Optical constants

Refractive index of Pb (Lead)

Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm

Data: tabulated nk
Range: 0.01759–2.48 µm
Points: 150
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.79964
Extinction coefficient k: 4.03215

Permittivity ε₁: -8.42019
Permittivity ε₂: 22.5772

Absorption coefficient α: 862312 cm⁻¹
Penetration depth δ = λ/(2πk): 23.1935 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 5.8493 µm⁻¹

Group index n_g: -0.637406
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — 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

# Pb (Lead): Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm
pb = ls.fetch_refractiveindex("main", "Pb", "Werner-DFT", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pb.range_nm)  # (17.586, 2479.68) nm
eps = pb.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_3c18de98871c/lightsmith"
pb = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pb.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (pb/werner-2009-dft).

# ... load pb as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=pb)],
    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"]).

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.

Comments and conditions

Theoretical density function theory (DFT) calculations.

References

W. S. M. Werner, K. Glantschnig, C. Ambrosch-Draxl. Optical constants and inelastic electron-scattering data for 17 elemental metals. J. Phys Chem Ref. Data 38, 1013-1092 (2009)

doi:10.1063/1.3243762 Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals, Journal of Physical and Chemical Reference Data (2009)

Cite

Wolfgang S. M. Werner, Kathrin Glantschnig and Claudia Ambrosch-Draxl. Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals. Journal of Physical and Chemical Reference Data, 38, 1013-1092 (2009), doi:10.1063/1.3243762; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

