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

Range 1.357–11.04 µm
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.

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 µm
n2−1=10.6684293λ2λ2−0.3015164852+0.0030434748λ2λ2−1.134751152+1.54133408λ2λ2−1104.02

Valid from 1.357 to 11.04 µm.

Coefficients as stored
CiValue
C10.0
C210.6684293
C30.301516485
C40.0030434748
C51.13475115
C61.54133408
C71104.0

Comments and conditions

26 °C, Unknown purity

References

1) C. D. Salzberg and J. J. Villa. Infrared refractive indexes of silicon, germanium and modified selenium glass. J. Opt. Soc. Am., 47, 244-246 (1957)
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
Si (Silicon), Salzberg and Villa 1957: n 1.36–11 µm: n and k versus wavelength
λ (µm)n
1.3573.497513
1.364153.496609
1.371333.495715
1.378563.494834
1.385823.493963
1.393123.493104
1.400463.492255
1.407833.491417
1.415253.490589
1.422713.489771
1.43023.488963
1.437733.488165
1.445313.487376
1.452923.486597
1.460573.485827
1.468273.485067
1.4763.484315
1.483783.483572
1.491593.482838
1.499453.482112
1.507353.481395
1.515293.480687
1.523273.479986
1.531293.479294
1.539363.478609
1.547473.477933
1.555623.477264
1.563813.476603
1.572053.475949
1.580333.475303
1.588663.474664
1.597033.474033
1.605443.473409
1.613893.472791
1.62243.472181
1.630943.471578
1.639533.470981
1.648173.470391
1.656853.469808
1.665583.469232
1.674353.468661
1.683173.468098
1.692043.46754
1.700953.466989
1.709913.466444
1.718923.465905
1.727973.465372
1.737083.464845
1.746233.464323
1.755423.463808
1.764673.463298
1.773973.462794
1.783313.462296
1.79273.461803
1.802153.461315
1.811643.460833
1.821183.460356
1.830783.459885
1.840423.459419
1.850123.458957
1.859863.458501
1.869663.45805
1.879513.457604
1.889413.457163
1.899363.456726
1.909363.456295
1.919423.455868
1.929533.455446
1.93973.455028
1.949913.454615
1.960193.454206
1.970513.453802
1.980893.453403
1.991333.453007
2.001823.452616
2.012363.45223
2.022963.451847
2.033623.451469
2.044333.451095
2.05513.450725
2.065923.450358
2.07683.449996
2.087743.449638
2.098743.449284
2.10983.448933
2.120913.448587
2.132083.448244
2.143313.447905
2.15463.447569
2.165953.447237
2.177363.446909
2.188833.446584
2.200363.446263
2.211953.445945
2.22363.445631
2.235323.44532
2.247093.445012
2.258933.444708
2.270833.444407
2.282793.444109
2.294813.443815
2.30693.443523
2.319053.443235
2.331273.44295
2.343553.442668
2.35593.442389
2.368313.442113
2.380783.44184
2.393323.44157
2.405933.441303
2.41863.441038
2.431343.440777
2.444153.440518
2.457023.440262
2.469973.440009
2.482983.439759
2.496063.439511
2.50923.439266
2.522423.439023
2.535713.438784
2.549073.438546
2.562493.438312
2.575993.438079
2.589563.43785
2.60323.437622
2.616913.437397
2.63073.437175
2.644563.436955
2.658493.436737
2.672493.436522
2.686573.436309
2.700723.436098
2.714953.435889
2.729253.435683
2.743623.435479
2.758083.435277
2.77263.435077
2.787213.434879
2.801893.434684
2.816653.43449
2.831493.434299
2.84643.434109
2.86143.433922
2.876473.433736
2.891623.433553
2.906853.433372
2.922163.433192
2.937563.433014
2.953033.432839
2.968593.432665
2.984223.432493
2.999943.432323
3.015753.432154
3.031633.431988
3.04763.431823
3.063653.43166
3.079793.431499
3.096023.431339
3.112323.431181
3.128723.431025
3.14523.43087
3.161773.430717
3.178423.430566
3.195163.430416
3.2123.430268
3.228913.430122
3.245923.429977
3.263023.429833
3.280213.429691
3.297493.429551
3.314863.429412
3.332323.429274
3.349873.429138
3.367523.429004
3.385263.428871
3.403093.428739
3.421023.428608
