Optical constants

Refractive index of BaF₂ (Barium fluoride)

Zheng et al. 2023: n 0.22–1.7 µm; 21 °C

Data: formula 1
Range: 0.22–1.7 µm
Temperature: 294.25 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.47442
Extinction coefficient k: 0

Permittivity ε₁: 2.17392
Permittivity ε₂: 0

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

Abbe number V_d: 85.189
Chromatic dispersion dn/dλ: -0.0286665 µm⁻¹

Group index n_g: 1.49127
Group velocity dispersion: 52.5415 fs²/mm

Dispersion parameter D: -286.642 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): Zheng et al. 2023: n 0.22–1.7 µm; 21 °C
baf2 = ls.fetch_refractiveindex("main", "BaF2", "Zheng-21C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(baf2.range_nm)  # (220, 1700) 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_598d294466c9/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/zheng-2023-21c).

# ... 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_598d294466c9/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 = \frac{0.64336 λ^{2}}{λ^{2} - {0.057789}^{2}} + \frac{0.5076 λ^{2}}{λ^{2} - {0.10664}^{2}} + \frac{3.8261 λ^{2}}{λ^{2} - {46.386}^{2}}

Valid from 0.22 to 1.7 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.64336
C3	0.057789
C4	0.5076
C5	0.10664
C6	3.8261
C7	46.386

Comments and conditions

21.1 °C. The supplementary materials of the original publication contain coefficients of the Sellmeier formula for multiple temperatures in the range of 21 °C to 368 °C.

Conditions

temperature: 294.25 K

References

Q. Zheng, X. Wang, D. Thompson. Temperature-dependent optical properties of monocrystalline CaF₂, BaF₂, and MgF₂. Opt. Mater. Express 13, 2380–2391 (2023) (See Supplementary materials)

doi:10.1364/ome.496246 Temperature-dependent optical properties of monocrystalline CaF2, BaF2, and MgF2, Optical Materials Express (2023)