150 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Pb (Lead), Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm: n and k versus wavelength
λ (µm)	n	k
0.017586	0.8845	0.0475
0.017712	0.8846	0.0503
0.017839	0.884	0.0588
0.017969	0.8876	0.0614
0.0181	0.8908	0.0589
0.018233	0.8852	0.0593
0.018368	0.8837	0.0622
0.018505	0.8848	0.0763
0.018644	0.8976	0.0685
0.018785	0.8982	0.0612
0.018929	0.8893	0.0529
0.019074	0.8763	0.0531
0.019222	0.8699	0.069
0.019373	0.8768	0.0696
0.019525	0.874	0.0698
0.01968	0.8752	0.0703
0.019837	0.8681	0.0674
0.019997	0.8625	0.0696
0.02016	0.8536	0.075
0.020325	0.8458	0.0857
0.020493	0.8548	0.0983
0.020664	0.8542	0.0931
0.020838	0.8524	0.0927
0.021014	0.8383	0.0984
0.021194	0.8339	0.1115
0.021377	0.8441	0.1161
0.021562	0.8262	0.1168
0.021752	0.8138	0.1524
0.021944	0.8536	0.157
0.02214	0.8479	0.1515
0.022339	0.8567	0.1611
0.022543	0.8404	0.1559
0.022749	0.831	0.1962
0.02296	0.899	0.2219
0.023175	0.9213	0.1699
0.023393	0.9047	0.1498
0.023616	0.8916	0.1379
0.023843	0.8715	0.14
0.024075	0.865	0.1619
0.024311	0.8809	0.1447
0.024551	0.856	0.1332
0.024797	0.8389	0.1293
0.025047	0.7849	0.1306
0.025303	0.7381	0.2425
0.025564	0.8238	0.2804
0.02583	0.8882	0.2387
0.026102	0.86	0.1965
0.02638	0.785	0.2006
0.026663	0.7443	0.3493
0.026953	0.8765	0.3965
0.027249	0.988	0.3163
0.027552	0.9183	0.2668
0.027862	0.9237	0.302
0.028178	0.9105	0.2845
0.028502	0.9488	0.2904
0.028834	0.926	0.2819
0.029173	0.8958	0.3137
0.02952	0.9496	0.3817
0.029876	0.9828	0.3404
0.03024	1.0753	0.3213
0.030613	1.015	0.2798
0.030996	1.0061	0.2778
0.031388	0.9972	0.2973
0.031791	1.0243	0.2885
0.032204	1.0159	0.283
0.032627	1.0317	0.2854
0.033062	1.0308	0.258
0.033509	0.9992	0.2747
0.033968	1.0299	0.2874
0.03444	1.0102	0.289
0.034925	1.0456	0.3228
0.035424	1.0825	0.2928
0.035937	1.067	0.2676
0.036466	1.0701	0.2864
0.03701	1.0895	0.274
0.037571	1.0961	0.2614
0.038149	1.099	0.2484
0.038745	1.1036	0.2388
0.03936	1.1028	0.2262
0.039995	1.108	0.2184
0.040651	1.1076	0.1946
0.041328	1.0927	0.1844
0.042029	1.0903	0.1784
0.042753	1.0765	0.1547
0.043503	1.0455	0.155
0.04428	1.0399	0.1745
0.045085	1.0407	0.1821
0.04592	1.0556	0.1767
0.046786	1.0395	0.1366
0.047686	0.9885	0.1386
0.048621	0.971	0.1921
0.049594	0.9968	0.2067
0.050606	1.0177	0.1916
0.05166	0.9913	0.1695
0.052759	0.968	0.1787
0.053906	0.9527	0.1863
0.055104	0.9316	0.2023
0.056356	0.9247	0.2282
0.057667	0.9192	0.2529
0.05904	0.9356	0.2816
0.06048	0.9487	0.2883
0.061992	0.9598	0.2969
0.063582	0.9715	0.3047
0.065255	0.9958	0.3093
0.067018	1.0286	0.2722
0.06888	1.0015	0.2386
0.070848	0.9767	0.2406
0.072932	0.9734	0.244
0.075142	0.9808	0.2345
0.07749	0.99	0.1586
0.07999	0.8773	0.1248
0.082656	0.7988	0.1452
0.085506	0.7342	0.1846
0.08856	0.6828	0.2241
0.09184	0.6258	0.262
0.095372	0.562	0.3238
0.099187	0.5081	0.4015
0.10332	0.468	0.5
0.107812	0.4522	0.607
0.112713	0.4562	0.7114
0.11808	0.4768	0.8095
0.123984	0.5081	0.8945
0.13051	0.5449	0.9726
0.13776	0.5934	0.9985
0.145864	0.5591	1.0624
0.15498	0.5738	1.1275
0.165312	0.5465	1.1518
0.17712	0.3649	1.2455
0.190745	0.2649	1.5268
0.20664	0.2671	1.8405
0.225426	0.3311	2.1734
0.247968	0.4602	2.5237
0.261019	0.5535	2.7071
0.27552	0.6721	2.8932
0.291728	0.8224	3.0735
0.30996	1.0114	3.2213
0.330625	1.1551	3.2426
0.354241	1.083	3.4608
0.38149	1.2351	3.8739
0.413281	1.6192	4.2951
0.450852	2.4048	4.4145
0.495937	2.6246	3.9718
0.551041	2.5858	4.0788
0.619921	2.9887	3.9909
0.708481	2.4455	3.4574
0.826561	1.3904	4.3534
0.991874	1.026	5.7882
1.239842	0.7878	7.8228
1.653123	0.9004	11.1859
2.479684	1.8247	17.3182

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: —

Pb (Lead): all datasets

Experimental data

Models and simulations

Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm n,k 0.01759–2.48 µm

About Pb (Lead)

Lead (Pb) is a heavy metal that is known for its malleability, ductility, and resistance to corrosion. Historically, lead has had various applications including in batteries, pipes, cable sheathing, and as a radiation shield. In terms of optics, lead has been utilized in the manufacture of certain types of optical glasses, known as flint glasses. These glasses have high refractive indices and dispersive power. Lead-based glasses have been traditionally used in lenses and prisms to correct chromatic aberration in optical systems. However, the use of lead in consumer products has decreased significantly due to environmental and health concerns. In many regions, regulations have limited the use of lead in electronics and other products.

More about Pb (Lead) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Pb/nk/Werner-DFT.yml
ID: ds_3c18de98871c
API: /v1/datasets/ds_3c18de98871c

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