3.439043.428479
3.457153.428352
3.475363.428226
3.493673.428101
3.512073.427977
3.530573.427855
3.549173.427734
3.567873.427614
3.586663.427496
3.605553.427378
3.624543.427263
3.643643.427148
3.662833.427034
3.682123.426922
3.701523.426811
3.721023.426701
3.740623.426592
3.760323.426484
3.780133.426378
3.800043.426273
3.820063.426168
3.840183.426065
3.860413.425963
3.880753.425862
3.901193.425762
3.921743.425663
3.94243.425565
3.963163.425468
3.984043.425373
4.005033.425278
4.026123.425184
4.047333.425091
4.068653.425
4.090083.424909
4.111633.424819
4.133293.42473
4.155063.424642
4.176953.424555
4.198953.424469
4.221073.424383
4.24333.424299
4.265653.424216
4.288123.424133
4.310713.424051
4.333423.42397
4.356243.42389
4.379193.423811
4.402263.423733
4.425453.423655
4.448763.423579
4.472193.423503
4.495753.423428
4.519433.423353
4.543243.42328
4.567173.423207
4.591233.423135
4.615413.423064
4.639733.422994
4.664173.422924
4.688733.422855
4.713433.422787
4.738263.422719
4.763223.422652
4.788313.422586
4.813533.422521
4.838893.422456
4.864383.422392
4.893.422328
4.915763.422266
4.941663.422204
4.967693.422142
4.993853.422081
5.020163.422021
5.04663.421962
5.073193.421903
5.099913.421844
5.126773.421787
5.153783.42173
5.180933.421673
5.208223.421617
5.235653.421562
5.263233.421507
5.290963.421453
5.318833.4214
5.346853.421347
5.375013.421294
5.403323.421242
5.431793.421191
5.46043.42114
5.489163.42109
5.518083.42104
5.547143.420991
5.576363.420942
5.605743.420894
5.635273.420846
5.664953.420799
5.694793.420753
5.724793.420706
5.754943.420661
5.785263.420615
5.815733.420571
5.846373.420526
5.877163.420482
5.908123.420439
5.939243.420396
5.970533.420354
6.001983.420312
6.03363.42027
6.065383.420229
6.097333.420188
6.129453.420148
6.161733.420108
6.194193.420069
6.226823.420029
6.259623.419991
6.292593.419953
6.325743.419915
6.359063.419877
6.392563.41984
6.426233.419804
6.460083.419767
6.494113.419731
6.528323.419696
6.562713.419661
6.597283.419626
6.632033.419591
6.666963.419557
6.702083.419524
6.737393.41949
6.772883.419457
6.808553.419425
6.844423.419392
6.880473.41936
6.916713.419329
6.953153.419297
6.989773.419266
7.026593.419236
7.063613.419205
7.100813.419175
7.138223.419145
7.175823.419116
7.213623.419087
7.251623.419058
7.289823.41903
7.328223.419001
7.366823.418973
7.405623.418946
7.444633.418919
7.483853.418891
7.523273.418865
7.56293.418838
7.602743.418812
7.642793.418786
7.683043.41876
7.723523.418735
7.76423.41871
7.80513.418685
7.846213.41866
7.887543.418636
7.929093.418612
7.970863.418588
8.012853.418564
8.055053.418541
8.097483.418518
8.140143.418495
8.183023.418472
8.226123.41845
8.269453.418428
8.313013.418406
8.35683.418384
8.400823.418362
8.445083.418341
8.489563.41832
8.534283.418299
8.579243.418278
8.624433.418258
8.669863.418238
8.715533.418218
8.761443.418198
8.807593.418178
8.853983.418159
8.900623.41814
8.947513.418121
8.994643.418102
9.042023.418083
9.089653.418065
9.137533.418047
9.185663.418029
9.234053.418011
9.282693.417993
9.331583.417976
9.380743.417958
9.430153.417941
9.479833.417924
9.529763.417908
9.579963.417891
9.630433.417875
9.681153.417858
9.732153.417842
9.783423.417826
9.834953.41781
9.886763.417795
9.938843.417779
9.991193.417764
10.04383.417749
10.09673.417734
10.14993.417719
10.20343.417704
10.25713.41769
10.31123.417675
10.36553.417661
10.42013.417647
10.4753.417633
10.53013.417619
10.58563.417606
10.64143.417592
10.69743.417579
10.75383.417566
10.81043.417552
10.86743.417539
10.92463.417527
10.98223.417514
11.043.417501

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—