Optical constants

Refractive index of Si (Silicon)

Karaman et al. 2025: n,k 0.21–2.5 µm; 220 °C

Data
tabulated nk
Range
0.21–2.5 µm
Points
1041
Temperature
493 K
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.21–2.5 µm
Refractive index n
4.77953
Extinction coefficient k
0.46612
Permittivity ε1
22.6266
Permittivity ε2
4.45566
Absorption coefficient α
99684 cm⁻¹
Penetration depth δ = λ/(2πk)
200.634 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-3.001 µm⁻¹
Group index ng
6.54291
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): Karaman et al. 2025: n,k 0.21–2.5 µm; 220 °C
si = ls.fetch_refractiveindex("main", "Si", "Karaman-220C", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(si.range_nm)  # (210, 2500) nm
eps = si.eps([633])  # 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.

Comments and conditions

Amorphous silicon (a-Si), 220 °C. 100 nm film on fused silica substrate.

Conditions

temperature
493 K
film thickness
100e-9
substrate
SiO2

References

O. C. Karaman, G. N. Naidu, A. R. Bowman, E. N. Dayi, G. Tagliabue. Decoupling optical and thermal dynamics in dielectric metasurfaces for self-encoded photonic control. Laser Photonics Rev., e01014 (2025) (Numerical data kindly provided by Omer Can Karaman)
  • doi:10.1002/lpor.202501014 Decoupling Optical and Thermal Dynamics in Dielectric Metasurfaces for Self‐Encoded Photonic Control, Laser & Photonics Reviews (2025)

