Optical constants
Refractive index of He (Helium)
Ermolov et al. 2015: n 0.09–1.00 µm
- Data
- formula 2
- Range
- 0.09–1 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
- 259.06
- Chromatic dispersion dn/dλ
- -6.93198e-07 µm⁻¹
- Group index ng
- 1.00004
- Group velocity dispersion
- 0.00128936 fs²/mm
- Dispersion parameter D
- -0.00703415 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): Ermolov et al. 2015: n 0.09–1.00 µm
he = ls.fetch_refractiveindex("main", "He", "Ermolov", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(he.range_nm) # (90, 1000) 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_179667675a4a/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/ermolov-2015).
# ... 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=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.
Dispersion formula
Sellmeier (C in µm²) (formula 2), λ in µmValid from 0.09 to 1.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 2.16463842e-05 |
| C3 | -0.000680769781 |
| C4 | 2.10561127e-07 |
| C5 | 0.00513251289 |
| C6 | 4.7509272e-05 |
| C7 | 0.00318621354 |
Comments and conditions
Conditions
- temperature
- 273.15 K
- pressure
- 101325
References
- doi:10.1103/physreva.92.033821 Supercontinuum generation in the vacuum ultraviolet through dispersive-wave and soliton-plasma interaction in a noble-gas-filled hollow-core photonic crystal fiber, Physical Review A (2015)
Cite
A. Ermolov, K. F. Mak, M. H. Frosz, J. C. Travers and P. St. J. Russell. Supercontinuum generation in the vacuum ultraviolet through dispersive-wave and soliton-plasma interaction in a noble-gas-filled hollow-core photonic crystal fiber. Physical Review A, 92, 033821 (2015), doi:10.1103/physreva.92.033821; 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 |
|---|---|
| 0.09 | 1.000049 |
| 0.0905448 | 1.000049 |
| 0.0910929 | 1.000049 |
| 0.0916443 | 1.000049 |
| 0.092199 | 1.000048 |
| 0.0927571 | 1.000048 |
| 0.0933186 | 1.000048 |
| 0.0938835 | 1.000048 |
| 0.0944518 | 1.000047 |
| 0.0950235 | 1.000047 |
| 0.0955987 | 1.000047 |
| 0.0961774 | 1.000047 |
| 0.0967596 | 1.000046 |
| 0.0973453 | 1.000046 |
| 0.0979345 | 1.000046 |
| 0.0985273 | 1.000046 |
| 0.0991237 | 1.000045 |
| 0.0997237 | 1.000045 |
| 0.100327 | 1.000045 |
| 0.100935 | 1.000045 |
| 0.101546 | 1.000045 |
| 0.10216 | 1.000045 |
| 0.102779 | 1.000044 |
| 0.103401 | 1.000044 |
| 0.104027 | 1.000044 |
| 0.104656 | 1.000044 |
| 0.10529 | 1.000044 |
| 0.105927 | 1.000044 |
| 0.106569 | 1.000043 |
| 0.107214 | 1.000043 |
| 0.107863 | 1.000043 |
| 0.108516 | 1.000043 |
| 0.109172 | 1.000043 |
| 0.109833 | 1.000043 |
| 0.110498 | 1.000043 |
| 0.111167 | 1.000042 |
| 0.11184 | 1.000042 |
| 0.112517 | 1.000042 |
| 0.113198 | 1.000042 |
| 0.113883 | 1.000042 |
| 0.114572 | 1.000042 |
| 0.115266 | 1.000042 |
| 0.115964 | 1.000042 |
| 0.116666 | 1.000041 |
