Optical constants
Refractive index of Si (Silicon)
Salzberg and Villa 1957: n 1.36–11 µm
- Data
- formula 1
- Range
- 1.357–11.04 µm
- State
- crystalline
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.42592
- Extinction coefficient k
- 0
- Permittivity ε1
- 11.7369
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.00496932 µm⁻¹
- Group index ng
- 3.44515
- Group velocity dispersion
- 397.931 fs²/mm
- Dispersion parameter D
- -50.048 ps/(nm·km)
- Photon energy
- 0.320373 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): Salzberg and Villa 1957: n 1.36–11 µm
si = ls.fetch_refractiveindex("main", "Si", "Salzberg", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm) # (1357, 11040) nm
eps = si.eps([3870]) # 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_8343dc91ed79/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/salzberg-villa-1957).
# ... 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=1357, stop_nm=11040, 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"]).
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_8343dc91ed79/lightsmith?model=drude_lorentz"
si_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))
A dispersive Drude–Lorentz model for time-domain solvers.
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
Sellmeier (formula 1), λ in µmValid from 1.357 to 11.04 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 10.6684293 |
| C3 | 0.301516485 |
| C4 | 0.0030434748 |
| C5 | 1.13475115 |
| C6 | 1.54133408 |
| C7 | 1104.0 |
Comments and conditions
References
2) B. Tatian. Fitting refractive-index data with the Sellmeier dispersion formula. Appl. Opt. 23, 4477-4485 (1984)
* Ref. 2 provides a dispersion formula based on data from Ref. 1
- doi:10.1364/josa.47.000244 Infrared Refractive Indexes of Silicon Germanium and Modified Selenium Glass*, Journal of the Optical Society of America (1957)
- doi:10.1364/ao.23.004477 Fitting refractive-index data with the Sellmeier dispersion formula, Applied Optics (1984)
Cite
Calvin D. Salzberg and John J. Villa. Infrared Refractive Indexes of Silicon Germanium and Modified Selenium Glass*. Journal of the Optical Society of America, 47, 244 (1957), doi:10.1364/josa.47.000244; Berge Tatian. Fitting refractive-index data with the Sellmeier dispersion formula. Applied Optics, 23, 4477 (1984), doi:10.1364/ao.23.004477; 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| λ (µm) | n |
|---|---|
| 1.357 | 3.497513 |
| 1.36415 | 3.496609 |
| 1.37133 | 3.495715 |
| 1.37856 | 3.494834 |
| 1.38582 | 3.493963 |
| 1.39312 | 3.493104 |
| 1.40046 | 3.492255 |
| 1.40783 | 3.491417 |
| 1.41525 | 3.490589 |
| 1.42271 | 3.489771 |
| 1.4302 | 3.488963 |
| 1.43773 | 3.488165 |
| 1.44531 | 3.487376 |
| 1.45292 | 3.486597 |
| 1.46057 | 3.485827 |
| 1.46827 | 3.485067 |
| 1.476 | 3.484315 |
| 1.48378 | 3.483572 |
| 1.49159 | 3.482838 |
| 1.49945 | 3.482112 |
| 1.50735 | 3.481395 |
