Optical constants
Refractive index of He (Helium)
Mansfield and Peck 1969: n 0.480–2.06 µm
- Data
- formula 6
- Range
- 0.4801–2.059 µm
- Temperature
- 273.15 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.00003
- Extinction coefficient k
- 0
- Permittivity ε1
- 1.00007
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 220.11
- Chromatic dispersion dn/dλ
- -8.17320e-07 µm⁻¹
- Group index ng
- 1.00004
- Group velocity dispersion
- 0.00151293 fs²/mm
- Dispersion parameter D
- -0.00825384 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
# He (Helium): Mansfield and Peck 1969: n 0.480–2.06 µm
he = ls.fetch_refractiveindex("main", "He", "Mansfield", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(he.range_nm) # (480.1, 2058.6) nm
eps = he.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_6647ed4988e9/lightsmith"
he = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(he.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (he/mansfield-peck-1969).
# ... load he as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=he)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=481, 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.
Dispersion formula
Gases (formula 6), λ in µmValid from 0.4801 to 2.0586 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 0.01470091 |
| C3 | 423.98 |
Comments and conditions
Conditions
- temperature
- 273.15 K
- pressure
- 101325
References
- doi:10.1364/josa.59.000199 Dispersion of Helium, Journal of the Optical Society of America (1969)
Cite
Charles R. Mansfield and Edson R. Peck. Dispersion of Helium. Journal of the Optical Society of America, 59, 199 (1969), doi:10.1364/josa.59.000199; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
Computed on 400 wavelengths, the same grid as the API and the library| λ (µm) | n |
|---|---|
| 0.4801 | 1.000035 |
| 0.481855 | 1.000035 |
| 0.483616 | 1.000035 |
| 0.485384 | 1.000035 |
| 0.487158 | 1.000035 |
| 0.488939 | 1.000035 |
| 0.490726 | 1.000035 |
| 0.49252 | 1.000035 |
| 0.49432 | 1.000035 |
| 0.496127 | 1.000035 |
| 0.49794 | 1.000035 |
| 0.49976 | 1.000035 |
| 0.501587 | 1.000035 |
| 0.503421 | 1.000035 |
| 0.505261 | 1.000035 |
| 0.507108 | 1.000035 |
| 0.508961 | 1.000035 |
| 0.510822 | 1.000035 |
| 0.512689 | 1.000035 |
| 0.514563 | 1.000035 |
| 0.516444 | 1.000035 |
| 0.518331 | 1.000035 |
| 0.520226 | 1.000035 |
| 0.522128 | 1.000035 |
| 0.524036 | 1.000035 |
| 0.525952 | 1.000035 |
| 0.527874 | 1.000035 |
| 0.529804 | 1.000035 |
| 0.53174 | 1.000035 |
| 0.533684 | 1.000035 |
| 0.535635 | 1.000035 |
| 0.537592 | 1.000035 |
| 0.539557 | 1.000035 |
| 0.54153 | 1.000035 |
| 0.543509 | 1.000035 |
| 0.545496 | 1.000035 |
| 0.54749 | 1.000035 |
| 0.549491 | 1.000035 |
| 0.551499 | 1.000035 |
| 0.553515 | 1.000035 |
| 0.555539 | 1.000035 |
| 0.557569 | 1.000035 |
