Optical constants
Refractive index of Bombyx mori (silkworm) silk
Bucciarelli et al. 2018: Pure fibroin film, formed using water; 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
- 1.54713
- Extinction coefficient k
- 0
- Permittivity ε1
- 2.39362
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 51.066
- Chromatic dispersion dn/dλ
- -0.0538094 µm⁻¹
- Group index ng
- 1.57875
- Group velocity dispersion
- 112.666 fs²/mm
- Dispersion parameter D
- -614.655 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 water; n 0.4–1.5 µm
bombyx_mori = ls.fetch_refractiveindex("other", "Bombyx_mori", "Bucciarelli-rSF_H2O", 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_01e2d0f6ee27/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-h2o).
# ... 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 | 1.533 |
| C2 | 0.0043 |
| C3 | -2.0 |
| C4 | 0.0002 |
| 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 | 1.567687 |
| 0.401327 | 1.567407 |
| 0.402659 | 1.567129 |
| 0.403995 | 1.566854 |
| 0.405336 | 1.566581 |
| 0.406681 | 1.566311 |
| 0.40803 | 1.566043 |
| 0.409384 | 1.565778 |
| 0.410742 | 1.565514 |
| 0.412105 | 1.565254 |
| 0.413473 | 1.564995 |
| 0.414845 | 1.564739 |
| 0.416221 | 1.564485 |
| 0.417602 | 1.564233 |
| 0.418988 | 1.563984 |
| 0.420378 | 1.563737 |
| 0.421773 | 1.563492 |
| 0.423173 | 1.563249 |
| 0.424577 | 1.563008 |
| 0.425985 | 1.56277 |
| 0.427399 | 1.562533 |
| 0.428817 | 1.562299 |
| 0.43024 | 1.562067 |
| 0.431668 | 1.561837 |
| 0.4331 | 1.561608 |
| 0.434537 | 1.561382 |
| 0.435979 | 1.561158 |
| 0.437426 | 1.560936 |
| 0.438877 | 1.560715 |
| 0.440333 | 1.560497 |
| 0.441794 | 1.560281 |
| 0.44326 | 1.560066 |
| 0.444731 | 1.559853 |
| 0.446207 | 1.559642 |
| 0.447687 | 1.559433 |
| 0.449173 | 1.559226 |
| 0.450663 | 1.559021 |
| 0.452159 | 1.558817 |
| 0.453659 | 1.558615 |
| 0.455164 | 1.558415 |
| 0.456675 | 1.558217 |
| 0.45819 | 1.55802 |
| 0.45971 | 1.557825 |
| 0.461236 | 1.557632 |
| 0.462766 | 1.55744 |
| 0.464302 | 1.55725 |
| 0.465842 | 1.557062 |
| 0.467388 | 1.556875 |
| 0.468939 | 1.55669 |
| 0.470495 | 1.556506 |
| 0.472056 | 1.556324 |
| 0.473623 | 1.556144 |
| 0.475194 | 1.555965 |
| 0.476771 | 1.555788 |
| 0.478353 | 1.555612 |
| 0.47994 | 1.555437 |
| 0.481533 | 1.555264 |
| 0.483131 | 1.555093 |
| 0.484734 | 1.554923 |
| 0.486342 | 1.554755 |
| 0.487956 | 1.554587 |
| 0.489575 | 1.554422 |
| 0.491199 | 1.554257 |
| 0.492829 | 1.554095 |
| 0.494465 | 1.553933 |
| 0.496105 | 1.553773 |
| 0.497751 | 1.553614 |
| 0.499403 | 1.553456 |
| 0.50106 | 1.5533 |
| 0.502723 | 1.553145 |
