Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.3764
Extinction coefficient k: 0

Permittivity ε₁: 1.89447
Permittivity ε₂: 0

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

Abbe number V_d: 106.46
Chromatic dispersion dn/dλ: -0.0184167 µm⁻¹

Group index n_g: 1.38722
Group velocity dispersion: 30.3346 fs²/mm

Dispersion parameter D: -165.491 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

# MgF2 (Magnesium fluoride): Zheng et al. 2023: n(o) 0.22–1.7 µm; 186 °C
mgf2 = ls.fetch_refractiveindex("main", "MgF2", "Zheng-o-186C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mgf2.range_nm)  # (220, 1700) nm
eps = mgf2.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_a8e567550a78/lightsmith"
mgf2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(mgf2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (mgf2/zheng-2023-o-186c).

# ... load mgf2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=mgf2)],
    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_a8e567550a78/lightsmith?model=drude_lorentz"
mgf2_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{0.4876 λ^{2}}{λ^{2} - {0.043384}^{2}} + \frac{0.39509 λ^{2}}{λ^{2} - {0.094614}^{2}} + \frac{2.312 λ^{2}}{λ^{2} - {23.794}^{2}}

Valid from 0.22 to 1.7 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.4876
C3	0.043384
C4	0.39509
C5	0.094614
C6	2.312
C7	23.794

Comments and conditions

Ordinary ray (o). 186.4 °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: 459.55 K
direction: o

