Optical constants

Refractive index of SrTiO₃ (Strontium titanate, STO)

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: 2.06
Extinction coefficient k: 0

Permittivity ε₁: 4.24361
Permittivity ε₂: 0

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

Abbe number V_d: 19.985
Chromatic dispersion dn/dλ: -0.267806 µm⁻¹

Group index n_g: 2.21737
Group velocity dispersion: 544.179 fs²/mm

Dispersion parameter D: -2968.78 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

# SrTiO3 (Strontium titanate, STO): Wöhlecke et al. 1977: Microcrystalline; n 0.3–1.0 µm
srtio3 = ls.fetch_refractiveindex("main", "SrTiO3", "Wohlecke-mx", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(srtio3.range_nm)  # (300, 1000) nm
eps = srtio3.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_fc218047b009/lightsmith"
srtio3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(srtio3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (srtio3/wohlecke-1977-mx).

# ... load srtio3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=srtio3)],
    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_fc218047b009/lightsmith?model=drude_lorentz"
srtio3_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{2.9489 λ^{2}}{λ^{2} - {0.17712}^{2}}

Valid from 0.3 to 1.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	2.9489
C3	0.17712

Comments and conditions

Microcrystalline 1–4 µm thin film. Prepared by RF sputter deposition at 500 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

SrTiO3 (Strontium titanate, STO), Wöhlecke et al. 1977: Microcrystalline; n 0.3–1.0 µm: n and k versus wavelength
λ (µm)	n
0.3	2.35092
0.300907	2.347828
0.301816	2.344771
0.302728	2.341747
0.303643	2.338756
0.304561	2.335798
0.305481	2.332872
0.306404	2.329978
0.30733	2.327115
0.308259	2.324283
0.30919	2.321482
0.310125	2.31871
0.311062	2.315968
0.312002	2.313254
0.312945	2.31057
0.313891	2.307913
0.314839	2.305285
0.315791	2.302683
0.316745	2.300109
0.317702	2.297562
0.318662	2.295041
0.319625	2.292545
0.320591	2.290076
0.32156	2.287631
0.322532	2.285212
0.323507	2.282817
0.324484	2.280446
0.325465	2.278099
0.326448	2.275775
0.327435	2.273475
0.328424	2.271198
0.329417	2.268943
0.330412	2.266711
0.331411	2.264501
0.332412	2.262312
0.333417	2.260145
0.334425	2.258
0.335435	2.255875
0.336449	2.25377
0.337466	2.251687
0.338486	2.249623
0.339508	2.247579
0.340535	2.245555
0.341564	2.24355
0.342596	2.241564
0.343631	2.239597
0.34467	2.237649
0.345711	2.235719
0.346756	2.233807
0.347804	2.231914
0.348855	2.230038
0.349909	2.228179
0.350967	2.226338
0.352027	2.224514
0.353091	2.222707
0.354158	2.220917
0.355228	2.219143
0.356302	2.217386
0.357379	2.215644
0.358459	2.213919
0.359542	2.212209
0.360629	2.210515
0.361718	2.208836
0.362812	2.207172
0.363908	2.205523
0.365008	2.20389
0.366111	2.20227
0.367217	2.200666
0.368327	2.199075
0.36944	2.197499
0.370556	2.195937
0.371676	2.194388
0.372799	2.192854
0.373926	2.191333
0.375056	2.189825
0.37619	2.18833
0.377326	2.186849
0.378467	2.18538
0.37961	2.183925
0.380758	2.182482
0.381908	2.181051
0.383062	2.179633
0.38422	2.178227
0.385381	2.176833
0.386546	2.175451
0.387714	2.174081
0.388886	2.172723
0.390061	2.171376
0.39124	2.170041
0.392422	2.168717
0.393608	2.167405
0.394797	2.166103
0.395991	2.164812
0.397187	2.163533
0.398388	2.162264
