Optical constants

Refractive index of PbF₂ (Lead difluoride)

Malitson and Dodge 1969: n 0.3–11.9 µm

Data: formula 1
Range: 0.3–11.9 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.76651
Extinction coefficient k: 0

Permittivity ε₁: 3.12058
Permittivity ε₂: 0

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

Abbe number V_d: 28.51
Chromatic dispersion dn/dλ: -0.135486 µm⁻¹

Group index n_g: 1.84613
Group velocity dispersion: 275.902 fs²/mm

Dispersion parameter D: -1505.19 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

# PbF2 (Lead difluoride): Malitson and Dodge 1969: n 0.3–11.9 µm
pbf2 = ls.fetch_refractiveindex("main", "PbF2", "Malitson", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pbf2.range_nm)  # (300, 11900) nm
eps = pbf2.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_293815d446b4/lightsmith"
pbf2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pbf2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (pbf2/malitson-dodge-1969).

# ... load pbf2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=pbf2)],
    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_293815d446b4/lightsmith?model=drude_lorentz"
pbf2_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{0.66959342 λ^{2}}{λ^{2} - {0.00034911}^{2}} + \frac{1.3086319 λ^{2}}{λ^{2} - {0.17144455}^{2}} + \frac{0.01670641 λ^{2}}{λ^{2} - {0.28125513}^{2}} + \frac{2007.8865 λ^{2}}{λ^{2} - {796.67469}^{2}}

Valid from 0.3 to 11.9 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.66959342
C3	0.00034911
C4	1.3086319
C5	0.17144455
C6	0.01670641
C7	0.28125513
C8	2007.8865
C9	796.67469

References

I. H. Malitson and M. J. Dodge. Refraction and dispersion of lead fluoride, J. Opt. Soc. Am. 59, 500A (1969) (as cited in Handbook of Optics, 2nd edition, Vol. 2. McGraw-Hill 1994)

Cite

I. H. Malitson and M. J. Dodge. Refraction and dispersion of lead fluoride, J. Opt. Soc. Am. 59, 500A (1969) (as cited in Handbook of Optics, 2nd edition, Vol. 2. McGraw-Hill 1994); 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

