Optical constants
Refractive index of Si (Silicon)
Šik et al. 1998: n,k 0.29–0.62 µm; 250 °C
- Data
- tabulated nk
- Range
- 0.2883–0.6199 µm
- Points
- 47
- Temperature
- 523 K
- State
- crystalline
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 4.08099
- Extinction coefficient k
- 0.104899
- Permittivity ε1
- 16.6435
- Permittivity ε2
- 0.856179
- Absorption coefficient α
- 22433.5 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 891.523 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.78102 µm⁻¹
- Group index ng
- 5.71512
- 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
# Si (Silicon): Šik et al. 1998: n,k 0.29–0.62 µm; 250 °C
si = ls.fetch_refractiveindex("main", "Si", "Sik-250C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (288.3, 619.9) nm
eps = si.eps([423]) # 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_66b9270f1ddf/lightsmith"
si = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(si.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (si/sik-1998-250c).
# ... load si as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=si)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=619, 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
Conditions
- temperature
- 523 K
References
- doi:10.1063/1.368951 Optical functions of silicon at high temperatures, Journal of Applied Physics (1998)
Cite
J. Šik, J. Hora and J. Humlı́ček. Optical functions of silicon at high temperatures. Journal of Applied Physics, 84, 6291-6298 (1998), doi:10.1063/1.368951; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
47 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.2883 | 3.6357 | 5.1613 |
| 0.2917 | 3.9398 | 5.0904 |
| 0.2952 | 4.3119 | 4.9317 |
| 0.2988 | 4.6142 | 4.6638 |
| 0.3024 | 4.8106 | 4.3591 |
| 0.3061 | 4.9182 | 4.0889 |
| 0.31 | 4.9793 | 3.854 |
| 0.3139 | 5.0177 | 3.663 |
| 0.3179 | 5.0385 | 3.508 |
| 0.322 | 5.055 | 3.3798 |
| 0.3263 | 5.0794 | 3.2711 |
| 0.3306 | 5.1125 | 3.1746 |
| 0.3351 | 5.148 | 3.0905 |
| 0.3397 | 5.192 | 3.0162 |
| 0.3444 | 5.248 | 2.9516 |
| 0.3493 | 5.3152 | 2.902 |
| 0.3542 | 5.4097 | 2.868 |
| 0.3594 | 5.5622 | 2.8298 |
| 0.3647 | 5.7863 | 2.7461 |
| 0.3701 | 6.054 | 2.5653 |
| 0.3757 | 6.2898 | 2.2497 |
| 0.3815 | 6.4122 | 1.8239 |
| 0.3875 | 6.3626 | 1.3831 |
| 0.3936 | 6.1816 | 1.0256 |
| 0.3999 | 5.9552 | 0.7775 |
| 0.4065 | 5.7376 | 0.6083 |
| 0.4133 | 5.5428 | 0.4925 |
| 0.4203 | 5.3703 | 0.4125 |
| 0.4275 | 5.2187 | 0.3526 |
| 0.435 | 5.0856 | 0.3048 |
| 0.4428 | 4.9702 | 0.2706 |
| 0.4509 | 4.8691 | 0.2413 |
| 0.4592 | 4.7777 | 0.2156 |
| 0.4679 | 4.6924 | 0.1971 |
| 0.4769 | 4.6157 | 0.1852 |
| 0.4862 | 4.5453 | 0.1716 |
| 0.4959 | 4.4795 | 0.1596 |
| 0.5061 | 4.4172 | 0.1483 |
| 0.5166 | 4.3577 | 0.1411 |
| 0.5276 | 4.301 | 0.1372 |
| 0.5391 | 4.2481 | 0.1283 |
| 0.551 | 4.1993 | 0.1191 |
| 0.5636 | 4.1537 | 0.1144 |
| 0.5767 | 4.1113 | 0.1119 |
| 0.5904 | 4.0732 | 0.1031 |
| 0.6048 | 4.0372 | 0.0929 |
| 0.6199 | 4.0013 | 0.1012 |
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
- —
Temperature: 250 °C (523 K).