| 1.51529 | 3.480687 |
| 1.52327 | 3.479986 |
| 1.53129 | 3.479294 |
| 1.53936 | 3.478609 |
| 1.54747 | 3.477933 |
| 1.55562 | 3.477264 |
| 1.56381 | 3.476603 |
| 1.57205 | 3.475949 |
| 1.58033 | 3.475303 |
| 1.58866 | 3.474664 |
| 1.59703 | 3.474033 |
| 1.60544 | 3.473409 |
| 1.61389 | 3.472791 |
| 1.6224 | 3.472181 |
| 1.63094 | 3.471578 |
| 1.63953 | 3.470981 |
| 1.64817 | 3.470391 |
| 1.65685 | 3.469808 |
| 1.66558 | 3.469232 |
| 1.67435 | 3.468661 |
| 1.68317 | 3.468098 |
| 1.69204 | 3.46754 |
| 1.70095 | 3.466989 |
| 1.70991 | 3.466444 |
| 1.71892 | 3.465905 |
| 1.72797 | 3.465372 |
| 1.73708 | 3.464845 |
| 1.74623 | 3.464323 |
| 1.75542 | 3.463808 |
| 1.76467 | 3.463298 |
| 1.77397 | 3.462794 |
| 1.78331 | 3.462296 |
| 1.7927 | 3.461803 |
| 1.80215 | 3.461315 |
| 1.81164 | 3.460833 |
| 1.82118 | 3.460356 |
| 1.83078 | 3.459885 |
| 1.84042 | 3.459419 |
| 1.85012 | 3.458957 |
| 1.85986 | 3.458501 |
| 1.86966 | 3.45805 |
| 1.87951 | 3.457604 |
| 1.88941 | 3.457163 |
| 1.89936 | 3.456726 |
| 1.90936 | 3.456295 |
| 1.91942 | 3.455868 |
| 1.92953 | 3.455446 |
| 1.9397 | 3.455028 |
| 1.94991 | 3.454615 |
| 1.96019 | 3.454206 |
| 1.97051 | 3.453802 |
| 1.98089 | 3.453403 |
| 1.99133 | 3.453007 |
| 2.00182 | 3.452616 |
| 2.01236 | 3.45223 |
| 2.02296 | 3.451847 |
| 2.03362 | 3.451469 |
| 2.04433 | 3.451095 |
| 2.0551 | 3.450725 |
| 2.06592 | 3.450358 |
| 2.0768 | 3.449996 |
| 2.08774 | 3.449638 |
| 2.09874 | 3.449284 |
| 2.1098 | 3.448933 |
| 2.12091 | 3.448587 |
| 2.13208 | 3.448244 |
| 2.14331 | 3.447905 |
| 2.1546 | 3.447569 |
| 2.16595 | 3.447237 |
| 2.17736 | 3.446909 |
| 2.18883 | 3.446584 |
| 2.20036 | 3.446263 |
| 2.21195 | 3.445945 |
| 2.2236 | 3.445631 |
| 2.23532 | 3.44532 |
| 2.24709 | 3.445012 |
| 2.25893 | 3.444708 |
| 2.27083 | 3.444407 |
| 2.28279 | 3.444109 |
| 2.29481 | 3.443815 |
| 2.3069 | 3.443523 |
| 2.31905 | 3.443235 |
| 2.33127 | 3.44295 |
| 2.34355 | 3.442668 |
| 2.3559 | 3.442389 |
| 2.36831 | 3.442113 |
| 2.38078 | 3.44184 |
| 2.39332 | 3.44157 |
| 2.40593 | 3.441303 |
| 2.4186 | 3.441038 |
| 2.43134 | 3.440777 |
| 2.44415 | 3.440518 |
| 2.45702 | 3.440262 |
| 2.46997 | 3.440009 |
| 2.48298 | 3.439759 |
| 2.49606 | 3.439511 |
| 2.5092 | 3.439266 |
| 2.52242 | 3.439023 |
| 2.53571 | 3.438784 |
| 2.54907 | 3.438546 |
| 2.56249 | 3.438312 |
| 2.57599 | 3.438079 |
| 2.58956 | 3.43785 |
| 2.6032 | 3.437622 |
| 2.61691 | 3.437397 |
| 2.6307 | 3.437175 |
| 2.64456 | 3.436955 |
| 2.65849 | 3.436737 |
| 2.67249 | 3.436522 |
| 2.68657 | 3.436309 |
| 2.70072 | 3.436098 |
| 2.71495 | 3.435889 |
| 2.72925 | 3.435683 |
| 2.74362 | 3.435479 |
| 2.75808 | 3.435277 |
| 2.7726 | 3.435077 |
| 2.78721 | 3.434879 |
| 2.80189 | 3.434684 |
| 2.81665 | 3.43449 |
| 2.83149 | 3.434299 |
| 2.8464 | 3.434109 |
| 2.8614 | 3.433922 |
| 2.87647 | 3.433736 |
| 2.89162 | 3.433553 |
| 2.90685 | 3.433372 |
| 2.92216 | 3.433192 |
| 2.93756 | 3.433014 |
| 2.95303 | 3.432839 |