| 0.559607 | 1.000035 |
| 0.561653 | 1.000035 |
| 0.563706 | 1.000035 |
| 0.565766 | 1.000035 |
| 0.567834 | 1.000035 |
| 0.56991 | 1.000035 |
| 0.571993 | 1.000035 |
| 0.574084 | 1.000035 |
| 0.576182 | 1.000035 |
| 0.578288 | 1.000035 |
| 0.580402 | 1.000035 |
| 0.582524 | 1.000035 |
| 0.584653 | 1.000035 |
| 0.58679 | 1.000035 |
| 0.588935 | 1.000035 |
| 0.591087 | 1.000035 |
| 0.593248 | 1.000035 |
| 0.595417 | 1.000035 |
| 0.597593 | 1.000035 |
| 0.599777 | 1.000035 |
| 0.60197 | 1.000035 |
| 0.60417 | 1.000035 |
| 0.606378 | 1.000035 |
| 0.608595 | 1.000035 |
| 0.610819 | 1.000035 |
| 0.613052 | 1.000035 |
| 0.615293 | 1.000035 |
| 0.617542 | 1.000035 |
| 0.619799 | 1.000035 |
| 0.622065 | 1.000035 |
| 0.624339 | 1.000035 |
| 0.626621 | 1.000035 |
| 0.628911 | 1.000035 |
| 0.63121 | 1.000035 |
| 0.633517 | 1.000035 |
| 0.635833 | 1.000035 |
| 0.638157 | 1.000035 |
| 0.64049 | 1.000035 |
| 0.642831 | 1.000035 |
| 0.645181 | 1.000035 |
| 0.647539 | 1.000035 |
| 0.649906 | 1.000035 |
| 0.652281 | 1.000035 |
| 0.654666 | 1.000035 |
| 0.657059 | 1.000035 |
| 0.65946 | 1.000035 |
| 0.661871 | 1.000035 |
| 0.66429 | 1.000035 |
| 0.666718 | 1.000035 |
| 0.669155 | 1.000035 |
| 0.671601 | 1.000035 |
| 0.674056 | 1.000035 |
| 0.67652 | 1.000035 |
| 0.678993 | 1.000035 |
| 0.681475 | 1.000035 |
| 0.683966 | 1.000035 |
| 0.686466 | 1.000035 |
| 0.688975 | 1.000035 |
| 0.691493 | 1.000035 |
| 0.694021 | 1.000035 |
| 0.696558 | 1.000035 |
| 0.699104 | 1.000035 |
| 0.701659 | 1.000035 |
| 0.704224 | 1.000035 |
| 0.706798 | 1.000035 |
| 0.709381 | 1.000035 |
| 0.711974 | 1.000035 |
| 0.714577 | 1.000035 |
| 0.717189 | 1.000035 |
| 0.71981 | 1.000035 |
| 0.722441 | 1.000035 |
| 0.725082 | 1.000035 |
| 0.727733 | 1.000035 |
| 0.730393 | 1.000035 |
| 0.733062 | 1.000035 |
| 0.735742 | 1.000035 |
| 0.738431 | 1.000035 |
| 0.74113 | 1.000035 |
| 0.743839 | 1.000035 |
| 0.746558 | 1.000035 |
| 0.749287 | 1.000035 |
| 0.752026 | 1.000035 |
| 0.754775 | 1.000035 |
| 0.757534 | 1.000035 |
| 0.760303 | 1.000035 |
| 0.763082 | 1.000035 |
| 0.765871 | 1.000035 |
| 0.76867 | 1.000035 |
| 0.77148 | 1.000035 |
| 0.7743 | 1.000035 |
| 0.77713 | 1.000035 |
| 0.779971 | 1.000035 |
| 0.782822 | 1.000035 |
| 0.785683 | 1.000035 |
| 0.788555 | 1.000035 |
| 0.791438 | 1.000035 |
| 0.794331 | 1.000035 |
| 0.797234 | 1.000035 |
| 0.800148 | 1.000035 |
| 0.803073 | 1.000035 |
| 0.806008 | 1.000035 |
| 0.808954 | 1.000035 |
| 0.811911 | 1.000035 |
| 0.814879 | 1.000035 |
| 0.817858 | 1.000035 |
| 0.820847 | 1.000035 |
| 0.823848 | 1.000035 |
| 0.826859 | 1.000035 |
| 0.829881 | 1.000035 |
| 0.832915 | 1.000035 |
| 0.835959 | 1.000035 |
| 0.839015 | 1.000035 |
| 0.842082 | 1.000035 |
| 0.84516 | 1.000035 |
| 0.848249 | 1.000035 |
| 0.85135 | 1.000035 |
| 0.854462 | 1.000035 |
| 0.857585 | 1.000035 |
