Optical constants
Refractive index of CsBr (Cesium bromide)
Rodney and Spindler 1953: n 0.365–39 µm; 27 °C
- Data
- formula 1
- Range
- 0.365–39 µm
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.69706
- Extinction coefficient k
- 0
- Permittivity ε1
- 2.88
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 34.108
- Chromatic dispersion dn/dλ
- -0.103672 µm⁻¹
- Group index ng
- 1.75797
- Group velocity dispersion
- 206.312 fs²/mm
- Dispersion parameter D
- -1125.54 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
# CsBr (Cesium bromide): Rodney and Spindler 1953: n 0.365–39 µm; 27 °C
csbr = ls.fetch_refractiveindex("main", "CsBr", "Rodney", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(csbr.range_nm) # (365, 39000) nm
eps = csbr.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_51a710a88bab/lightsmith"
csbr = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(csbr.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (csbr/rodney-spindler-1953).
# ... load csbr as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=csbr)],
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"]).
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_51a710a88bab/lightsmith?model=drude_lorentz"
csbr_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))
A dispersive Drude–Lorentz model for time-domain solvers.
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
Sellmeier (formula 1), λ in µmValid from 0.365 to 39.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 0.9533786 |
| C3 | 0.0905643 |
| C4 | 0.8303809 |
| C5 | 0.1671517 |
| C6 | 2.847172 |
| C7 | 119.0155 |
Comments and conditions
References
Cite
W. S. Rodney and R. J. Spindler. Refractive index of cesium bromide for ultraviolet, visible, and infrared wavelengths, J. Res. Nat. Bur. Stand. 51, 123-126 (1953); 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 |
|---|---|
| 0.365 | 1.751181 |
| 0.369298 | 1.748909 |
| 0.373648 | 1.746709 |
| 0.378048 | 1.744578 |
| 0.3825 | 1.742514 |
| 0.387005 | 1.740515 |
| 0.391562 | 1.738578 |
| 0.396173 | 1.7367 |
| 0.400839 | 1.734879 |
| 0.40556 | 1.733113 |
| 0.410336 | 1.731401 |
| 0.415168 | 1.72974 |
| 0.420057 | 1.728127 |
| 0.425004 | 1.726563 |
| 0.430009 | 1.725044 |
| 0.435073 | 1.72357 |
| 0.440197 | 1.722138 |
| 0.445381 | 1.720748 |
| 0.450626 | 1.719398 |
| 0.455933 | 1.718086 |
| 0.461302 | 1.716811 |
| 0.466735 | 1.715572 |
| 0.472232 | 1.714368 |
| 0.477793 | 1.713198 |
| 0.48342 | 1.71206 |
| 0.489113 | 1.710953 |
| 0.494873 | 1.709878 |
| 0.500701 | 1.708831 |
| 0.506597 | 1.707814 |
| 0.512563 | 1.706824 |
| 0.518599 | 1.705861 |
| 0.524707 | 1.704924 |
| 0.530886 | 1.704012 |
| 0.537138 | 1.703124 |
| 0.543464 | 1.70226 |
| 0.549864 | 1.70142 |
| 0.55634 | 1.700601 |
| 0.562891 | 1.699805 |
