Optical constants
Refractive index of BN (Boron nitride)
Rah et al. 2019: h-BN; n(e) 0.4–1.6 µm
- Data
- formula 2
- Range
- 0.4–1.6 µm
- Optical axis
- e
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.85875
- Extinction coefficient k
- 0
- Permittivity ε1
- 3.45494
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 22.829
- Chromatic dispersion dn/dλ
- -0.190533 µm⁻¹
- Group index ng
- 1.9707
- Group velocity dispersion
- 381.973 fs²/mm
- Dispersion parameter D
- -2083.86 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
# BN (Boron nitride): Rah et al. 2019: h-BN; n(e) 0.4–1.6 µm
bn = ls.fetch_refractiveindex("main", "BN", "Rah-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bn.range_nm) # (400, 1600) nm
eps = bn.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_492f1e773bcd/lightsmith"
bn = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bn.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (bn/rah-2019-e).
# ... load bn as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bn)],
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_492f1e773bcd/lightsmith?model=drude_lorentz"
bn_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 (C in µm²) (formula 2), λ in µmValid from 0.4 to 1.6 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 0.0 |
| C2 | 2.2631 |
| C3 | 0.026981 |
Comments and conditions
Conditions
- direction
- e
References
- doi:10.1364/ol.44.003797 Optical analysis of the refractive index and birefringence of hexagonal boron nitride from the visible to near-infrared, Optics Letters (2019)
Cite
Yoonhyuk Rah, Yeonghoon Jin, Sejeong Kim and Kyoungsik Yu. Optical analysis of the refractive index and birefringence of hexagonal boron nitride from the visible to near-infrared. Optics Letters, 44, 3797 (2019), doi:10.1364/ol.44.003797; 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 | 1.929284 |
| 0.401392 | 1.928294 |
| 0.402789 | 1.927314 |
| 0.404191 | 1.926342 |
| 0.405598 | 1.925379 |
| 0.40701 | 1.924425 |
| 0.408426 | 1.92348 |
| 0.409848 | 1.922543 |
| 0.411274 | 1.921615 |
| 0.412706 | 1.920695 |
| 0.414142 | 1.919784 |
| 0.415583 | 1.918881 |
| 0.41703 | 1.917986 |
| 0.418481 | 1.917099 |
| 0.419938 | 1.91622 |
| 0.421399 | 1.915348 |
| 0.422866 | 1.914485 |
| 0.424338 | 1.913629 |
| 0.425815 | 1.912781 |
| 0.427297 | 1.911941 |
| 0.428784 | 1.911108 |
| 0.430276 | 1.910282 |
| 0.431774 | 1.909464 |
| 0.433277 | 1.908653 |
| 0.434785 | 1.907849 |
| 0.436298 | 1.907052 |
| 0.437816 | 1.906262 |
| 0.43934 | 1.905479 |
| 0.440869 | 1.904703 |
| 0.442404 | 1.903933 |
| 0.443943 | 1.903171 |
| 0.445489 | 1.902415 |
| 0.447039 | 1.901666 |
| 0.448595 | 1.900923 |
| 0.450156 | 1.900186 |
| 0.451723 | 1.899456 |
| 0.453295 | 1.898733 |
| 0.454873 | 1.898015 |
| 0.456456 | 1.897304 |
| 0.458045 | 1.896599 |
| 0.459639 | 1.895899 |
| 0.461239 | 1.895206 |
| 0.462844 | 1.894519 |
| 0.464455 | 1.893838 |
| 0.466072 | 1.893162 |
| 0.467694 | 1.892493 |
| 0.469321 | 1.891829 |
| 0.470955 | 1.89117 |
| 0.472594 | 1.890518 |
| 0.474239 | 1.88987 |
| 0.475889 | 1.889229 |
| 0.477546 | 1.888592 |
| 0.479208 | 1.887961 |
| 0.480876 | 1.887336 |
| 0.482549 | 1.886715 |
| 0.484229 | 1.8861 |
| 0.485914 | 1.88549 |
