Optical constants
Refractive index of TlBr-TlCl (Thallium bromo-chloride, KRS-6)
Hettner and Leisegang 1948: n 0.6–24 µm
- Data
- formula 4
- Range
- 0.6–24 µm
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.19284
- Extinction coefficient k
- 0
- Permittivity ε1
- 4.80854
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.00153174 µm⁻¹
- Group index ng
- 2.19864
- Group velocity dispersion
- -37.4398 fs²/mm
- Dispersion parameter D
- 4.90971 ps/(nm·km)
- Photon energy
- 0.327135 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
# TlBr-TlCl (Thallium bromo-chloride, KRS-6): Hettner and Leisegang 1948: n 0.6–24 µm
tlbr_tlcl = ls.fetch_refractiveindex("other", "TlBr-TlCl", "Hettner", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tlbr_tlcl.range_nm) # (600, 24000) nm
eps = tlbr_tlcl.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_daae50a99e67/lightsmith"
tlbr_tlcl = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(tlbr_tlcl.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (tlbr-tlcl/hettner-leisegang-1948).
# ... load tlbr_tlcl as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=tlbr_tlcl)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=600, 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
RefractiveIndex.INFO (formula 4), λ in µmValid from 0.6 to 24.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 1.0 |
| C2 | 3.821 |
| C3 | 2.0 |
| C4 | 0.02234 |
| C5 | 2.0 |
| C6 | 0.0 |
| C7 | 0.0 |
| C8 | 0.0 |
| C9 | 1.0 |
| C10 | -0.000877 |
| C11 | 2.0 |
References
Cite
G. Hettner and G. Leisegang. Dispersion of the mixed crystals TlBr-TlI (KRS-5) and TlCl-TlBr (KRS-6) in the infrared, Optik, 3, 305-314 (1948) [in German], as cited in Handbook of Optics, 3rd edition, Vol. 4. McGraw-Hill 2009 (data fit by Handbook of Optics, corrected by refractiveindex.info); 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 |
|---|---|
| 0.6 | 2.196813 |
| 0.605573 | 2.19679 |
| 0.611198 | 2.196767 |
| 0.616874 | 2.196744 |
| 0.622604 | 2.196722 |
| 0.628387 | 2.1967 |
| 0.634224 | 2.196678 |
| 0.640114 | 2.196657 |
| 0.64606 | 2.196636 |
| 0.652061 | 2.196615 |
| 0.658117 | 2.196595 |
| 0.66423 | 2.196575 |
| 0.670399 | 2.196555 |
| 0.676626 | 2.196536 |
| 0.682911 | 2.196516 |
| 0.689254 | 2.196498 |
| 0.695656 | 2.196479 |
| 0.702117 | 2.196461 |
| 0.708638 | 2.196443 |
| 0.71522 | 2.196425 |
| 0.721863 | 2.196408 |
| 0.728568 | 2.19639 |
| 0.735335 | 2.196373 |
| 0.742165 | 2.196357 |
| 0.749059 | 2.19634 |
| 0.756016 | 2.196324 |
| 0.763038 | 2.196308 |
| 0.770125 | 2.196292 |
| 0.777278 | 2.196276 |
| 0.784498 | 2.196261 |
| 0.791784 | 2.196246 |
| 0.799139 | 2.19623 |
| 0.806561 | 2.196216 |
| 0.814053 | 2.196201 |
| 0.821614 | 2.196186 |
| 0.829245 | 2.196172 |
| 0.836947 | 2.196158 |