| 2.96859 | 3.432665 |
| 2.98422 | 3.432493 |
| 2.99994 | 3.432323 |
| 3.01575 | 3.432154 |
| 3.03163 | 3.431988 |
| 3.0476 | 3.431823 |
| 3.06365 | 3.43166 |
| 3.07979 | 3.431499 |
| 3.09602 | 3.431339 |
| 3.11232 | 3.431181 |
| 3.12872 | 3.431025 |
| 3.1452 | 3.43087 |
| 3.16177 | 3.430717 |
| 3.17842 | 3.430566 |
| 3.19516 | 3.430416 |
| 3.212 | 3.430268 |
| 3.22891 | 3.430122 |
| 3.24592 | 3.429977 |
| 3.26302 | 3.429833 |
| 3.28021 | 3.429691 |
| 3.29749 | 3.429551 |
| 3.31486 | 3.429412 |
| 3.33232 | 3.429274 |
| 3.34987 | 3.429138 |
| 3.36752 | 3.429004 |
| 3.38526 | 3.428871 |
| 3.40309 | 3.428739 |
| 3.42102 | 3.428608 |
| 3.43904 | 3.428479 |
| 3.45715 | 3.428352 |
| 3.47536 | 3.428226 |
| 3.49367 | 3.428101 |
| 3.51207 | 3.427977 |
| 3.53057 | 3.427855 |
| 3.54917 | 3.427734 |
| 3.56787 | 3.427614 |
| 3.58666 | 3.427496 |
| 3.60555 | 3.427378 |
| 3.62454 | 3.427263 |
| 3.64364 | 3.427148 |
| 3.66283 | 3.427034 |
| 3.68212 | 3.426922 |
| 3.70152 | 3.426811 |
| 3.72102 | 3.426701 |
| 3.74062 | 3.426592 |
| 3.76032 | 3.426484 |
| 3.78013 | 3.426378 |
| 3.80004 | 3.426273 |
| 3.82006 | 3.426168 |
| 3.84018 | 3.426065 |
| 3.86041 | 3.425963 |
| 3.88075 | 3.425862 |
| 3.90119 | 3.425762 |
| 3.92174 | 3.425663 |
| 3.9424 | 3.425565 |
| 3.96316 | 3.425468 |
| 3.98404 | 3.425373 |
| 4.00503 | 3.425278 |
| 4.02612 | 3.425184 |
| 4.04733 | 3.425091 |
| 4.06865 | 3.425 |
| 4.09008 | 3.424909 |
| 4.11163 | 3.424819 |
| 4.13329 | 3.42473 |
| 4.15506 | 3.424642 |
| 4.17695 | 3.424555 |
| 4.19895 | 3.424469 |
| 4.22107 | 3.424383 |
| 4.2433 | 3.424299 |
| 4.26565 | 3.424216 |
| 4.28812 | 3.424133 |
| 4.31071 | 3.424051 |
| 4.33342 | 3.42397 |
| 4.35624 | 3.42389 |
| 4.37919 | 3.423811 |
| 4.40226 | 3.423733 |
| 4.42545 | 3.423655 |
| 4.44876 | 3.423579 |
| 4.47219 | 3.423503 |
| 4.49575 | 3.423428 |
| 4.51943 | 3.423353 |
| 4.54324 | 3.42328 |
| 4.56717 | 3.423207 |
| 4.59123 | 3.423135 |
| 4.61541 | 3.423064 |
| 4.63973 | 3.422994 |
| 4.66417 | 3.422924 |
| 4.68873 | 3.422855 |
| 4.71343 | 3.422787 |
| 4.73826 | 3.422719 |
| 4.76322 | 3.422652 |
| 4.78831 | 3.422586 |
| 4.81353 | 3.422521 |
| 4.83889 | 3.422456 |
| 4.86438 | 3.422392 |
| 4.89 | 3.422328 |
| 4.91576 | 3.422266 |
| 4.94166 | 3.422204 |
| 4.96769 | 3.422142 |
| 4.99385 | 3.422081 |
| 5.02016 | 3.422021 |
| 5.0466 | 3.421962 |
| 5.07319 | 3.421903 |
| 5.09991 | 3.421844 |
| 5.12677 | 3.421787 |
| 5.15378 | 3.42173 |
| 5.18093 | 3.421673 |
| 5.20822 | 3.421617 |
| 5.23565 | 3.421562 |
| 5.26323 | 3.421507 |
| 5.29096 | 3.421453 |
| 5.31883 | 3.4214 |
| 5.34685 | 3.421347 |
| 5.37501 | 3.421294 |
| 5.40332 | 3.421242 |
| 5.43179 | 3.421191 |
| 5.4604 | 3.42114 |
| 5.48916 | 3.42109 |
| 5.51808 | 3.42104 |
| 5.54714 | 3.420991 |
| 5.57636 | 3.420942 |
| 5.60574 | 3.420894 |
| 5.63527 | 3.420846 |
| 5.66495 | 3.420799 |
| 5.69479 | 3.420753 |
| 5.72479 | 3.420706 |
| 5.75494 | 3.420661 |