| 0.117372 | 1.000041 |
| 0.118082 | 1.000041 |
| 0.118797 | 1.000041 |
| 0.119516 | 1.000041 |
| 0.12024 | 1.000041 |
| 0.120968 | 1.000041 |
| 0.1217 | 1.000041 |
| 0.122436 | 1.000041 |
| 0.123178 | 1.000041 |
| 0.123923 | 1.00004 |
| 0.124673 | 1.00004 |
| 0.125428 | 1.00004 |
| 0.126187 | 1.00004 |
| 0.126951 | 1.00004 |
| 0.12772 | 1.00004 |
| 0.128493 | 1.00004 |
| 0.12927 | 1.00004 |
| 0.130053 | 1.00004 |
| 0.13084 | 1.00004 |
| 0.131632 | 1.00004 |
| 0.132429 | 1.00004 |
| 0.133231 | 1.00004 |
| 0.134037 | 1.000039 |
| 0.134848 | 1.000039 |
| 0.135665 | 1.000039 |
| 0.136486 | 1.000039 |
| 0.137312 | 1.000039 |
| 0.138143 | 1.000039 |
| 0.138979 | 1.000039 |
| 0.139821 | 1.000039 |
| 0.140667 | 1.000039 |
| 0.141519 | 1.000039 |
| 0.142375 | 1.000039 |
| 0.143237 | 1.000039 |
| 0.144104 | 1.000039 |
| 0.144976 | 1.000039 |
| 0.145854 | 1.000039 |
| 0.146737 | 1.000039 |
| 0.147625 | 1.000038 |
| 0.148519 | 1.000038 |
| 0.149418 | 1.000038 |
| 0.150322 | 1.000038 |
| 0.151232 | 1.000038 |
| 0.152147 | 1.000038 |
| 0.153068 | 1.000038 |
| 0.153995 | 1.000038 |
| 0.154927 | 1.000038 |
| 0.155865 | 1.000038 |
| 0.156808 | 1.000038 |
| 0.157758 | 1.000038 |
| 0.158713 | 1.000038 |
| 0.159673 | 1.000038 |
| 0.16064 | 1.000038 |
| 0.161612 | 1.000038 |
| 0.162591 | 1.000038 |
| 0.163575 | 1.000038 |
| 0.164565 | 1.000038 |
| 0.165561 | 1.000038 |
| 0.166563 | 1.000038 |
| 0.167571 | 1.000037 |
| 0.168586 | 1.000037 |
| 0.169606 | 1.000037 |
| 0.170633 | 1.000037 |
| 0.171666 | 1.000037 |
| 0.172705 | 1.000037 |
| 0.17375 | 1.000037 |
| 0.174802 | 1.000037 |
| 0.17586 | 1.000037 |
| 0.176925 | 1.000037 |
| 0.177996 | 1.000037 |
| 0.179073 | 1.000037 |
| 0.180157 | 1.000037 |
| 0.181248 | 1.000037 |
| 0.182345 | 1.000037 |
| 0.183448 | 1.000037 |
| 0.184559 | 1.000037 |
| 0.185676 | 1.000037 |
| 0.1868 | 1.000037 |
| 0.187931 | 1.000037 |
| 0.189068 | 1.000037 |
| 0.190213 | 1.000037 |
| 0.191364 | 1.000037 |
| 0.192523 | 1.000037 |
| 0.193688 | 1.000037 |
| 0.19486 | 1.000037 |
| 0.19604 | 1.000037 |
| 0.197227 | 1.000037 |
| 0.19842 | 1.000037 |
| 0.199622 | 1.000037 |
| 0.20083 | 1.000037 |
| 0.202046 | 1.000037 |
| 0.203269 | 1.000037 |
| 0.204499 | 1.000036 |
| 0.205737 | 1.000036 |
| 0.206982 | 1.000036 |
| 0.208235 | 1.000036 |
| 0.209496 | 1.000036 |
| 0.210764 | 1.000036 |
| 0.21204 | 1.000036 |
| 0.213323 | 1.000036 |
| 0.214614 | 1.000036 |
| 0.215913 | 1.000036 |
| 0.21722 | 1.000036 |
| 0.218535 | 1.000036 |
| 0.219858 | 1.000036 |
| 0.221189 | 1.000036 |
| 0.222528 | 1.000036 |
| 0.223875 | 1.000036 |
| 0.22523 | 1.000036 |
| 0.226593 | 1.000036 |
| 0.227965 | 1.000036 |
| 0.229345 | 1.000036 |
| 0.230733 | 1.000036 |
| 0.23213 | 1.000036 |
| 0.233535 | 1.000036 |
| 0.234949 | 1.000036 |
| 0.236371 | 1.000036 |
| 0.237802 | 1.000036 |
| 0.239241 | 1.000036 |
