Optical constants

Refractive index of BaTiO₃ (Barium titanate)

Wöhlecke et al. 1977: Microcrystalline; n 0.3–1.0 µm

Data: formula 1
Range: 0.3–1 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.05207
Extinction coefficient k: 0

Permittivity ε₁: 4.21101
Permittivity ε₂: 0

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

Abbe number V_d: 20.605
Chromatic dispersion dn/dλ: -0.257988 µm⁻¹

Group index n_g: 2.20367
Group velocity dispersion: 522.694 fs²/mm

Dispersion parameter D: -2851.58 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

# BaTiO3 (Barium titanate): Wöhlecke et al. 1977: Microcrystalline; n 0.3–1.0 µm
batio3 = ls.fetch_refractiveindex("main", "BaTiO3", "Wohlecke-mx", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(batio3.range_nm)  # (300, 1000) nm
eps = batio3.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_b1769e8bbe01/lightsmith"
batio3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(batio3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (batio3/wohlecke-1977-mx).

# ... load batio3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=batio3)],
    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_b1769e8bbe01/lightsmith?model=drude_lorentz"
batio3_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{2.9274 λ^{2}}{λ^{2} - {0.17463}^{2}}

Valid from 0.3 to 1.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	2.9274
C3	0.17463

Comments and conditions

Microcrystalline 1–4 µm thin film. Prepared by RF sputter deposition at 600 K substrate temperature.

References

M. Wöhlecke, V. Marrello, A. Onton. Refractive index of BaTiO₃ and SrTiO₃ films. J. Appl. Phys. 48, 1748–1750 (1977)

doi:10.1063/1.323822 Refractive index of BaTiO3 and SrTiO3 films, Journal of Applied Physics (1977)

Cite

M. Wöhlecke, V. Marrello and A. Onton. Refractive index of BaTiO3 and SrTiO3 films. Journal of Applied Physics, 48, 1748-1750 (1977), doi:10.1063/1.323822; 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