Cite

Qifan Zheng, Xinchao Wang and Dakotah Thompson. Temperature-dependent optical properties of monocrystalline CaF2, BaF2, and MgF2. Optical Materials Express, 13, 2380 (2023), doi:10.1364/ome.496246; 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), Zheng et al. 2023: n 0.22–1.7 µm; 21 °C: n and k versus wavelength
λ (µm)	n
0.22	1.534422
0.22113	1.533576
0.222266	1.532743
0.223408	1.531923
0.224556	1.531114
0.22571	1.530317
0.22687	1.529532
0.228035	1.528758
0.229207	1.527996
0.230385	1.527244
0.231568	1.526504
0.232758	1.525774
0.233954	1.525054
0.235156	1.524344
0.236364	1.523645
0.237578	1.522955
0.238799	1.522275
0.240026	1.521605
0.241259	1.520944
0.242499	1.520292
0.243745	1.519649
0.244997	1.519015
0.246256	1.51839
0.247521	1.517773
0.248793	1.517165
0.250071	1.516565
0.251356	1.515973
0.252647	1.515389
0.253945	1.514813
0.25525	1.514245
0.256562	1.513684
0.25788	1.513131
0.259205	1.512585
0.260536	1.512046
0.261875	1.511515
0.263221	1.510991
0.264573	1.510473
0.265932	1.509962
0.267299	1.509458
0.268672	1.508961
0.270052	1.50847
0.27144	1.507985
0.272834	1.507507
0.274236	1.507035
0.275645	1.506568
0.277061	1.506108
0.278485	1.505654
0.279916	1.505206
0.281354	1.504763
0.282799	1.504326
0.284252	1.503894
0.285713	1.503468
0.287181	1.503047
0.288656	1.502632
0.290139	1.502222
0.29163	1.501817
0.293128	1.501417
0.294634	1.501022
0.296148	1.500632
0.29767	1.500246
0.299199	1.499866
0.300736	1.49949
0.302282	1.499119
0.303835	1.498752
0.305396	1.49839
0.306965	1.498032
0.308542	1.497679
0.310127	1.49733
0.311721	1.496985
0.313322	1.496645
0.314932	1.496309
0.31655	1.495976
0.318176	1.495648
0.319811	1.495324
0.321454	1.495003
0.323106	1.494686
0.324766	1.494374
0.326435	1.494065
0.328112	1.493759
0.329798	1.493457
0.331492	1.493159
0.333195	1.492865
0.334907	1.492574
0.336628	1.492286
0.338357	1.492002
0.340096	1.491721
0.341843	1.491443
0.343599	1.491169
0.345365	1.490898
0.347139	1.49063
0.348923	1.490365
0.350716	1.490103
0.352517	1.489845
0.354329	1.489589
0.356149	1.489336
0.357979	1.489086
0.359818	1.48884
0.361667	1.488596
0.363525	1.488354
0.365393	1.488116
0.36727	1.48788
0.369157	1.487647
0.371054	1.487417
0.37296	1.487189
0.374876	1.486964
0.376803	1.486742
0.378738	1.486522
0.380684	1.486305
0.38264	1.48609
0.384606	1.485877
0.386582	1.485667
0.388568	1.485459
0.390565	1.485254
0.392572	1.485051
0.394589	1.48485
0.396616	1.484652
0.398654	1.484456
0.400702	1.484262
0.402761	1.48407
0.40483	1.48388
0.40691	1.483692
0.409001	1.483507
0.411102	1.483323
0.413214	1.483142
0.415337	1.482963
0.417471	1.482785
0.419616	1.48261
0.421772	1.482437
0.423939	1.482265
0.426117	1.482095
0.428306	1.481928
0.430507	1.481762
0.432719	1.481598
0.434942	1.481435
0.437177	1.481275
0.439423	1.481116
0.441681	1.480959
0.44395	1.480804
0.446231	1.48065
0.448524	1.480499
0.450828	1.480348
0.453144	1.4802
0.455472	1.480053
0.457813	1.479907
0.460165	1.479764
0.462529	1.479621
0.464905	1.479481
0.467294	1.479341
0.469695	1.479204
0.472108	1.479068
0.474534	1.478933
0.476972	1.4788
0.479422	1.478668
0.481886	1.478537
0.484362	1.478408
0.48685	1.478281
0.489351	1.478155
0.491866	1.47803
0.494393	1.477906
0.496933	1.477784
0.499486	1.477663
0.502052	1.477543
0.504632	1.477425
0.507225	1.477308
0.509831	1.477192
0.51245	1.477077
0.515083	1.476964
0.517729	1.476851
0.520389	1.47674
0.523063	1.47663
0.525751	1.476522
0.528452	1.476414
0.531167	1.476307
0.533896	1.476202
0.536639	1.476098
0.539396	1.475995
0.542168	1.475893
0.544953	1.475791
0.547753	1.475692
0.550567	1.475593
0.553396	1.475495
0.556239	1.475398
0.559097	1.475302
0.56197	1.475207
0.564857	1.475113
0.567759	1.47502
0.570676	1.474928
0.573608	1.474837
0.576555	1.474747
0.579518	1.474658
0.582495	1.474569
