Optical constants

Refractive index of Si (Silicon)

Edwards and Ochoa 1980: n 2.5–25 µm

Data
formula 7
Range
2.437–25 µm
State
crystalline
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 2.437–25 µm
Refractive index n
3.42249
Extinction coefficient k
0
Permittivity ε1
11.7134
Permittivity ε2
0
Absorption coefficient α
0 cm⁻¹
Penetration depth δ = λ/(2πk)
— nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.000638884 µm⁻¹
Group index ng
3.42748
Group velocity dispersion
209.641 fs²/mm
Dispersion parameter D
-6.47404 ps/(nm·km)
Photon energy
0.158751 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): Edwards and Ochoa 1980: n 2.5–25 µm
si = ls.fetch_refractiveindex("main", "Si", "Edwards", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (2437.3, 25000) nm
eps = si.eps([7810])  # 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

Herzberger (formula 7), λ in µm
n=3.41983+0.159906λ2−0.028−0.123109⁢(1λ2−0.028)2+1.26878×10-6⁢λ2−1.95104×10-9⁢λ4

Valid from 2.4373 to 25.0 µm.

Coefficients as stored
CiValue
C13.41983
C20.159906
C3-0.123109
C41.26878e-06
C5-1.95104e-09

Comments and conditions

26 °C, crystal orientation <111>; 3-4 Ω-cm, n-type (phosporous-dopped)