| 0.504391 | 1.552992 |
| 0.506065 | 1.55284 |
| 0.507744 | 1.552689 |
| 0.509429 | 1.552539 |
| 0.511119 | 1.55239 |
| 0.512815 | 1.552243 |
| 0.514516 | 1.552097 |
| 0.516224 | 1.551952 |
| 0.517937 | 1.551809 |
| 0.519655 | 1.551666 |
| 0.52138 | 1.551525 |
| 0.52311 | 1.551385 |
| 0.524845 | 1.551246 |
| 0.526587 | 1.551108 |
| 0.528334 | 1.550971 |
| 0.530087 | 1.550836 |
| 0.531846 | 1.550702 |
| 0.533611 | 1.550568 |
| 0.535382 | 1.550436 |
| 0.537158 | 1.550305 |
| 0.53894 | 1.550175 |
| 0.540729 | 1.550046 |
| 0.542523 | 1.549918 |
| 0.544323 | 1.549791 |
| 0.546129 | 1.549665 |
| 0.547941 | 1.549541 |
| 0.54976 | 1.549417 |
| 0.551584 | 1.549294 |
| 0.553414 | 1.549172 |
| 0.55525 | 1.549051 |
| 0.557093 | 1.548932 |
| 0.558941 | 1.548813 |
| 0.560796 | 1.548695 |
| 0.562657 | 1.548578 |
| 0.564524 | 1.548462 |
| 0.566397 | 1.548347 |
| 0.568276 | 1.548233 |
| 0.570162 | 1.54812 |
| 0.572054 | 1.548008 |
| 0.573952 | 1.547896 |
| 0.575856 | 1.547786 |
| 0.577767 | 1.547676 |
| 0.579684 | 1.547568 |
| 0.581608 | 1.54746 |
| 0.583538 | 1.547353 |
| 0.585474 | 1.547247 |
| 0.587417 | 1.547141 |
| 0.589366 | 1.547037 |
| 0.591321 | 1.546933 |
| 0.593284 | 1.546831 |
| 0.595252 | 1.546729 |
| 0.597227 | 1.546628 |
| 0.599209 | 1.546527 |
| 0.601197 | 1.546428 |
| 0.603192 | 1.546329 |
| 0.605194 | 1.546231 |
| 0.607202 | 1.546134 |
| 0.609217 | 1.546038 |
| 0.611238 | 1.545942 |
| 0.613266 | 1.545847 |
| 0.615301 | 1.545753 |
| 0.617343 | 1.54566 |
| 0.619391 | 1.545567 |
| 0.621447 | 1.545475 |
| 0.623509 | 1.545384 |
| 0.625577 | 1.545294 |
| 0.627653 | 1.545204 |
| 0.629736 | 1.545115 |
| 0.631825 | 1.545026 |
| 0.633922 | 1.544939 |
| 0.636025 | 1.544852 |
| 0.638136 | 1.544766 |
| 0.640253 | 1.54468 |
| 0.642378 | 1.544595 |
| 0.644509 | 1.544511 |
| 0.646648 | 1.544427 |
| 0.648794 | 1.544344 |
| 0.650946 | 1.544262 |
| 0.653106 | 1.54418 |
| 0.655273 | 1.544099 |
| 0.657448 | 1.544019 |
| 0.659629 | 1.543939 |
| 0.661818 | 1.54386 |
| 0.664014 | 1.543781 |
| 0.666217 | 1.543703 |
| 0.668428 | 1.543626 |
| 0.670646 | 1.543549 |
| 0.672871 | 1.543473 |
| 0.675104 | 1.543398 |
| 0.677344 | 1.543323 |
| 0.679592 | 1.543248 |
| 0.681847 | 1.543174 |
| 0.684109 | 1.543101 |
| 0.686379 | 1.543028 |
| 0.688657 | 1.542956 |
| 0.690942 | 1.542885 |
| 0.693234 | 1.542814 |
| 0.695535 | 1.542743 |
| 0.697842 | 1.542673 |
| 0.700158 | 1.542604 |
| 0.702481 | 1.542535 |
| 0.704812 | 1.542467 |
| 0.707151 | 1.542399 |
| 0.709497 | 1.542331 |
| 0.711852 | 1.542265 |
| 0.714214 | 1.542198 |
| 0.716583 | 1.542133 |
| 0.718961 | 1.542067 |
| 0.721347 | 1.542002 |
