Optical constants
Refractive index of Si (Silicon)
Pierce and Spicer 1972: n,k 0.0103–2.07 µm
- Data
- tabulated nk
- Range
- 0.1033–2.066 µm
- Points
- 46
- State
- amorphous
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 4.30458
- Extinction coefficient k
- 0.59238
- Permittivity ε1
- 18.1785
- Permittivity ε2
- 5.0999
- Absorption coefficient α
- 126686 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 157.871 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.30906 µm⁻¹
- Group index ng
- 5.66139
- 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): Pierce and Spicer 1972: n,k 0.0103–2.07 µm
si = ls.fetch_refractiveindex("main", "Si", "Pierce", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (103.3, 2066) nm
eps = si.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_705e135f14df/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/pierce-spicer-1972).
# ... 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=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.
Comments and conditions
References
2) Handbook of Optical Constants of Solids, Edward D. Palik, ed. Academic Press, Boston, 1985
* Ref. 2 provides numerical values for the graphical data reported in Ref. 1
- doi:10.1103/physrevb.5.3017 Electronic Structure of Amorphous Si from Photoemission and Optical Studies, Physical Review B (1972)
Cite
D. T. Pierce and W. E. Spicer. Electronic Structure of Amorphous Si from Photoemission and Optical Studies. Physical Review B, 5, 3017-3029 (1972), doi:10.1103/physrevb.5.3017; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
46 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.1033 | 0.327 | 0.726 |
| 0.1078 | 0.363 | 0.847 |
| 0.1127 | 0.392 | 0.946 |
| 0.1181 | 0.423 | 1.04 |
| 0.124 | 0.459 | 1.14 |
| 0.1305 | 0.497 | 1.24 |
| 0.1378 | 0.543 | 1.35 |
| 0.1459 | 0.597 | 1.47 |
| 0.155 | 0.66 | 1.6 |
| 0.1653 | 0.735 | 1.74 |
| 0.1771 | 0.832 | 1.89 |
| 0.1907 | 0.951 | 2.07 |
| 0.2066 | 1.11 | 2.28 |
| 0.2254 | 1.35 | 2.51 |
| 0.248 | 1.69 | 2.76 |
| 0.2583 | 1.86 | 2.85 |
| 0.2695 | 2.07 | 2.93 |
| 0.2818 | 2.3 | 2.99 |
| 0.2952 | 2.56 | 3.04 |
| 0.31 | 2.87 | 3.06 |
| 0.3263 | 3.21 | 3.0 |
| 0.3444 | 3.55 | 2.88 |
| 0.3543 | 3.73 | 2.79 |
| 0.3647 | 3.9 | 2.66 |
| 0.3875 | 4.17 | 2.38 |
| 0.4133 | 4.38 | 2.02 |
| 0.4428 | 4.47 | 1.64 |
| 0.4769 | 4.49 | 1.28 |
| 0.496 | 4.47 | 1.12 |
| 0.5166 | 4.46 | 0.969 |
| 0.5636 | 4.36 | 0.69 |
| 0.6199 | 4.23 | 0.461 |
| 0.6526 | 4.17 | 0.363 |
| 0.6888 | 4.09 | 0.271 |
| 0.7293 | 4.01 | 0.199 |
| 0.7749 | 3.93 | 0.136 |
| 0.8266 | 3.86 | 0.0812 |
| 0.8856 | 3.77 | 0.0401 |
| 0.9538 | 3.68 | 0.0 |
| 1.033 | 3.61 | 0.0 |
| 1.127 | 3.57 | 0.0 |
| 1.24 | 3.54 | 0.0 |
| 1.378 | 3.5 | 0.0 |
| 1.55 | 3.48 | 0.0 |
| 1.771 | 3.45 | 0.0 |
| 2.066 | 3.44 | 0.0 |
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
- —
Amorphous silicon (α-Si or a-Si). 60-nm film.