References

D. F. Edwards and E. Ochoa. Infrared Refractive Indexes of Silicon. Appl. Opt., 19, 4130-4131 (1980)

Cite

David F. Edwards and Ellen Ochoa. Infrared refractive index of silicon. Applied Optics, 19, 4130 (1980), doi:10.1364/ao.19.004130; 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), Edwards and Ochoa 1980: n 2.5–25 µm: n and k versus wavelength
λ (µm)n
2.43733.443361
2.451563.443128
2.465913.442896
2.480343.442666
2.494853.442438
2.509453.442212
2.524133.441987
2.53893.441764
2.553763.441544
2.56873.441324
2.583743.441107
2.598853.440891
2.614063.440678
2.629363.440466
2.644743.440255
2.660223.440047
2.675793.43984
2.691443.439635
2.707193.439432
2.723043.43923
2.738973.439031
2.7553.438833
2.771123.438636
2.787333.438442
2.803643.438249
2.820053.438058
2.836553.437868
2.853153.437681
2.869853.437495
2.886643.43731
2.903533.437128
2.920523.436947
2.937613.436767
2.95483.436589
2.972093.436413
2.989483.436239
3.006983.436066
3.024573.435895
3.042273.435725
3.060073.435557
3.077983.435391
3.095993.435226
3.114113.435062
3.132333.434901
3.150663.43474
3.169093.434582
3.187643.434424
3.206293.434269
3.225053.434114
3.243923.433962
3.262913.433811
3.2823.433661
3.30123.433513
3.320523.433366
3.339953.43322
3.35953.433076
3.379153.432934
3.398933.432793
3.418823.432653
3.438823.432514
3.458953.432377
3.479193.432242
3.499543.432108
3.520023.431975
3.540623.431843
3.561343.431713
3.582183.431584
3.603143.431456
3.624223.43133
3.645433.431205
3.666763.431081
3.688223.430958
3.70983.430837
3.731513.430717
3.753353.430598
3.775313.430481
3.79743.430364
3.819623.430249
3.841973.430135
3.864453.430022
3.887073.42991
3.909813.4298
3.932693.429691
3.95573.429582
3.978853.429475
4.002133.429369
4.025553.429264
4.049113.429161
4.07283.429058
4.096633.428956
4.120613.428856
4.144723.428756
4.168973.428658
4.193373.42856
4.21793.428464
4.242593.428369
4.267413.428274
4.292383.428181
4.31753.428089
4.342763.427997
4.368183.427907
4.393743.427818
4.419453.427729
4.445313.427642
4.471323.427555
4.497493.42747
4.52383.427385
4.550273.427301
4.57693.427218
4.603683.427136
4.630623.427055
4.657723.426975
4.684973.426895
4.712393.426817
4.739963.426739
4.76773.426662
4.79563.426586
4.823663.426511
4.851893.426437
4.880283.426363
4.908843.426291
4.937563.426219
4.966453.426148
4.995513.426077
5.024753.426008
5.054153.425939
5.083723.425871
5.113473.425803
5.143393.425737
5.173493.425671
5.203763.425606
5.234213.425542
5.264843.425478
5.295653.425415
5.326643.425353
5.357813.425291
5.389163.42523
5.42073.42517
5.452413.42511
5.484323.425051
5.516413.424993
5.548693.424936
5.581163.424879
5.613823.424822
5.646673.424767
5.679713.424712
5.712953.424657
5.746383.424603
5.783.42455
5.813823.424498
5.847843.424445
5.882063.424394
5.916483.424343
5.95113.424293
5.985933.424243
6.020963.424194
6.056193.424145
6.091633.424097
6.127273.42405
6.163133.424003
6.199193.423956
6.235473.42391
6.271953.423865
6.308653.42382
6.345573.423776
6.38273.423732
6.420053.423689
6.457623.423646
6.495413.423603
6.533413.423562
6.571643.42352
6.61013.423479
6.648783.423439
6.687693.423399
6.726823.423359
6.766183.42332
6.805773.423282
6.84563.423243
6.885663.423206
6.925953.423168
6.966483.423131
7.007243.423095
7.048253.423059
7.089493.423023
7.130973.422988
7.17273.422953
7.214673.422919
7.256893.422885
7.299363.422851
7.342073.422818
7.385033.422785
7.428253.422753
7.471713.422721
7.515433.422689
7.559413.422658
7.603653.422627
7.648143.422597
7.692893.422566
7.737913.422537
7.783193.422507
7.828733.422478
7.874543.422449
7.920623.422421
7.966973.422392
8.013593.422365
8.060483.422337
8.107653.42231
8.155093.422283
8.202813.422257
8.250813.422231
8.299093.422205
8.347653.422179
8.39653.422154
8.445643.422129
8.495063.422104
8.544773.42208
8.594773.422056
8.645063.422032
8.695653.422009
8.746533.421986
8.797713.421963
8.849193.42194
8.900973.421918
8.953063.421896
9.005453.421874
9.058143.421852
9.111153.421831
9.164463.42181
9.218093.421789
9.272033.421769
9.326293.421748
9.380863.421728
9.435753.421709
9.490973.421689
9.546513.42167
9.602373.421651
9.658563.421632
9.715083.421613
9.771923.421595
9.829113.421577
9.886623.421559
9.944483.421541
10.00273.421524
10.06123.421507
10.12013.42149
10.17933.421473
10.23893.421456
10.29883.42144
10.3593.421424
10.41973.421408
10.48063.421392
10.5423.421376
10.60363.421361
10.66573.421346
10.72813.421331
10.79093.421316
10.8543.421301
10.91753.421287
10.98143.421272
11.04573.421258
11.11033.421245
11.17533.421231
11.24073.421217
11.30653.421204
11.37273.421191
11.43923.421178
11.50613.421165
11.57353.421152
11.64123.42114
11.70933.421127
11.77783.421115
11.84683.421103
11.91613.421091
11.98583.421079
12.05593.421068
12.12653.421056
12.19743.421045
12.26883.421034
12.34063.421023
12.41283.421012
12.48553.421001
12.55853.420991
12.6323.42098
12.70593.42097
12.78033.42096
12.85513.42095
12.93033.42094
13.00593.42093
13.0823.42092
13.15863.420911
13.23563.420901
13.3133.420892
13.3913.420883
13.46933.420874
13.54813.420865
13.62743.420856
13.70713.420847
13.78743.420839
13.8683.42083
13.94923.420822
14.03083.420813
14.11293.420805
14.19553.420797
14.27863.420789
14.36213.420781
14.44623.420773
14.53073.420766
14.61573.420758
14.70123.42075
14.78733.420743
14.87383.420736
14.96083.420728
15.04843.420721
15.13643.420714
15.2253.420707
15.31413.4207
15.40373.420693
15.49383.420686
15.58453.420679
15.67573.420673
15.76743.420666
15.85973.42066
15.95253.420653
16.04583.420647
16.13973.42064
16.23423.420634
16.32923.420628
16.42473.420621
16.52083.420615
16.61753.420609
16.71483.420603
16.81263.420597
16.91093.420591
17.00993.420585
17.10943.420579
17.20963.420573
17.31033.420567
17.41163.420562
17.51343.420556
17.61593.42055
17.7193.420544
17.82273.420538
17.9273.420533
18.03193.420527
18.13743.420521
18.24353.420516
18.35033.42051
18.45773.420504
18.56573.420498
18.67433.420493
18.78363.420487
18.89353.420481
19.0043.420476
19.11533.42047
19.22713.420464
19.33963.420458
19.45283.420452
19.56663.420447
19.68113.420441
19.79633.420435
19.91213.420429
20.02863.420423
20.14583.420417
20.26373.420411
20.38233.420405
20.50163.420398
20.62153.420392
20.74223.420386
20.86363.420379
20.98573.420373
21.10853.420366
21.2323.42036
21.35623.420353
21.48123.420346
21.60693.420339
21.73333.420332
21.86053.420325
21.98843.420318
22.11713.42031
22.24653.420303
22.37673.420295
22.50763.420287
22.63933.420279
22.77183.420271
22.90513.420263
23.03913.420255
23.17393.420246
23.30953.420237
23.44593.420228
23.58313.420219
23.72113.42021
23.85993.420201
23.99953.420191
24.143.420181
24.28123.420171
24.42333.42016
24.56623.42015
24.713.420139
24.85463.420128
253.420116

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
—