Optical constants

Refractive index of BaF₂ (Barium fluoride)

Li 1980: n 0.15–15.0 µm

Data: formula 1
Range: 0.15–15 µm
Temperature: 293 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.47456
Extinction coefficient k: 0

Permittivity ε₁: 2.17432
Permittivity ε₂: 0

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

Abbe number V_d: 81.78
Chromatic dispersion dn/dλ: -0.0298476 µm⁻¹

Group index n_g: 1.4921
Group velocity dispersion: 54.9477 fs²/mm

Dispersion parameter D: -299.769 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

# BaF2 (Barium fluoride): Li 1980: n 0.15–15.0 µm
baf2 = ls.fetch_refractiveindex("main", "BaF2", "Li", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(baf2.range_nm)  # (150, 15000) nm
eps = baf2.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_466790190ac2/lightsmith"
baf2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(baf2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (baf2/li-1980).

# ... load baf2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=baf2)],
    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_466790190ac2/lightsmith?model=drude_lorentz"
baf2_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 = 0.33973 + \frac{0.8107 λ^{2}}{λ^{2} - {0.10065}^{2}} + \frac{0.19652 λ^{2}}{λ^{2} - {29.87}^{2}} + \frac{4.52469 λ^{2}}{λ^{2} - {53.82}^{2}}

Valid from 0.15 to 15.0 µm.

Coefficients as stored

C_i	Value
C1	0.33973
C2	0.8107
C3	0.10065
C4	0.19652
C5	29.87
C6	4.52469
C7	53.82

Comments and conditions

293 K (20 °C).

Conditions

temperature: 293 K

References

H. H. Li. Refractive index of alkaline earth halides and its wavelength and temperature derivatives. J. Phys. Chem. Ref. Data 9, 161-289 (1980) and references therein.
* Sellmeier formula is derived by critical analysis of experimental data from several sources.

doi:10.1063/1.555616 Refractive index of alkaline earth halides and its wavelength and temperature derivatives, Journal of Physical and Chemical Reference Data (1980)

Cite

H. H. Li. Refractive index of alkaline earth halides and its wavelength and temperature derivatives. Journal of Physical and Chemical Reference Data, 9, 161-290 (1980), doi:10.1063/1.555616; 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