| 0.487605 | 1.884885 |
| 0.489303 | 1.884285 |
| 0.491006 | 1.88369 |
| 0.492714 | 1.883101 |
| 0.494429 | 1.882516 |
| 0.49615 | 1.881936 |
| 0.497877 | 1.88136 |
| 0.49961 | 1.88079 |
| 0.501349 | 1.880224 |
| 0.503094 | 1.879663 |
| 0.504845 | 1.879107 |
| 0.506602 | 1.878555 |
| 0.508365 | 1.878008 |
| 0.510134 | 1.877465 |
| 0.51191 | 1.876927 |
| 0.513692 | 1.876393 |
| 0.515479 | 1.875864 |
| 0.517274 | 1.875339 |
| 0.519074 | 1.874818 |
| 0.52088 | 1.874301 |
| 0.522693 | 1.873789 |
| 0.524513 | 1.873281 |
| 0.526338 | 1.872777 |
| 0.52817 | 1.872277 |
| 0.530008 | 1.871781 |
| 0.531853 | 1.871289 |
| 0.533704 | 1.870802 |
| 0.535562 | 1.870318 |
| 0.537426 | 1.869838 |
| 0.539296 | 1.869362 |
| 0.541173 | 1.86889 |
| 0.543057 | 1.868421 |
| 0.544947 | 1.867957 |
| 0.546843 | 1.867496 |
| 0.548747 | 1.867039 |
| 0.550657 | 1.866585 |
| 0.552573 | 1.866136 |
| 0.554496 | 1.865689 |
| 0.556426 | 1.865247 |
| 0.558363 | 1.864808 |
| 0.560306 | 1.864372 |
| 0.562256 | 1.86394 |
| 0.564213 | 1.863511 |
| 0.566177 | 1.863086 |
| 0.568148 | 1.862664 |
| 0.570125 | 1.862246 |
| 0.572109 | 1.861831 |
| 0.5741 | 1.861419 |
| 0.576099 | 1.86101 |
| 0.578104 | 1.860605 |
| 0.580116 | 1.860203 |
| 0.582135 | 1.859804 |
| 0.584161 | 1.859408 |
| 0.586194 | 1.859015 |
| 0.588234 | 1.858626 |
| 0.590282 | 1.858239 |
| 0.592336 | 1.857856 |
| 0.594398 | 1.857475 |
| 0.596466 | 1.857098 |
| 0.598542 | 1.856723 |
| 0.600626 | 1.856352 |
| 0.602716 | 1.855983 |
| 0.604814 | 1.855618 |
| 0.606919 | 1.855255 |
| 0.609031 | 1.854895 |
| 0.611151 | 1.854537 |
| 0.613278 | 1.854183 |
| 0.615413 | 1.853831 |
| 0.617554 | 1.853482 |
| 0.619704 | 1.853136 |
| 0.621861 | 1.852793 |
| 0.624025 | 1.852452 |
| 0.626197 | 1.852114 |
| 0.628376 | 1.851778 |
| 0.630563 | 1.851445 |
| 0.632758 | 1.851115 |
| 0.63496 | 1.850787 |
| 0.63717 | 1.850462 |
| 0.639388 | 1.850139 |
| 0.641613 | 1.849818 |
| 0.643847 | 1.849501 |
| 0.646087 | 1.849185 |
| 0.648336 | 1.848872 |
| 0.650593 | 1.848562 |
| 0.652857 | 1.848254 |
| 0.655129 | 1.847948 |
| 0.657409 | 1.847645 |
| 0.659697 | 1.847344 |
| 0.661993 | 1.847045 |
| 0.664298 | 1.846748 |
| 0.66661 | 1.846454 |
| 0.66893 | 1.846162 |
| 0.671258 | 1.845872 |
| 0.673594 | 1.845585 |
| 0.675939 | 1.8453 |
| 0.678291 | 1.845017 |
| 0.680652 | 1.844736 |
| 0.683021 | 1.844457 |
| 0.685398 | 1.84418 |
| 0.687784 | 1.843905 |
| 0.690177 | 1.843633 |
| 0.69258 | 1.843363 |
| 0.69499 | 1.843094 |
| 0.697409 | 1.842828 |
| 0.699836 | 1.842564 |
| 0.702272 | 1.842301 |
| 0.704716 | 1.842041 |
| 0.707169 | 1.841783 |
| 0.70963 | 1.841526 |
| 0.7121 | 1.841272 |
| 0.714579 | 1.841019 |
| 0.717066 | 1.840769 |
| 0.719561 | 1.84052 |
| 0.722066 | 1.840273 |
| 0.724579 | 1.840028 |
| 0.727101 | 1.839785 |
| 0.729631 | 1.839544 |
| 0.732171 | 1.839304 |
| 0.734719 | 1.839067 |
| 0.737276 | 1.838831 |
| 0.739842 | 1.838597 |
| 0.742417 | 1.838364 |
| 0.745001 | 1.838134 |
| 0.747594 | 1.837905 |
| 0.750196 | 1.837678 |
| 0.752807 | 1.837452 |
| 0.755427 | 1.837228 |
| 0.758057 | 1.837006 |
| 0.760695 | 1.836786 |
| 0.763343 | 1.836567 |
| 0.765999 | 1.83635 |
| 0.768665 | 1.836134 |
| 0.771341 | 1.83592 |
| 0.774025 | 1.835708 |
| 0.776719 | 1.835497 |
| 0.779423 | 1.835288 |