| 0.844721 | 2.196144 |
| 0.852567 | 2.19613 |
| 0.860486 | 2.196117 |
| 0.868478 | 2.196103 |
| 0.876544 | 2.19609 |
| 0.884686 | 2.196076 |
| 0.892903 | 2.196063 |
| 0.901197 | 2.19605 |
| 0.909567 | 2.196038 |
| 0.918015 | 2.196025 |
| 0.926542 | 2.196012 |
| 0.935148 | 2.196 |
| 0.943834 | 2.195987 |
| 0.9526 | 2.195975 |
| 0.961448 | 2.195963 |
| 0.970378 | 2.195951 |
| 0.979391 | 2.195939 |
| 0.988488 | 2.195927 |
| 0.997669 | 2.195915 |
| 1.00694 | 2.195904 |
| 1.01629 | 2.195892 |
| 1.02573 | 2.19588 |
| 1.03526 | 2.195869 |
| 1.04487 | 2.195857 |
| 1.05458 | 2.195846 |
| 1.06437 | 2.195835 |
| 1.07426 | 2.195824 |
| 1.08423 | 2.195812 |
| 1.09431 | 2.195801 |
| 1.10447 | 2.19579 |
| 1.11473 | 2.195779 |
| 1.12508 | 2.195768 |
| 1.13553 | 2.195757 |
| 1.14608 | 2.195746 |
| 1.15672 | 2.195735 |
| 1.16747 | 2.195724 |
| 1.17831 | 2.195713 |
| 1.18926 | 2.195702 |
| 1.2003 | 2.195691 |
| 1.21145 | 2.19568 |
| 1.2227 | 2.19567 |
| 1.23406 | 2.195659 |
| 1.24552 | 2.195648 |
| 1.25709 | 2.195637 |
| 1.26877 | 2.195626 |
| 1.28055 | 2.195615 |
| 1.29244 | 2.195604 |
| 1.30445 | 2.195593 |
| 1.31656 | 2.195582 |
| 1.32879 | 2.195571 |
| 1.34114 | 2.19556 |
| 1.35359 | 2.195549 |
| 1.36616 | 2.195538 |
| 1.37885 | 2.195526 |
| 1.39166 | 2.195515 |
| 1.40459 | 2.195504 |
| 1.41763 | 2.195492 |
| 1.4308 | 2.195481 |
| 1.44409 | 2.195469 |
| 1.4575 | 2.195458 |
| 1.47104 | 2.195446 |
| 1.4847 | 2.195434 |
| 1.49849 | 2.195423 |
| 1.51241 | 2.195411 |
| 1.52646 | 2.195399 |
| 1.54064 | 2.195387 |
| 1.55495 | 2.195374 |
| 1.56939 | 2.195362 |
| 1.58397 | 2.19535 |
| 1.59868 | 2.195337 |
| 1.61353 | 2.195324 |
| 1.62851 | 2.195312 |
| 1.64364 | 2.195299 |
| 1.65891 | 2.195286 |
| 1.67431 | 2.195273 |
| 1.68987 | 2.195259 |
| 1.70556 | 2.195246 |
| 1.7214 | 2.195232 |
| 1.73739 | 2.195219 |
| 1.75353 | 2.195205 |
| 1.76982 | 2.195191 |
| 1.78625 | 2.195176 |
| 1.80285 | 2.195162 |
| 1.81959 | 2.195147 |
| 1.83649 | 2.195133 |
| 1.85355 | 2.195118 |
| 1.87077 | 2.195103 |
| 1.88814 | 2.195087 |
| 1.90568 | 2.195072 |
| 1.92338 | 2.195056 |
| 1.94124 | 2.19504 |
| 1.95927 | 2.195024 |
| 1.97747 | 2.195008 |
| 1.99584 | 2.194991 |
| 2.01438 | 2.194974 |
| 2.03309 | 2.194957 |
| 2.05197 | 2.19494 |
| 2.07103 | 2.194922 |
| 2.09027 | 2.194904 |
| 2.10968 | 2.194886 |
| 2.12928 | 2.194868 |
| 2.14905 | 2.194849 |
| 2.16901 | 2.19483 |
| 2.18916 | 2.194811 |
| 2.20949 | 2.194791 |
| 2.23002 | 2.194772 |
| 2.25073 | 2.194751 |
| 2.27163 | 2.194731 |
| 2.29273 | 2.19471 |
| 2.31403 | 2.194689 |
| 2.33552 | 2.194668 |
| 2.35721 | 2.194646 |
| 2.37911 | 2.194624 |
| 2.40121 | 2.194601 |
| 2.42351 | 2.194578 |
| 2.44602 | 2.194555 |
| 2.46874 | 2.194531 |
| 2.49167 | 2.194507 |
| 2.51481 | 2.194483 |
| 2.53817 | 2.194458 |
| 2.56174 | 2.194433 |
