Optical constants
Refractive index of Al (Aluminium)
Rakić 1995: n,k 0.000124–200 µm
- Data
- tabulated nk
- Range
- 0.000124–200 µm
- Points
- 206
- Licence
- CC0-1.0
- Lightsmith
- bundled
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.19781
- Extinction coefficient k
- 7.0488
- Permittivity ε1
- -48.2509
- Permittivity ε2
- 16.8863
- Absorption coefficient α
- 1.50745e+06 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 13.2674 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 5.20227 µm⁻¹
- Group index ng
- -1.85904
- 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
# Al (Aluminium): Rakić 1995: n,k 0.000124–200 µm
al = ls.LibraryMaterial(name="Al", dataset="Rakic-1995")
print(al.range_nm) # (0.12399, 200000) nm
eps = al.eps([633]) # complex permittivity
Ships with the library: works offline.
import lightsmith as ls
# Al (Aluminium): Rakić 1995: n,k 0.000124–200 µm
al = ls.fetch_refractiveindex("main", "Al", "Rakic", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(al.range_nm) # (0.12399, 200000) nm
eps = al.eps([633]) # complex permittivity
Downloads 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_6275ef04b3e3/lightsmith"
al = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(al.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (al/rakic-1995).
# ... 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=400, stop_nm=1000, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelength
Same 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
- doi:10.1364/ao.34.004755 Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum, Applied Optics (1995)
Cite
Aleksandar D. Rakić. Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum. Applied Optics, 34, 4755 (1995), doi:10.1364/ao.34.004755; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
206 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.00012399 | 0.9999946 | 8.241e-08 |
| 0.00013051 | 0.999994 | 1.272e-07 |
| 0.00013776 | 0.999993 | 1.2488e-07 |
| 0.00015498 | 0.999991 | 1.9173e-07 |
| 0.00017712 | 0.999989 | 3.1463e-07 |
| 0.00020664 | 0.999984 | 5.5102e-07 |
| 0.00024797 | 0.99998 | 1.0726e-06 |
| 0.00030996 | 0.99997 | 2.4843e-06 |
| 0.00035424 | 0.99995 | 4.0484e-06 |
| 0.00041328 | 0.99994 | 7.1408e-06 |
| 0.00049594 | 0.99991 | 1.3642e-05 |
| 0.00061993 | 0.99987 | 3.2079e-05 |
| 0.00065255 | 0.99986 | 3.8497e-05 |
| 0.00068881 | 0.99985 | 4.7138e-05 |
| 0.00072932 | 0.99984 | 5.7974e-05 |
| 0.00074021 | 0.99984 | 6.1633e-05 |
| 0.00077734 | 0.99986 | 7.4862e-05 |
| 0.00078472 | 0.99987 | 7.848e-05 |
| 0.00079274 | 0.9999 | 8.5418e-05 |
| 0.00079376 | 0.99992 | 7.1847e-05 |
| 0.00079478 | 0.99993 | 4.9998e-05 |
| 0.00079529 | 0.99992 | 4.1131e-05 |
| 0.0007958 | 0.99992 | 3.2911e-05 |
| 0.00079785 | 0.99991 | 2.3687e-05 |
| 0.00079887 | 0.99991 | 1.1026e-05 |
| 0.0007999 | 0.99989 | 6.0484e-06 |
| 0.0008051 | 0.99987 | 6.1901e-06 |
| 0.00081569 | 0.99985 | 6.4818e-06 |
| 0.00082657 | 0.99983 | 6.8049e-06 |