| 0.72374 | 1.541938 |
| 0.726142 | 1.541874 |
| 0.728551 | 1.541811 |
| 0.730969 | 1.541748 |
| 0.733394 | 1.541686 |
| 0.735828 | 1.541624 |
| 0.738269 | 1.541563 |
| 0.740719 | 1.541502 |
| 0.743177 | 1.541441 |
| 0.745643 | 1.541381 |
| 0.748117 | 1.541321 |
| 0.750599 | 1.541262 |
| 0.75309 | 1.541204 |
| 0.755589 | 1.541145 |
| 0.758096 | 1.541088 |
| 0.760612 | 1.54103 |
| 0.763135 | 1.540973 |
| 0.765668 | 1.540917 |
| 0.768208 | 1.540861 |
| 0.770757 | 1.540805 |
| 0.773315 | 1.54075 |
| 0.775881 | 1.540695 |
| 0.778455 | 1.54064 |
| 0.781038 | 1.540586 |
| 0.78363 | 1.540533 |
| 0.78623 | 1.54048 |
| 0.788839 | 1.540427 |
| 0.791456 | 1.540374 |
| 0.794083 | 1.540322 |
| 0.796718 | 1.540271 |
| 0.799361 | 1.540219 |
| 0.802014 | 1.540168 |
| 0.804675 | 1.540118 |
| 0.807345 | 1.540068 |
| 0.810024 | 1.540018 |
| 0.812712 | 1.539969 |
| 0.815408 | 1.53992 |
| 0.818114 | 1.539871 |
| 0.820829 | 1.539823 |
| 0.823552 | 1.539775 |
| 0.826285 | 1.539727 |
| 0.829027 | 1.53968 |
| 0.831777 | 1.539633 |
| 0.834537 | 1.539586 |
| 0.837307 | 1.53954 |
| 0.840085 | 1.539494 |
| 0.842872 | 1.539449 |
| 0.845669 | 1.539404 |
| 0.848475 | 1.539359 |
| 0.851291 | 1.539314 |
| 0.854115 | 1.53927 |
| 0.856949 | 1.539226 |
| 0.859793 | 1.539183 |
| 0.862646 | 1.53914 |
| 0.865508 | 1.539097 |
| 0.86838 | 1.539054 |
| 0.871262 | 1.539012 |
| 0.874153 | 1.53897 |
| 0.877053 | 1.538928 |
| 0.879963 | 1.538887 |
| 0.882883 | 1.538846 |
| 0.885813 | 1.538805 |
| 0.888752 | 1.538764 |
| 0.891701 | 1.538724 |
| 0.89466 | 1.538684 |
| 0.897629 | 1.538645 |
| 0.900607 | 1.538605 |
| 0.903595 | 1.538566 |
| 0.906594 | 1.538528 |
| 0.909602 | 1.538489 |
| 0.91262 | 1.538451 |
| 0.915648 | 1.538413 |
| 0.918687 | 1.538376 |
| 0.921735 | 1.538338 |
| 0.924793 | 1.538301 |
| 0.927862 | 1.538264 |
| 0.930941 | 1.538228 |
| 0.93403 | 1.538192 |
| 0.937129 | 1.538156 |
| 0.940239 | 1.53812 |
| 0.943359 | 1.538084 |
| 0.946489 | 1.538049 |
| 0.949629 | 1.538014 |
| 0.95278 | 1.537979 |
| 0.955942 | 1.537945 |
| 0.959114 | 1.537911 |
| 0.962296 | 1.537877 |
| 0.965489 | 1.537843 |
| 0.968693 | 1.53781 |
| 0.971907 | 1.537776 |
| 0.975132 | 1.537743 |
| 0.978368 | 1.537711 |
| 0.981614 | 1.537678 |
| 0.984871 | 1.537646 |
| 0.988139 | 1.537614 |
| 0.991418 | 1.537582 |
| 0.994708 | 1.53755 |
| 0.998009 | 1.537519 |
| 1.00132 | 1.537488 |
| 1.00464 | 1.537457 |
| 1.00798 | 1.537426 |
| 1.01132 | 1.537395 |
| 1.01468 | 1.537365 |
| 1.01804 | 1.537335 |
| 1.02142 | 1.537305 |
| 1.02481 | 1.537276 |
| 1.02821 | 1.537246 |
| 1.03162 | 1.537217 |
| 1.03505 | 1.537188 |
| 1.03848 | 1.537159 |
