Optical constants

Refractive index of Bombyx mori (silkworm) silk

Bucciarelli et al. 2018: Pure fibroin film, formed using formic acid; n 0.4–1.5 µm

Data
formula 5
Range
0.4–1.5 µm
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.4–1.5 µm
Refractive index n
1.54545
Extinction coefficient k
0
Permittivity ε1
2.3884
Permittivity ε2
0
Absorption coefficient α
0 cm⁻¹
Penetration depth δ = λ/(2πk)
— nm
Abbe number Vd
38.258
Chromatic dispersion dn/dλ
-0.0713491 µm⁻¹
Group index ng
1.58737
Group velocity dispersion
151.822 fs²/mm
Dispersion parameter D
-828.268 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

# Bombyx mori (silkworm) silk: Bucciarelli et al. 2018: Pure fibroin film, formed using formic acid; n 0.4–1.5 µm
bombyx_mori = ls.fetch_refractiveindex("other", "Bombyx_mori", "Bucciarelli-rSF_FA", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bombyx_mori.range_nm)  # (400, 1500) nm
eps = bombyx_mori.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.

Dispersion formula

Cauchy (formula 5), λ in µm
n=1.527+0.0055⁢λ−2.0+0.0003⁢λ−4.0

Valid from 0.4 to 1.5 µm.

Coefficients as stored
CiValue
C11.527
C20.0055
C3-2.0
C40.0003
C5-4.0

Comments and conditions

Pure fibroin (regenerated silk fibroin) film. Formed using formic acid.

References

A. Bucciarelli, V. Mulloni, D.Maniglio, R. K. Pal, V. K. Yadavalli, A. Motta, A. Quarant. A comparative study of the refractive index of silk protein thin films towards biomaterial based optical devices. Opt. Mater. 78, 407-414 (2018)
  • doi:10.1016/j.optmat.2018.02.058 A comparative study of the refractive index of silk protein thin films towards biomaterial based optical devices, Optical Materials (2018)

