Optical constants

Refractive index of Pb (Lead)

Golovashkin and Motulevich 1968: n,k 0.54–12 µm; 4.2 K

Data: tabulated nk
Range: 0.54–12 µm
Points: 70
Temperature: 4.2 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.1556
Extinction coefficient k: 3.52

Permittivity ε₁: -7.74379
Permittivity ε₂: 15.1754

Absorption coefficient α: 752785 cm⁻¹
Penetration depth δ = λ/(2πk): 26.568 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 6 µm⁻¹

Group index n_g: -1.37
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): Golovashkin and Motulevich 1968: n,k 0.54–12 µm; 4.2 K
pb = ls.fetch_refractiveindex("main", "Pb", "Golovashkin-4.2K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pb.range_nm)  # (540, 12000) 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_1ccad6d0a02d/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/golovashkin-motulevich-1968-4-2k).

# ... 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=540, 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

4.2 K (-268.95 °C)

Conditions

temperature: 4.2 K

References

A. I. Golovashkin and G. P. Motulevich. Optical properties of lead in the visible and infrared spectral ranges, Sov. Phys. JETP 26, 881-887 (1968)

Cite

A. I. Golovashkin and G. P. Motulevich. Optical properties of lead in the visible and infrared spectral ranges, Sov. Phys. JETP 26, 881-887 (1968); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

70 rows as published

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

Pb (Lead), Golovashkin and Motulevich 1968: n,k 0.54–12 µm; 4.2 K: n and k versus wavelength
λ (µm)	n	k
0.54	1.82	3.46
0.55	1.88	3.5
0.56	1.97	3.51
0.57	2.04	3.52
0.58	2.11	3.52
0.59	2.17	3.52
0.6	2.26	3.5
0.61	2.29	3.45
0.62	2.34	3.38
0.63	2.39	3.27
0.64	2.39	3.16
0.65	2.34	3.09
0.66	2.28	3.02
0.67	2.18	2.93
0.68	2.09	2.89
0.69	1.97	2.84
0.7	1.85	2.82
0.71	1.67	2.83
0.72	1.54	2.89
0.73	1.4	2.97
0.74	1.3	3.06
0.75	1.24	3.15
0.76	1.17	3.26
0.78	1.09	3.46
0.79	1.07	3.58
0.8	1.04	3.61
0.81	1.02	3.75
0.82	1.0	3.78
0.84	0.989	3.92
0.85	0.976	3.97
0.86	0.965	4.04
0.88	0.94	4.16
0.9	0.904	4.27
0.92	0.87	4.39
0.95	0.821	4.57
0.98	0.771	4.76
1.0	0.721	4.9
1.05	0.656	5.22
1.1	0.574	5.58
1.15	0.485	5.92
1.2	0.417	6.29
1.25	0.346	6.66
1.3	0.312	6.96
1.35	0.294	7.26
1.4	0.285	7.59
1.45	0.29	7.9
1.5	0.275	8.24
1.6	0.3	8.94
1.7	0.312	9.57
1.8	0.336	10.3
1.9	0.338	11.0
2.0	0.387	11.5
2.1	0.382	12.1
2.2	0.448	12.7
2.3	0.409	13.3
2.4	0.541	13.9
2.5	0.586	14.5
2.55	0.597	14.7
2.6	0.614	15.0
3.0	0.81	17.3
3.5	1.1	20.1
4.0	1.49	23.1
5.0	2.15	28.6
6.0	2.95	34.4
7.0	3.75	39.9
8.0	4.5	45.5
9.0	5.56	50.6
10.0	6.7	55.9
11.0	7.9	61.3
12.0	9.2	66.5

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/Golovashkin-4.2K.yml
ID: ds_1ccad6d0a02d
API: /v1/datasets/ds_1ccad6d0a02d

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