PbF2 (Lead difluoride), Malitson and Dodge 1969: n 0.3–11.9 µm: n and k versus wavelength
λ (µm)	n
0.3	1.936648
0.30278	1.928044
0.305586	1.920496
0.308418	1.913727
0.311276	1.907557
0.314161	1.901866
0.317072	1.896567
0.32001	1.891598
0.322976	1.886913
0.325969	1.882474
0.32899	1.878254
0.332038	1.87423
0.335115	1.870382
0.338221	1.866694
0.341355	1.863155
0.344518	1.859752
0.347711	1.856476
0.350933	1.853318
0.354185	1.850271
0.357468	1.847328
0.36078	1.844483
0.364124	1.841731
0.367498	1.839066
0.370904	1.836485
0.374341	1.833984
0.37781	1.831558
0.381311	1.829204
0.384845	1.82692
0.388411	1.824701
0.39201	1.822546
0.395643	1.820452
0.39931	1.818416
0.40301	1.816436
0.406745	1.81451
0.410514	1.812636
0.414318	1.810812
0.418158	1.809036
0.422033	1.807307
0.425944	1.805623
0.429891	1.803982
0.433875	1.802383
0.437896	1.800825
0.441954	1.799305
0.446049	1.797824
0.450183	1.796379
0.454354	1.79497
0.458565	1.793596
0.462815	1.792254
0.467103	1.790946
0.471432	1.789668
0.475801	1.788421
0.48021	1.787203
0.48466	1.786014
0.489152	1.784853
0.493685	1.783719
0.49826	1.782611
0.502877	1.781529
0.507537	1.780471
0.51224	1.779438
0.516987	1.778428
0.521778	1.777441
0.526614	1.776476
0.531494	1.775533
0.536419	1.77461
0.54139	1.773708
0.546407	1.772826
0.551471	1.771963
0.556581	1.77112
0.561739	1.770294
0.566945	1.769487
0.572199	1.768697
0.577501	1.767923
0.582853	1.767167
0.588254	1.766427
0.593706	1.765702
0.599207	1.764993
0.60476	1.764298
0.610365	1.763618
0.616021	1.762953
0.62173	1.762301
0.627491	1.761663
0.633306	1.761038
0.639175	1.760426
0.645098	1.759827
0.651076	1.75924
0.65711	1.758665
0.663199	1.758101
0.669345	1.757549
0.675548	1.757009
0.681808	1.756479
0.688127	1.755959
0.694504	1.75545
0.70094	1.754952
0.707435	1.754463
0.713991	1.753983
0.720608	1.753514
0.727285	1.753053
0.734025	1.752602
0.740827	1.752159
0.747693	1.751725
0.754622	1.751299
0.761615	1.750882
0.768673	1.750472
0.775796	1.750071
0.782985	1.749677
0.790241	1.74929
0.797564	1.748911
0.804955	1.748539
0.812415	1.748174
0.819943	1.747816
0.827542	1.747465
0.835211	1.74712
0.842951	1.746781
0.850762	1.746449
0.858646	1.746123
0.866603	1.745803
0.874634	1.745488
0.882739	1.74518
0.89092	1.744877
0.899176	1.744579
0.907509	1.744286
0.915919	1.743999
0.924406	1.743717
0.932973	1.74344
0.941619	1.743168
0.950345	1.7429
0.959152	1.742637
0.96804	1.742379
0.977011	1.742125
0.986065	1.741875
0.995203	1.741629
1.00443	1.741388
1.01373	1.741151
1.02313	1.740917
1.03261	1.740688
1.04218	1.740462
1.05184	1.74024
1.06158	1.740021
1.07142	1.739806
1.08135	1.739594
1.09137	1.739386
1.10148	1.739181
1.11169	1.738979
1.12199	1.73878
1.13239	1.738584
1.14289	1.738391
1.15348	1.738201
1.16417	1.738013
1.17495	1.737829
1.18584	1.737647
1.19683	1.737467
1.20792	1.73729
1.21912	1.737116
1.23041	1.736944
1.24182	1.736774
1.25332	1.736607
1.26494	1.736441
1.27666	1.736278
1.28849	1.736117
1.30043	1.735958
1.31248	1.7358
1.32465	1.735645
1.33692	1.735492
1.34931	1.73534
1.36182	1.73519
1.37444	1.735042
1.38717	1.734895
1.40003	1.73475
1.413	1.734606
1.4261	1.734464
1.43931	1.734323
1.45265	1.734183
1.46611	1.734045
1.4797	1.733908
1.49341	1.733773
1.50725	1.733638
1.52122	1.733505
1.53531	1.733372
1.54954	1.733241
1.5639	1.73311
1.57839	1.732981
1.59302	1.732852
1.60778	1.732724
1.62268	1.732597
1.63772	1.732471
1.6529	1.732345
1.66822	1.73222
1.68367	1.732095
1.69928	1.731972
1.71502	1.731848
1.73092	1.731725
1.74696	1.731603
1.76315	1.731481
1.77949	1.731359
1.79598	1.731237
1.81262	1.731116
1.82942	1.730995
1.84637	1.730874
1.86348	1.730753
1.88075	1.730633
1.89818	1.730512
1.91577	1.730391
1.93352	1.730271
1.95144	1.73015
1.96952	1.730029
1.98778	1.729908
2.0062	1.729786
2.02479	1.729665
2.04355	1.729543
2.06249	1.729421
2.0816	1.729298
2.10089	1.729175
2.12036	1.729052
2.14001	1.728928
2.15984	1.728803
2.17986	1.728678
2.20006	1.728552
2.22045	1.728426
2.24102	1.728298
2.26179	1.72817
2.28275	1.728041
2.30391	1.727912
2.32526	1.727781
2.3468	1.72765