BaTiO3 (Barium titanate), Wöhlecke et al. 1977: Microcrystalline; n 0.3–1.0 µm: n and k versus wavelength
λ (µm)	n
0.3	2.329737
0.300907	2.326814
0.301816	2.323923
0.302728	2.321063
0.303643	2.318234
0.304561	2.315435
0.305481	2.312666
0.306404	2.309927
0.30733	2.307216
0.308259	2.304534
0.30919	2.301881
0.310125	2.299255
0.311062	2.296657
0.312002	2.294086
0.312945	2.291541
0.313891	2.289023
0.314839	2.286531
0.315791	2.284064
0.316745	2.281622
0.317702	2.279206
0.318662	2.276813
0.319625	2.274446
0.320591	2.272102
0.32156	2.269781
0.322532	2.267484
0.323507	2.26521
0.324484	2.262958
0.325465	2.260729
0.326448	2.258521
0.327435	2.256336
0.328424	2.254172
0.329417	2.252029
0.330412	2.249907
0.331411	2.247805
0.332412	2.245724
0.333417	2.243663
0.334425	2.241622
0.335435	2.239601
0.336449	2.237599
0.337466	2.235616
0.338486	2.233652
0.339508	2.231707
0.340535	2.22978
0.341564	2.227871
0.342596	2.22598
0.343631	2.224107
0.34467	2.222251
0.345711	2.220413
0.346756	2.218592
0.347804	2.216788
0.348855	2.215
0.349909	2.213229
0.350967	2.211474
0.352027	2.209735
0.353091	2.208013
0.354158	2.206306
0.355228	2.204614
0.356302	2.202938
0.357379	2.201277
0.358459	2.199631
0.359542	2.198
0.360629	2.196383
0.361718	2.194781
0.362812	2.193193
0.363908	2.19162
0.365008	2.19006
0.366111	2.188514
0.367217	2.186982
0.368327	2.185464
0.36944	2.183959
0.370556	2.182467
0.371676	2.180988
0.372799	2.179522
0.373926	2.178068
0.375056	2.176628
0.37619	2.1752
0.377326	2.173784
0.378467	2.172381
0.37961	2.170989
0.380758	2.16961
0.381908	2.168242
0.383062	2.166887
0.38422	2.165542
0.385381	2.164209
0.386546	2.162888
0.387714	2.161578
0.388886	2.160279
0.390061	2.15899
0.39124	2.157713
0.392422	2.156446
0.393608	2.15519
0.394797	2.153945
0.395991	2.15271
0.397187	2.151485
0.398388	2.150271
0.399591	2.149066
0.400799	2.147872
0.40201	2.146687
0.403225	2.145513
0.404444	2.144347
0.405666	2.143192
0.406892	2.142046
0.408122	2.140909
0.409355	2.139782
0.410592	2.138664
0.411833	2.137555
0.413077	2.136455
0.414326	2.135364
0.415578	2.134281
0.416834	2.133208
0.418093	2.132143
0.419357	2.131087
0.420624	2.130039
0.421895	2.129
0.42317	2.127969
0.424449	2.126946
0.425732	2.125931
0.427018	2.124925
0.428309	2.123926
0.429603	2.122936
0.430902	2.121953
0.432204	2.120978
0.43351	2.120011
0.43482	2.119051
0.436134	2.118099
0.437452	2.117154
0.438774	2.116217
0.4401	2.115287
0.44143	2.114365
0.442764	2.11345
0.444102	2.112541
0.445444	2.11164
0.44679	2.110746
0.44814	2.109859
0.449495	2.108979
0.450853	2.108105
0.452216	2.107238
0.453582	2.106378
0.454953	2.105525
0.456328	2.104678
0.457707	2.103837
0.45909	2.103003
0.460478	2.102176
0.461869	2.101354
0.463265	2.100539
0.464665	2.099731
0.466069	2.098928
0.467478	2.098132
0.46889	2.097341
0.470307	2.096557
0.471729	2.095778
0.473154	2.095005
0.474584	2.094238
0.476018	2.093477
0.477457	2.092722
0.4789	2.091972
0.480347	2.091228
0.481799	2.09049
0.483255	2.089757
0.484715	2.089029
0.48618	2.088307
0.487649	2.08759
0.489123	2.086879
0.490601	2.086173
0.492084	2.085472
0.493571	2.084776
0.495062	2.084086
0.496558	2.083401
0.498059	2.08272
0.499564	2.082045
0.501074	2.081375
0.502588	2.080709
0.504107	2.080049
0.50563	2.079393
0.507158	2.078742
0.508691	2.078096
0.510228	2.077455
0.51177	2.076818
0.513317	2.076186
0.514868	2.075559
0.516424	2.074936
0.517985	2.074317
0.51955	2.073703
0.52112	2.073094
0.522695	2.072489
0.524275	2.071888
0.525859	2.071292
0.527448	2.0707
0.529042	2.070112
0.530641	2.069529
0.532244	2.06895
0.533853	2.068375
0.535466	2.067804
0.537084	2.067237
0.538708	2.066674
0.540335	2.066115
0.541968	2.06556
0.543606	2.065009
0.545249	2.064462
0.546897	2.063919
0.54855	2.06338
0.550207	2.062845
0.55187	2.062313
0.553538	2.061786
0.555211	2.061262
0.556888	2.060741
0.558571	2.060225
0.560259	2.059712
0.561953	2.059202
0.563651	2.058697
0.565354	2.058194
0.567063	2.057696
0.568776	2.057201
0.570495	2.056709
0.572219	2.056221
0.573949	2.055736
0.575683	2.055255
0.577423	2.054777
0.579168	2.054302
0.580918	2.05383
0.582674	2.053362
0.584434	2.052898
0.586201	2.052436
0.587972	2.051978
0.589749	2.051522
0.591531	2.05107
0.593319	2.050622
0.595112	2.050176
0.59691	2.049733
0.598714	2.049294
0.600524	2.048857
0.602338	2.048423
0.604159	2.047993
0.605984	2.047565
0.607816	2.047141
0.609653	2.046719
0.611495	2.0463
0.613343	2.045884
0.615196	2.045471
0.617056	2.045061
0.61892	2.044654
0.620791	2.044249
0.622667	2.043847
0.624549	2.043448
0.626436	2.043052
0.628329	2.042658
0.630228	2.042267
0.632132	2.041879
0.634043	2.041493
0.635959	2.04111
0.637881	2.04073
0.639808	2.040352
0.641742	2.039977
0.643681	2.039604
0.645627	2.039234
0.647578	2.038866
0.649535	2.038501
0.651498	2.038138
0.653466	2.037778
0.655441	2.03742
0.657422	2.037065
0.659409	2.036712
0.661402	2.036361
0.6634	2.036013
0.665405	2.035667
0.667416	2.035324
0.669433	2.034982
0.671456	2.034643
0.673485	2.034307
0.67552	2.033972
0.677562	2.03364
0.67961	2.03331
0.681663	2.032982
0.683723	2.032657
0.68579	2.032334
0.687862	2.032012
0.689941	2.031693
0.692026	2.031376
0.694117	2.031062
0.696215	2.030749
0.698319	2.030438
0.700429	2.03013
0.702546	2.029823
0.704669	2.029519
0.706798	2.029217
0.708934	2.028916
0.711077	2.028618
0.713226	2.028321
0.715381	2.028027
0.717543	2.027734
0.719711	2.027444
0.721886	2.027155
0.724068	2.026868
0.726256	2.026584
0.728451	2.026301
0.730652	2.026019
0.73286	2.02574
0.735075	2.025463
0.737297	2.025187
0.739525	2.024914
0.74176	2.024642
0.744001	2.024372
0.74625	2.024103
0.748505	2.023837
0.750767	2.023572
0.753036	2.023309
0.755311	2.023047
0.757594	2.022788
0.759883	2.02253
0.76218	2.022273
0.764483	2.022019
0.766793	2.021766
0.769111	2.021515
0.771435	2.021265
0.773766	2.021017
0.776105	2.020771
0.77845	2.020526
0.780803	2.020283
0.783162	2.020041
0.785529	2.019801
0.787903	2.019563
0.790284	2.019326
0.792672	2.019091
0.795068	2.018857
0.79747	2.018625
0.79988	2.018394
0.802298	2.018165
0.804722	2.017937
0.807154	2.017711
0.809593	2.017486
0.81204	2.017262
0.814494	2.017041
0.816955	2.01682
0.819424	2.016601
0.821901	2.016383
0.824384	2.016167
0.826876	2.015952
0.829374	2.015739
0.831881	2.015527
0.834395	2.015316
0.836916	2.015107
0.839446	2.014899
0.841982	2.014692
0.844527	2.014487
0.847079	2.014283
0.849639	2.014081
0.852207	2.013879
0.854782	2.013679
0.857365	2.013481
0.859956	2.013283
0.862555	2.013087
0.865162	2.012892
0.867776	2.012698
0.870399	2.012506
0.873029	2.012315
0.875667	2.012125
0.878314	2.011936
0.880968	2.011748
0.88363	2.011562
0.886301	2.011377
0.888979	2.011193
0.891666	2.01101
0.89436	2.010829
0.897063	2.010648
0.899774	2.010469
0.902493	2.010291
0.905221	2.010114
0.907956	2.009938
0.9107	2.009763
0.913452	2.009589
0.916213	2.009417
0.918981	2.009246
0.921759	2.009075
0.924544	2.008906
0.927338	2.008738
0.930141	2.008571
0.932952	2.008405
0.935771	2.00824
0.938599	2.008076
0.941435	2.007913
0.94428	2.007751
0.947134	2.00759
0.949996	2.007431
0.952867	2.007272
0.955747	2.007114
0.958635	2.006957
0.961532	2.006802
0.964438	2.006647
0.967353	2.006493
0.970276	2.00634
0.973208	2.006188
0.976149	2.006037
0.979099	2.005888
0.982058	2.005739
0.985026	2.005591
0.988003	2.005443
0.990988	2.005297
0.993983	2.005152
0.996987	2.005008
1	2.004864