| 0.240689 | 1.000036 |
| 0.242146 | 1.000036 |
| 0.243612 | 1.000036 |
| 0.245087 | 1.000036 |
| 0.24657 | 1.000036 |
| 0.248063 | 1.000036 |
| 0.249564 | 1.000036 |
| 0.251075 | 1.000036 |
| 0.252595 | 1.000036 |
| 0.254124 | 1.000036 |
| 0.255662 | 1.000036 |
| 0.25721 | 1.000036 |
| 0.258767 | 1.000036 |
| 0.260333 | 1.000036 |
| 0.261909 | 1.000036 |
| 0.263494 | 1.000036 |
| 0.265089 | 1.000036 |
| 0.266694 | 1.000036 |
| 0.268308 | 1.000036 |
| 0.269932 | 1.000036 |
| 0.271566 | 1.000036 |
| 0.27321 | 1.000036 |
| 0.274864 | 1.000036 |
| 0.276528 | 1.000036 |
| 0.278201 | 1.000036 |
| 0.279885 | 1.000036 |
| 0.28158 | 1.000036 |
| 0.283284 | 1.000036 |
| 0.284999 | 1.000036 |
| 0.286724 | 1.000036 |
| 0.28846 | 1.000036 |
| 0.290206 | 1.000036 |
| 0.291962 | 1.000036 |
| 0.29373 | 1.000036 |
| 0.295508 | 1.000036 |
| 0.297297 | 1.000035 |
| 0.299096 | 1.000035 |
| 0.300907 | 1.000035 |
| 0.302728 | 1.000035 |
| 0.304561 | 1.000035 |
| 0.306404 | 1.000035 |
| 0.308259 | 1.000035 |
| 0.310125 | 1.000035 |
| 0.312002 | 1.000035 |
| 0.313891 | 1.000035 |
| 0.315791 | 1.000035 |
| 0.317702 | 1.000035 |
| 0.319625 | 1.000035 |
| 0.32156 | 1.000035 |
| 0.323507 | 1.000035 |
| 0.325465 | 1.000035 |
| 0.327435 | 1.000035 |
| 0.329417 | 1.000035 |
| 0.331411 | 1.000035 |
| 0.333417 | 1.000035 |
| 0.335435 | 1.000035 |
| 0.337466 | 1.000035 |
| 0.339508 | 1.000035 |
| 0.341564 | 1.000035 |
| 0.343631 | 1.000035 |
| 0.345711 | 1.000035 |
| 0.347804 | 1.000035 |
| 0.349909 | 1.000035 |
| 0.352027 | 1.000035 |
| 0.354158 | 1.000035 |
| 0.356302 | 1.000035 |
| 0.358459 | 1.000035 |
| 0.360629 | 1.000035 |
| 0.362812 | 1.000035 |
| 0.365008 | 1.000035 |
| 0.367217 | 1.000035 |
| 0.36944 | 1.000035 |
| 0.371676 | 1.000035 |
| 0.373926 | 1.000035 |
| 0.37619 | 1.000035 |
| 0.378467 | 1.000035 |
| 0.380758 | 1.000035 |
| 0.383062 | 1.000035 |
| 0.385381 | 1.000035 |
| 0.387714 | 1.000035 |
| 0.390061 | 1.000035 |
| 0.392422 | 1.000035 |
| 0.394797 | 1.000035 |
| 0.397187 | 1.000035 |
| 0.399591 | 1.000035 |
| 0.40201 | 1.000035 |
| 0.404444 | 1.000035 |
| 0.406892 | 1.000035 |
| 0.409355 | 1.000035 |
| 0.411833 | 1.000035 |
| 0.414326 | 1.000035 |
| 0.416834 | 1.000035 |
| 0.419357 | 1.000035 |
| 0.421895 | 1.000035 |
| 0.424449 | 1.000035 |
| 0.427018 | 1.000035 |
| 0.429603 | 1.000035 |
| 0.432204 | 1.000035 |
| 0.43482 | 1.000035 |
| 0.437452 | 1.000035 |
| 0.4401 | 1.000035 |
| 0.442764 | 1.000035 |
| 0.445444 | 1.000035 |
| 0.44814 | 1.000035 |
| 0.450853 | 1.000035 |
| 0.453582 | 1.000035 |
| 0.456328 | 1.000035 |
| 0.45909 | 1.000035 |
| 0.461869 | 1.000035 |
| 0.464665 | 1.000035 |
| 0.467478 | 1.000035 |
| 0.470307 | 1.000035 |
| 0.473154 | 1.000035 |
| 0.476018 | 1.000035 |
| 0.4789 | 1.000035 |
| 0.481799 | 1.000035 |
| 0.484715 | 1.000035 |
| 0.487649 | 1.000035 |
| 0.490601 | 1.000035 |
| 0.493571 | 1.000035 |