BaF2 (Barium fluoride), Li 1980: n 0.15–15.0 µm: n and k versus wavelength
λ (µm)	n
0.15	1.677598
0.151741	1.669515
0.153503	1.661863
0.155285	1.654608
0.157087	1.647722
0.158911	1.64118
0.160756	1.634958
0.162622	1.629035
0.16451	1.62339
0.166419	1.618006
0.168351	1.612866
0.170306	1.607956
0.172283	1.603261
0.174283	1.598769
0.176306	1.594468
0.178353	1.590347
0.180423	1.586396
0.182517	1.582605
0.184636	1.578967
0.18678	1.575472
0.188948	1.572114
0.191141	1.568885
0.19336	1.565779
0.195605	1.562789
0.197875	1.559911
0.200173	1.557138
0.202496	1.554465
0.204847	1.551889
0.207225	1.549404
0.209631	1.547006
0.212064	1.544691
0.214526	1.542457
0.217016	1.540298
0.219536	1.538212
0.222084	1.536196
0.224662	1.534247
0.22727	1.532362
0.229908	1.530538
0.232577	1.528774
0.235277	1.527065
0.238009	1.525411
0.240771	1.52381
0.243567	1.522258
0.246394	1.520755
0.249254	1.519297
0.252148	1.517885
0.255075	1.516515
0.258036	1.515187
0.261031	1.513899
0.264062	1.512649
0.267127	1.511436
0.270228	1.510259
0.273365	1.509117
0.276538	1.508007
0.279749	1.50693
0.282996	1.505884
0.286281	1.504867
0.289605	1.50388
0.292967	1.50292
0.296368	1.501988
0.299808	1.501081
0.303288	1.5002
0.306809	1.499344
0.310371	1.498511
0.313974	1.497701
0.317619	1.496913
0.321306	1.496146
0.325036	1.495401
0.328809	1.494675
0.332626	1.493969
0.336487	1.493282
0.340393	1.492613
0.344345	1.491962
0.348342	1.491329
0.352386	1.490712
0.356477	1.490111
0.360615	1.489526
0.364801	1.488956
0.369036	1.488401
0.37332	1.487861
0.377654	1.487334
0.382038	1.486821
0.386473	1.486321
0.390959	1.485834
0.395498	1.485359
0.400089	1.484897
0.404733	1.484446
0.409432	1.484006
0.414185	1.483578
0.418993	1.48316
0.423857	1.482753
0.428777	1.482356
0.433755	1.481968
0.43879	1.481591
0.443884	1.481223
0.449037	1.480863
0.454249	1.480513
0.459523	1.480171
0.464857	1.479838
0.470253	1.479513
0.475712	1.479195
0.481235	1.478885
0.486821	1.478583
0.492473	1.478288
0.498189	1.478001
0.503973	1.47772
0.509823	1.477446
0.515742	1.477178
0.521729	1.476917
0.527785	1.476662
0.533912	1.476412
0.54011	1.476169
0.54638	1.475932
0.552723	1.4757
0.559139	1.475473
0.56563	1.475252
0.572196	1.475036
0.578839	1.474825
0.585558	1.474619
0.592356	1.474417
0.599232	1.47422
0.606188	1.474028
0.613225	1.47384
0.620344	1.473656
0.627545	1.473476
0.63483	1.473301
0.6422	1.473129
0.649655	1.472961
0.657197	1.472797
0.664826	1.472637
0.672543	1.47248
0.680351	1.472326
0.688249	1.472176
0.696238	1.472029
0.704321	1.471885
0.712497	1.471745
0.720768	1.471607
0.729135	1.471472
0.737599	1.47134
0.746162	1.471211
0.754824	1.471084
0.763586	1.470961
0.772451	1.470839
0.781418	1.47072
0.790489	1.470604
0.799665	1.47049
0.808948	1.470378
0.818339	1.470268
0.827839	1.47016
0.837449	1.470055
0.847171	1.469951
0.857005	1.46985
0.866954	1.46975
0.877018	1.469653
0.887199	1.469557
0.897498	1.469462
0.907917	1.46937
0.918457	1.469279
0.929119	1.469189
0.939905	1.469101
0.950816	1.469015
0.961853	1.46893
0.973019	1.468847
0.984314	1.468764
0.995741	1.468683
1.0073	1.468604
1.01899	1.468525
1.03082	1.468448
1.04279	1.468371
1.05489	1.468296
1.06714	1.468222
1.07953	1.468149
1.09206	1.468077
1.10474	1.468005
1.11756	1.467935
1.13054	1.467865
1.14366	1.467796
1.15694	1.467728
1.17037	1.467661
1.18395	1.467594
1.1977	1.467528
1.2116	1.467462
1.22567	1.467397
1.23989	1.467333
1.25429	1.467269
1.26885	1.467205
1.28358	1.467142
1.29848	1.46708
1.31355	1.467018
1.3288	1.466956
1.34423	1.466894
1.35983	1.466832
1.37562	1.466771
1.39159	1.46671
1.40774	1.466649
1.42408	1.466589
1.44061	1.466528
1.45734	1.466467
1.47425	1.466407
1.49137	1.466346
1.50868	1.466286
1.5262	1.466225
1.54391	1.466164
1.56183	1.466103
1.57997	1.466042
1.59831	1.465981
1.61686	1.465919
1.63563	1.465857
1.65462	1.465795
1.67383	1.465733
1.69326	1.46567
1.71291	1.465607
1.7328	1.465543
1.75291	1.465479
1.77326	1.465414
1.79385	1.465349
1.81467	1.465283
1.83574	1.465216
1.85705	1.465149
1.87861	1.465082
1.90041	1.465013
1.92247	1.464944
1.94479	1.464874
1.96737	1.464803
1.99021	1.464731
2.01331	1.464658
2.03668	1.464585
2.06033	1.46451
2.08424	1.464434
2.10844	1.464357
2.13291	1.46428
2.15767	1.4642
2.18272	1.46412
2.20806	1.464039
