Optical constants

Refractive index of He (Helium)

Cuthbertson and Cuthbertson 1936: n 0.275–0.546 µm

Data
formula 6
Range
0.2753–0.5462 µm
Temperature
273.15 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.2753–0.5462 µm
Refractive index n
1.00004
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
—
Chromatic dispersion dn/dλ
-2.86879e-06 µm⁻¹
Group index ng
1.00004
Group velocity dispersion
0.00234279 fs²/mm
Dispersion parameter D
-0.0293137 ps/(nm·km)
Photon energy
3.19547 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): Cuthbertson and Cuthbertson 1936: n 0.275–0.546 µm
he = ls.fetch_refractiveindex("main", "He", "Cuthbertson", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(he.range_nm)  # (275.3, 546.2) nm
eps = he.eps([388])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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 µm
n−1=0.014755297426.2974−λ−2

Valid from 0.2753 to 0.5462 µm.

Coefficients as stored
CiValue
C10.0
C20.014755297
C3426.2974

Comments and conditions

Standard conditions: 0 °C, 760 torr (101.325 kPa).

Conditions

temperature
273.15 K
pressure
101325

References

1) C. Cuthbertson and M. Cuthbertson. The refraction and dispersion of neon and helium. Proc. R. Soc. London A 135, 40-47 (1936)
2) C. Cuthbertson and M. Cuthbertson. On the refraction and dispersion of neon. Proc. R. Soc. London A 83, 149-151 (1910)
* Ref. 1 doesn't cite gas temperature and pressure. See the earlier publication by the same authors (ref. 2) instead.
  • doi:10.1098/rspa.1932.0019 The refraction and dispersion of neon and helium, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character (1932)
  • doi:10.1098/rspa.1910.0001 On the refraction and dispersion of neon, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character (1910)

