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
- 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.
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_bc0e80ed7d4f/lightsmith"
bombyx_mori = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bombyx_mori.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (bombyx-mori/bucciarelli-2018-rsf-fa).
# ... load bombyx_mori as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bombyx_mori)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, 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"]).
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 µmValid from 0.4 to 1.5 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 1.527 |
| C2 | 0.0055 |
| C3 | -2.0 |
| C4 | 0.0003 |
| C5 | -4.0 |
Comments and conditions
References
- 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| λ (µm) | n |
|---|---|
| 0.4 | 1.573094 |
| 0.401327 | 1.572712 |
| 0.402659 | 1.572335 |
| 0.403995 | 1.571961 |
| 0.405336 | 1.57159 |
| 0.406681 | 1.571222 |
| 0.40803 | 1.570858 |
| 0.409384 | 1.570498 |
| 0.410742 | 1.570141 |
| 0.412105 | 1.569787 |
| 0.413473 | 1.569436 |
| 0.414845 | 1.569088 |
| 0.416221 | 1.568744 |
| 0.417602 | 1.568403 |
| 0.418988 | 1.568064 |
| 0.420378 | 1.567729 |
| 0.421773 | 1.567398 |
| 0.423173 | 1.567069 |
| 0.424577 | 1.566743 |
| 0.425985 | 1.56642 |
| 0.427399 | 1.5661 |
| 0.428817 | 1.565782 |
| 0.43024 | 1.565468 |
| 0.431668 | 1.565157 |
| 0.4331 | 1.564848 |
| 0.434537 | 1.564542 |
| 0.435979 | 1.564239 |
| 0.437426 | 1.563939 |
| 0.438877 | 1.563641 |
| 0.440333 | 1.563346 |
| 0.441794 | 1.563054 |
| 0.44326 | 1.562764 |
| 0.444731 | 1.562477 |
| 0.446207 | 1.562192 |
| 0.447687 | 1.56191 |
| 0.449173 | 1.561631 |
| 0.450663 | 1.561354 |
| 0.452159 | 1.561079 |
| 0.453659 | 1.560807 |
| 0.455164 | 1.560537 |
| 0.456675 | 1.56027 |
| 0.45819 | 1.560005 |
| 0.45971 | 1.559742 |
| 0.461236 | 1.559482 |
| 0.462766 | 1.559224 |
| 0.464302 | 1.558968 |
| 0.465842 | 1.558715 |
| 0.467388 | 1.558464 |
| 0.468939 | 1.558215 |
| 0.470495 | 1.557968 |
| 0.472056 | 1.557723 |
| 0.473623 | 1.557481 |
| 0.475194 | 1.55724 |
| 0.476771 | 1.557002 |
| 0.478353 | 1.556766 |
| 0.47994 | 1.556532 |
| 0.481533 | 1.5563 |
| 0.483131 | 1.55607 |
| 0.484734 | 1.555841 |
| 0.486342 | 1.555615 |
| 0.487956 | 1.555391 |
| 0.489575 | 1.555169 |
| 0.491199 | 1.554949 |
| 0.492829 | 1.55473 |
| 0.494465 | 1.554514 |
| 0.496105 | 1.554299 |
| 0.497751 | 1.554087 |
| 0.499403 | 1.553876 |
| 0.50106 | 1.553667 |
| 0.502723 | 1.553459 |
| 0.504391 | 1.553254 |
| 0.506065 | 1.55305 |
| 0.507744 | 1.552848 |