| 0.860719 | 1.000035 |
| 0.863866 | 1.000035 |
| 0.867023 | 1.000035 |
| 0.870192 | 1.000035 |
| 0.873373 | 1.000035 |
| 0.876566 | 1.000035 |
| 0.87977 | 1.000035 |
| 0.882985 | 1.000035 |
| 0.886213 | 1.000035 |
| 0.889452 | 1.000035 |
| 0.892704 | 1.000035 |
| 0.895967 | 1.000035 |
| 0.899242 | 1.000035 |
| 0.902529 | 1.000035 |
| 0.905828 | 1.000035 |
| 0.909139 | 1.000035 |
| 0.912462 | 1.000035 |
| 0.915797 | 1.000035 |
| 0.919144 | 1.000035 |
| 0.922504 | 1.000035 |
| 0.925876 | 1.000035 |
| 0.92926 | 1.000035 |
| 0.932657 | 1.000035 |
| 0.936066 | 1.000035 |
| 0.939488 | 1.000035 |
| 0.942922 | 1.000035 |
| 0.946368 | 1.000035 |
| 0.949828 | 1.000035 |
| 0.9533 | 1.000035 |
| 0.956784 | 1.000035 |
| 0.960281 | 1.000035 |
| 0.963791 | 1.000035 |
| 0.967314 | 1.000035 |
| 0.97085 | 1.000035 |
| 0.974399 | 1.000035 |
| 0.97796 | 1.000035 |
| 0.981535 | 1.000035 |
| 0.985123 | 1.000035 |
| 0.988724 | 1.000035 |
| 0.992338 | 1.000035 |
| 0.995965 | 1.000035 |
| 0.999606 | 1.000035 |
| 1.00326 | 1.000035 |
| 1.00693 | 1.000035 |
| 1.01061 | 1.000035 |
| 1.0143 | 1.000035 |
| 1.01801 | 1.000035 |
| 1.02173 | 1.000035 |
| 1.02546 | 1.000035 |
| 1.02921 | 1.000035 |
| 1.03297 | 1.000035 |
| 1.03675 | 1.000035 |
| 1.04054 | 1.000035 |
| 1.04434 | 1.000035 |
| 1.04816 | 1.000035 |
| 1.05199 | 1.000035 |
| 1.05584 | 1.000035 |
| 1.0597 | 1.000035 |
| 1.06357 | 1.000035 |
| 1.06746 | 1.000035 |
| 1.07136 | 1.000035 |
| 1.07528 | 1.000035 |
| 1.07921 | 1.000035 |
| 1.08315 | 1.000035 |
| 1.08711 | 1.000035 |
| 1.09108 | 1.000035 |
| 1.09507 | 1.000035 |
| 1.09907 | 1.000035 |
| 1.10309 | 1.000035 |
| 1.10712 | 1.000035 |
| 1.11117 | 1.000035 |
| 1.11523 | 1.000035 |
| 1.11931 | 1.000035 |
| 1.1234 | 1.000035 |
| 1.12751 | 1.000035 |
| 1.13163 | 1.000035 |
| 1.13576 | 1.000035 |
| 1.13992 | 1.000035 |
| 1.14408 | 1.000035 |
| 1.14826 | 1.000035 |
| 1.15246 | 1.000035 |
| 1.15667 | 1.000035 |
| 1.1609 | 1.000035 |
| 1.16515 | 1.000035 |
| 1.1694 | 1.000035 |
| 1.17368 | 1.000035 |
| 1.17797 | 1.000035 |
| 1.18228 | 1.000035 |
| 1.1866 | 1.000035 |
| 1.19093 | 1.000035 |
| 1.19529 | 1.000035 |
| 1.19966 | 1.000035 |
| 1.20404 | 1.000035 |
| 1.20844 | 1.000035 |
| 1.21286 | 1.000035 |
| 1.21729 | 1.000035 |
| 1.22174 | 1.000035 |
| 1.22621 | 1.000035 |
| 1.23069 | 1.000035 |
| 1.23519 | 1.000035 |
| 1.2397 | 1.000035 |
| 1.24423 | 1.000035 |
| 1.24878 | 1.000035 |
| 1.25335 | 1.000035 |
| 1.25793 | 1.000035 |
| 1.26253 | 1.000035 |
| 1.26714 | 1.000035 |
| 1.27177 | 1.000035 |
| 1.27642 | 1.000035 |
| 1.28109 | 1.000035 |
| 1.28577 | 1.000035 |
| 1.29047 | 1.000035 |
| 1.29519 | 1.000035 |
| 1.29992 | 1.000035 |
| 1.30467 | 1.000035 |
| 1.30944 | 1.000035 |
| 1.31423 | 1.000035 |
| 1.31903 | 1.000035 |
| 1.32385 | 1.000035 |
| 1.32869 | 1.000035 |
| 1.33355 | 1.000035 |
