0666} + \frac{8.9543 λ^{2}}{λ^{2} - 416.08}

Valid from 0.4 to 5.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	2.9804
C3	0.02047
C4	0.5981
C5	0.0666
C6	8.9543
C7	416.08

Comments and conditions

21 °C. Extraordinary ray (e). Congruently grown lithium niobate (CLN).

Conditions

temperature: 294 K
direction: e

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

LiNbO3 (Lithium niobate), Zelmon et al. 1997: n(e) 0.4–5.0 µm: n and k versus wavelength
λ (µm)	n
0.4	2.33212
0.40254	2.328805
0.405096	2.325566
0.407669	2.3224
0.410258	2.319304
0.412863	2.316277
0.415485	2.313316
0.418123	2.310419
0.420778	2.307584
0.42345	2.304809
0.426139	2.302092
0.428845	2.299432
0.431569	2.296826
0.434309	2.294274
0.437067	2.291773
0.439843	2.289322
0.442636	2.28692
0.445446	2.284566
0.448275	2.282257
0.451122	2.279993
0.453987	2.277773
0.456869	2.275595
0.459771	2.273459
0.46269	2.271363
0.465628	2.269306
0.468585	2.267287
0.471561	2.265305
0.474555	2.263359
0.477569	2.261449
0.480602	2.259573
0.483654	2.257731
0.486725	2.255922
0.489816	2.254145
0.492926	2.252399
0.496056	2.250683
0.499206	2.248998
0.502376	2.247341
0.505567	2.245713
0.508777	2.244113
0.512008	2.24254
0.515259	2.240994
0.518531	2.239473
0.521824	2.237978
0.525138	2.236508
0.528473	2.235062
0.531829	2.233639
0.535206	2.23224
0.538604	2.230864
0.542025	2.22951
0.545467	2.228178
0.548931	2.226868
0.552416	2.225578
0.555924	2.224308
0.559455	2.223059
0.563007	2.221829
0.566582	2.220619
0.57018	2.219427
0.573801	2.218254
0.577445	2.217099
0.581112	2.215962
0.584802	2.214842
0.588516	2.213739
0.592253	2.212653
0.596014	2.211583
0.599799	2.21053
0.603607	2.209492
0.607441	2.20847
0.611298	2.207462
0.61518	2.20647
0.619086	2.205492
0.623018	2.204529
0.626974	2.203579
0.630955	2.202644
0.634962	2.201722
0.638994	2.200813
0.643052	2.199917
0.647136	2.199034
0.651245	2.198163
0.655381	2.197305
0.659542	2.196459
0.663731	2.195625
0.667945	2.194802
0.672187	2.193991
0.676456	2.193191
0.680751	2.192403
0.685074	2.191625
0.689424	2.190857
0.693802	2.1901
0.698208	2.189354
0.702642	2.188617
0.707104	2.18789
0.711594	2.187173
0.716113	2.186466
0.720661	2.185768
0.725237	2.185079
0.729842	2.184399
0.734477	2.183728
0.739141	2.183066
0.743835	2.182412
0.748558	2.181767
0.753312	2.18113
0.758096	2.180502
0.76291	2.179881
0.767754	2.179268
0.77263	2.178662
0.777536	2.178065
0.782474	2.177475
0.787442	2.176892
0.792443	2.176316
0.797475	2.175747
0.802539	2.175185
0.807636	2.17463
0.812764	2.174082
0.817925	2.17354
0.823119	2.173005
0.828346	2.172476
0.833607	2.171953
0.8389	2.171436
0.844227	2.170925
0.849588	2.170421
0.854984	2.169921
0.860413	2.169428
0.865877	2.16894
0.871375	2.168458
0.876909	2.167981
0.882477	2.167509
0.888081	2.167043
0.893721	2.166581
0.899396	2.166125
0.905107	2.165674
0.910855	2.165227
0.916639	2.164785
0.92246	2.164347
0.928318	2.163915
0.934213	2.163486
0.940145	2.163062
0.946115	2.162643
0.952123	2.162227
0.95817	2.161816
0.964254	2.161408
0.970377	2.161005
0.97654	2.160605
0.982741	2.16021
0.988981	2.159818
0.995262	2.159429
1.00158	2.159045
1.00794	2.158663
1.01434	2.158286
1.02078	2.157911
1.02727	2.15754
1.03379	2.157172
1.04035	2.156807
1.04696	2.156445
1.05361	2.156087
1.0603	2.155731
1.06703	2.155378
1.07381	2.155028
1.08063	2.154681
1.08749	2.154336
1.0944	2.153994
1.10135	2.153655
1.10834	2.153318
1.11538	2.152983
1.12246	2.152651
1.12959	2.152321
1.13676	2.151994
1.14398	2.151668
1.15124	2.151345
1.15856	2.151024
1.16591	2.150705
1.17332	2.150387
1.18077	2.150072
1.18827	2.149758
1.19581	2.149447
1.2034	2.149137
1.21105	2.148828
1.21874	2.148522
1.22648	2.148217
1.23426	2.147913
1.2421	2.147611
1.24999	2.14731
1.25793	2.147011
1.26592	2.146713
1.27395	2.146416
1.28204	2.14612
1.29019	2.145826
1.29838	2.145532
1.30662	2.14524
1.31492	2.144949
1.32327	2.144658
1.33167	2.144369
1.34013	2.14408
1.34864	2.143792
1.35721	2.143505
1.36582	2.143218
1.3745	2.142932
1.38323	2.142647
1.39201	2.142362
1.40085	2.142078
1.40974	2.141794
1.4187	2.14151
1.42771	2.141227
1.43677	2.140944
1.4459	2.140662
1.45508	2.140379
1.46432	2.140097
1.47362	2.139815
1.48297	2.139533
1.49239	2.139251
1.50187	2.138968
1.51141	2.138686
1.521	2.138404
1.53066	2.138121