| 5.78526 | 3.420615 |
| 5.81573 | 3.420571 |
| 5.84637 | 3.420526 |
| 5.87716 | 3.420482 |
| 5.90812 | 3.420439 |
| 5.93924 | 3.420396 |
| 5.97053 | 3.420354 |
| 6.00198 | 3.420312 |
| 6.0336 | 3.42027 |
| 6.06538 | 3.420229 |
| 6.09733 | 3.420188 |
| 6.12945 | 3.420148 |
| 6.16173 | 3.420108 |
| 6.19419 | 3.420069 |
| 6.22682 | 3.420029 |
| 6.25962 | 3.419991 |
| 6.29259 | 3.419953 |
| 6.32574 | 3.419915 |
| 6.35906 | 3.419877 |
| 6.39256 | 3.41984 |
| 6.42623 | 3.419804 |
| 6.46008 | 3.419767 |
| 6.49411 | 3.419731 |
| 6.52832 | 3.419696 |
| 6.56271 | 3.419661 |
| 6.59728 | 3.419626 |
| 6.63203 | 3.419591 |
| 6.66696 | 3.419557 |
| 6.70208 | 3.419524 |
| 6.73739 | 3.41949 |
| 6.77288 | 3.419457 |
| 6.80855 | 3.419425 |
| 6.84442 | 3.419392 |
| 6.88047 | 3.41936 |
| 6.91671 | 3.419329 |
| 6.95315 | 3.419297 |
| 6.98977 | 3.419266 |
| 7.02659 | 3.419236 |
| 7.06361 | 3.419205 |
| 7.10081 | 3.419175 |
| 7.13822 | 3.419145 |
| 7.17582 | 3.419116 |
| 7.21362 | 3.419087 |
| 7.25162 | 3.419058 |
| 7.28982 | 3.41903 |
| 7.32822 | 3.419001 |
| 7.36682 | 3.418973 |
| 7.40562 | 3.418946 |
| 7.44463 | 3.418919 |
| 7.48385 | 3.418891 |
| 7.52327 | 3.418865 |
| 7.5629 | 3.418838 |
| 7.60274 | 3.418812 |
| 7.64279 | 3.418786 |
| 7.68304 | 3.41876 |
| 7.72352 | 3.418735 |
| 7.7642 | 3.41871 |
| 7.8051 | 3.418685 |
| 7.84621 | 3.41866 |
| 7.88754 | 3.418636 |
| 7.92909 | 3.418612 |
| 7.97086 | 3.418588 |
| 8.01285 | 3.418564 |
| 8.05505 | 3.418541 |
| 8.09748 | 3.418518 |
| 8.14014 | 3.418495 |
| 8.18302 | 3.418472 |
| 8.22612 | 3.41845 |
| 8.26945 | 3.418428 |
| 8.31301 | 3.418406 |
| 8.3568 | 3.418384 |
| 8.40082 | 3.418362 |
| 8.44508 | 3.418341 |
| 8.48956 | 3.41832 |
| 8.53428 | 3.418299 |
| 8.57924 | 3.418278 |
| 8.62443 | 3.418258 |
| 8.66986 | 3.418238 |
| 8.71553 | 3.418218 |
| 8.76144 | 3.418198 |
| 8.80759 | 3.418178 |
| 8.85398 | 3.418159 |
| 8.90062 | 3.41814 |
| 8.94751 | 3.418121 |
| 8.99464 | 3.418102 |
| 9.04202 | 3.418083 |
| 9.08965 | 3.418065 |
| 9.13753 | 3.418047 |
| 9.18566 | 3.418029 |
| 9.23405 | 3.418011 |
| 9.28269 | 3.417993 |
| 9.33158 | 3.417976 |
| 9.38074 | 3.417958 |
| 9.43015 | 3.417941 |
| 9.47983 | 3.417924 |
| 9.52976 | 3.417908 |
| 9.57996 | 3.417891 |
| 9.63043 | 3.417875 |
| 9.68115 | 3.417858 |
| 9.73215 | 3.417842 |
| 9.78342 | 3.417826 |
| 9.83495 | 3.41781 |
| 9.88676 | 3.417795 |
| 9.93884 | 3.417779 |
| 9.99119 | 3.417764 |
| 10.0438 | 3.417749 |
| 10.0967 | 3.417734 |
| 10.1499 | 3.417719 |
| 10.2034 | 3.417704 |
| 10.2571 | 3.41769 |
| 10.3112 | 3.417675 |
| 10.3655 | 3.417661 |
| 10.4201 | 3.417647 |
| 10.475 | 3.417633 |
| 10.5301 | 3.417619 |
| 10.5856 | 3.417606 |
| 10.6414 | 3.417592 |
| 10.6974 | 3.417579 |
| 10.7538 | 3.417566 |
| 10.8104 | 3.417552 |
| 10.8674 | 3.417539 |
| 10.9246 | 3.417527 |
| 10.9822 | 3.417514 |
| 11.04 | 3.417501 |
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
- —
26 °C, Unknown purity