Optical constants
Refractive index of Nb (Niobium)
Golovashkin et al. 1969: n,k 0.40–10 µm; 293 K
- Data
- tabulated nk
- Range
- 0.4–10 µm
- Points
- 65
- Temperature
- 293 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.2824
- Extinction coefficient k
- 3.2376
- Permittivity ε1
- -5.2727
- Permittivity ε2
- 14.779
- Absorption coefficient α
- 692391 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 28.8854 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1 µm⁻¹
- Group index ng
- 2.87
- 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
# Nb (Niobium): Golovashkin et al. 1969: n,k 0.40–10 µm; 293 K
nb = ls.fetch_refractiveindex("main", "Nb", "Golovashkin-293K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(nb.range_nm) # (400, 10000) nm
eps = nb.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_40a9045882d5/lightsmith"
nb = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(nb.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (nb/golovashkin-1969-293k).
# ... load nb as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=nb)],
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
- 293 K
References
Cite
A. I. Golovashkin, I. E. Leksina, G. P. Motulevich and A. A. Shubin. The optical properties of niobium, Sov. Phys. JETP 29, 27-34 (1969); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
65 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.4 | 1.5 | 2.99 |
| 0.42 | 1.61 | 2.95 |
| 0.44 | 1.91 | 2.98 |
| 0.46 | 2.0 | 3.0 |
| 0.48 | 2.02 | 3.04 |
| 0.5 | 2.13 | 3.07 |
| 0.52 | 2.2 | 3.08 |
| 0.54 | 2.23 | 3.15 |
| 0.56 | 2.29 | 3.17 |
| 0.58 | 2.29 | 3.23 |
| 0.6 | 2.27 | 3.25 |
| 0.62 | 2.28 | 3.25 |
| 0.64 | 2.27 | 3.3 |
| 0.66 | 2.27 | 3.36 |
| 0.68 | 2.23 | 3.38 |
| 0.7 | 2.22 | 3.41 |
| 0.72 | 2.17 | 3.44 |
| 0.74 | 2.13 | 3.47 |
| 0.76 | 2.11 | 3.62 |
| 0.78 | 2.06 | 3.72 |
| 0.8 | 2.05 | 3.85 |
| 0.82 | 2.01 | 3.9 |
| 0.84 | 2.0 | 4.03 |
| 0.85 | 1.92 | 4.06 |
| 0.88 | 1.86 | 4.16 |
| 0.9 | 1.83 | 4.32 |
| 0.92 | 1.8 | 4.41 |
| 0.95 | 1.71 | 4.62 |
| 0.98 | 1.71 | 4.8 |
| 1.0 | 1.66 | 4.94 |
| 1.05 | 1.59 | 5.37 |
| 1.1 | 1.52 | 5.66 |
| 1.2 | 1.43 | 6.31 |
| 1.3 | 1.38 | 7.04 |
| 1.4 | 1.35 | 7.64 |
| 1.5 | 1.39 | 8.24 |
| 1.6 | 1.48 | 8.96 |
| 1.7 | 1.49 | 9.61 |
| 1.8 | 1.68 | 10.3 |
| 1.9 | 1.67 | 11.0 |
| 2.0 | 1.75 | 11.6 |
| 2.1 | 1.83 | 12.2 |
| 2.2 | 2.26 | 13.1 |
| 2.3 | 2.33 | 13.6 |
| 2.4 | 2.51 | 14.0 |
| 2.5 | 2.4 | 14.4 |
| 2.6 | 2.58 | 15.3 |
| 2.8 | 3.17 | 16.3 |
| 3.0 | 3.65 | 17.3 |
| 3.5 | 4.55 | 19.8 |
| 4.0 | 5.62 | 22.2 |
| 4.22 | 5.79 | 23.4 |
| 4.5 | 6.72 | 25.1 |
| 4.7 | 7.46 | 26.8 |
| 5.0 | 8.06 | 27.7 |
| 5.5 | 9.2 | 29.6 |
| 6.0 | 10.4 | 31.0 |
| 6.2 | 10.7 | 32.7 |
| 6.5 | 11.5 | 33.9 |
| 6.8 | 12.5 | 34.8 |
| 7.0 | 13.1 | 36.2 |
| 7.5 | 15.1 | 37.4 |
| 8.0 | 16.3 | 38.8 |
| 9.0 | 19.2 | 41.0 |
| 10.0 | 22.4 | 44.3 |
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
- —
293 K (19.85 °C)