| 0.00085507 | 0.99981 | 7.8422e-06 |
| 0.00088561 | 0.99979 | 8.94e-06 |
| 0.00095373 | 0.99974 | 1.1636e-05 |
| 0.0010332 | 0.99968 | 1.5628e-05 |
| 0.0011271 | 0.99961 | 2.1586e-05 |
| 0.0012399 | 0.99953 | 3.1115e-05 |
| 0.0013776 | 0.9994 | 4.6771e-05 |
| 0.0015498 | 0.99924 | 7.2992e-05 |
| 0.0017712 | 0.99898 | 0.00011811 |
| 0.0020664 | 0.9986 | 0.00022001 |
| 0.0024797 | 0.99797 | 0.00043503 |
| 0.0030996 | 0.99694 | 0.00096887 |
| 0.0041328 | 0.9948 | 0.0023492 |
| 0.0049594 | 0.99313 | 0.0041863 |
| 0.0061993 | 0.99111 | 0.0075099 |
| 0.0065255 | 0.99054 | 0.0084716 |
| 0.0068881 | 0.99007 | 0.0096517 |
| 0.0072932 | 0.98909 | 0.010987 |
| 0.0077491 | 0.98912 | 0.013728 |
| 0.0082657 | 0.98966 | 0.014773 |
| 0.0085507 | 0.98934 | 0.015437 |
| 0.0088561 | 0.98883 | 0.016304 |
| 0.0091841 | 0.98793 | 0.017765 |
| 0.0095373 | 0.98761 | 0.020606 |
| 0.0099188 | 0.98941 | 0.023421 |
| 0.010332 | 0.99139 | 0.024063 |
| 0.010781 | 0.99233 | 0.024928 |
| 0.011271 | 0.99415 | 0.025452 |
| 0.011808 | 0.99285 | 0.024415 |
| 0.012399 | 0.99123 | 0.02992 |
| 0.012652 | 0.99265 | 0.033061 |
| 0.012915 | 0.99652 | 0.035883 |
| 0.01319 | 1.0012 | 0.035311 |
| 0.013477 | 1.0041 | 0.033392 |
| 0.013776 | 1.0058 | 0.030918 |
| 0.014089 | 1.006 | 0.028956 |
| 0.014417 | 1.0065 | 0.028232 |
| 0.01476 | 1.0074 | 0.026826 |
| 0.01512 | 1.0077 | 0.02546 |
| 0.015498 | 1.0075 | 0.024476 |
| 0.015694 | 1.0075 | 0.024501 |
| 0.015896 | 1.0078 | 0.024757 |
| 0.016102 | 1.0095 | 0.02518 |
| 0.016314 | 1.0106 | 0.023853 |
| 0.016422 | 1.011 | 0.023955 |
| 0.016531 | 1.0118 | 0.02402 |
| 0.016642 | 1.0132 | 0.024343 |
| 0.016755 | 1.0151 | 0.024184 |
| 0.016777 | 1.0156 | 0.024228 |
| 0.0168 | 1.0161 | 0.024282 |
| 0.016823 | 1.0167 | 0.024375 |
| 0.016846 | 1.0173 | 0.024499 |
| 0.016869 | 1.0181 | 0.024831 |
| 0.016892 | 1.0194 | 0.025432 |
| 0.016915 | 1.0219 | 0.026018 |
| 0.016938 | 1.0259 | 0.024227 |
| 0.016961 | 1.0262 | 0.019564 |
| 0.016984 | 1.0246 | 0.019145 |
| 0.017008 | 1.0255 | 0.020012 |
| 0.017031 | 1.0305 | 0.020072 |
| 0.017054 | 1.0349 | 0.012476 |
| 0.017078 | 1.0305 | 0.0041164 |
| 0.017101 | 1.0249 | 0.0036218 |
| 0.017125 | 1.0226 | 0.0034141 |
| 0.017149 | 1.0206 | 0.00344 |
| 0.017172 | 1.0192 | 0.0034767 |
| 0.017196 | 1.0179 | 0.0034877 |
| 0.017208 | 1.0174 | 0.0035108 |
| 0.01722 | 1.0169 | 0.0035249 |
| 0.017463 | 1.0108 | 0.0034957 |
| 0.017712 | 1.007 | 0.0035425 |
| 0.018233 | 1.0019 | 0.003673 |
| 0.018786 | 0.99791 | 0.0038926 |
| 0.019373 | 0.99457 | 0.0041092 |
| 0.019998 | 0.99143 | 0.0042397 |
| 0.020664 | 0.98827 | 0.0043696 |
| 0.022543 | 0.97998 | 0.0050004 |
| 0.024797 | 0.97048 | 0.0057469 |
| 0.027552 | 0.95834 | 0.0066191 |
| 0.030996 | 0.94189 | 0.0078466 |
| 0.035424 | 0.91802 | 0.0093121 |
| 0.041328 | 0.88013 | 0.011651 |
| 0.049594 | 0.81512 | 0.015894 |
| 0.061993 | 0.67912 | 0.02234 |
| 0.065255 | 0.63242 | 0.02477 |
| 0.068881 | 0.57251 | 0.027681 |
| 0.072932 | 0.49131 | 0.032409 |
| 0.077491 | 0.37197 | 0.044202 |