| 1.33842 | 1.000035 |
| 1.34332 | 1.000035 |
| 1.34823 | 1.000035 |
| 1.35315 | 1.000035 |
| 1.3581 | 1.000035 |
| 1.36306 | 1.000035 |
| 1.36805 | 1.000035 |
| 1.37305 | 1.000035 |
| 1.37807 | 1.000035 |
| 1.3831 | 1.000035 |
| 1.38816 | 1.000035 |
| 1.39323 | 1.000035 |
| 1.39833 | 1.000035 |
| 1.40344 | 1.000035 |
| 1.40857 | 1.000035 |
| 1.41372 | 1.000035 |
| 1.41888 | 1.000035 |
| 1.42407 | 1.000035 |
| 1.42927 | 1.000035 |
| 1.4345 | 1.000035 |
| 1.43974 | 1.000035 |
| 1.44501 | 1.000035 |
| 1.45029 | 1.000035 |
| 1.45559 | 1.000035 |
| 1.46091 | 1.000035 |
| 1.46625 | 1.000035 |
| 1.47161 | 1.000035 |
| 1.47699 | 1.000035 |
| 1.48239 | 1.000035 |
| 1.4878 | 1.000035 |
| 1.49324 | 1.000035 |
| 1.4987 | 1.000035 |
| 1.50418 | 1.000035 |
| 1.50968 | 1.000035 |
| 1.5152 | 1.000035 |
| 1.52073 | 1.000035 |
| 1.52629 | 1.000035 |
| 1.53187 | 1.000035 |
| 1.53747 | 1.000035 |
| 1.54309 | 1.000035 |
| 1.54873 | 1.000035 |
| 1.55439 | 1.000035 |
| 1.56007 | 1.000035 |
| 1.56578 | 1.000035 |
| 1.5715 | 1.000035 |
| 1.57724 | 1.000035 |
| 1.58301 | 1.000035 |
| 1.5888 | 1.000035 |
| 1.5946 | 1.000035 |
| 1.60043 | 1.000035 |
| 1.60628 | 1.000035 |
| 1.61215 | 1.000035 |
| 1.61805 | 1.000035 |
| 1.62396 | 1.000035 |
| 1.6299 | 1.000035 |
| 1.63585 | 1.000035 |
| 1.64183 | 1.000035 |
| 1.64783 | 1.000035 |
| 1.65386 | 1.000035 |
| 1.6599 | 1.000035 |
| 1.66597 | 1.000035 |
| 1.67206 | 1.000035 |
| 1.67817 | 1.000035 |
| 1.68431 | 1.000035 |
| 1.69046 | 1.000035 |
| 1.69664 | 1.000035 |
| 1.70284 | 1.000035 |
| 1.70907 | 1.000035 |
| 1.71531 | 1.000035 |
| 1.72158 | 1.000035 |
| 1.72788 | 1.000035 |
| 1.73419 | 1.000035 |
| 1.74053 | 1.000035 |
| 1.74689 | 1.000035 |
| 1.75328 | 1.000035 |
| 1.75969 | 1.000035 |
| 1.76612 | 1.000035 |
| 1.77258 | 1.000035 |
| 1.77906 | 1.000035 |
| 1.78556 | 1.000035 |
| 1.79209 | 1.000035 |
| 1.79864 | 1.000035 |
| 1.80521 | 1.000035 |
| 1.81181 | 1.000035 |
| 1.81843 | 1.000035 |
| 1.82508 | 1.000035 |
| 1.83175 | 1.000035 |
| 1.83844 | 1.000035 |
| 1.84516 | 1.000035 |
| 1.85191 | 1.000035 |
| 1.85868 | 1.000035 |
| 1.86547 | 1.000035 |
| 1.87229 | 1.000035 |
| 1.87913 | 1.000035 |
| 1.886 | 1.000035 |
| 1.8929 | 1.000035 |
| 1.89982 | 1.000035 |
| 1.90676 | 1.000035 |
| 1.91373 | 1.000035 |
| 1.92073 | 1.000035 |
| 1.92775 | 1.000035 |
| 1.93479 | 1.000035 |
| 1.94186 | 1.000035 |
| 1.94896 | 1.000035 |
| 1.95609 | 1.000035 |
| 1.96324 | 1.000035 |
| 1.97041 | 1.000035 |
| 1.97762 | 1.000035 |
| 1.98484 | 1.000035 |
| 1.9921 | 1.000035 |
| 1.99938 | 1.000035 |
| 2.00669 | 1.000035 |
| 2.01402 | 1.000035 |
| 2.02139 | 1.000035 |
| 2.02877 | 1.000035 |
| 2.03619 | 1.000035 |
| 2.04363 | 1.000035 |
| 2.0511 | 1.000035 |
| 2.0586 | 1.000035 |
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
- —
Standard conditions: 0 °C, 760 torr (101.325 kPa).