| 2.58554 | 2.194407 |
| 2.60955 | 2.194381 |
| 2.63379 | 2.194354 |
| 2.65825 | 2.194327 |
| 2.68294 | 2.1943 |
| 2.70786 | 2.194272 |
| 2.73302 | 2.194244 |
| 2.7584 | 2.194215 |
| 2.78402 | 2.194185 |
| 2.80988 | 2.194155 |
| 2.83598 | 2.194125 |
| 2.86232 | 2.194094 |
| 2.8889 | 2.194062 |
| 2.91574 | 2.19403 |
| 2.94282 | 2.193998 |
| 2.97015 | 2.193964 |
| 2.99774 | 2.193931 |
| 3.02558 | 2.193896 |
| 3.05369 | 2.193861 |
| 3.08205 | 2.193825 |
| 3.11068 | 2.193789 |
| 3.13957 | 2.193752 |
| 3.16873 | 2.193715 |
| 3.19816 | 2.193676 |
| 3.22787 | 2.193637 |
| 3.25785 | 2.193598 |
| 3.28811 | 2.193558 |
| 3.31865 | 2.193516 |
| 3.34947 | 2.193475 |
| 3.38058 | 2.193432 |
| 3.41198 | 2.193389 |
| 3.44367 | 2.193345 |
| 3.47566 | 2.1933 |
| 3.50794 | 2.193254 |
| 3.54052 | 2.193207 |
| 3.57341 | 2.19316 |
| 3.6066 | 2.193112 |
| 3.6401 | 2.193063 |
| 3.67391 | 2.193013 |
| 3.70803 | 2.192962 |
| 3.74247 | 2.19291 |
| 3.77723 | 2.192857 |
| 3.81232 | 2.192803 |
| 3.84773 | 2.192748 |
| 3.88346 | 2.192692 |
| 3.91953 | 2.192636 |
| 3.95594 | 2.192578 |
| 3.99268 | 2.192519 |
| 4.02977 | 2.192459 |
| 4.0672 | 2.192398 |
| 4.10497 | 2.192336 |
| 4.1431 | 2.192272 |
| 4.18158 | 2.192208 |
| 4.22042 | 2.192142 |
| 4.25962 | 2.192075 |
| 4.29919 | 2.192007 |
| 4.33912 | 2.191937 |
| 4.37942 | 2.191867 |
| 4.4201 | 2.191795 |
| 4.46115 | 2.191721 |
| 4.50259 | 2.191647 |
| 4.54441 | 2.19157 |
| 4.58662 | 2.191493 |
| 4.62922 | 2.191414 |
| 4.67222 | 2.191334 |
| 4.71561 | 2.191252 |
| 4.75941 | 2.191168 |
| 4.80362 | 2.191083 |
| 4.84824 | 2.190997 |
| 4.89327 | 2.190909 |
| 4.93872 | 2.190819 |
| 4.98459 | 2.190727 |
| 5.03089 | 2.190634 |
| 5.07761 | 2.190539 |
| 5.12478 | 2.190443 |
| 5.17238 | 2.190344 |
| 5.22042 | 2.190244 |
| 5.26891 | 2.190142 |
| 5.31784 | 2.190038 |
| 5.36724 | 2.189932 |
| 5.41709 | 2.189824 |
| 5.4674 | 2.189714 |
| 5.51819 | 2.189602 |
| 5.56944 | 2.189488 |
| 5.62117 | 2.189372 |
| 5.67338 | 2.189254 |
| 5.72608 | 2.189133 |
| 5.77926 | 2.18901 |
| 5.83294 | 2.188885 |
| 5.88712 | 2.188758 |
| 5.9418 | 2.188628 |
| 5.99699 | 2.188496 |
| 6.05269 | 2.188361 |
| 6.10891 | 2.188224 |
| 6.16565 | 2.188084 |
| 6.22291 | 2.187941 |
| 6.28071 | 2.187796 |
| 6.33905 | 2.187649 |
| 6.39793 | 2.187498 |
| 6.45735 | 2.187345 |
| 6.51733 | 2.187189 |
| 6.57786 | 2.187029 |
| 6.63896 | 2.186867 |
| 6.70062 | 2.186702 |
| 6.76286 | 2.186534 |
| 6.82568 | 2.186363 |
| 6.88907 | 2.186188 |
| 6.95306 | 2.18601 |
| 7.01764 | 2.185829 |
| 7.08282 | 2.185645 |
| 7.14861 | 2.185457 |
| 7.21501 | 2.185265 |
| 7.28202 | 2.18507 |
| 7.34966 | 2.184871 |
| 7.41792 | 2.184669 |
| 7.48682 | 2.184462 |
| 7.55636 | 2.184252 |
| 7.62655 | 2.184038 |
| 7.69738 | 2.18382 |
| 7.76888 | 2.183598 |
| 7.84104 | 2.183372 |
| 7.91387 | 2.183141 |