| 1.04193 | 1.537131 |
| 1.04538 | 1.537102 |
| 1.04885 | 1.537074 |
| 1.05233 | 1.537046 |
| 1.05582 | 1.537018 |
| 1.05933 | 1.536991 |
| 1.06284 | 1.536963 |
| 1.06637 | 1.536936 |
| 1.06991 | 1.536909 |
| 1.07346 | 1.536882 |
| 1.07702 | 1.536856 |
| 1.08059 | 1.536829 |
| 1.08418 | 1.536803 |
| 1.08778 | 1.536777 |
| 1.09139 | 1.536751 |
| 1.09501 | 1.536725 |
| 1.09864 | 1.5367 |
| 1.10229 | 1.536674 |
| 1.10594 | 1.536649 |
| 1.10961 | 1.536624 |
| 1.1133 | 1.5366 |
| 1.11699 | 1.536575 |
| 1.1207 | 1.53655 |
| 1.12441 | 1.536526 |
| 1.12815 | 1.536502 |
| 1.13189 | 1.536478 |
| 1.13564 | 1.536454 |
| 1.13941 | 1.536431 |
| 1.14319 | 1.536407 |
| 1.14699 | 1.536384 |
| 1.15079 | 1.536361 |
| 1.15461 | 1.536338 |
| 1.15844 | 1.536315 |
| 1.16229 | 1.536293 |
| 1.16614 | 1.53627 |
| 1.17001 | 1.536248 |
| 1.1739 | 1.536226 |
| 1.17779 | 1.536204 |
| 1.1817 | 1.536182 |
| 1.18562 | 1.53616 |
| 1.18955 | 1.536139 |
| 1.1935 | 1.536117 |
| 1.19746 | 1.536096 |
| 1.20143 | 1.536075 |
| 1.20542 | 1.536054 |
| 1.20942 | 1.536033 |
| 1.21343 | 1.536013 |
| 1.21746 | 1.535992 |
| 1.2215 | 1.535972 |
| 1.22555 | 1.535952 |
| 1.22962 | 1.535931 |
| 1.2337 | 1.535912 |
| 1.23779 | 1.535892 |
| 1.2419 | 1.535872 |
| 1.24602 | 1.535853 |
| 1.25016 | 1.535833 |
| 1.2543 | 1.535814 |
| 1.25847 | 1.535795 |
| 1.26264 | 1.535776 |
| 1.26683 | 1.535757 |
| 1.27104 | 1.535738 |
| 1.27525 | 1.53572 |
| 1.27948 | 1.535701 |
| 1.28373 | 1.535683 |
| 1.28799 | 1.535665 |
| 1.29226 | 1.535647 |
| 1.29655 | 1.535629 |
| 1.30085 | 1.535611 |
| 1.30517 | 1.535593 |
| 1.3095 | 1.535576 |
| 1.31385 | 1.535558 |
| 1.3182 | 1.535541 |
| 1.32258 | 1.535524 |
| 1.32697 | 1.535507 |
| 1.33137 | 1.53549 |
| 1.33579 | 1.535473 |
| 1.34022 | 1.535456 |
| 1.34467 | 1.535439 |
| 1.34913 | 1.535423 |
| 1.35361 | 1.535406 |
| 1.3581 | 1.53539 |
| 1.3626 | 1.535374 |
| 1.36713 | 1.535358 |
| 1.37166 | 1.535342 |
| 1.37621 | 1.535326 |
| 1.38078 | 1.53531 |
| 1.38536 | 1.535295 |
| 1.38996 | 1.535279 |
| 1.39457 | 1.535264 |
| 1.3992 | 1.535249 |
| 1.40384 | 1.535233 |
| 1.4085 | 1.535218 |
| 1.41317 | 1.535203 |
| 1.41786 | 1.535188 |
| 1.42257 | 1.535174 |
| 1.42729 | 1.535159 |
| 1.43202 | 1.535144 |
| 1.43677 | 1.53513 |
| 1.44154 | 1.535116 |
| 1.44632 | 1.535101 |
| 1.45112 | 1.535087 |
| 1.45594 | 1.535073 |
| 1.46077 | 1.535059 |
| 1.46562 | 1.535045 |
| 1.47048 | 1.535031 |
| 1.47536 | 1.535018 |
| 1.48026 | 1.535004 |
| 1.48517 | 1.534991 |
| 1.49009 | 1.534977 |
| 1.49504 | 1.534964 |
| 1.5 | 1.534951 |
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 water.