Optical constants
Refractive index of Pb (Lead)
Mathewson and Myers 1971: n,k 0.344–1.77 µm; 140 K
- Data
- tabulated nk
- Range
- 0.3444–1.771 µm
- Points
- 59
- Temperature
- 140 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.95444
- Extinction coefficient k
- 4.02429
- Permittivity ε1
- -7.46615
- Permittivity ε2
- 23.779
- Absorption coefficient α
- 860631 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 23.2388 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -41.9752 µm⁻¹
- Group index ng
- 27.6191
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 2.11001 eV
ε = (n + ik)², α = 4πk/λ, ng = 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): Mathewson and Myers 1971: n,k 0.344–1.77 µm; 140 K
pb = ls.fetch_refractiveindex("main", "Pb", "Mathewson-140K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pb.range_nm) # (344.4, 1771.2) nm
eps = pb.eps([633]) # complex permittivityDownloads 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_0479d4c4ade5/lightsmith"
pb = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pb.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (pb/mathewson-myers-1971-140k).
# ... 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 wavelengthSame spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
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
Conditions
- temperature
- 140 K
References
- doi:10.1088/0031-8949/4/6/009 Absolute Values of the Optical Constants of Some Pure Metals, Physica Scripta (1971)
Cite
A G Mathewson and H P Myers. Absolute Values of the Optical Constants of Some Pure Metals. Physica Scripta, 4, 291-292 (1971), doi:10.1088/0031-8949/4/6/009; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
59 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.3444 | 1.0467 | 3.53491 |
| 0.34925 | 1.07006 | 3.59792 |
| 0.35424 | 1.08921 | 3.67238 |
| 0.35937 | 1.12397 | 3.73675 |
| 0.36466 | 1.15787 | 3.80009 |
| 0.3701 | 1.20277 | 3.86609 |
| 0.37571 | 1.24647 | 3.93112 |
| 0.38149 | 1.28905 | 3.9952 |
| 0.38745 | 1.35278 | 4.06571 |
| 0.3936 | 1.42544 | 4.13907 |
| 0.39995 | 1.49962 | 4.20106 |
| 0.40651 | 1.60651 | 4.2639 |
| 0.41328 | 1.72407 | 4.32116 |
| 0.42029 | 1.83252 | 4.36556 |
| 0.42753 | 1.95095 | 4.38249 |
| 0.43503 | 2.0713 | 4.36924 |
| 0.4428 | 2.18636 | 4.34513 |
| 0.45085 | 2.28794 | 4.30519 |
| 0.4592 | 2.35826 | 4.26162 |
| 0.46786 | 2.4064 | 4.21791 |
| 0.47686 | 2.43219 | 4.17319 |
| 0.48621 | 2.42473 | 4.14479 |
| 0.49594 | 2.42629 | 4.12152 |
| 0.50606 | 3.08465 | 3.25807 |
| 0.5166 | 3.10883 | 3.28098 |
| 0.52759 | 3.14121 | 3.32674 |
| 0.53906 | 3.18114 | 3.37929 |
| 0.55104 | 3.25749 | 3.40753 |
| 0.56356 | 3.33975 | 3.4284 |
| 0.57667 | 3.41323 | 3.42784 |
| 0.5904 | 2.83691 | 4.17708 |
| 0.6048 | 2.89589 | 4.10928 |
| 0.61992 | 2.92983 | 4.01047 |
| 0.63582 | 2.89008 | 3.89263 |
| 0.65255 | 2.82065 | 3.77572 |
| 0.67018 | 2.70821 | 3.69248 |
| 0.6888 | 2.49997 | 3.64004 |
| 0.70848 | 2.25499 | 3.65855 |
| 0.72932 | 2.01941 | 3.73872 |
| 0.75142 | 1.81541 | 3.91097 |
| 0.7749 | 1.65467 | 4.1398 |
| 0.7999 | 1.55455 | 4.40643 |
| 0.82656 | 1.48451 | 4.64799 |
| 0.85506 | 1.44917 | 4.79584 |
| 0.8856 | 1.36769 | 5.15467 |
| 0.9184 | 1.31995 | 5.41685 |
| 0.95372 | 1.264 | 5.65665 |
| 0.99187 | 1.18324 | 5.95819 |
| 1.0332 | 1.07303 | 6.47699 |
| 1.07812 | 0.99398 | 6.94176 |
| 1.12713 | 0.93074 | 7.35977 |
| 1.1808 | 0.89136 | 7.79708 |
| 1.23984 | 0.84813 | 8.25344 |
| 1.3051 | 0.81387 | 8.8466 |
| 1.3776 | 0.80359 | 9.45758 |
| 1.45864 | 0.82378 | 9.89336 |
| 1.5498 | 0.7979 | 11.0289 |
| 1.65312 | 0.83169 | 11.90343 |
| 1.7712 | 0.90683 | 12.68157 |
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —
140 K (-133.15 °C)