| 0.56952 | 1.699029 |
| 0.576227 | 1.698273 |
| 0.583013 | 1.697538 |
| 0.589879 | 1.696821 |
| 0.596826 | 1.696123 |
| 0.603855 | 1.695444 |
| 0.610966 | 1.694782 |
| 0.618161 | 1.694137 |
| 0.625441 | 1.693508 |
| 0.632807 | 1.692896 |
| 0.640259 | 1.692299 |
| 0.647799 | 1.691718 |
| 0.655428 | 1.691152 |
| 0.663147 | 1.690599 |
| 0.670956 | 1.690061 |
| 0.678858 | 1.689537 |
| 0.686852 | 1.689025 |
| 0.694941 | 1.688527 |
| 0.703125 | 1.688041 |
| 0.711406 | 1.687567 |
| 0.719784 | 1.687105 |
| 0.72826 | 1.686655 |
| 0.736837 | 1.686216 |
| 0.745514 | 1.685788 |
| 0.754294 | 1.68537 |
| 0.763177 | 1.684963 |
| 0.772165 | 1.684566 |
| 0.781258 | 1.684178 |
| 0.790459 | 1.683801 |
| 0.799768 | 1.683432 |
| 0.809186 | 1.683073 |
| 0.818716 | 1.682722 |
| 0.828357 | 1.68238 |
| 0.838113 | 1.682046 |
| 0.847983 | 1.68172 |
| 0.857969 | 1.681403 |
| 0.868073 | 1.681093 |
| 0.878296 | 1.68079 |
| 0.888639 | 1.680495 |
| 0.899105 | 1.680207 |
| 0.909693 | 1.679926 |
| 0.920406 | 1.679652 |
| 0.931245 | 1.679384 |
| 0.942212 | 1.679123 |
| 0.953308 | 1.678868 |
| 0.964535 | 1.678619 |
| 0.975894 | 1.678376 |
| 0.987387 | 1.678139 |
| 0.999015 | 1.677908 |
| 1.01078 | 1.677682 |
| 1.02268 | 1.677461 |
| 1.03473 | 1.677246 |
| 1.04691 | 1.677036 |
| 1.05924 | 1.676831 |
| 1.07172 | 1.67663 |
| 1.08434 | 1.676434 |
| 1.09711 | 1.676243 |
| 1.11003 | 1.676057 |
| 1.1231 | 1.675875 |
| 1.13633 | 1.675697 |
| 1.14971 | 1.675523 |
| 1.16325 | 1.675353 |
| 1.17695 | 1.675188 |
| 1.19081 | 1.675026 |
| 1.20483 | 1.674868 |
| 1.21902 | 1.674713 |
| 1.23338 | 1.674562 |
| 1.2479 | 1.674415 |
| 1.2626 | 1.674271 |
| 1.27747 | 1.67413 |
| 1.29251 | 1.673993 |
| 1.30773 | 1.673858 |
| 1.32313 | 1.673727 |
| 1.33871 | 1.673599 |
| 1.35448 | 1.673474 |
| 1.37043 | 1.673351 |
| 1.38657 | 1.673231 |
| 1.4029 | 1.673114 |
| 1.41942 | 1.673 |
| 1.43614 | 1.672888 |
| 1.45305 | 1.672779 |
| 1.47016 | 1.672672 |
| 1.48748 | 1.672567 |
| 1.50499 | 1.672465 |
| 1.52272 | 1.672365 |
| 1.54065 | 1.672268 |
| 1.55879 | 1.672172 |
| 1.57715 | 1.672079 |
| 1.59572 | 1.671987 |
| 1.61452 | 1.671898 |
| 1.63353 | 1.67181 |
| 1.65277 | 1.671724 |
| 1.67223 | 1.671641 |
| 1.69192 | 1.671559 |
| 1.71185 | 1.671478 |
| 1.73201 | 1.6714 |
| 1.75241 | 1.671323 |
| 1.77304 | 1.671247 |
| 1.79392 | 1.671174 |
| 1.81505 | 1.671101 |
| 1.83643 | 1.67103 |
| 1.85805 | 1.670961 |
| 1.87993 | 1.670893 |
| 1.90207 | 1.670826 |
| 1.92447 | 1.670761 |
| 1.94714 | 1.670697 |
| 1.97007 | 1.670634 |
| 1.99327 | 1.670573 |
| 2.01674 | 1.670512 |
| 2.04049 | 1.670453 |
| 2.06452 | 1.670395 |
| 2.08884 | 1.670338 |
| 2.11344 | 1.670282 |
| 2.13832 | 1.670227 |
| 2.16351 | 1.670173 |
| 2.18899 | 1.67012 |
| 2.21476 | 1.670068 |
| 2.24085 | 1.670017 |
| 2.26724 | 1.669966 |
| 2.29394 | 1.669917 |