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

MgF2 (Magnesium fluoride), Zheng et al. 2023: n(o) 0.22–1.7 µm; 186 °C: n and k versus wavelength
λ (µm)	n
0.22	1.411339
0.22113	1.410867
0.222266	1.410403
0.223408	1.409944
0.224556	1.409492
0.22571	1.409046
0.22687	1.408606
0.228035	1.408172
0.229207	1.407744
0.230385	1.407321
0.231568	1.406904
0.232758	1.406493
0.233954	1.406088
0.235156	1.405687
0.236364	1.405292
0.237578	1.404903
0.238799	1.404518
0.240026	1.404138
0.241259	1.403764
0.242499	1.403394
0.243745	1.403029
0.244997	1.402669
0.246256	1.402314
0.247521	1.401963
0.248793	1.401616
0.250071	1.401274
0.251356	1.400937
0.252647	1.400604
0.253945	1.400275
0.25525	1.39995
0.256562	1.399629
0.25788	1.399313
0.259205	1.399
0.260536	1.398691
0.261875	1.398387
0.263221	1.398086
0.264573	1.397788
0.265932	1.397495
0.267299	1.397205
0.268672	1.396919
0.270052	1.396636
0.27144	1.396357
0.272834	1.396081
0.274236	1.395809
0.275645	1.395539
0.277061	1.395274
0.278485	1.395011
0.279916	1.394752
0.281354	1.394496
0.282799	1.394243
0.284252	1.393993
0.285713	1.393746
0.287181	1.393502
0.288656	1.39326
0.290139	1.393022
0.29163	1.392787
0.293128	1.392554
0.294634	1.392325
0.296148	1.392098
0.29767	1.391873
0.299199	1.391652
0.300736	1.391433
0.302282	1.391216
0.303835	1.391002
0.305396	1.390791
0.306965	1.390582
0.308542	1.390375
0.310127	1.390171
0.311721	1.38997
0.313322	1.38977
0.314932	1.389573
0.31655	1.389379
0.318176	1.389186
0.319811	1.388996
0.321454	1.388808
0.323106	1.388622
0.324766	1.388438
0.326435	1.388257
0.328112	1.388077
0.329798	1.3879
0.331492	1.387724
0.333195	1.387551
0.334907	1.387379
0.336628	1.38721
0.338357	1.387042
0.340096	1.386876
0.341843	1.386713
0.343599	1.386551
0.345365	1.38639
0.347139	1.386232
0.348923	1.386075
0.350716	1.38592
0.352517	1.385767
0.354329	1.385616
0.356149	1.385466
0.357979	1.385318
0.359818	1.385172
0.361667	1.385027
0.363525	1.384884
0.365393	1.384742
0.36727	1.384602
0.369157	1.384464
0.371054	1.384327
0.37296	1.384191
0.374876	1.384057
0.376803	1.383925
0.378738	1.383794
0.380684	1.383664
0.38264	1.383536
0.384606	1.383409
0.386582	1.383283
0.388568	1.383159
0.390565	1.383036
0.392572	1.382915
0.394589	1.382795
0.396616	1.382676
0.398654	1.382558
0.400702	1.382442
0.402761	1.382327
0.40483	1.382213
0.40691	1.3821
0.409001	1.381989
0.411102	1.381879
0.413214	1.38177
0.415337	1.381662
0.417471	1.381555
0.419616	1.381449
0.421772	1.381344
0.423939	1.381241
0.426117	1.381139
0.428306	1.381037
0.430507	1.380937
0.432719	1.380838
0.434942	1.38074
0.437177	1.380642
0.439423	1.380546
0.441681	1.380451
0.44395	1.380357
0.446231	1.380264
0.448524	1.380171
0.450828	1.38008
0.453144	1.379989
0.455472	1.3799
0.457813	1.379811
0.460165	1.379724
0.462529	1.379637
0.464905	1.379551
0.467294	1.379466
0.469695	1.379382
0.472108	1.379298
0.474534	1.379216
0.476972	1.379134
0.479422	1.379053
0.481886	1.378973
0.484362	1.378894
0.48685	1.378815
0.489351	1.378738
0.491866	1.378661
0.494393	1.378584
0.496933	1.378509
0.499486	1.378434
0.502052	1.37836
0.504632	1.378287
0.507225	1.378214
0.509831	1.378142
0.51245	1.378071
0.515083	1.378001
0.517729	1.377931
0.520389	1.377862
0.523063	1.377793
0.525751	1.377725
0.528452	1.377658
0.531167	1.377591
0.533896	1.377525
0.536639	1.37746
0.539396	1.377395
0.542168	1.377331
0.544953	1.377268
0.547753	1.377205
0.550567	1.377142
0.553396	1.37708
0.556239	1.377019
0.559097	1.376958
0.56197	1.376898
0.564857	1.376839
0.567759	1.37678
0.570676	1.376721
0.573608	1.376663
0.576555	1.376605
0.579518	1.376548
0.582495	1.376492
0.585488	1.376436
0.588496	1.37638
0.59152	1.376325