2.36855	1.727517
2.3905	1.727384
2.41265	1.727249
2.43501	1.727113
2.45758	1.726976
2.48035	1.726838
2.50334	1.726698
2.52654	1.726557
2.54995	1.726415
2.57358	1.726272
2.59743	1.726126
2.6215	1.72598
2.64579	1.725832
2.67031	1.725682
2.69506	1.72553
2.72003	1.725377
2.74524	1.725222
2.77068	1.725065
2.79636	1.724906
2.82227	1.724746
2.84842	1.724583
2.87482	1.724418
2.90146	1.724251
2.92835	1.724082
2.95549	1.723911
2.98287	1.723737
3.01052	1.723561
3.03842	1.723383
3.06657	1.723202
3.09499	1.723019
3.12367	1.722833
3.15262	1.722645
3.18183	1.722453
3.21132	1.722259
3.24108	1.722062
3.27112	1.721862
3.30143	1.721659
3.33202	1.721453
3.3629	1.721244
3.39406	1.721032
3.42552	1.720816
3.45726	1.720597
3.4893	1.720375
3.52164	1.720149
3.55427	1.71992
3.58721	1.719686
3.62045	1.719449
3.654	1.719209
3.68786	1.718964
3.72204	1.718715
3.75653	1.718463
3.79134	1.718206
3.82648	1.717944
3.86194	1.717679
3.89773	1.717409
3.93385	1.717134
3.9703	1.716855
4.00709	1.716571
4.04423	1.716282
4.08171	1.715989
4.11953	1.71569
4.15771	1.715386
4.19624	1.715077
4.23512	1.714762
4.27437	1.714442
4.31398	1.714117
4.35396	1.713785
4.39431	1.713448
4.43503	1.713105
4.47613	1.712756
4.51761	1.712401
4.55947	1.71204
4.60173	1.711672
4.64437	1.711297
4.68741	1.710916
4.73085	1.710528
4.77469	1.710133
4.81894	1.709731
4.86359	1.709322
4.90866	1.708905
4.95415	1.708481
5.00006	1.708049
5.0464	1.707609
5.09316	1.707161
5.14036	1.706706
5.188	1.706241
5.23608	1.705769
5.2846	1.705287
5.33357	1.704797
5.383	1.704298
5.43288	1.70379
5.48323	1.703272
5.53404	1.702745
5.58532	1.702208
5.63708	1.701662
5.68932	1.701105
5.74205	1.700538
5.79526	1.69996
5.84896	1.699371
5.90316	1.698772
5.95787	1.698162
6.01308	1.69754
6.0688	1.696906
6.12504	1.696261
6.18181	1.695604
6.23909	1.694934
6.29691	1.694252
6.35526	1.693557
6.41416	1.692849
6.4736	1.692128
6.53359	1.691393
6.59414	1.690644
6.65524	1.689881
6.71692	1.689104
6.77916	1.688313
6.84199	1.687506
6.90539	1.686684
6.96938	1.685846
7.03397	1.684993
7.09915	1.684123
7.16494	1.683237
7.23134	1.682334
7.29835	1.681414
7.36598	1.680477
7.43425	1.679522
7.50314	1.678548
7.57267	1.677556
7.64285	1.676545
7.71367	1.675514
7.78516	1.674464
7.8573	1.673394
7.93011	1.672303
8.0036	1.671192
8.07777	1.670059
8.15263	1.668904
8.22818	1.667727
8.30443	1.666528
8.38139	1.665305
8.45906	1.664059
8.53745	1.662788
8.61657	1.661494
8.69642	1.660174
8.777	1.658828
8.85834	1.657457
8.94043	1.656058
9.02328	1.654633
9.1069	1.65318
9.1913	1.651699
9.27647	1.650189
9.36244	1.648649
9.4492	1.64708
9.53676	1.645479
9.62514	1.643848
9.71434	1.642184
9.80436	1.640488
9.89522	1.638758
9.98692	1.636995
10.0795	1.635196
10.1729	1.633363
10.2671	1.631493
10.3623	1.629586
10.4583	1.627641
10.5552	1.625658
10.6531	1.623636
10.7518	1.621573
10.8514	1.619469
10.952	1.617324
11.0535	1.615135
11.1559	1.612903
11.2593	1.610626
11.3636	1.608303
11.4689	1.605934
11.5752	1.603517
11.6825	1.601052
11.7907	1.598536
11.9	1.59597

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: —

PbF₂ (Lead difluoride): all datasets

Malitson and Dodge 1969: n 0.3–11.9 µm n 0.3–11.9 µm default

About PbF2 (Lead difluoride)

Lead difluoride (PbF₂) is a crystalline compound that exhibits notable optical properties. It has a wide transmission range, spanning from the ultraviolet to the far-infrared region, making it an attractive choice for certain optical applications. In addition, PbF₂ is used in the fabrication of specialty glass, especially in combination with heavy metals, to produce glasses with unique refractive properties. Its optical properties have also led to its consideration in infrared optics, such as in the production of lenses and windows for IR systems. However, due to the presence of lead, precautions should be taken when handling or working with PbF₂ to minimize exposure.

More about PbF2 (Lead difluoride) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/PbF2/nk/Malitson.yml
ID: ds_293815d446b4
API: /v1/datasets/ds_293815d446b4

Plot