Cite

A. Bucciarelli et al.. A comparative study of the refractive index of silk protein thin films towards biomaterial based optical devices. Optical Materials, 78, 407-414 (2018), doi:10.1016/j.optmat.2018.02.058; 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
Bombyx mori (silkworm) silk, Bucciarelli et al. 2018: Pure fibroin film, formed using formic acid; n 0.4–1.5 µm: n and k versus wavelength
λ (µm)n
0.41.573094
0.4013271.572712
0.4026591.572335
0.4039951.571961
0.4053361.57159
0.4066811.571222
0.408031.570858
0.4093841.570498
0.4107421.570141
0.4121051.569787
0.4134731.569436
0.4148451.569088
0.4162211.568744
0.4176021.568403
0.4189881.568064
0.4203781.567729
0.4217731.567398
0.4231731.567069
0.4245771.566743
0.4259851.56642
0.4273991.5661
0.4288171.565782
0.430241.565468
0.4316681.565157
0.43311.564848
0.4345371.564542
0.4359791.564239
0.4374261.563939
0.4388771.563641
0.4403331.563346
0.4417941.563054
0.443261.562764
0.4447311.562477
0.4462071.562192
0.4476871.56191
0.4491731.561631
0.4506631.561354
0.4521591.561079
0.4536591.560807
0.4551641.560537
0.4566751.56027
0.458191.560005
0.459711.559742
0.4612361.559482
0.4627661.559224
0.4643021.558968
0.4658421.558715
0.4673881.558464
0.4689391.558215
0.4704951.557968
0.4720561.557723
0.4736231.557481
0.4751941.55724
0.4767711.557002
0.4783531.556766
0.479941.556532
0.4815331.5563
0.4831311.55607
0.4847341.555841
0.4863421.555615
0.4879561.555391
0.4895751.555169
0.4911991.554949
0.4928291.55473
0.4944651.554514
0.4961051.554299
0.4977511.554087
0.4994031.553876
0.501061.553667
0.5027231.553459
0.5043911.553254
0.5060651.55305
0.5077441.552848
0.5094291.552648
0.5111191.552449
0.5128151.552252
0.5145161.552057
0.5162241.551863
0.5179371.551671
0.5196551.551481
0.521381.551293
0.523111.551106
0.5248451.55092
0.5265871.550736
0.5283341.550554
0.5300871.550373
0.5318461.550194
0.5336111.550016
0.5353821.54984
0.5371581.549665
0.538941.549492
0.5407291.54932
0.5425231.549149
0.5443231.54898
0.5461291.548813
0.5479411.548647
0.549761.548482
0.5515841.548319
0.5534141.548156
0.555251.547996
0.5570931.547836
0.5589411.547678
0.5607961.547522
0.5626571.547366
0.5645241.547212
0.5663971.547059
0.5682761.546908
0.5701621.546757
0.5720541.546608
0.5739521.54646
0.5758561.546314
0.5777671.546168
0.5796841.546024
0.5816081.545881
0.5835381.545739
0.5854741.545599
0.5874171.545459
0.5893661.545321
0.5913211.545183
0.5932841.545047
0.5952521.544912
0.5972271.544778
0.5992091.544645
0.6011971.544513
0.6031921.544383
0.6051941.544253
0.6072021.544124
0.6092171.543997
0.6112381.54387
0.6132661.543745
0.6153011.54362
0.6173431.543497
0.6193911.543374
0.6214471.543253
0.6235091.543132
0.6255771.543013
0.6276531.542894
0.6297361.542777
0.6318251.54266
0.6339221.542544
0.6360251.542429
0.6381361.542315
0.6402531.542202
0.6423781.54209
0.6445091.541979
0.6466481.541869
0.6487941.541759
0.6509461.541651
0.6531061.541543
0.6552731.541436
0.6574481.54133
0.6596291.541225
0.6618181.541121
0.6640141.541017
0.6662171.540915
0.6684281.540813
0.6706461.540712
0.6728711.540611
0.6751041.540512
0.6773441.540413
0.6795921.540315
0.6818471.540218
0.6841091.540122
0.6863791.540026
0.6886571.539931
0.6909421.539837
0.6932341.539744
0.6955351.539651
0.6978421.539559
0.7001581.539468
0.7024811.539377
0.7048121.539287
0.7071511.539198
0.7094971.53911
0.7118521.539022
0.7142141.538935
0.7165831.538849
0.7189611.538763
0.7213471.538678
0.723741.538594
0.7261421.53851
0.7285511.538427
0.7309691.538344
0.7333941.538263
0.7358281.538181
0.7382691.538101
0.7407191.538021
0.7431771.537942
0.7456431.537863
0.7481171.537785
0.7505991.537707
0.753091.53763
0.7555891.537554
0.7580961.537478
0.7606121.537403
0.7631351.537329
0.7656681.537255
0.7682081.537181
0.7707571.537108
0.7733151.537036
0.7758811.536964
0.7784551.536893
0.7810381.536822
0.783631.536752
0.786231.536683
0.7888391.536613
0.7914561.536545
0.7940831.536477
0.7967181.536409
0.7993611.536342
0.8020141.536276
0.8046751.53621
0.8073451.536144
0.8100241.536079
0.8127121.536015
0.8154081.535951
0.8181141.535887
0.8208291.535824
0.8235521.535761
0.8262851.535699
0.8290271.535638
0.8317771.535576
0.8345371.535516
0.8373071.535455
0.8400851.535396
0.8428721.535336
0.8456691.535277
0.8484751.535219
0.8512911.535161
0.8541151.535103
0.8569491.535046
0.8597931.534989
0.8626461.534933
0.8655081.534877
0.868381.534821
0.8712621.534766
0.8741531.534711
0.8770531.534657
0.8799631.534603
0.8828831.53455
0.8858131.534497
0.8887521.534444
0.8917011.534392
0.894661.53434
0.8976291.534288
0.9006071.534237
0.9035951.534186
0.9065941.534136
0.9096021.534086
0.912621.534036
0.9156481.533987
0.9186871.533938
0.9217351.533889
0.9247931.533841
0.9278621.533793
0.9309411.533746
0.934031.533699
0.9371291.533652
0.9402391.533605
0.9433591.533559
0.9464891.533513
0.9496291.533468
0.952781.533423
0.9559421.533378
0.9591141.533333
0.9622961.533289
0.9654891.533245
0.9686931.533202
0.9719071.533159
0.9751321.533116
0.9783681.533073
0.9816141.533031
0.9848711.532989
0.9881391.532947
0.9914181.532906
0.9947081.532865
0.9980091.532824
1.001321.532784
1.004641.532744
1.007981.532704
1.011321.532664
1.014681.532625
1.018041.532586
1.021421.532547
1.024811.532509
1.028211.532471
1.031621.532433
1.035051.532395
1.038481.532358
1.041931.532321
1.045381.532284
1.048851.532247
1.052331.532211
1.055821.532175
1.059331.532139
1.062841.532104
1.066371.532069
1.069911.532034
1.073461.531999
1.077021.531964
1.080591.53193
1.084181.531896
1.087781.531862
1.091391.531829
1.095011.531796
1.098641.531763
1.102291.53173
1.105941.531697
1.109611.531665
1.11331.531633
1.116991.531601
1.12071.531569
1.124411.531538
1.128151.531507
1.131891.531476
1.135641.531445
1.139411.531414
1.143191.531384
1.146991.531354
1.150791.531324
1.154611.531294
1.158441.531265
1.162291.531236
1.166141.531207
1.170011.531178
1.17391.531149
1.177791.531121
1.18171.531093
1.185621.531064
1.189551.531037
1.19351.531009
1.197461.530982
1.201431.530954
1.205421.530927
1.209421.5309
1.213431.530874
1.217461.530847
1.22151.530821
1.225551.530795
1.229621.530769
1.23371.530743
1.237791.530718
1.24191.530692
1.246021.530667
1.250161.530642
1.25431.530617
1.258471.530592
1.262641.530568
1.266831.530544
1.271041.530519
1.275251.530495
1.279481.530472
1.283731.530448
1.287991.530424
1.292261.530401
1.296551.530378
1.300851.530355
1.305171.530332
1.30951.530309
1.313851.530287
1.31821.530265
1.322581.530242
1.326971.53022
1.331371.530198
1.335791.530177
1.340221.530155
1.344671.530134
1.349131.530112
1.353611.530091
1.35811.53007
1.36261.530049
1.367131.530029
1.371661.530008
1.376211.529988
1.380781.529967
1.385361.529947
1.389961.529927
1.394571.529907
1.39921.529888
1.403841.529868
1.40851.529849
1.413171.529829
1.417861.52981
1.422571.529791
1.427291.529772
1.432021.529753
1.436771.529735
1.441541.529716
1.446321.529698
1.451121.52968
1.455941.529661
1.460771.529643
1.465621.529626
1.470481.529608
1.475361.52959
1.480261.529573
1.485171.529555
1.490091.529538
1.495041.529521
1.51.529504

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
—