| 0.509429 | 1.552648 |
| 0.511119 | 1.552449 |
| 0.512815 | 1.552252 |
| 0.514516 | 1.552057 |
| 0.516224 | 1.551863 |
| 0.517937 | 1.551671 |
| 0.519655 | 1.551481 |
| 0.52138 | 1.551293 |
| 0.52311 | 1.551106 |
| 0.524845 | 1.55092 |
| 0.526587 | 1.550736 |
| 0.528334 | 1.550554 |
| 0.530087 | 1.550373 |
| 0.531846 | 1.550194 |
| 0.533611 | 1.550016 |
| 0.535382 | 1.54984 |
| 0.537158 | 1.549665 |
| 0.53894 | 1.549492 |
| 0.540729 | 1.54932 |
| 0.542523 | 1.549149 |
| 0.544323 | 1.54898 |
| 0.546129 | 1.548813 |
| 0.547941 | 1.548647 |
| 0.54976 | 1.548482 |
| 0.551584 | 1.548319 |
| 0.553414 | 1.548156 |
| 0.55525 | 1.547996 |
| 0.557093 | 1.547836 |
| 0.558941 | 1.547678 |
| 0.560796 | 1.547522 |
| 0.562657 | 1.547366 |
| 0.564524 | 1.547212 |
| 0.566397 | 1.547059 |
| 0.568276 | 1.546908 |
| 0.570162 | 1.546757 |
| 0.572054 | 1.546608 |
| 0.573952 | 1.54646 |
| 0.575856 | 1.546314 |
| 0.577767 | 1.546168 |
| 0.579684 | 1.546024 |
| 0.581608 | 1.545881 |
| 0.583538 | 1.545739 |
| 0.585474 | 1.545599 |
| 0.587417 | 1.545459 |
| 0.589366 | 1.545321 |
| 0.591321 | 1.545183 |
| 0.593284 | 1.545047 |
| 0.595252 | 1.544912 |
| 0.597227 | 1.544778 |
| 0.599209 | 1.544645 |
| 0.601197 | 1.544513 |
| 0.603192 | 1.544383 |
| 0.605194 | 1.544253 |
| 0.607202 | 1.544124 |
| 0.609217 | 1.543997 |
| 0.611238 | 1.54387 |
| 0.613266 | 1.543745 |
| 0.615301 | 1.54362 |
| 0.617343 | 1.543497 |
| 0.619391 | 1.543374 |
| 0.621447 | 1.543253 |
| 0.623509 | 1.543132 |
| 0.625577 | 1.543013 |
| 0.627653 | 1.542894 |
| 0.629736 | 1.542777 |
| 0.631825 | 1.54266 |
| 0.633922 | 1.542544 |
| 0.636025 | 1.542429 |
| 0.638136 | 1.542315 |
| 0.640253 | 1.542202 |
| 0.642378 | 1.54209 |
| 0.644509 | 1.541979 |
| 0.646648 | 1.541869 |
| 0.648794 | 1.541759 |
| 0.650946 | 1.541651 |
| 0.653106 | 1.541543 |
| 0.655273 | 1.541436 |
| 0.657448 | 1.54133 |
| 0.659629 | 1.541225 |
| 0.661818 | 1.541121 |
| 0.664014 | 1.541017 |
| 0.666217 | 1.540915 |
| 0.668428 | 1.540813 |
| 0.670646 | 1.540712 |
| 0.672871 | 1.540611 |
| 0.675104 | 1.540512 |
| 0.677344 | 1.540413 |
| 0.679592 | 1.540315 |
| 0.681847 | 1.540218 |
| 0.684109 | 1.540122 |
| 0.686379 | 1.540026 |
| 0.688657 | 1.539931 |
| 0.690942 | 1.539837 |
| 0.693234 | 1.539744 |
| 0.695535 | 1.539651 |
| 0.697842 | 1.539559 |
| 0.700158 | 1.539468 |
| 0.702481 | 1.539377 |
| 0.704812 | 1.539287 |
| 0.707151 | 1.539198 |
| 0.709497 | 1.53911 |
| 0.711852 | 1.539022 |
| 0.714214 | 1.538935 |
| 0.716583 | 1.538849 |
| 0.718961 | 1.538763 |
| 0.721347 | 1.538678 |
| 0.72374 | 1.538594 |
| 0.726142 | 1.53851 |
| 0.728551 | 1.538427 |
