Optical constants
Refractive index of Pb (Lead)
Mathewson and Myers 1971: n,k 0.344–1.77 µm; 298 K
- Data
- tabulated nk
- Range
- 0.3444–1.771 µm
- Points
- 59
- Temperature
- 298 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.5947
- Extinction coefficient k
- 4.17767
- Permittivity ε1
- -10.7204
- Permittivity ε2
- 21.6796
- Absorption coefficient α
- 893433 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 22.3856 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 1.01966 µm⁻¹
- Group index ng
- 1.99555
- 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; 298 K
pb = ls.fetch_refractiveindex("main", "Pb", "Mathewson-298K", 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_e518c407e09a/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-1971-298k).
# ... 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
- 298 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 | 1.17059 | 3.45981 |
| 0.34925 | 1.19607 | 3.51149 |
| 0.35424 | 1.21679 | 3.57499 |
| 0.35937 | 1.24136 | 3.62505 |
| 0.36466 | 1.27765 | 3.67864 |
| 0.3701 | 1.32504 | 3.73574 |
| 0.37571 | 1.37126 | 3.79214 |
| 0.38149 | 1.41637 | 3.84787 |
| 0.38745 | 1.47166 | 3.90715 |
| 0.3936 | 1.52979 | 3.95478 |
| 0.39995 | 1.58664 | 4.00218 |
| 0.40651 | 1.65717 | 4.04304 |
| 0.41328 | 1.71581 | 4.07971 |
| 0.42029 | 1.79827 | 4.11507 |
| 0.42753 | 1.86905 | 4.14649 |
| 0.43503 | 1.95301 | 4.17304 |
| 0.4428 | 2.03525 | 4.17639 |
| 0.45085 | 2.11192 | 4.19049 |
| 0.4592 | 2.18315 | 4.1912 |
| 0.46786 | 2.25385 | 4.19283 |
| 0.47686 | 2.30983 | 4.19944 |
| 0.48621 | 2.36141 | 4.19241 |
| 0.49594 | 2.40388 | 4.18074 |
| 0.50606 | 2.44112 | 4.17841 |
| 0.5166 | 2.47301 | 4.18518 |
| 0.52759 | 2.49592 | 4.18684 |
| 0.53906 | 2.51876 | 4.18857 |
| 0.55104 | 2.54683 | 4.18167 |
| 0.56356 | 2.56955 | 4.18361 |
| 0.57667 | 2.58356 | 4.18028 |
| 0.5904 | 2.59756 | 4.177 |
| 0.6048 | 2.60618 | 4.18237 |
| 0.61992 | 2.60294 | 4.16837 |
| 0.63582 | 2.5943 | 4.16298 |
| 0.65255 | 2.57157 | 4.16088 |
| 0.67018 | 2.52934 | 4.17104 |
| 0.6888 | 2.45892 | 4.18883 |
| 0.70848 | 2.37327 | 4.23467 |
| 0.72932 | 2.27887 | 4.30038 |
| 0.75142 | 2.1818 | 4.40003 |
| 0.7749 | 2.09878 | 4.55026 |
| 0.7999 | 2.01129 | 4.74819 |
| 0.82656 | 1.9583 | 4.95328 |
| 0.85506 | 1.91905 | 5.18486 |
| 0.8856 | 1.88041 | 5.39777 |
| 0.9184 | 1.85222 | 5.64187 |
| 0.95372 | 1.84405 | 5.85667 |
| 0.99187 | 1.81906 | 6.15703 |
| 1.0332 | 1.80417 | 6.48498 |
| 1.07812 | 1.80918 | 6.74338 |
| 1.12713 | 1.79546 | 7.12907 |
| 1.1808 | 1.82482 | 7.39797 |
| 1.23984 | 1.80484 | 7.97856 |
| 1.3051 | 1.84979 | 8.43337 |
| 1.3776 | 1.88333 | 8.9469 |
| 1.45864 | 1.94706 | 9.47581 |
| 1.5498 | 2.04976 | 10.04995 |
| 1.65312 | 2.17508 | 10.80421 |
| 1.7712 | 2.26234 | 11.58094 |
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
- —
298 K (24.85 °C)