0.585488	1.474482
0.588496	1.474395
0.59152	1.47431
0.594559	1.474225
0.597614	1.474141
0.600684	1.474058
0.60377	1.473976
0.606872	1.473895
0.60999	1.473814
0.613124	1.473734
0.616275	1.473655
0.619441	1.473577
0.622623	1.4735
0.625822	1.473423
0.629038	1.473347
0.63227	1.473272
0.635518	1.473198
0.638783	1.473124
0.642065	1.473052
0.645364	1.472979
0.64868	1.472908
0.652013	1.472837
0.655363	1.472767
0.65873	1.472698
0.662114	1.472629
0.665516	1.472561
0.668936	1.472494
0.672373	1.472427
0.675827	1.472361
0.679299	1.472296
0.68279	1.472231
0.686298	1.472167
0.689824	1.472103
0.693368	1.47204
0.69693	1.471978
0.700511	1.471916
0.70411	1.471855
0.707728	1.471795
0.711364	1.471735
0.715019	1.471675
0.718693	1.471617
0.722385	1.471558
0.726097	1.471501
0.729827	1.471443
0.733577	1.471387
0.737346	1.471331
0.741134	1.471275
0.744942	1.47122
0.74877	1.471165
0.752617	1.471111
0.756483	1.471057
0.76037	1.471004
0.764277	1.470952
0.768204	1.4709
0.77215	1.470848
0.776118	1.470797
0.780105	1.470746
0.784113	1.470696
0.788142	1.470646
0.792191	1.470596
0.796262	1.470547
0.800353	1.470499
0.804465	1.470451
0.808598	1.470403
0.812752	1.470356
0.816928	1.470309
0.821125	1.470262
0.825344	1.470216
0.829585	1.470171
0.833847	1.470125
0.838131	1.47008
0.842437	1.470036
0.846766	1.469992
0.851116	1.469948
0.855489	1.469904
0.859885	1.469861
0.864303	1.469819
0.868743	1.469776
0.873207	1.469734
0.877693	1.469693
0.882203	1.469651
0.886735	1.46961
0.891291	1.46957
0.89587	1.469529
0.900473	1.469489
0.9051	1.469449
0.90975	1.46941
0.914424	1.469371
0.919122	1.469332
0.923845	1.469294
0.928591	1.469255
0.933362	1.469217
0.938158	1.46918
0.942978	1.469142
0.947823	1.469105
0.952693	1.469068
0.957587	1.469032
0.962507	1.468996
0.967453	1.468959
0.972423	1.468924
0.977419	1.468888
0.982441	1.468853
0.987489	1.468818
0.992562	1.468783
0.997662	1.468748
1.00279	1.468714
1.00794	1.46868
1.01312	1.468646
1.01832	1.468612
1.02356	1.468579
1.02881	1.468546
1.0341	1.468513
1.03941	1.46848
1.04475	1.468447
1.05012	1.468415
1.05552	1.468382
1.06094	1.46835
1.06639	1.468318
1.07187	1.468287
1.07738	1.468255
1.08291	1.468224
1.08848	1.468193
1.09407	1.468162
1.09969	1.468131
1.10534	1.4681
1.11102	1.46807
1.11673	1.46804
1.12247	1.468009
1.12823	1.467979
1.13403	1.467949
1.13986	1.46792
1.14571	1.46789
1.1516	1.467861
1.15752	1.467831
1.16346	1.467802
1.16944	1.467773
1.17545	1.467744
1.18149	1.467715
1.18756	1.467687
1.19366	1.467658
1.19979	1.46763
1.20596	1.467601
1.21215	1.467573
1.21838	1.467545
1.22464	1.467517
1.23093	1.467489
1.23726	1.467461
1.24361	1.467433
1.25	1.467406
1.25643	1.467378
1.26288	1.46735
1.26937	1.467323
1.27589	1.467296
1.28245	1.467268
1.28904	1.467241
1.29566	1.467214
1.30232	1.467187
1.30901	1.46716
1.31573	1.467133
1.32249	1.467106
1.32929	1.467079
1.33612	1.467052
1.34298	1.467026
1.34988	1.466999
1.35682	1.466972
1.36379	1.466946
1.37079	1.466919
1.37784	1.466893
1.38492	1.466866
1.39203	1.46684
1.39918	1.466813
1.40637	1.466787
1.4136	1.46676
1.42086	1.466734
1.42816	1.466707
1.4355	1.466681
1.44288	1.466655
1.45029	1.466628
1.45774	1.466602
1.46523	1.466576
1.47276	1.466549
1.48032	1.466523
1.48793	1.466496
1.49557	1.46647
1.50326	1.466444
1.51098	1.466417
1.51875	1.466391
1.52655	1.466364
1.53439	1.466338
1.54228	1.466311
1.5502	1.466285
1.55816	1.466258
1.56617	1.466231
1.57422	1.466205
1.5823	1.466178
1.59043	1.466151
1.59861	1.466125
1.60682	1.466098
1.61507	1.466071
1.62337	1.466044
1.63171	1.466017
1.6401	1.46599
1.64852	1.465962
1.65699	1.465935
1.66551	1.465908
1.67406	1.465881
1.68267	1.465853
1.69131	1.465826
1.7	1.465798

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/Zheng-21C.yml
ID: ds_598d294466c9
API: /v1/datasets/ds_598d294466c9

Plot