| 0.730969 | 1.538344 |
| 0.733394 | 1.538263 |
| 0.735828 | 1.538181 |
| 0.738269 | 1.538101 |
| 0.740719 | 1.538021 |
| 0.743177 | 1.537942 |
| 0.745643 | 1.537863 |
| 0.748117 | 1.537785 |
| 0.750599 | 1.537707 |
| 0.75309 | 1.53763 |
| 0.755589 | 1.537554 |
| 0.758096 | 1.537478 |
| 0.760612 | 1.537403 |
| 0.763135 | 1.537329 |
| 0.765668 | 1.537255 |
| 0.768208 | 1.537181 |
| 0.770757 | 1.537108 |
| 0.773315 | 1.537036 |
| 0.775881 | 1.536964 |
| 0.778455 | 1.536893 |
| 0.781038 | 1.536822 |
| 0.78363 | 1.536752 |
| 0.78623 | 1.536683 |
| 0.788839 | 1.536613 |
| 0.791456 | 1.536545 |
| 0.794083 | 1.536477 |
| 0.796718 | 1.536409 |
| 0.799361 | 1.536342 |
| 0.802014 | 1.536276 |
| 0.804675 | 1.53621 |
| 0.807345 | 1.536144 |
| 0.810024 | 1.536079 |
| 0.812712 | 1.536015 |
| 0.815408 | 1.535951 |
| 0.818114 | 1.535887 |
| 0.820829 | 1.535824 |
| 0.823552 | 1.535761 |
| 0.826285 | 1.535699 |
| 0.829027 | 1.535638 |
| 0.831777 | 1.535576 |
| 0.834537 | 1.535516 |
| 0.837307 | 1.535455 |
| 0.840085 | 1.535396 |
| 0.842872 | 1.535336 |
| 0.845669 | 1.535277 |
| 0.848475 | 1.535219 |
| 0.851291 | 1.535161 |
| 0.854115 | 1.535103 |
| 0.856949 | 1.535046 |
| 0.859793 | 1.534989 |
| 0.862646 | 1.534933 |
| 0.865508 | 1.534877 |
| 0.86838 | 1.534821 |
| 0.871262 | 1.534766 |
| 0.874153 | 1.534711 |
| 0.877053 | 1.534657 |
| 0.879963 | 1.534603 |
| 0.882883 | 1.53455 |
| 0.885813 | 1.534497 |
| 0.888752 | 1.534444 |
| 0.891701 | 1.534392 |
| 0.89466 | 1.53434 |
| 0.897629 | 1.534288 |
| 0.900607 | 1.534237 |
| 0.903595 | 1.534186 |
| 0.906594 | 1.534136 |
| 0.909602 | 1.534086 |
| 0.91262 | 1.534036 |
| 0.915648 | 1.533987 |
| 0.918687 | 1.533938 |
| 0.921735 | 1.533889 |
| 0.924793 | 1.533841 |
| 0.927862 | 1.533793 |
| 0.930941 | 1.533746 |
| 0.93403 | 1.533699 |
| 0.937129 | 1.533652 |
| 0.940239 | 1.533605 |
| 0.943359 | 1.533559 |
| 0.946489 | 1.533513 |
| 0.949629 | 1.533468 |
| 0.95278 | 1.533423 |
| 0.955942 | 1.533378 |
| 0.959114 | 1.533333 |
| 0.962296 | 1.533289 |
| 0.965489 | 1.533245 |
| 0.968693 | 1.533202 |
| 0.971907 | 1.533159 |
| 0.975132 | 1.533116 |
| 0.978368 | 1.533073 |
| 0.981614 | 1.533031 |
| 0.984871 | 1.532989 |
| 0.988139 | 1.532947 |
| 0.991418 | 1.532906 |
| 0.994708 | 1.532865 |
| 0.998009 | 1.532824 |
| 1.00132 | 1.532784 |
| 1.00464 | 1.532744 |
| 1.00798 | 1.532704 |
| 1.01132 | 1.532664 |
| 1.01468 | 1.532625 |
| 1.01804 | 1.532586 |
| 1.02142 | 1.532547 |
| 1.02481 | 1.532509 |
| 1.02821 | 1.532471 |
| 1.03162 | 1.532433 |
| 1.03505 | 1.532395 |
| 1.03848 | 1.532358 |
| 1.04193 | 1.532321 |
| 1.04538 | 1.532284 |