2.23369	1.463956
2.25962	1.463872
2.28585	1.463786
2.31239	1.463699
2.33923	1.463611
2.36639	1.463521
2.39386	1.46343
2.42165	1.463336
2.44976	1.463242
2.4782	1.463145
2.50697	1.463047
2.53607	1.462947
2.56551	1.462845
2.59529	1.462741
2.62542	1.462635
2.6559	1.462527
2.68673	1.462417
2.71792	1.462304
2.74947	1.46219
2.78139	1.462073
2.81368	1.461954
2.84634	1.461832
2.87938	1.461708
2.91281	1.461581
2.94662	1.461452
2.98083	1.46132
3.01543	1.461185
3.05044	1.461048
3.08585	1.460907
3.12167	1.460764
3.15791	1.460617
3.19457	1.460467
3.23165	1.460314
3.26917	1.460158
3.30712	1.459998
3.34551	1.459834
3.38435	1.459668
3.42363	1.459497
3.46338	1.459323
3.50358	1.459144
3.54425	1.458962
3.5854	1.458776
3.62702	1.458585
3.66912	1.45839
3.71172	1.458191
3.75481	1.457987
3.79839	1.457779
3.84249	1.457566
3.88709	1.457348
3.93222	1.457125
3.97787	1.456897
4.02404	1.456663
4.07076	1.456425
4.11801	1.45618
4.16582	1.455931
4.21418	1.455675
4.2631	1.455413
4.31259	1.455145
4.36265	1.454871
4.41329	1.454591
4.46453	1.454304
4.51635	1.454011
4.56878	1.45371
4.62182	1.453402
4.67547	1.453088
4.72975	1.452765
4.78466	1.452435
4.8402	1.452098
4.89639	1.451752
4.95323	1.451398
5.01073	1.451036
5.0689	1.450665
5.12774	1.450285
5.18726	1.449896
5.24748	1.449498
5.3084	1.44909
5.37002	1.448673
5.43236	1.448245
5.49542	1.447807
5.55922	1.447359
5.62375	1.4469
5.68904	1.44643
5.75508	1.445948
5.82189	1.445455
5.88947	1.44495
5.95784	1.444432
6.027	1.443902
6.09697	1.443359
6.16774	1.442803
6.23934	1.442233
6.31177	1.441649
6.38504	1.441051
6.45917	1.440439
6.53415	1.439811
6.61	1.439168
6.68673	1.438508
6.76436	1.437833
6.84288	1.437141
6.92232	1.436432
7.00268	1.435705
7.08397	1.43496
7.16621	1.434197
7.2494	1.433414
7.33355	1.432612
7.41868	1.43179
7.5048	1.430947
7.59193	1.430084
7.68006	1.429198
7.76921	1.42829
7.8594	1.427359
7.95064	1.426404
8.04294	1.425426
8.1363	1.424422
8.23075	1.423392
8.3263	1.422337
8.42296	1.421254
8.52074	1.420144
8.61965	1.419005
8.71971	1.417836
8.82094	1.416637
8.92334	1.415408
9.02693	1.414146
9.13172	1.412851
9.23772	1.411522
9.34496	1.410159
9.45344	1.40876
9.56318	1.407323
9.6742	1.405849
9.7865	1.404336
9.90011	1.402782
10.015	1.401187
10.1313	1.399549
10.2489	1.397866
10.3679	1.396139
10.4882	1.394364
10.61	1.392541
10.7332	1.390669
10.8578	1.388745
10.9838	1.386768
11.1113	1.384736
11.2403	1.382648
11.3708	1.380501
11.5028	1.378295
11.6363	1.376026
11.7714	1.373693
11.908	1.371294
12.0463	1.368826
12.1861	1.366287
12.3276	1.363674
12.4707	1.360986
12.6155	1.358219
12.7619	1.355371
12.9101	1.352439
13.0599	1.349419
13.2115	1.346309
13.3649	1.343104
13.5201	1.339803
13.677	1.336401
13.8358	1.332894
13.9964	1.329277
14.1589	1.325548
14.3232	1.321701
14.4895	1.317732
14.6577	1.313636
14.8279	1.309407
15	1.30504

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: —

BaF₂ (Barium fluoride): all datasets

About BaF2 (Barium fluoride)

BaF₂, or barium fluoride, is a crystal that offers a wide transmission range, spanning from the ultraviolet into the mid-infrared regions. This material is commonly used in specialized optical applications such as scintillators in high-energy physics experiments, and as windows and lenses in infrared spectroscopy systems. It possesses a relatively low refractive index and high resistance to radiation damage, which makes it especially useful in extreme conditions. Additionally, BaF₂ has fast scintillation response times, making it advantageous in fast-timing applications. One drawback, however, is that the crystal is hygroscopic, making it sensitive to moisture and requiring proper storage and handling to maintain its optical properties. It also has a lower resistance to thermal and mechanical shock compared to other fluoride crystals, which can be a consideration depending on the intended application. Despite these limitations, BaF₂ remains a highly valuable material for specialized optical and photonic applications, owing to its broad transmission range and resilience to high-energy radiation.

More about BaF2 (Barium fluoride) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/BaF2/nk/Li.yml
ID: ds_466790190ac2
API: /v1/datasets/ds_466790190ac2

Plot