Optical constants
Refractive index of Si (Silicon)
Green 2008: n,k 0.25–1.45 µm
- Data
- tabulated nk
- Range
- 0.25–1.45 µm
- Points
- 121
- Temperature
- 300 K
- State
- crystalline
- Licence
- CC0-1.0
- Lightsmith
- bundled, default
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.969
- Extinction coefficient k
- 0.0214273
- Permittivity ε1
- 15.7525
- Permittivity ε2
- 0.17009
- Absorption coefficient α
- 4582.43 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 4364.5 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.5 µm⁻¹
- Group index ng
- 5.438
- 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): Green 2008: n,k 0.25–1.45 µm
si = ls.LibraryMaterial(name="Si", dataset="Green-2008")
print(si.range_nm) # (250, 1450) nm
eps = si.eps([633]) # complex permittivity
Ships with the library: works offline and is the library's own default dataset choice.
import lightsmith as ls
# Si (Silicon): Green 2008: n,k 0.25–1.45 µm
si = ls.fetch_refractiveindex("main", "Si", "Green-2008", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (250, 1450) 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_aa67cc1ecd1b/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/green-2008).
# ... 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
Conditions
- temperature
- 300 K
References
- doi:10.1016/j.solmat.2008.06.009 Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients, Solar Energy Materials and Solar Cells (2008)
Cite
Martin A. Green. Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients. Solar Energy Materials and Solar Cells, 92, 1305-1310 (2008), doi:10.1016/j.solmat.2008.06.009; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
121 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.25 | 1.665 | 3.665 |
| 0.26 | 1.757 | 4.084 |
| 0.27 | 2.068 | 4.68 |
| 0.28 | 2.959 | 5.287 |
| 0.29 | 4.356 | 5.286 |
| 0.3 | 4.976 | 4.234 |
| 0.31 | 5.121 | 3.598 |
| 0.32 | 5.112 | 3.303 |
| 0.33 | 5.195 | 3.1 |
| 0.34 | 5.301 | 2.977 |
| 0.35 | 5.494 | 2.938 |
| 0.36 | 6.026 | 2.966 |
| 0.37 | 6.891 | 2.171 |
| 0.38 | 6.616 | 0.946 |
| 0.39 | 6.039 | 0.445 |
| 0.4 | 5.613 | 0.296 |
| 0.41 | 5.33 | 0.227 |
| 0.42 | 5.119 | 0.176 |
| 0.43 | 4.949 | 0.138 |
| 0.44 | 4.812 | 0.107 |
| 0.45 | 4.691 | 0.086302 |
| 0.46 | 4.587 | 0.071381 |
| 0.47 | 4.497 | 0.062086 |
| 0.48 | 4.419 | 0.055004 |
| 0.49 | 4.35 | 0.049131 |
| 0.5 | 4.294 | 0.044165 |
| 0.51 | 4.241 | 0.039367 |
| 0.52 | 4.193 | 0.036415 |
| 0.53 | 4.151 | 0.033108 |
| 0.54 | 4.112 | 0.030295 |
| 0.55 | 4.077 | 0.027968 |
| 0.56 | 4.045 | 0.025758 |
| 0.57 | 4.015 | 0.024131 |
| 0.58 | 3.988 | 0.022524 |
| 0.59 | 3.963 | 0.021081 |