| 7.98737 | 2.182906 |
| 8.06156 | 2.182667 |
| 8.13644 | 2.182423 |
| 8.21201 | 2.182175 |
| 8.28828 | 2.181922 |
| 8.36527 | 2.181664 |
| 8.44297 | 2.181401 |
| 8.52139 | 2.181134 |
| 8.60053 | 2.180861 |
| 8.68042 | 2.180583 |
| 8.76104 | 2.1803 |
| 8.84242 | 2.180012 |
| 8.92455 | 2.179719 |
| 9.00744 | 2.179419 |
| 9.0911 | 2.179115 |
| 9.17554 | 2.178804 |
| 9.26077 | 2.178488 |
| 9.34678 | 2.178166 |
| 9.4336 | 2.177837 |
| 9.52122 | 2.177503 |
| 9.60965 | 2.177162 |
| 9.69891 | 2.176815 |
| 9.78899 | 2.176461 |
| 9.87991 | 2.1761 |
| 9.97168 | 2.175733 |
| 10.0643 | 2.175359 |
| 10.1578 | 2.174978 |
| 10.2521 | 2.17459 |
| 10.3473 | 2.174194 |
| 10.4435 | 2.173791 |
| 10.5405 | 2.17338 |
| 10.6384 | 2.172962 |
| 10.7372 | 2.172535 |
| 10.8369 | 2.172101 |
| 10.9376 | 2.171658 |
| 11.0391 | 2.171208 |
| 11.1417 | 2.170748 |
| 11.2452 | 2.17028 |
| 11.3496 | 2.169803 |
| 11.455 | 2.169317 |
| 11.5614 | 2.168822 |
| 11.6688 | 2.168317 |
| 11.7772 | 2.167803 |
| 11.8866 | 2.16728 |
| 11.997 | 2.166746 |
| 12.1084 | 2.166202 |
| 12.2209 | 2.165648 |
| 12.3344 | 2.165084 |
| 12.449 | 2.164509 |
| 12.5646 | 2.163923 |
| 12.6813 | 2.163325 |
| 12.7991 | 2.162717 |
| 12.918 | 2.162097 |
| 13.0379 | 2.161465 |
| 13.159 | 2.160821 |
| 13.2813 | 2.160166 |
| 13.4046 | 2.159497 |
| 13.5291 | 2.158816 |
| 13.6548 | 2.158122 |
| 13.7816 | 2.157415 |
| 13.9096 | 2.156694 |
| 14.0388 | 2.15596 |
| 14.1692 | 2.155212 |
| 14.3008 | 2.154449 |
| 14.4336 | 2.153672 |
| 14.5677 | 2.15288 |
| 14.703 | 2.152073 |
| 14.8396 | 2.151251 |
| 14.9774 | 2.150413 |
| 15.1165 | 2.149559 |
| 15.2569 | 2.148689 |
| 15.3986 | 2.147803 |
| 15.5417 | 2.146899 |
| 15.686 | 2.145978 |
| 15.8317 | 2.145039 |
| 15.9788 | 2.144083 |
| 16.1272 | 2.143108 |
| 16.277 | 2.142115 |
| 16.4281 | 2.141102 |
| 16.5807 | 2.14007 |
| 16.7347 | 2.139019 |
| 16.8902 | 2.137947 |
| 17.0471 | 2.136855 |
| 17.2054 | 2.135742 |
| 17.3652 | 2.134607 |
| 17.5265 | 2.133451 |
| 17.6893 | 2.132272 |
| 17.8536 | 2.131071 |
| 18.0194 | 2.129846 |
| 18.1868 | 2.128598 |
| 18.3557 | 2.127326 |
| 18.5262 | 2.12603 |
| 18.6983 | 2.124708 |
| 18.8719 | 2.123361 |
| 19.0472 | 2.121988 |
| 19.2241 | 2.120588 |
| 19.4027 | 2.119162 |
| 19.5829 | 2.117707 |
| 19.7648 | 2.116225 |
| 19.9484 | 2.114714 |
| 20.1337 | 2.113173 |
| 20.3207 | 2.111603 |
| 20.5094 | 2.110002 |
| 20.6999 | 2.10837 |
| 20.8922 | 2.106706 |
| 21.0862 | 2.10501 |
| 21.2821 | 2.10328 |
| 21.4797 | 2.101517 |
| 21.6792 | 2.09972 |
| 21.8806 | 2.097887 |
| 22.0838 | 2.096019 |
| 22.289 | 2.094114 |
| 22.496 | 2.092171 |
| 22.7049 | 2.090191 |
| 22.9158 | 2.088172 |
| 23.1287 | 2.086113 |
| 23.3435 | 2.084013 |
| 23.5603 | 2.081872 |
| 23.7791 | 2.079689 |
| 24 | 2.077463 |
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
- —