Optical constants
Refractive index of Al (Aluminium)
Larruquert et al. 1996: n,k 0.077–0.114 µm
- Data
- tabulated nk
- Range
- 0.077–0.1135 µm
- Points
- 13
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.0419545
- Extinction coefficient k
- 0.600909
- Permittivity ε1
- -0.359332
- Permittivity ε2
- 0.0504217
- Absorption coefficient α
- 807620 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 24.7641 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1.36364 µm⁻¹
- Group index ng
- 0.169455
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 13.2603 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
# Al (Aluminium): Larruquert et al. 1996: n,k 0.077–0.114 µm
al = ls.fetch_refractiveindex("main", "Al", "Larruquert", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(al.range_nm) # (77, 113.5) nm
eps = al.eps([93.5]) # 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_6afe925ca38b/lightsmith"
al = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(al.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (al/larruquert-1996).
# ... load al as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=al)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=77, stop_nm=113, 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
References
2) J. I. Larruquert, J. A. Méndez, J. A. Aznárez. Far-ultraviolet reflectance measurements and optical constants of unoxidized aluminum films. Appl. Opt. 34, 4892-4899 (1995)
- doi:10.1364/ao.35.005692 Optical constants of aluminum films in the extreme ultraviolet interval of 82–77 nm, Applied Optics (1996)
- doi:10.1364/ao.34.004892 Far-ultraviolet reflectance measurements and optical constants of unoxidized aluminum films, Applied Optics (1995)
Cite
J. I. Larruquert, J. A. Méndez and J. A. Aznárez. Optical constants of aluminum films in the extreme ultraviolet interval of 82–77 nm. Applied Optics, 35, 5692 (1996), doi:10.1364/ao.35.005692; J. I. Larruquert, J. A. Méndez and J. A. Aznárez. Far-ultraviolet reflectance measurements and optical constants of unoxidized aluminum films. Applied Optics, 34, 4892 (1995), doi:10.1364/ao.34.004892; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
13 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.077 | 0.367 | 0.047 |
| 0.078 | 0.339 | 0.052 |
| 0.079 | 0.302 | 0.06 |
| 0.08 | 0.255 | 0.075 |
| 0.081 | 0.207 | 0.093 |
| 0.082 | 0.161 | 0.12 |
| 0.0826 | 0.115 | 0.138 |
| 0.0835 | 0.092 | 0.18 |
| 0.0868 | 0.053 | 0.39 |
| 0.092 | 0.044 | 0.56 |
| 0.0964 | 0.038 | 0.68 |
| 0.1048 | 0.031 | 0.88 |
| 0.1135 | 0.026 | 0.97 |
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
- —
Optical constants are obtained from reflectance measurements versus angle of incidence. Film deposited at room temperature.