0.594559	1.376271
0.597614	1.376216
0.600684	1.376163
0.60377	1.376109
0.606872	1.376057
0.60999	1.376004
0.613124	1.375952
0.616275	1.375901
0.619441	1.37585
0.622623	1.375799
0.625822	1.375749
0.629038	1.375699
0.63227	1.37565
0.635518	1.375601
0.638783	1.375552
0.642065	1.375504
0.645364	1.375456
0.64868	1.375409
0.652013	1.375362
0.655363	1.375315
0.65873	1.375268
0.662114	1.375222
0.665516	1.375177
0.668936	1.375131
0.672373	1.375086
0.675827	1.375042
0.679299	1.374997
0.68279	1.374953
0.686298	1.374909
0.689824	1.374866
0.693368	1.374823
0.69693	1.37478
0.700511	1.374737
0.70411	1.374695
0.707728	1.374653
0.711364	1.374612
0.715019	1.37457
0.718693	1.374529
0.722385	1.374488
0.726097	1.374448
0.729827	1.374407
0.733577	1.374367
0.737346	1.374327
0.741134	1.374288
0.744942	1.374248
0.74877	1.374209
0.752617	1.37417
0.756483	1.374132
0.76037	1.374093
0.764277	1.374055
0.768204	1.374017
0.77215	1.373979
0.776118	1.373942
0.780105	1.373904
0.784113	1.373867
0.788142	1.37383
0.792191	1.373793
0.796262	1.373757
0.800353	1.37372
0.804465	1.373684
0.808598	1.373648
0.812752	1.373612
0.816928	1.373576
0.821125	1.373541
0.825344	1.373505
0.829585	1.37347
0.833847	1.373435
0.838131	1.3734
0.842437	1.373365
0.846766	1.37333
0.851116	1.373296
0.855489	1.373261
0.859885	1.373227
0.864303	1.373193
0.868743	1.373159
0.873207	1.373125
0.877693	1.373091
0.882203	1.373057
0.886735	1.373024
0.891291	1.37299
0.89587	1.372957
0.900473	1.372923
0.9051	1.37289
0.90975	1.372857
0.914424	1.372824
0.919122	1.372791
0.923845	1.372758
0.928591	1.372725
0.933362	1.372692
0.938158	1.37266
0.942978	1.372627
0.947823	1.372595
0.952693	1.372562
0.957587	1.372529
0.962507	1.372497
0.967453	1.372465
0.972423	1.372432
0.977419	1.3724
0.982441	1.372368
0.987489	1.372335
0.992562	1.372303
0.997662	1.372271
1.00279	1.372239
1.00794	1.372207
1.01312	1.372174
1.01832	1.372142
1.02356	1.37211
1.02881	1.372078
1.0341	1.372046
1.03941	1.372014
1.04475	1.371982
1.05012	1.371949
1.05552	1.371917
1.06094	1.371885
1.06639	1.371853
1.07187	1.37182
1.07738	1.371788
1.08291	1.371756
1.08848	1.371723
1.09407	1.371691
1.09969	1.371659
1.10534	1.371626
1.11102	1.371594
1.11673	1.371561
1.12247	1.371528
1.12823	1.371496
1.13403	1.371463
1.13986	1.37143
1.14571	1.371397
1.1516	1.371364
1.15752	1.371331
1.16346	1.371298
1.16944	1.371265
1.17545	1.371231
1.18149	1.371198
1.18756	1.371164
1.19366	1.371131
1.19979	1.371097
1.20596	1.371063
1.21215	1.371029
1.21838	1.370995
1.22464	1.370961
1.23093	1.370927
1.23726	1.370892
1.24361	1.370858
1.25	1.370823
1.25643	1.370788
1.26288	1.370753
1.26937	1.370718
1.27589	1.370683
1.28245	1.370648
1.28904	1.370612
1.29566	1.370576
1.30232	1.37054
1.30901	1.370504
1.31573	1.370468
1.32249	1.370432
1.32929	1.370395
1.33612	1.370359
1.34298	1.370322
1.34988	1.370284
1.35682	1.370247
1.36379	1.37021
1.37079	1.370172
1.37784	1.370134
1.38492	1.370096
1.39203	1.370057
1.39918	1.370019
1.40637	1.36998
1.4136	1.369941
1.42086	1.369902
1.42816	1.369862
1.4355	1.369823
1.44288	1.369783
1.45029	1.369742
1.45774	1.369702
1.46523	1.369661
1.47276	1.36962
1.48032	1.369579
1.48793	1.369537
1.49557	1.369495
1.50326	1.369453
1.51098	1.369411
1.51875	1.369368
1.52655	1.369325
1.53439	1.369282
1.54228	1.369239
1.5502	1.369195
1.55816	1.36915
1.56617	1.369106
1.57422	1.369061
1.5823	1.369016
1.59043	1.368971
1.59861	1.368925
1.60682	1.368879
1.61507	1.368832
1.62337	1.368785
1.63171	1.368738
1.6401	1.36869
1.64852	1.368642
1.65699	1.368594
1.66551	1.368545
1.67406	1.368496
1.68267	1.368447
1.69131	1.368397
1.7	1.368347

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: —

Plot