Optical constants
Refractive index of Nb (Niobium)
Golovashkin et al. 1969: n,k 0.40–9.2 µm; 4.2 K
- Data
- tabulated nk
- Range
- 0.4–9.2 µm
- Points
- 78
- Temperature
- 4.2 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.3572
- Extinction coefficient k
- 3.1224
- Permittivity ε1
- -4.19299
- Permittivity ε2
- 14.7202
- Absorption coefficient α
- 667754 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 29.9511 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -3 µm⁻¹
- Group index ng
- 4.12
- 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 0.40–9.2 µm; 4.2 K
nb = ls.fetch_refractiveindex("main", "Nb", "Golovashkin-4.2K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(nb.range_nm) # (400, 9200) 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_e27f7d92aa47/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-1969-4-2k).
# ... 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
- 4.2 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
78 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.4 | 1.1 | 3.11 |
| 0.41 | 1.33 | 2.94 |
| 0.42 | 1.54 | 3.0 |
| 0.43 | 1.66 | 3.01 |
| 0.44 | 1.8 | 3.03 |
| 0.45 | 1.87 | 3.08 |
| 0.46 | 1.98 | 3.12 |
| 0.48 | 2.08 | 3.0 |
| 0.5 | 2.24 | 3.12 |
| 0.52 | 2.28 | 3.14 |
| 0.53 | 2.31 | 3.12 |
| 0.54 | 2.35 | 3.12 |
| 0.55 | 2.35 | 3.12 |
| 0.56 | 2.32 | 3.09 |
| 0.57 | 2.37 | 3.12 |
| 0.58 | 2.38 | 3.13 |
| 0.59 | 2.35 | 3.12 |
| 0.6 | 2.3 | 3.07 |
| 0.62 | 2.3 | 3.12 |
| 0.64 | 2.31 | 3.1 |
| 0.66 | 2.28 | 3.13 |
| 0.68 | 2.26 | 3.14 |
| 0.7 | 2.17 | 3.19 |
| 0.72 | 2.14 | 3.25 |
| 0.74 | 2.11 | 3.24 |
| 0.76 | 2.02 | 3.4 |
| 0.78 | 1.85 | 3.62 |
| 0.8 | 1.69 | 3.69 |
| 0.82 | 1.64 | 3.72 |
| 0.84 | 1.6 | 3.78 |
| 0.85 | 1.63 | 4.06 |
| 0.86 | 1.51 | 4.05 |
| 0.88 | 1.49 | 4.1 |
| 0.9 | 1.47 | 4.19 |
| 0.92 | 1.39 | 4.33 |
| 0.94 | 1.31 | 4.4 |
| 0.95 | 1.33 | 4.47 |
| 0.98 | 1.24 | 4.67 |
| 1.0 | 1.23 | 4.82 |
| 1.05 | 1.1 | 5.15 |
| 1.1 | 1.01 | 5.6 |
| 1.15 | 0.97 | 6.15 |
| 1.2 | 0.82 | 6.28 |
| 1.3 | 0.78 | 7.03 |
| 1.4 | 0.75 | 7.51 |
| 1.45 | 0.62 | 8.0 |
| 1.5 | 0.56 | 8.24 |
| 1.55 | 0.45 | 8.52 |
| 1.6 | 0.41 | 8.9 |
| 1.7 | 0.41 | 9.92 |
| 1.75 | 0.28 | 10.0 |
| 1.8 | 0.28 | 10.4 |
| 1.85 | 0.22 | 10.6 |
| 1.9 | 0.23 | 11.0 |
| 1.95 | 0.19 | 11.4 |
| 2.0 | 0.18 | 11.8 |
| 2.05 | 0.28 | 12.2 |
| 2.1 | 0.4 | 12.6 |
| 2.15 | 0.45 | 12.9 |
| 2.2 | 0.63 | 13.2 |
| 2.25 | 0.55 | 13.5 |
| 2.3 | 0.48 | 14.1 |
| 2.35 | 0.4 | 14.3 |
| 2.4 | 0.34 | 14.4 |
| 2.45 | 0.33 | 15.0 |
| 2.5 | 0.3 | 15.3 |
| 2.55 | 0.45 | 15.7 |
| 2.6 | 0.83 | 16.1 |
| 2.75 | 0.9 | 16.6 |
| 3.0 | 1.1 | 17.3 |
| 3.3 | 1.26 | 17.7 |
| 3.5 | 1.53 | 18.5 |
| 4.22 | 1.82 | 24.7 |
| 4.7 | 2.04 | 28.4 |
| 5.9 | 2.1 | 35.9 |
| 6.7 | 3.4 | 38.4 |
| 8.2 | 4.04 | 51.0 |
| 9.2 | 4.99 | 58.8 |
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
- —
4.2 K (-268.95 °C)