0.399591	2.161006
0.400799	2.159758
0.40201	2.15852
0.403225	2.157293
0.404444	2.156077
0.405666	2.15487
0.406892	2.153673
0.408122	2.152486
0.409355	2.151309
0.410592	2.150142
0.411833	2.148984
0.413077	2.147836
0.414326	2.146697
0.415578	2.145568
0.416834	2.144448
0.418093	2.143336
0.419357	2.142234
0.420624	2.141141
0.421895	2.140057
0.42317	2.138981
0.424449	2.137914
0.425732	2.136856
0.427018	2.135806
0.428309	2.134765
0.429603	2.133731
0.430902	2.132707
0.432204	2.13169
0.43351	2.130681
0.43482	2.129681
0.436134	2.128688
0.437452	2.127704
0.438774	2.126727
0.4401	2.125757
0.44143	2.124796
0.442764	2.123842
0.444102	2.122895
0.445444	2.121956
0.44679	2.121024
0.44814	2.1201
0.449495	2.119183
0.450853	2.118273
0.452216	2.11737
0.453582	2.116474
0.454953	2.115585
0.456328	2.114702
0.457707	2.113827
0.45909	2.112958
0.460478	2.112097
0.461869	2.111241
0.463265	2.110393
0.464665	2.10955
0.466069	2.108715
0.467478	2.107885
0.46889	2.107062
0.470307	2.106246
0.471729	2.105435
0.473154	2.104631
0.474584	2.103832
0.476018	2.10304
0.477457	2.102254
0.4789	2.101474
0.480347	2.100699
0.481799	2.099931
0.483255	2.099168
0.484715	2.098411
0.48618	2.09766
0.487649	2.096914
0.489123	2.096174
0.490601	2.095439
0.492084	2.09471
0.493571	2.093987
0.495062	2.093268
0.496558	2.092555
0.498059	2.091848
0.499564	2.091145
0.501074	2.090448
0.502588	2.089756
0.504107	2.089069
0.50563	2.088388
0.507158	2.087711
0.508691	2.087039
0.510228	2.086372
0.51177	2.08571
0.513317	2.085053
0.514868	2.084401
0.516424	2.083753
0.517985	2.08311
0.51955	2.082472
0.52112	2.081839
0.522695	2.08121
0.524275	2.080585
0.525859	2.079966
0.527448	2.07935
0.529042	2.07874
0.530641	2.078133
0.532244	2.077531
0.533853	2.076934
0.535466	2.07634
0.537084	2.075751
0.538708	2.075166
0.540335	2.074586
0.541968	2.074009
0.543606	2.073437
0.545249	2.072869
0.546897	2.072305
0.54855	2.071745
0.550207	2.071189
0.55187	2.070636
0.553538	2.070088
0.555211	2.069544
0.556888	2.069004
0.558571	2.068467
0.560259	2.067934
0.561953	2.067405
0.563651	2.06688
0.565354	2.066358
0.567063	2.065841
0.568776	2.065326
0.570495	2.064816
0.572219	2.064309
0.573949	2.063806
0.575683	2.063306
0.577423	2.062809
0.579168	2.062317
0.580918	2.061827
0.582674	2.061341
0.584434	2.060859
0.586201	2.06038
0.587972	2.059904
0.589749	2.059431
0.591531	2.058962
0.593319	2.058496
0.595112	2.058034
0.59691	2.057574
0.598714	2.057118
0.600524	2.056665
0.602338	2.056215
0.604159	2.055768
0.605984	2.055324
0.607816	2.054884
0.609653	2.054446
0.611495	2.054011
0.613343	2.05358
0.615196	2.053151
0.617056	2.052726
0.61892	2.052303
0.620791	2.051883
0.622667	2.051466
0.624549	2.051052
0.626436	2.050641
0.628329	2.050233
0.630228	2.049827
0.632132	2.049424
0.634043	2.049024
0.635959	2.048627
0.637881	2.048232
0.639808	2.04784
0.641742	2.047451
0.643681	2.047064
0.645627	2.046681
0.647578	2.046299
0.649535	2.04592
0.651498	2.045544
0.653466	2.045171
0.655441	2.0448
0.657422	2.044431
0.659409	2.044065
0.661402	2.043701
0.6634	2.04334
0.665405	2.042982
0.667416	2.042625
0.669433	2.042271
0.671456	2.04192
0.673485	2.041571
0.67552	2.041224
0.677562	2.04088
0.67961	2.040538
0.681663	2.040198
0.683723	2.03986
0.68579	2.039525
0.687862	2.039192
0.689941	2.038861
0.692026	2.038533
0.694117	2.038207
0.696215	2.037882
0.698319	2.03756
0.700429	2.037241