Cite

Omer Can Karaman, Gopal Narmada Naidu, Alan R. Bowman, Elif Nur Dayi and Giulia Tagliabue. Decoupling Optical and Thermal Dynamics in Dielectric Metasurfaces for Self‐Encoded Photonic Control. Laser & Photonics Reviews, 19, e01014 (2025), doi:10.1002/lpor.202501014; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1041 rows as published
Si (Silicon), Karaman et al. 2025: n,k 0.21–2.5 µm; 220 °C: n and k versus wavelength
λ (µm)nk
0.211.0791482.946963
0.2111.09452.965008
0.2121.1100562.983019
0.2131.1258183.000994
0.2141.1417873.018931
0.2151.1579673.036827
0.2161.174363.05468
0.2171.1909673.072486
0.2181.2077913.090243
0.2191.2248343.107947
0.221.2420993.125596
0.2211.2595873.143187
0.2221.27733.160716
0.2231.2952413.178179
0.2241.3134123.195574
0.2251.3318143.212896
0.2261.350453.230143
0.2271.3693213.247309
0.2281.3884293.264392
0.2291.4077773.281387
0.231.4273663.29829
0.2311.4471983.315097
0.2321.4672743.331803
0.2331.4875963.348404
0.2341.5081653.364895
0.2351.5289843.381272
0.2361.5500533.397529
0.2371.5713743.413662
0.2381.5929473.429666
0.2391.6147743.445535
0.241.6368573.461265
0.2411.6591953.476849
0.2421.6817893.492282
0.2431.7046413.507559
0.2441.7277513.522674
0.2451.7511193.53762
0.2461.7747453.552392
0.2471.798633.566985
0.2481.8227743.58139
0.2491.8471763.595603
0.251.8718353.609617
0.2511.8967533.623426
0.2521.9219273.637022
0.2531.9473583.650399
0.2541.9730433.663551
0.2551.9989823.67647
0.2562.0251733.68915
0.2572.0516143.701583
0.2582.0783053.713763
0.2592.1052423.725683
0.262.1324233.737335
0.2612.1598463.748712
0.2622.1875073.759808
0.2632.2154053.770613
0.2642.2435363.781123
0.2652.2718953.791328
0.2662.3004793.801222
0.2672.3292853.810798
0.2682.3583083.820049
0.2692.3875433.828966
0.272.4169863.837544
0.2712.4466313.845774
0.2722.4764733.85365
0.2732.5065053.861165
0.2742.5367243.868312
0.2752.5671213.875084
0.2762.597693.881475
0.2772.6284253.887477
0.2782.6593183.893085
0.2792.6903623.898293
0.282.7215493.903093
0.2812.7528723.907481
0.2822.7843223.91145
0.2832.8158913.914996
0.2842.8475693.918112
0.2852.8793493.920794
0.2862.911223.923037
0.2872.9431733.924837
0.2882.9751993.926188
0.2893.0072873.927088
0.293.0394273.927533
0.2913.071613.927518
0.2923.1038243.927042
0.2933.1360593.926102
0.2943.1683033.924694
0.2953.2005473.922818
0.2963.2327793.920471
0.2973.2649873.917653
0.2983.297163.914362
0.2993.3292873.910598
0.33.3613563.906361
0.3013.3933563.901652
0.3023.4252753.89647
0.3033.4571023.890817
0.3043.4888243.884695
0.3053.5204313.878105
0.3063.551913.871051
0.3073.5832513.863533
0.3083.6144413.855557
0.3093.645473.847126
0.313.6763273.838242
0.3113.7073.828912
0.3123.7374783.819139
0.3133.7677523.808928
0.3143.7978093.798286
0.3153.827643.787218
0.3163.8572353.77573
0.3173.8865853.763829
0.3183.9156783.751523
0.3193.9445063.738817
0.323.9730613.725719
0.3214.0013323.712239
0.3224.0293123.698382
0.3234.0569933.684159
0.3244.0843663.669577
0.3254.1114243.654646
0.3264.1381613.639374
0.3274.1645693.623771
0.3284.1906413.607846
0.3294.2163733.591609
0.334.2417573.57507
0.3314.2667893.558238
0.3324.2914653.541124
0.3334.3157783.523737
0.3344.3397253.506088
0.3354.3633023.488187
0.3364.3865063.470044
0.3374.4093333.45167
0.3384.4317813.433074
0.3394.4538483.414268
0.344.4755313.395261
0.3414.4968293.376064
0.3424.517743.356687
0.3434.5382653.33714
0.3444.5584013.317432
0.3454.5781483.297575
0.3464.5975073.277578
0.3474.6164793.257451
0.3484.6350633.237202
0.3494.653263.216843
0.354.6710723.196381
0.3514.6885013.175827
0.3524.7055473.155189
0.3534.7222143.134477
0.3544.7385033.113698
0.3554.7544163.092861
0.3564.7699563.071975
0.3574.7851273.051048
0.3584.7999313.030088
0.3594.8143713.009102
0.364.8284512.988097
0.3614.8421752.967083
0.3624.8555462.946064
0.3634.8685672.925049
0.3644.8812452.904043
0.3654.8935812.883054
0.3664.9055812.862087
0.3674.9172492.84115
0.3684.9285882.820246
0.3694.9396052.799383
0.374.9503042.778565
0.3714.9606882.757798
0.3724.9707632.737087
0.3734.9805342.716436
0.3744.9900052.69585
