Optical constants
Refractive index of Na (Sodium)
Althoff and Hertz 1967: n,k 2.25–10.2 µm
- Data
- tabulated nk
- Range
- 2.25–10.15 µm
- Points
- 8
- State
- solid
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.73388
- Extinction coefficient k
- 22.4298
- Permittivity ε1
- -500.089
- Permittivity ε2
- 77.781
- Absorption coefficient α
- 589668 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 33.9174 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.795918 µm⁻¹
- Group index ng
- -2.07061
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.259381 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
# Na (Sodium): Althoff and Hertz 1967: n,k 2.25–10.2 µm
na = ls.fetch_refractiveindex("main", "Na", "Althoff", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(na.range_nm) # (2250, 10150) nm
eps = na.eps([4780]) # 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_dfa22203a0da/lightsmith"
na = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(na.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (na/althoff-hertz-1967).
# ... load na as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=na)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=2250, stop_nm=10150, 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.
References
- doi:10.1016/0020-0891(67)90025-5 Measurement of the optical constants of Na and K in the range of wavelength from 2.5 to 10 μ, Infrared Physics (1967)
Cite
R. Althoff and J.H. Hertz. Measurement of the optical constants of Na and K in the range of wavelength from 2.5 to 10 μ. Infrared Physics, 7, 11-16 (1967), doi:10.1016/0020-0891(67)90025-5; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
8 rows as published| λ (µm) | n | k |
|---|---|---|
| 2.25 | 0.41 | 11.6 |
| 2.5 | 0.5 | 12.5 |
| 3.0 | 0.61 | 14.7 |
| 3.5 | 0.81 | 17.2 |
| 4.0 | 1.02 | 19.4 |
| 4.75 | 1.71 | 22.3 |
| 7.2 | 3.66 | 32.9 |
| 10.15 | 6.43 | 44.5 |
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
- —