| 0.6 | 3.94 | 0.019934 |
| 0.61 | 3.918 | 0.018446 |
| 0.62 | 3.898 | 0.017367 |
| 0.63 | 3.879 | 0.016444 |
| 0.64 | 3.861 | 0.015432 |
| 0.65 | 3.844 | 0.014431 |
| 0.66 | 3.828 | 0.013498 |
| 0.67 | 3.813 | 0.012743 |
| 0.68 | 3.798 | 0.011905 |
| 0.69 | 3.784 | 0.011201 |
| 0.7 | 3.772 | 0.010528 |
| 0.71 | 3.759 | 0.010057 |
| 0.72 | 3.748 | 0.0096257 |
| 0.73 | 3.737 | 0.0089461 |
| 0.74 | 3.727 | 0.008362 |
| 0.75 | 3.717 | 0.0078185 |
| 0.76 | 3.708 | 0.007197 |
| 0.77 | 3.699 | 0.0067402 |
| 0.78 | 3.691 | 0.0063933 |
| 0.79 | 3.683 | 0.005834 |
| 0.8 | 3.675 | 0.0054113 |
| 0.81 | 3.668 | 0.0049955 |
| 0.82 | 3.661 | 0.0046134 |
| 0.83 | 3.654 | 0.0042734 |
| 0.84 | 3.647 | 0.0039439 |
| 0.85 | 3.641 | 0.003612 |
| 0.86 | 3.635 | 0.0032781 |
| 0.87 | 3.63 | 0.0029839 |
| 0.88 | 3.624 | 0.0026821 |
| 0.89 | 3.619 | 0.0024293 |
| 0.9 | 3.614 | 0.0021701 |
| 0.91 | 3.609 | 0.0019625 |
| 0.92 | 3.604 | 0.0017571 |
| 0.93 | 3.6 | 0.0015467 |
| 0.94 | 3.595 | 0.0013689 |
| 0.95 | 3.591 | 0.0011793 |
| 0.96 | 3.587 | 0.0010237 |
| 0.97 | 3.583 | 0.00087225 |
| 0.98 | 3.579 | 0.00074866 |
| 0.99 | 3.575 | 0.00062238 |
| 1.0 | 3.572 | 0.0005093 |
| 1.01 | 3.568 | 0.00041071 |
| 1.02 | 3.565 | 0.00032386 |
| 1.03 | 3.562 | 0.00024753 |
| 1.04 | 3.559 | 0.00018704 |
| 1.05 | 3.556 | 0.0001362 |
| 1.06 | 3.553 | 9.3631e-05 |
| 1.07 | 3.55 | 6.8118e-05 |
| 1.08 | 3.547 | 5.3285e-05 |
| 1.09 | 3.545 | 4.0768e-05 |
| 1.1 | 3.542 | 3.0637e-05 |
| 1.11 | 3.54 | 2.3849e-05 |
| 1.12 | 3.537 | 1.7825e-05 |
| 1.13 | 3.535 | 1.3488e-05 |
| 1.14 | 3.532 | 9.0718e-06 |
| 1.15 | 3.53 | 6.223e-06 |
| 1.16 | 3.528 | 3.877e-06 |
| 1.17 | 3.526 | 2.0483e-06 |
| 1.18 | 3.524 | 6.1036e-07 |
| 1.19 | 3.522 | 3.4091e-07 |
| 1.2 | 3.52 | 2.1008e-07 |
| 1.21 | 3.518 | 1.2518e-07 |
| 1.22 | 3.517 | 7.9609e-08 |
| 1.23 | 3.515 | 4.6004e-08 |
| 1.24 | 3.513 | 2.3682e-08 |
| 1.25 | 3.511 | 9.9472e-09 |
| 1.26 | 3.509 | 3.6096e-09 |
| 1.27 | 3.508 | 2.0213e-09 |
| 1.28 | 3.506 | 1.2223e-09 |
| 1.29 | 3.505 | 7.2885e-10 |
| 1.3 | 3.503 | 4.6553e-10 |
| 1.31 | 3.502 | 2.8147e-10 |
| 1.32 | 3.5 | 1.6807e-10 |
| 1.33 | 3.499 | 8.467e-11 |
| 1.34 | 3.497 | 3.7322e-11 |
| 1.35 | 3.496 | 1.8263e-11 |
| 1.36 | 3.495 | 1.0281e-11 |
| 1.37 | 3.494 | 6.5413e-12 |
| 1.38 | 3.492 | 4.173e-12 |
| 1.39 | 3.491 | 2.5441e-12 |
| 1.4 | 3.49 | 1.5597e-12 |
| 1.41 | 3.489 | 9.5374e-13 |
| 1.42 | 3.488 | 5.65e-13 |
| 1.43 | 3.487 | 2.8449e-13 |
| 1.44 | 3.486 | 2.0626e-13 |
| 1.45 | 3.485 | 1.3846e-13 |
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
- —
Combination of data sets enforcing KK consistency. 300 K (27 °C). k is for band-to-band absorption.