0.3754.9991812.675334
0.3765.0080672.654891
0.3775.0166692.634527
0.3785.024992.614244
0.3795.0330362.594046
0.385.0408122.573936
0.3815.0483232.553919
0.3825.0555732.533996
0.3835.0625682.514172
0.3845.0693122.494448
0.3855.075812.474828
0.3865.0820672.455314
0.3875.0880892.435908
0.3885.0938792.416612
0.3895.0994422.397428
0.395.1047832.378359
0.3915.1099072.359406
0.3925.1148182.34057
0.3935.1195212.321854
0.3945.124022.303258
0.3955.128322.284784
0.3965.1324252.266432
0.3975.136342.248205
0.3985.1400682.230103
0.3995.1436142.212126
0.45.1469832.194275
0.4015.1501772.176552
0.4025.1532022.158956
0.4035.156062.141489
0.4045.1587572.12415
0.4055.1612952.106939
0.4065.163682.089858
0.4075.1659132.072906
0.4085.1679992.056082
0.4095.1699422.039388
0.415.1717452.022824
0.4115.1734112.006388
0.4125.1749441.990082
0.4135.1763471.973904
0.4145.1776231.957854
0.4155.1787761.941933
0.4165.1798091.926139
0.4175.1807241.910473
0.4185.1815251.894933
0.4195.1822141.87952
0.425.1827951.864233
0.4215.183271.849071
0.4225.1836421.834034
0.4235.1839131.819121
0.4245.1840871.804332
0.4255.1841651.789665
0.4265.1841511.77512
0.4275.1840471.760697
0.4285.1838541.746394
0.4295.1835761.732211
0.435.1832151.718147
0.4315.1827731.704201
0.4325.1822511.690373
0.4335.1816531.676661
0.4345.1809811.663065
0.4355.1802361.649583
0.4365.179421.636216
0.4375.1785351.622962
0.4385.1775841.60982
0.4395.1765671.596789
0.445.1754871.583868
0.4415.1743451.571057
0.4425.1731441.558354
0.4435.1718851.545759
0.4445.1705691.533271
0.4455.1691991.520889
0.4465.1677741.508611
0.4475.1662981.496437
0.4485.1647721.484366
0.4495.1631961.472397
0.455.1615731.460528
0.4515.1599041.448761
0.4525.1581891.437092
0.4535.1564311.425521
0.4545.154631.414048
0.4555.1527881.402671
0.4565.1509071.391389
0.4575.1489861.380203
0.4585.1470271.369109
0.4595.1450321.358109
0.465.1430021.3472
0.4615.1409361.336382
0.4625.1388381.325654
0.4635.1367071.315015
0.4645.1345441.304464
0.4655.132351.294001
0.4665.1301271.283624
0.4675.1278751.273332
0.4685.1255951.263125
0.4695.1232881.253003
0.475.1209551.242963
0.4715.1185961.233005
0.4725.1162121.223129
0.4735.1138041.213333
0.4745.1113731.203616
0.4755.1089191.193979
0.4765.1064431.18442
0.4775.1039471.174938
0.4785.1014291.165532
0.4795.0988931.156202
0.485.0963361.146947
0.4815.0937611.137766
0.4825.0911681.128659
0.4835.0885571.119624
0.4845.0859291.110661
0.4855.0832851.101769
0.4865.0806251.092948
0.4875.077951.084196
0.4885.0752591.075514
0.4895.0725551.066899
0.495.0698361.058353
0.4915.0671041.049873
0.4925.0643591.041459
0.4935.0616011.033111
0.4945.0588311.024828
0.4955.0560491.016609
0.4965.0532571.008453
0.4975.0504531.000361
0.4985.0476380.992331
0.4995.0448130.984363
0.55.0419780.976455
0.5015.0391340.968608
0.5025.0362810.960821
0.5035.0334180.953093
0.5045.0305470.945424
0.5055.0276680.937813
0.5065.0247810.93026
0.5075.0218860.922763
0.5085.0189840.915323
0.5095.0160750.907939
0.515.0131590.90061
0.5115.0102360.893335
0.5125.0073080.886115
0.5135.0043730.878949
0.5145.0014310.871836
0.5154.9984850.864775
0.5164.9955330.857767
0.5174.9925770.85081
0.5184.9896150.843905
0.5194.9866480.83705
0.524.9836770.830246
0.5214.9807020.823491
0.5224.9777220.816785
0.5234.9747390.810129
0.5244.9717520.80352
0.5254.9687610.79696
0.5264.9657670.790447
0.5274.962770.783981
0.5284.9597690.777562
0.5294.9567660.771189
0.534.953760.764861
0.5314.9507510.758579
0.5324.947740.752343
0.5334.9447260.74615
0.5344.941710.740002
0.5354.9386920.733897
0.5364.9356720.727836
0.5374.9326510.721818
0.5384.9296270.715843
0.5394.9266030.709909
0.544.9235760.704018
0.5414.9205490.698168
0.5424.917520.69236
0.5434.914490.686592
0.5444.9114590.680864
0.5454.9084280.675177
0.5464.9053950.66953
0.5474.9023610.663922
0.5484.8993280.658353
0.5494.8962930.652823
0.554.8932590.647332
0.5514.8902230.641878
0.5524.8871870.636463
0.5534.8841520.631085
0.5544.8811160.625745
0.5554.8780810.620441
0.5564.8750450.615174
0.5574.8720090.609944
0.5584.8689740.604749
0.5594.8659390.599591
0.564.8629050.594468