| 2.32095 | 1.669868 |
| 2.34828 | 1.66982 |
| 2.37594 | 1.669773 |
| 2.40392 | 1.669727 |
| 2.43223 | 1.669681 |
| 2.46087 | 1.669636 |
| 2.48985 | 1.669591 |
| 2.51918 | 1.669548 |
| 2.54884 | 1.669504 |
| 2.57886 | 1.669462 |
| 2.60923 | 1.66942 |
| 2.63996 | 1.669378 |
| 2.67105 | 1.669337 |
| 2.7025 | 1.669297 |
| 2.73433 | 1.669257 |
| 2.76653 | 1.669217 |
| 2.79911 | 1.669178 |
| 2.83208 | 1.669139 |
| 2.86543 | 1.669101 |
| 2.89917 | 1.669063 |
| 2.93332 | 1.669025 |
| 2.96786 | 1.668987 |
| 3.00281 | 1.66895 |
| 3.03818 | 1.668913 |
| 3.07396 | 1.668877 |
| 3.11016 | 1.66884 |
| 3.14678 | 1.668804 |
| 3.18384 | 1.668768 |
| 3.22134 | 1.668732 |
| 3.25927 | 1.668697 |
| 3.29766 | 1.668661 |
| 3.33649 | 1.668626 |
| 3.37578 | 1.668591 |
| 3.41554 | 1.668555 |
| 3.45576 | 1.66852 |
| 3.49646 | 1.668485 |
| 3.53764 | 1.66845 |
| 3.5793 | 1.668415 |
| 3.62145 | 1.66838 |
| 3.6641 | 1.668344 |
| 3.70725 | 1.668309 |
| 3.75091 | 1.668274 |
| 3.79508 | 1.668238 |
| 3.83977 | 1.668203 |
| 3.88499 | 1.668167 |
| 3.93075 | 1.668131 |
| 3.97704 | 1.668095 |
| 4.02387 | 1.668059 |
| 4.07126 | 1.668022 |
| 4.11921 | 1.667985 |
| 4.16772 | 1.667948 |
| 4.2168 | 1.667911 |
| 4.26646 | 1.667874 |
| 4.3167 | 1.667836 |
| 4.36754 | 1.667797 |
| 4.41897 | 1.667759 |
| 4.47101 | 1.66772 |
| 4.52367 | 1.66768 |
| 4.57694 | 1.667641 |
| 4.63084 | 1.6676 |
| 4.68538 | 1.667559 |
| 4.74056 | 1.667518 |
| 4.79638 | 1.667476 |
| 4.85287 | 1.667434 |
| 4.91002 | 1.667391 |
| 4.96784 | 1.667348 |
| 5.02635 | 1.667304 |
| 5.08554 | 1.667259 |
| 5.14543 | 1.667213 |
| 5.20603 | 1.667167 |
| 5.26734 | 1.66712 |
| 5.32937 | 1.667073 |
| 5.39213 | 1.667025 |
| 5.45563 | 1.666975 |
| 5.51988 | 1.666926 |
| 5.58488 | 1.666875 |
| 5.65066 | 1.666823 |
| 5.7172 | 1.66677 |
| 5.78453 | 1.666717 |
| 5.85265 | 1.666663 |
| 5.92158 | 1.666607 |
| 5.99131 | 1.666551 |
| 6.06187 | 1.666493 |
| 6.13326 | 1.666434 |
| 6.20549 | 1.666375 |
| 6.27857 | 1.666314 |
| 6.35251 | 1.666251 |
| 6.42732 | 1.666188 |
| 6.50301 | 1.666124 |
| 6.5796 | 1.666058 |
| 6.65708 | 1.66599 |
| 6.73548 | 1.665922 |
| 6.8148 | 1.665852 |
| 6.89506 | 1.66578 |
| 6.97626 | 1.665707 |
| 7.05841 | 1.665633 |
| 7.14154 | 1.665557 |
| 7.22564 | 1.665479 |
| 7.31073 | 1.6654 |
| 7.39683 | 1.665319 |
| 7.48394 | 1.665236 |
| 7.57207 | 1.665151 |
| 7.66125 | 1.665065 |
| 7.75147 | 1.664977 |
| 7.84276 | 1.664886 |
| 7.93512 | 1.664794 |
| 8.02857 | 1.6647 |
| 8.12312 | 1.664603 |
| 8.21878 | 1.664505 |
| 8.31557 | 1.664404 |
| 8.4135 | 1.664301 |
| 8.51258 | 1.664196 |
| 8.61283 | 1.664088 |
| 8.71426 | 1.663978 |
| 8.81689 | 1.663865 |
| 8.92072 | 1.66375 |
| 9.02577 | 1.663632 |
| 9.13207 | 1.663511 |
| 9.23961 | 1.663388 |
| 9.34842 | 1.663262 |
| 9.45852 | 1.663132 |
| 9.56991 | 1.663 |