| 1.04885 | 1.532247 |
| 1.05233 | 1.532211 |
| 1.05582 | 1.532175 |
| 1.05933 | 1.532139 |
| 1.06284 | 1.532104 |
| 1.06637 | 1.532069 |
| 1.06991 | 1.532034 |
| 1.07346 | 1.531999 |
| 1.07702 | 1.531964 |
| 1.08059 | 1.53193 |
| 1.08418 | 1.531896 |
| 1.08778 | 1.531862 |
| 1.09139 | 1.531829 |
| 1.09501 | 1.531796 |
| 1.09864 | 1.531763 |
| 1.10229 | 1.53173 |
| 1.10594 | 1.531697 |
| 1.10961 | 1.531665 |
| 1.1133 | 1.531633 |
| 1.11699 | 1.531601 |
| 1.1207 | 1.531569 |
| 1.12441 | 1.531538 |
| 1.12815 | 1.531507 |
| 1.13189 | 1.531476 |
| 1.13564 | 1.531445 |
| 1.13941 | 1.531414 |
| 1.14319 | 1.531384 |
| 1.14699 | 1.531354 |
| 1.15079 | 1.531324 |
| 1.15461 | 1.531294 |
| 1.15844 | 1.531265 |
| 1.16229 | 1.531236 |
| 1.16614 | 1.531207 |
| 1.17001 | 1.531178 |
| 1.1739 | 1.531149 |
| 1.17779 | 1.531121 |
| 1.1817 | 1.531093 |
| 1.18562 | 1.531064 |
| 1.18955 | 1.531037 |
| 1.1935 | 1.531009 |
| 1.19746 | 1.530982 |
| 1.20143 | 1.530954 |
| 1.20542 | 1.530927 |
| 1.20942 | 1.5309 |
| 1.21343 | 1.530874 |
| 1.21746 | 1.530847 |
| 1.2215 | 1.530821 |
| 1.22555 | 1.530795 |
| 1.22962 | 1.530769 |
| 1.2337 | 1.530743 |
| 1.23779 | 1.530718 |
| 1.2419 | 1.530692 |
| 1.24602 | 1.530667 |
| 1.25016 | 1.530642 |
| 1.2543 | 1.530617 |
| 1.25847 | 1.530592 |
| 1.26264 | 1.530568 |
| 1.26683 | 1.530544 |
| 1.27104 | 1.530519 |
| 1.27525 | 1.530495 |
| 1.27948 | 1.530472 |
| 1.28373 | 1.530448 |
| 1.28799 | 1.530424 |
| 1.29226 | 1.530401 |
| 1.29655 | 1.530378 |
| 1.30085 | 1.530355 |
| 1.30517 | 1.530332 |
| 1.3095 | 1.530309 |
| 1.31385 | 1.530287 |
| 1.3182 | 1.530265 |
| 1.32258 | 1.530242 |
| 1.32697 | 1.53022 |
| 1.33137 | 1.530198 |
| 1.33579 | 1.530177 |
| 1.34022 | 1.530155 |
| 1.34467 | 1.530134 |
| 1.34913 | 1.530112 |
| 1.35361 | 1.530091 |
| 1.3581 | 1.53007 |
| 1.3626 | 1.530049 |
| 1.36713 | 1.530029 |
| 1.37166 | 1.530008 |
| 1.37621 | 1.529988 |
| 1.38078 | 1.529967 |
| 1.38536 | 1.529947 |
| 1.38996 | 1.529927 |
| 1.39457 | 1.529907 |
| 1.3992 | 1.529888 |
| 1.40384 | 1.529868 |
| 1.4085 | 1.529849 |
| 1.41317 | 1.529829 |
| 1.41786 | 1.52981 |
| 1.42257 | 1.529791 |
| 1.42729 | 1.529772 |
| 1.43202 | 1.529753 |
| 1.43677 | 1.529735 |
| 1.44154 | 1.529716 |
| 1.44632 | 1.529698 |
| 1.45112 | 1.52968 |
| 1.45594 | 1.529661 |
| 1.46077 | 1.529643 |
| 1.46562 | 1.529626 |
| 1.47048 | 1.529608 |
| 1.47536 | 1.52959 |
| 1.48026 | 1.529573 |
| 1.48517 | 1.529555 |
| 1.49009 | 1.529538 |
| 1.49504 | 1.529521 |
| 1.5 | 1.529504 |
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
- —
Pure fibroin (regenerated silk fibroin) film. Formed using formic acid.