0.5614.859870.58938
0.5624.8568370.584327
0.5634.8538040.579309
0.5644.8507710.574325
0.5654.8477390.569376
0.5664.8447080.56446
0.5674.8416780.559579
0.5684.8386480.55473
0.5694.835620.549915
0.574.8325920.545133
0.5714.8295660.540384
0.5724.8265410.535667
0.5734.8235170.530982
0.5744.8204940.526329
0.5754.8174720.521708
0.5764.8144520.517119
0.5774.8114320.512561
0.5784.8084150.508034
0.5794.8053990.503538
0.584.8023840.499072
0.5814.7993710.494637
0.5824.796360.490233
0.5834.7933490.485858
0.5844.7903410.481513
0.5854.7873340.477198
0.5864.784330.472912
0.5874.7813270.468656
0.5884.7783260.464429
0.5894.7753270.46023
0.594.7723290.456061
0.5914.7693340.451919
0.5924.7663410.447806
0.5934.763350.443722
0.5944.760360.439665
0.5954.7573730.435636
0.5964.7543880.431634
0.5974.7514060.42766
0.5984.7484250.423713
0.5994.7454470.419793
0.64.7424710.415901
0.6014.7394980.412035
0.6024.7365260.408195
0.6034.7335580.404382
0.6044.7305910.400595
0.6054.7276280.396835
0.6064.7246670.3931
0.6074.7217080.389391
0.6084.7187510.385708
0.6094.7157980.38205
0.614.7128470.378417
0.6114.7098990.37481
0.6124.7069540.371228
0.6134.7040110.367671
0.6144.7010710.364138
0.6154.6981340.36063
0.6164.6951990.357147
0.6174.6922680.353688
0.6184.689340.350253
0.6194.6864140.346842
0.624.6834920.343455
0.6214.6805730.340092
0.6224.6776560.336753
0.6234.6747430.333437
0.6244.6718330.330145
0.6254.6689250.326876
0.6264.6660210.32363
0.6274.6631210.320407
0.6284.6602230.317207
0.6294.6573290.314029
0.634.6544380.310875
0.6314.651550.307743
0.6324.6486660.304633
0.6334.6457850.301546
0.6344.6429080.298481
0.6354.6400340.295438
0.6364.6371630.292417
0.6374.6342960.289417
0.6384.6314330.28644
0.6394.6285720.283484
0.644.6257160.280549
0.6414.6228640.277636
0.6424.6200150.274745
0.6434.6171690.271874
0.6444.6143280.269025
0.6454.611490.266196
0.6464.6086560.263388
0.6474.6058260.260601
0.6484.6030.257835
0.6494.6001770.255089
0.654.5973590.252364
0.6514.5945440.249659
0.6524.5917330.246974
0.6534.5889270.244309
0.6544.5861240.241665
0.6554.5833260.23904
0.6564.5805310.236435
0.6574.5777410.23385
0.6584.5749550.231284
0.6594.5721730.228738
0.664.5693950.226212
0.6614.5666220.223704
0.6624.5638530.221216
0.6634.5610880.218747
0.6644.5583270.216298
0.6654.5555710.213867
0.6664.5528190.211455
0.6674.5500720.209062
0.6684.5473290.206687
0.6694.5445910.204331
0.674.5418570.201994
0.6714.5391280.199675
0.6724.5364030.197374
0.6734.5336830.195092
0.6744.5309680.192827
0.6754.5282570.190581
0.6764.5255510.188353
0.6774.522850.186142
0.6784.5201530.18395
0.6794.5174610.181775
0.684.5147740.179617
0.6814.5120920.177477
0.6824.5094150.175355
0.6834.5067430.17325
0.6844.5040760.171162
0.6854.5014130.169092
0.6864.4987560.167038
0.6874.4961030.165002
0.6884.4934560.162982
0.6894.4908140.16098
0.694.4881770.158994
0.6914.4855450.157024
0.6924.4829180.155072
0.6934.4802970.153136
0.6944.4776810.151216
0.6954.475070.149313
0.6964.4724640.147426
0.6974.4698630.145555
0.6984.4672680.1437
0.6994.4646790.141861
0.74.4620950.140038
0.7014.4595160.138232
0.7024.4569430.13644
0.7034.4543750.134665
0.7044.4518120.132905
0.7054.4492550.131161
0.7064.4467040.129432
0.7074.4441590.127719
0.7084.4416180.126021
0.7094.4390840.124338
0.714.4365550.12267
0.7114.4340320.121018
0.7124.4315150.11938
0.7134.4290040.117758
0.7144.4264980.11615
0.7154.4239980.114557
0.7164.4215040.112978
0.7174.4190160.111415
0.7184.4165340.109865
0.7194.4140580.108331
0.724.4115870.10681
0.7214.4091230.105304
0.7224.4066640.103813
0.7234.4042120.102335
0.7244.4017650.100871
0.7254.3993250.099422
0.7264.3968910.097986
0.7274.3944630.096565
0.7284.3920410.095157
0.7294.3896250.093762
0.734.3872150.092382
0.7314.3848120.091015
0.7324.3824150.089661
0.7334.3800230.088321
0.7344.3776390.086994
0.7354.375260.085681
0.7364.3728890.084381
0.7374.3705230.083093
0.7384.3681640.081819
0.7394.365810.080558
0.744.3634640.07931
0.7414.3611240.078074
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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
—