Optical constants
Refractive index of C (Carbon, diamond, graphite, graphene, carbon nanotubes)
Hagemann et al. 1974: n,k 0.0000413–124 µm
- Data
- tabulated nk
- Range
- 4.133e-05–124 µm
- Points
- 100
- State
- amorphous
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.86025
- Extinction coefficient k
- 0.727799
- Permittivity ε1
- 2.93082
- Permittivity ε2
- 2.70777
- Absorption coefficient α
- 155647 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 128.496 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.580645 µm⁻¹
- Group index ng
- 1.51906
- 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
# C (Carbon, diamond, graphite, graphene, carbon nanotubes): Hagemann et al. 1974: n,k 0.0000413–124 µm
c = ls.fetch_refractiveindex("main", "C", "Hagemann", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(c.range_nm) # (0.04133, 124000) nm
eps = c.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_a271953943e0/lightsmith"
c = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(c.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (c/hagemann-1974).
# ... load c as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=c)],
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.
References
2) H.-J. Hagemann, W. Gudat, and C. Kunz. DESY report SR-74/7 (1974)
- doi:10.1364/josa.65.000742 Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3, Journal of the Optical Society of America (1975)
Cite
H.-J. Hagemann, W. Gudat and C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3. Journal of the Optical Society of America, 65, 742 (1975), doi:10.1364/josa.65.000742; H.-J. Hagemann, W. Gudat, and C. Kunz. DESY report SR-74/7 (1974); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
100 rows as published| λ (µm) | n | k |
|---|---|---|
| 4.133e-05 | 1.0 | 3.29e-11 |
| 6.199e-05 | 1.0 | 2.17e-10 |
| 8.266e-05 | 1.0 | 7.2e-10 |
| 0.0001378 | 1.0 | 5e-09 |
| 0.0001771 | 1.0 | 1.34e-08 |
| 0.000248 | 1.0 | 5.38e-08 |
| 0.0004133 | 1.0 | 4.48e-07 |
| 0.0006199 | 1.0 | 2.41e-06 |
| 0.0008266 | 1.0 | 8.62e-06 |
| 0.00124 | 1.0 | 4.22e-05 |
| 0.00155 | 0.999 | 9.85e-05 |
| 0.002066 | 0.999 | 0.000332 |
| 0.00248 | 0.999 | 0.000569 |
| 0.002755 | 0.998 | 0.000839 |
| 0.003542 | 0.998 | 0.00213 |
| 0.003647 | 0.998 | 0.00236 |
| 0.003757 | 0.998 | 0.00277 |
| 0.003875 | 0.998 | 0.00368 |
| 0.003999 | 0.999 | 0.00497 |
| 0.004133 | 1.002 | 0.00354 |
| 0.004275 | 1.001 | 0.000794 |
| 0.004592 | 0.999 | 0.000206 |
| 0.004959 | 0.998 | 0.000272 |
| 0.006199 | 0.995 | 0.000585 |
| 0.006888 | 0.994 | 0.000848 |
| 0.007749 | 0.992 | 0.00121 |
| 0.008856 | 0.989 | 0.00193 |
| 0.009537 | 0.987 | 0.00235 |
| 0.01033 | 0.985 | 0.00282 |
| 0.01127 | 0.982 | 0.00377 |
| 0.0124 | 0.978 | 0.00519 |
| 0.01305 | 0.976 | 0.00613 |
| 0.01378 | 0.973 | 0.00725 |
| 0.01459 | 0.97 | 0.00858 |
| 0.0155 | 0.966 | 0.0102 |
| 0.01653 | 0.961 | 0.0121 |
| 0.01771 | 0.955 | 0.015 |
| 0.01907 | 0.948 | 0.02 |
| 0.02066 | 0.94 | 0.027 |
| 0.02254 | 0.932 | 0.035 |
| 0.0248 | 0.922 | 0.045 |
| 0.02695 | 0.914 | 0.058 |
| 0.02818 | 0.911 | 0.063 |
| 0.02952 | 0.904 | 0.065 |
| 0.031 | 0.893 | 0.073 |
| 0.03263 | 0.883 | 0.086 |
| 0.03444 | 0.879 | 0.102 |
| 0.03647 | 0.873 | 0.109 |
| 0.03875 | 0.857 | 0.118 |
| 0.04133 | 0.837 | 0.14 |
| 0.04428 | 0.816 | 0.166 |
| 0.04769 | 0.794 | 0.207 |
| 0.05166 | 0.772 | 0.255 |
| 0.05636 | 0.735 | 0.314 |
| 0.06199 | 0.707 | 0.451 |
| 0.06888 | 0.733 | 0.631 |
| 0.07749 | 0.908 | 0.903 |
| 0.07999 | 1.005 | 0.938 |
| 0.08266 | 1.099 | 0.955 |
| 0.08551 | 1.191 | 0.96 |
| 0.08856 | 1.284 | 0.956 |
| 0.09184 | 1.378 | 0.934 |
| 0.09537 | 1.463 | 0.894 |
| 0.09919 | 1.542 | 0.851 |
| 0.1033 | 1.608 | 0.786 |
| 0.1078 | 1.663 | 0.73 |
| 0.1127 | 1.723 | 0.669 |
| 0.1181 | 1.785 | 0.582 |
| 0.124 | 1.811 | 0.449 |
| 0.1305 | 1.791 | 0.334 |
| 0.1378 | 1.736 | 0.223 |
| 0.1459 | 1.649 | 0.144 |
| 0.155 | 1.531 | 0.0869 |
| 0.1653 | 1.399 | 0.101 |
| 0.1771 | 1.28 | 0.158 |
| 0.1907 | 1.196 | 0.28 |
| 0.2066 | 1.158 | 0.415 |
| 0.2254 | 1.195 | 0.61 |
| 0.248 | 1.344 | 0.754 |
| 0.2755 | 1.518 | 0.764 |
| 0.31 | 1.638 | 0.723 |
| 0.3542 | 1.706 | 0.681 |
| 0.4133 | 1.752 | 0.678 |
| 0.4959 | 1.807 | 0.696 |
| 0.6199 | 1.879 | 0.739 |
| 0.8266 | 1.974 | 0.816 |
| 1.24 | 2.204 | 1.04 |
| 2.48 | 2.698 | 1.18 |
| 3.1 | 2.831 | 1.22 |
| 4.133 | 2.949 | 1.29 |
| 6.199 | 3.0 | 1.51 |
| 12.4 | 2.87 | 2.79 |
| 15.5 | 2.932 | 3.56 |
| 20.66 | 3.159 | 4.65 |
| 31.0 | 3.472 | 6.86 |
| 41.33 | 4.054 | 9.31 |
| 49.59 | 4.997 | 11.2 |
| 61.99 | 7.115 | 12.4 |
| 82.66 | 7.489 | 13.1 |
| 124.0 | 5.303 | 19.2 |
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
- —