1.54038	2.137838
1.55016	2.137555
1.56001	2.137271
1.56991	2.136987
1.57988	2.136703
1.58992	2.136418
1.60001	2.136133
1.61017	2.135847
1.6204	2.13556
1.63069	2.135273
1.64104	2.134985
1.65146	2.134696
1.66195	2.134407
1.6725	2.134116
1.68313	2.133825
1.69381	2.133532
1.70457	2.133239
1.71539	2.132944
1.72629	2.132649
1.73725	2.132352
1.74828	2.132054
1.75938	2.131754
1.77056	2.131454
1.7818	2.131152
1.79311	2.130848
1.8045	2.130543
1.81596	2.130237
1.82749	2.129929
1.8391	2.129619
1.85078	2.129307
1.86253	2.128994
1.87436	2.128679
1.88626	2.128362
1.89824	2.128043
1.91029	2.127723
1.92242	2.1274
1.93463	2.127075
1.94691	2.126748
1.95928	2.126419
1.97172	2.126087
1.98424	2.125753
1.99684	2.125417
2.00952	2.125079
2.02228	2.124737
2.03512	2.124394
2.04805	2.124048
2.06105	2.123699
2.07414	2.123347
2.08731	2.122993
2.10057	2.122636
2.11391	2.122276
2.12733	2.121912
2.14084	2.121546
2.15443	2.121177
2.16812	2.120805
2.18188	2.120429
2.19574	2.12005
2.20968	2.119668
2.22371	2.119282
2.23784	2.118893
2.25205	2.1185
2.26635	2.118104
2.28074	2.117704
2.29522	2.1173
2.3098	2.116892
2.32447	2.116481
2.33923	2.116065
2.35408	2.115645
2.36903	2.115221
2.38407	2.114793
2.39921	2.114361
2.41445	2.113924
2.42978	2.113483
2.44521	2.113037
2.46074	2.112587
2.47636	2.112132
2.49209	2.111672
2.50792	2.111208
2.52384	2.110738
2.53987	2.110264
2.556	2.109784
2.57223	2.109299
2.58856	2.108809
2.605	2.108313
2.62154	2.107812
2.63819	2.107306
2.65494	2.106793
2.6718	2.106275
2.68877	2.105752
2.70584	2.105222
2.72303	2.104686
2.74032	2.104144
2.75772	2.103596
2.77523	2.103041
2.79286	2.102481
2.81059	2.101913
2.82844	2.101339
2.8464	2.100758
2.86447	2.10017
2.88266	2.099575
2.90097	2.098974
2.91939	2.098364
2.93793	2.097748
2.95659	2.097124
2.97536	2.096493
2.99426	2.095854
3.01327	2.095207
3.03241	2.094552
3.05166	2.093889
3.07104	2.093218
3.09054	2.092539
3.11017	2.091851
3.12992	2.091154
3.14979	2.090449
3.1698	2.089735
3.18993	2.089012
3.21018	2.08828
3.23057	2.087539
3.25108	2.086788
3.27173	2.086028
3.2925	2.085257
3.31341	2.084477
3.33445	2.083687
3.35563	2.082887
3.37694	2.082077
3.39838	2.081255
3.41996	2.080424
3.44168	2.079581
3.46353	2.078727
3.48553	2.077862
3.50766	2.076986
3.52994	2.076098
3.55235	2.075198
3.57491	2.074287
3.59761	2.073363
3.62046	2.072427
3.64345	2.071479
3.66658	2.070517
3.68987	2.069543
3.7133	2.068556
3.73688	2.067555
3.76061	2.066541
3.78449	2.065513
3.80852	2.064471
3.83271	2.063415
3.85705	2.062345
3.88154	2.06126
3.90619	2.06016
3.93099	2.059044
3.95596	2.057914
3.98108	2.056767
4.00636	2.055605
4.0318	2.054427
4.0574	2.053232
4.08317	2.05202
4.1091	2.050792
4.13519	2.049546
4.16145	2.048283
4.18788	2.047002
4.21447	2.045703
4.24123	2.044385
4.26817	2.043049
4.29527	2.041694
4.32255	2.040319
4.34999	2.038925
4.37762	2.037511
4.40542	2.036076
4.43339	2.034621
4.46155	2.033144
4.48988	2.031647
4.51839	2.030127
4.54708	2.028586
4.57596	2.027022
4.60502	2.025435
4.63426	2.023824
4.66369	2.02219
4.6933	2.020532
4.72311	2.01885
4.7531	2.017143
4.78328	2.01541
4.81366	2.013651
4.84422	2.011866
4.87499	2.010055
4.90594	2.008216
4.9371	2.006349
4.96845	2.004455
5	2.002531

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: —

LiNbO₃ (Lithium niobate): all datasets

About LiNbO3 (Lithium niobate)

Lithium niobate (LiNbO₃) is a ferroelectric material with excellent electro-optic, piezoelectric, and nonlinear optical properties. It is widely used in integrated optics, optoelectronic devices, and telecommunication applications. LiNbO₃ crystals are often employed in modulators, switches, waveguide devices, and frequency doublers. Due to its strong Pockels effect, it is a popular choice for Q-switching in solid-state lasers and is a key material in the fabrication of surface acoustic wave (SAW) devices. The material is generally transparent in the wide wavelength range from the near-infrared to the ultraviolet, making it versatile for various optical applications.

Lithium niobate - Wikipedia

More about LiNbO3 (Lithium niobate) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/LiNbO3/nk/Zelmon-e.yml
ID: ds_621368c769f8
API: /v1/datasets/ds_621368c769f8

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