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: —

BaTiO₃ (Barium titanate): all datasets

Bulk

Thin film

About BaTiO3 (Barium titanate)

BaTiO₃, or barium titanate, is a ferroelectric crystal with a perovskite structure that is highly prized for its dielectric and piezoelectric properties. In the realm of optics, this material is particularly important for its electro-optic and nonlinear optical capabilities. It exhibits a high refractive index, and its electro-optic coefficients are among the highest of the known crystals, making it well-suited for applications such as optical modulators and beam deflectors. In addition to its electro-optic uses, BaTiO₃ is employed in the fabrication of photonic devices like waveguides and resonators. Its ferroelectric nature also enables applications in data storage and other memory devices. BaTiO₃ can be grown using various techniques such as the Bridgman or Czochralski methods and can be doped with different elements to fine-tune its properties. While it is a robust and versatile material, it is sensitive to defects and impurities, which can impact its optical performance. Overall, BaTiO₃ is a multifunctional material with a wide range of applications in both the electronic and optical domains, making it a subject of continued research and technological development.

Barium titanate - Wikipedia

More about BaTiO3 (Barium titanate) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/BaTiO3/nk/Wohlecke-mx.yml
ID: ds_b1769e8bbe01
API: /v1/datasets/ds_b1769e8bbe01

Plot