| 0.496558 | 1.000035 |
| 0.499564 | 1.000035 |
| 0.502588 | 1.000035 |
| 0.50563 | 1.000035 |
| 0.508691 | 1.000035 |
| 0.51177 | 1.000035 |
| 0.514868 | 1.000035 |
| 0.517985 | 1.000035 |
| 0.52112 | 1.000035 |
| 0.524275 | 1.000035 |
| 0.527448 | 1.000035 |
| 0.530641 | 1.000035 |
| 0.533853 | 1.000035 |
| 0.537084 | 1.000035 |
| 0.540335 | 1.000035 |
| 0.543606 | 1.000035 |
| 0.546897 | 1.000035 |
| 0.550207 | 1.000035 |
| 0.553538 | 1.000035 |
| 0.556888 | 1.000035 |
| 0.560259 | 1.000035 |
| 0.563651 | 1.000035 |
| 0.567063 | 1.000035 |
| 0.570495 | 1.000035 |
| 0.573949 | 1.000035 |
| 0.577423 | 1.000035 |
| 0.580918 | 1.000035 |
| 0.584434 | 1.000035 |
| 0.587972 | 1.000035 |
| 0.591531 | 1.000035 |
| 0.595112 | 1.000035 |
| 0.598714 | 1.000035 |
| 0.602338 | 1.000035 |
| 0.605984 | 1.000035 |
| 0.609653 | 1.000035 |
| 0.613343 | 1.000035 |
| 0.617056 | 1.000035 |
| 0.620791 | 1.000035 |
| 0.624549 | 1.000035 |
| 0.628329 | 1.000035 |
| 0.632132 | 1.000035 |
| 0.635959 | 1.000035 |
| 0.639808 | 1.000035 |
| 0.643681 | 1.000035 |
| 0.647578 | 1.000035 |
| 0.651498 | 1.000035 |
| 0.655441 | 1.000035 |
| 0.659409 | 1.000035 |
| 0.6634 | 1.000035 |
| 0.667416 | 1.000035 |
| 0.671456 | 1.000035 |
| 0.67552 | 1.000035 |
| 0.67961 | 1.000035 |
| 0.683723 | 1.000035 |
| 0.687862 | 1.000035 |
| 0.692026 | 1.000035 |
| 0.696215 | 1.000035 |
| 0.700429 | 1.000035 |
| 0.704669 | 1.000035 |
| 0.708934 | 1.000035 |
| 0.713226 | 1.000035 |
| 0.717543 | 1.000035 |
| 0.721886 | 1.000035 |
| 0.726256 | 1.000035 |
| 0.730652 | 1.000035 |
| 0.735075 | 1.000035 |
| 0.739525 | 1.000035 |
| 0.744001 | 1.000035 |
| 0.748505 | 1.000035 |
| 0.753036 | 1.000035 |
| 0.757594 | 1.000035 |
| 0.76218 | 1.000035 |
| 0.766793 | 1.000035 |
| 0.771435 | 1.000035 |
| 0.776105 | 1.000035 |
| 0.780803 | 1.000035 |
| 0.785529 | 1.000035 |
| 0.790284 | 1.000035 |
| 0.795068 | 1.000035 |
| 0.79988 | 1.000035 |
| 0.804722 | 1.000035 |
| 0.809593 | 1.000035 |
| 0.814494 | 1.000035 |
| 0.819424 | 1.000035 |
| 0.824384 | 1.000035 |
| 0.829374 | 1.000035 |
| 0.834395 | 1.000035 |
| 0.839446 | 1.000035 |
| 0.844527 | 1.000035 |
| 0.849639 | 1.000035 |
| 0.854782 | 1.000035 |
| 0.859956 | 1.000035 |
| 0.865162 | 1.000035 |
| 0.870399 | 1.000035 |
| 0.875667 | 1.000035 |
| 0.880968 | 1.000035 |
| 0.886301 | 1.000035 |
| 0.891666 | 1.000035 |
| 0.897063 | 1.000035 |
| 0.902493 | 1.000035 |
| 0.907956 | 1.000035 |
| 0.913452 | 1.000035 |
| 0.918981 | 1.000035 |
| 0.924544 | 1.000035 |
| 0.930141 | 1.000035 |
| 0.935771 | 1.000035 |
| 0.941435 | 1.000035 |
| 0.947134 | 1.000035 |
| 0.952867 | 1.000035 |
| 0.958635 | 1.000035 |
| 0.964438 | 1.000035 |
| 0.970276 | 1.000035 |
| 0.976149 | 1.000035 |
| 0.982058 | 1.000035 |
| 0.988003 | 1.000035 |
| 0.993983 | 1.000035 |
| 1 | 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).