Cite

Clive Cuthbertson and Maude Cuthbertson. The refraction and dispersion of neon and helium. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 135, 40-47 (1932), doi:10.1098/rspa.1932.0019; Clive Cuthbertson and Maude Cuthbertson. On the refraction and dispersion of neon. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 83, 149-151 (1910), doi:10.1098/rspa.1910.0001; 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
He (Helium), Cuthbertson and Cuthbertson 1936: n 0.275–0.546 µm: n and k versus wavelength
λ (µm)n
0.27531.000036
0.2757731.000036
0.2762471.000036
0.2767221.000036
0.2771971.000036
0.2776741.000036
0.2781511.000036
0.2786291.000036
0.2791081.000036
0.2795881.000036
0.2800681.000036
0.2805491.000036
0.2810311.000036
0.2815141.000036
0.2819981.000036
0.2824831.000036
0.2829681.000036
0.2834551.000036
0.2839421.000036
0.284431.000036
0.2849191.000036
0.2854081.000036
0.2858991.000036
0.286391.000036
0.2868821.000036
0.2873751.000036
0.2878691.000036
0.2883641.000036
0.2888591.000036
0.2893561.000036
0.2898531.000036
0.2903511.000036
0.290851.000036
0.291351.000036
0.2918511.000036
0.2923521.000036
0.2928551.000036
0.2933581.000036
0.2938621.000036
0.2943671.000036
0.2948731.000036
0.295381.000036
0.2958881.000036
0.2963961.000036
0.2969061.000036
0.2974161.000036
0.2979271.000036
0.2984391.000036
0.2989521.000036
0.2994661.000036
0.299981.000036
0.3004961.000036
0.3010121.000036
0.3015291.000036
0.3020481.000036
0.3025671.000036
0.3030871.000036
0.3036081.000036
0.3041291.000036
0.3046521.000036
0.3051761.000036
0.30571.000036
0.3062251.000036
0.3067521.000035
0.3072791.000035
0.3078071.000035
0.3083361.000035
0.3088661.000035
0.3093971.000035
0.3099281.000035
0.3104611.000035
0.3109951.000035
0.3115291.000035
0.3120641.000035
0.3126011.000035
0.3131381.000035
0.3136761.000035
0.3142151.000035
0.3147551.000035
0.3152961.000035
0.3158381.000035
0.3163811.000035
0.3169251.000035
0.3174691.000035
0.3180151.000035
0.3185611.000035
0.3191091.000035
0.3196571.000035
0.3202071.000035
0.3207571.000035
0.3213081.000035
0.321861.000035
0.3224131.000035
0.3229681.000035
0.3235231.000035
0.3240791.000035
0.3246361.000035
0.3251931.000035
0.3257521.000035
0.3263121.000035
0.3268731.000035
0.3274351.000035
0.3279971.000035
0.3285611.000035
0.3291261.000035
0.3296911.000035
0.3302581.000035
0.3308261.000035
0.3313941.000035
0.3319641.000035
0.3325341.000035
0.3331061.000035
0.3336781.000035
0.3342521.000035
0.3348261.000035
0.3354011.000035
0.3359781.000035
0.3365551.000035
0.3371341.000035
0.3377131.000035
0.3382931.000035
0.3388751.000035
0.3394571.000035
0.3400411.000035
0.3406251.000035
0.341211.000035
0.3417971.000035
0.3423841.000035
0.3429731.000035
0.3435621.000035
0.3441521.000035
0.3447441.000035
0.3453361.000035
0.345931.000035
0.3465241.000035
0.347121.000035
0.3477161.000035
0.3483141.000035
0.3489131.000035
0.3495121.000035
0.3501131.000035
0.3507151.000035
0.3513171.000035
0.3519211.000035
0.3525261.000035
0.3531321.000035
0.3537391.000035
0.3543471.000035
0.3549561.000035
0.3555661.000035
0.3561771.000035
0.3567891.000035
0.3574021.000035
0.3580161.000035
0.3586311.000035
0.3592481.000035
0.3598651.000035
0.3604841.000035
0.3611031.000035
0.3617241.000035
0.3623451.000035
0.3629681.000035
0.3635921.000035
0.3642171.000035
0.3648431.000035
0.365471.000035
0.3660981.000035
0.3667271.000035
0.3673571.000035
0.3679891.000035
0.3686211.000035
0.3692541.000035
0.3698891.000035
0.3705251.000035
0.3711611.000035
0.3717991.000035
0.3724381.000035
0.3730781.000035
0.373721.000035
0.3743621.000035
0.3750051.000035
0.375651.000035
0.3762951.000035
0.3769421.000035
0.377591.000035
0.3782391.000035
0.3788891.000035
0.379541.000035
0.3801921.000035
0.3808451.000035
0.38151.000035
0.3821561.000035
0.3828121.000035
0.383471.000035
0.3841291.000035
0.3847891.000035
0.3854511.000035
0.3861131.000035
0.3867771.000035
0.3874411.000035
0.3881071.000035
0.3887741.000035
0.3894421.000035
0.3901121.000035
0.3907821.000035
0.3914541.000035
0.3921261.000035
0.39281.000035
0.3934751.000035
0.3941521.000035
0.3948291.000035
0.3955081.000035
0.3961871.000035
0.3968681.000035
0.397551.000035
0.3982331.000035
0.3989181.000035
0.3996031.000035
0.400291.000035
0.4009781.000035
0.4016671.000035
0.4023581.000035
0.4030491.000035
0.4037421.000035
0.4044361.000035
0.4051311.000035
0.4058271.000035
0.4065241.000035
0.4072231.000035
0.4079231.000035
0.4086241.000035
0.4093261.000035
0.410031.000035
0.4107341.000035
0.411441.000035
0.4121471.000035
0.4128551.000035
0.4135651.000035
0.4142761.000035
0.4149881.000035
0.4157011.000035
0.4164151.000035
0.4171311.000035
0.4178481.000035
0.4185661.000035
0.4192851.000035
0.4200061.000035
0.4207281.000035
0.4214511.000035
0.4221751.000035
0.4229011.000035
0.4236271.000035
0.4243551.000035
0.4250851.000035
0.4258151.000035
0.4265471.000035
0.427281.000035
0.4280141.000035
0.428751.000035
0.4294871.000035
0.4302251.000035
0.4309641.000035
0.4317051.000035
0.4324471.000035
0.433191.000035
0.4339341.000035
0.434681.000035
0.4354271.000035
0.4361761.000035
0.4369251.000035
0.4376761.000035
0.4384281.000035
0.4391821.000035
0.4399361.000035
0.4406931.000035
0.441451.000035
0.4422091.000035
0.4429691.000035
0.443731.000035
0.4444921.000035
0.4452561.000035
0.4460211.000035
0.4467881.000035
0.4475561.000035
0.4483251.000035
0.4490951.000035
0.4498671.000035
0.450641.000035
0.4514151.000035
0.4521911.000035
0.4529681.000035
0.4537461.000035
0.4545261.000035
0.4553071.000035
0.456091.000035
0.4568741.000035
0.4576591.000035
0.4584451.000035
0.4592331.000035
0.4600221.000035
0.4608131.000035
0.4616051.000035
0.4623981.000035
0.4631931.000035
0.4639891.000035
0.4647861.000035
0.4655851.000035
0.4663851.000035
0.4671871.000035
0.467991.000035
0.4687941.000035
0.46961.000035
0.4704071.000035
0.4712151.000035
0.4720251.000035
0.4728361.000035
0.4736491.000035
0.4744631.000035
0.4752781.000035
0.4760951.000035
0.4769131.000035
0.4777331.000035
0.4785541.000035
0.4793761.000035
0.48021.000035
0.4810251.000035
0.4818521.000035
0.482681.000035
0.4835091.000035
0.484341.000035
0.4851731.000035
0.4860071.000035
0.4868421.000035
0.4876791.000035
0.4885171.000035
0.4893561.000035
0.4901971.000035
0.491041.000035
0.4918841.000035
0.4927291.000035
0.4935761.000035
0.4944241.000035
0.4952741.000035
0.4961251.000035
0.4969771.000035
0.4978321.000035
0.4986871.000035
0.4995441.000035
0.5004031.000035
0.5012631.000035
0.5021241.000035
0.5029871.000035
0.5038511.000035
0.5047171.000035
0.5055851.000035
0.5064541.000035
0.5073241.000035
0.5081961.000035
0.5090691.000035
0.5099441.000035
0.510821.000035
0.5116981.000035
0.5125781.000035
0.5134591.000035
0.5143411.000035
0.5152251.000035
0.516111.000035
0.5169971.000035
0.5178861.000035
0.5187761.000035
0.5196681.000035
0.5205611.000035
0.5214551.000035
0.5223511.000035
0.5232491.000035
0.5241481.000035
0.5250491.000035
0.5259511.000035
0.5268551.000035
0.5277611.000035
0.5286681.000035
0.5295761.000035
0.5304861.000035
0.5313981.000035
0.5323111.000035
0.5332261.000035
0.5341431.000035
0.5350611.000035
0.535981.000035
0.5369011.000035
0.5378241.000035
0.5387481.000035
0.5396741.000035
0.5406021.000035
0.5415311.000035
0.5424611.000035
0.5433941.000035
0.5443271.000035
0.5452631.000035
0.54621.000035

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—