| 0.078472 | 0.34031 | 0.04832 |
| 0.079478 | 0.30373 | 0.053349 |
| 0.07999 | 0.28271 | 0.056697 |
| 0.08051 | 0.25936 | 0.061407 |
| 0.081036 | 0.23344 | 0.068348 |
| 0.081569 | 0.20569 | 0.079959 |
| 0.082109 | 0.17943 | 0.094223 |
| 0.082657 | 0.15065 | 0.11041 |
| 0.083774 | 0.094517 | 0.16589 |
| 0.084921 | 0.067041 | 0.2342 |
| 0.086101 | 0.054863 | 0.29293 |
| 0.088561 | 0.044168 | 0.39115 |
| 0.095373 | 0.036437 | 0.59086 |
| 0.10332 | 0.035753 | 0.77163 |
| 0.11271 | 0.038468 | 0.95677 |
| 0.12399 | 0.046304 | 1.1555 |
| 0.13776 | 0.057167 | 1.3775 |
| 0.15498 | 0.072505 | 1.6366 |
| 0.17712 | 0.094236 | 1.9519 |
| 0.20664 | 0.12677 | 2.3563 |
| 0.24797 | 0.18137 | 2.9029 |
| 0.30996 | 0.28003 | 3.7081 |
| 0.32628 | 0.31474 | 3.9165 |
| 0.36466 | 0.39877 | 4.3957 |
| 0.41328 | 0.52135 | 5.0008 |
| 0.4428 | 0.6079 | 5.3676 |
| 0.47687 | 0.7278 | 5.7781 |
| 0.5166 | 0.8734 | 6.2418 |
| 0.56357 | 1.0728 | 6.7839 |
| 0.61993 | 1.366 | 7.4052 |
| 0.65225 | 1.5724 | 7.7354 |
| 0.68881 | 1.8301 | 8.0601 |
| 0.72932 | 2.1606 | 8.3565 |
| 0.77491 | 2.6154 | 8.4914 |
| 0.79478 | 2.7675 | 8.3866 |
| 0.81569 | 2.7668 | 8.2573 |
| 0.83774 | 2.6945 | 8.1878 |
| 0.88561 | 2.2802 | 8.1134 |
| 0.91166 | 1.9739 | 8.3058 |
| 0.93928 | 1.6784 | 8.597 |
| 0.96863 | 1.4867 | 9.0655 |
| 0.99988 | 1.4359 | 9.4939 |
| 1.0332 | 1.3998 | 9.8914 |
| 1.1271 | 1.3281 | 10.969 |
| 1.2399 | 1.3157 | 12.245 |
| 1.3776 | 1.3899 | 13.784 |
| 1.5498 | 1.5782 | 15.656 |
| 1.7712 | 1.9205 | 17.991 |
| 2.0664 | 2.4738 | 20.982 |
| 2.4797 | 3.3372 | 25.004 |
| 2.7552 | 3.938 | 27.58 |
| 3.0996 | 4.7097 | 30.737 |
| 3.2628 | 5.0735 | 32.183 |
| 3.444 | 5.4903 | 33.814 |
| 3.6466 | 5.9564 | 35.608 |
| 3.8745 | 6.4808 | 37.595 |
| 4.1328 | 7.0796 | 39.826 |
| 4.428 | 7.7757 | 42.367 |
| 4.7687 | 8.5881 | 45.257 |
| 5.166 | 9.558 | 48.593 |
| 5.6357 | 10.742 | 52.518 |
| 6.1993 | 12.195 | 57.156 |
| 6.8881 | 14.088 | 62.841 |
| 7.7491 | 16.755 | 69.857 |
| 8.8561 | 20.837 | 78.274 |
| 10.332 | 26.216 | 88.197 |
| 12.399 | 33.519 | 101.28 |
| 13.776 | 38.461 | 108.96 |
| 15.498 | 43.775 | 118.39 |
| 17.712 | 50.951 | 129.49 |
| 19.075 | 54.413 | 136.09 |
| 20.664 | 58.58 | 144.23 |
| 22.543 | 63.554 | 153.45 |
| 24.797 | 68.535 | 164.81 |
| 27.552 | 75.748 | 181.78 |
| 30.996 | 91.955 | 199.99 |
| 33.333 | 102.1 | 208.1 |
| 40.0 | 125.14 | 230.19 |
| 44.444 | 140.05 | 243.43 |
| 50.0 | 157.3 | 258.26 |
| 57.144 | 177.93 | 275.34 |
| 66.666 | 202.63 | 295.42 |
| 80.001 | 233.56 | 321.08 |
| 99.996 | 274.38 | 354.35 |
| 125.0 | 318.81 | 391.71 |
| 137.76 | 339.62 | 408.92 |
| 153.85 | 364.04 | 429.62 |
| 177.12 | 397.93 | 458.5 |
| 200.0 | 423.96 | 483.7 |
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 and electron-energy-loss data for evaporated-aluminum films have been critically analyzed and used in an iterative, self-consistent algorithm that represents a combination of the Kramers-Kronig analysis and the semiquantum-model application.""