| 9.68261 | 1.662865 |
| 9.79664 | 1.662727 |
| 9.91201 | 1.662585 |
| 10.0287 | 1.66244 |
| 10.1468 | 1.662292 |
| 10.2663 | 1.66214 |
| 10.3872 | 1.661985 |
| 10.5096 | 1.661826 |
| 10.6333 | 1.661663 |
| 10.7586 | 1.661496 |
| 10.8853 | 1.661326 |
| 11.0134 | 1.661151 |
| 11.1432 | 1.660973 |
| 11.2744 | 1.66079 |
| 11.4072 | 1.660602 |
| 11.5415 | 1.660411 |
| 11.6774 | 1.660214 |
| 11.8149 | 1.660013 |
| 11.9541 | 1.659807 |
| 12.0949 | 1.659597 |
| 12.2373 | 1.659381 |
| 12.3814 | 1.65916 |
| 12.5272 | 1.658933 |
| 12.6747 | 1.658702 |
| 12.824 | 1.658464 |
| 12.975 | 1.658221 |
| 13.1278 | 1.657972 |
| 13.2824 | 1.657717 |
| 13.4389 | 1.657456 |
| 13.5971 | 1.657188 |
| 13.7572 | 1.656915 |
| 13.9193 | 1.656634 |
| 14.0832 | 1.656346 |
| 14.249 | 1.656052 |
| 14.4168 | 1.65575 |
| 14.5866 | 1.655441 |
| 14.7584 | 1.655125 |
| 14.9322 | 1.6548 |
| 15.1081 | 1.654468 |
| 15.286 | 1.654127 |
| 15.466 | 1.653779 |
| 15.6481 | 1.653421 |
| 15.8324 | 1.653055 |
| 16.0189 | 1.65268 |
| 16.2075 | 1.652295 |
| 16.3984 | 1.651901 |
| 16.5915 | 1.651497 |
| 16.7869 | 1.651083 |
| 16.9846 | 1.650659 |
| 17.1846 | 1.650225 |
| 17.387 | 1.649779 |
| 17.5917 | 1.649323 |
| 17.7989 | 1.648855 |
| 18.0085 | 1.648375 |
| 18.2206 | 1.647883 |
| 18.4352 | 1.647379 |
| 18.6523 | 1.646863 |
| 18.872 | 1.646333 |
| 19.0942 | 1.64579 |
| 19.3191 | 1.645233 |
| 19.5466 | 1.644662 |
| 19.7768 | 1.644077 |
| 20.0097 | 1.643477 |
| 20.2453 | 1.642861 |
| 20.4837 | 1.64223 |
| 20.725 | 1.641583 |
| 20.969 | 1.640919 |
| 21.216 | 1.640239 |
| 21.4658 | 1.639541 |
| 21.7186 | 1.638824 |
| 21.9744 | 1.63809 |
| 22.2332 | 1.637336 |
| 22.495 | 1.636563 |
| 22.7599 | 1.63577 |
| 23.028 | 1.634956 |
| 23.2992 | 1.634121 |
| 23.5736 | 1.633265 |
| 23.8512 | 1.632385 |
| 24.1321 | 1.631483 |
| 24.4163 | 1.630557 |
| 24.7038 | 1.629607 |
| 24.9947 | 1.628631 |
| 25.2891 | 1.62763 |
| 25.5869 | 1.626602 |
| 25.8882 | 1.625547 |
| 26.1931 | 1.624463 |
| 26.5016 | 1.62335 |
| 26.8137 | 1.622208 |
| 27.1294 | 1.621034 |
| 27.4489 | 1.619829 |
| 27.7722 | 1.618591 |
| 28.0992 | 1.61732 |
| 28.4302 | 1.616013 |
| 28.765 | 1.614671 |
| 29.1037 | 1.613292 |
| 29.4465 | 1.611875 |
| 29.7932 | 1.610418 |
| 30.1441 | 1.608921 |
| 30.4991 | 1.607382 |
| 30.8583 | 1.6058 |
| 31.2217 | 1.604173 |
| 31.5894 | 1.602501 |
| 31.9614 | 1.60078 |
| 32.3378 | 1.599011 |
| 32.7186 | 1.597191 |
| 33.1039 | 1.595319 |
| 33.4938 | 1.593392 |
| 33.8882 | 1.591409 |
| 34.2873 | 1.589369 |
| 34.6911 | 1.587268 |
| 35.0997 | 1.585106 |
| 35.513 | 1.582879 |
| 35.9312 | 1.580585 |
| 36.3544 | 1.578223 |
| 36.7825 | 1.57579 |
| 37.2157 | 1.573282 |
| 37.654 | 1.570698 |
| 38.0974 | 1.568035 |
| 38.5461 | 1.565289 |
| 39 | 1.562457 |
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
- —
27 °C