0.702546	2.036923
0.704669	2.036607
0.706798	2.036294
0.708934	2.035982
0.711077	2.035673
0.713226	2.035366
0.715381	2.035061
0.717543	2.034758
0.719711	2.034456
0.721886	2.034157
0.724068	2.03386
0.726256	2.033565
0.728451	2.033272
0.730652	2.03298
0.73286	2.032691
0.735075	2.032404
0.737297	2.032118
0.739525	2.031834
0.74176	2.031553
0.744001	2.031273
0.74625	2.030995
0.748505	2.030718
0.750767	2.030444
0.753036	2.030171
0.755311	2.0299
0.757594	2.029631
0.759883	2.029364
0.76218	2.029099
0.764483	2.028835
0.766793	2.028573
0.769111	2.028313
0.771435	2.028054
0.773766	2.027797
0.776105	2.027542
0.77845	2.027288
0.780803	2.027036
0.783162	2.026786
0.785529	2.026538
0.787903	2.026291
0.790284	2.026045
0.792672	2.025801
0.795068	2.025559
0.79747	2.025319
0.79988	2.02508
0.802298	2.024842
0.804722	2.024606
0.807154	2.024372
0.809593	2.024139
0.81204	2.023908
0.814494	2.023678
0.816955	2.02345
0.819424	2.023223
0.821901	2.022997
0.824384	2.022773
0.826876	2.022551
0.829374	2.02233
0.831881	2.02211
0.834395	2.021892
0.836916	2.021675
0.839446	2.02146
0.841982	2.021246
0.844527	2.021033
0.847079	2.020822
0.849639	2.020612
0.852207	2.020404
0.854782	2.020197
0.857365	2.019991
0.859956	2.019787
0.862555	2.019583
0.865162	2.019382
0.867776	2.019181
0.870399	2.018982
0.873029	2.018784
0.875667	2.018587
0.878314	2.018392
0.880968	2.018197
0.88363	2.018005
0.886301	2.017813
0.888979	2.017622
0.891666	2.017433
0.89436	2.017245
0.897063	2.017058
0.899774	2.016873
0.902493	2.016688
0.905221	2.016505
0.907956	2.016323
0.9107	2.016142
0.913452	2.015962
0.916213	2.015784
0.918981	2.015606
0.921759	2.01543
0.924544	2.015255
0.927338	2.015081
0.930141	2.014908
0.932952	2.014736
0.935771	2.014565
0.938599	2.014395
0.941435	2.014227
0.94428	2.014059
0.947134	2.013893
0.949996	2.013727
0.952867	2.013563
0.955747	2.0134
0.958635	2.013238
0.961532	2.013076
0.964438	2.012916
0.967353	2.012757
0.970276	2.012599
0.973208	2.012442
0.976149	2.012285
0.979099	2.01213
0.982058	2.011976
0.985026	2.011823
0.988003	2.011671
0.990988	2.011519
0.993983	2.011369
0.996987	2.01122
1	2.011071

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: —

SrTiO₃ (Strontium titanate, STO): all datasets

Bulk

Bond 1965: n 0.43–3.8 µm n 0.43–3.8 µm default

Thin film

About SrTiO3 (Strontium titanate, STO)

Strontium titanate (SrTiO₃) is a crystalline solid that is often transparent or pale yellow. It possesses perovskite structure and has garnered significant attention in the field of materials science and solid-state physics due to its intriguing dielectric, ferroelectric, and optical properties. SrTiO₃ is widely used as a substrate material for growing high-temperature superconductors, magnetic films, and other oxide thin films. Its high refractive index has also made it popular as a diamond simulant in jewelry, although this use has decreased in favor of more modern materials. In addition, it's used in electronics as a high-k dielectric in DRAM capacitors. The compound can be naturally found in a mineral called perovskite, but most commercial SrTiO₃ is synthetically produced.

Strontium titanate - Wikipedia

More about SrTiO3 (Strontium titanate, STO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/SrTiO3/nk/Wohlecke-mx.yml
ID: ds_fc218047b009
API: /v1/datasets/ds_fc218047b009

Plot