| 0.782135 | 1.835081 |
| 0.784858 | 1.834875 |
| 0.787589 | 1.83467 |
| 0.790331 | 1.834467 |
| 0.793081 | 1.834266 |
| 0.795842 | 1.834066 |
| 0.798611 | 1.833867 |
| 0.801391 | 1.83367 |
| 0.80418 | 1.833474 |
| 0.806979 | 1.83328 |
| 0.809788 | 1.833088 |
| 0.812606 | 1.832896 |
| 0.815434 | 1.832707 |
| 0.818273 | 1.832518 |
| 0.821121 | 1.832331 |
| 0.823978 | 1.832146 |
| 0.826846 | 1.831961 |
| 0.829724 | 1.831778 |
| 0.832612 | 1.831597 |
| 0.83551 | 1.831417 |
| 0.838418 | 1.831238 |
| 0.841336 | 1.83106 |
| 0.844264 | 1.830884 |
| 0.847202 | 1.830709 |
| 0.850151 | 1.830535 |
| 0.85311 | 1.830363 |
| 0.856079 | 1.830192 |
| 0.859059 | 1.830022 |
| 0.862049 | 1.829853 |
| 0.865049 | 1.829686 |
| 0.86806 | 1.82952 |
| 0.871081 | 1.829355 |
| 0.874113 | 1.829191 |
| 0.877155 | 1.829029 |
| 0.880208 | 1.828867 |
| 0.883272 | 1.828707 |
| 0.886346 | 1.828548 |
| 0.889431 | 1.82839 |
| 0.892526 | 1.828234 |
| 0.895633 | 1.828078 |
| 0.89875 | 1.827924 |
| 0.901878 | 1.827771 |
| 0.905017 | 1.827619 |
| 0.908167 | 1.827468 |
| 0.911328 | 1.827318 |
| 0.9145 | 1.827169 |
| 0.917682 | 1.827021 |
| 0.920876 | 1.826875 |
| 0.924081 | 1.826729 |
| 0.927298 | 1.826585 |
| 0.930525 | 1.826441 |
| 0.933764 | 1.826299 |
| 0.937014 | 1.826157 |
| 0.940275 | 1.826017 |
| 0.943548 | 1.825878 |
| 0.946832 | 1.825739 |
| 0.950127 | 1.825602 |
| 0.953434 | 1.825466 |
| 0.956752 | 1.825331 |
| 0.960082 | 1.825196 |
| 0.963424 | 1.825063 |
| 0.966777 | 1.824931 |
| 0.970142 | 1.824799 |
| 0.973518 | 1.824669 |
| 0.976907 | 1.824539 |
| 0.980307 | 1.824411 |
| 0.983719 | 1.824283 |
| 0.987142 | 1.824156 |
| 0.990578 | 1.82403 |
| 0.994026 | 1.823906 |
| 0.997485 | 1.823782 |
| 1.00096 | 1.823659 |
| 1.00444 | 1.823536 |
| 1.00794 | 1.823415 |
| 1.01144 | 1.823295 |
| 1.01497 | 1.823175 |
| 1.0185 | 1.823056 |
| 1.02204 | 1.822939 |
| 1.0256 | 1.822822 |
| 1.02917 | 1.822706 |
| 1.03275 | 1.82259 |
| 1.03635 | 1.822476 |
| 1.03995 | 1.822362 |
| 1.04357 | 1.822249 |
| 1.0472 | 1.822137 |
| 1.05085 | 1.822026 |
| 1.05451 | 1.821916 |
| 1.05818 | 1.821806 |
| 1.06186 | 1.821697 |
| 1.06556 | 1.821589 |
| 1.06926 | 1.821482 |
| 1.07299 | 1.821376 |
| 1.07672 | 1.82127 |
| 1.08047 | 1.821165 |
| 1.08423 | 1.821061 |
| 1.088 | 1.820957 |
| 1.09179 | 1.820855 |
| 1.09559 | 1.820753 |
| 1.0994 | 1.820651 |
| 1.10323 | 1.820551 |
| 1.10707 | 1.820451 |
| 1.11092 | 1.820352 |
| 1.11479 | 1.820254 |
| 1.11867 | 1.820156 |
| 1.12256 | 1.820059 |
| 1.12647 | 1.819963 |
| 1.13039 | 1.819867 |
| 1.13432 | 1.819773 |
| 1.13827 | 1.819678 |
| 1.14223 | 1.819585 |
| 1.14621 | 1.819492 |
| 1.1502 | 1.8194 |
| 1.1542 | 1.819308 |
| 1.15822 | 1.819217 |
| 1.16225 | 1.819127 |
| 1.16629 | 1.819038 |
| 1.17035 | 1.818949 |
| 1.17443 | 1.81886 |
| 1.17851 | 1.818773 |
| 1.18262 | 1.818686 |
| 1.18673 | 1.818599 |
| 1.19086 | 1.818514 |
| 1.19501 | 1.818428 |
| 1.19917 | 1.818344 |
| 1.20334 | 1.81826 |
| 1.20753 | 1.818176 |
| 1.21173 | 1.818094 |
| 1.21595 | 1.818012 |
| 1.22018 | 1.81793 |
| 1.22443 | 1.817849 |
| 1.22869 | 1.817768 |
| 1.23297 | 1.817689 |
| 1.23726 | 1.817609 |
| 1.24156 | 1.817531 |
| 1.24588 | 1.817452 |
| 1.25022 | 1.817375 |
| 1.25457 | 1.817298 |
| 1.25894 | 1.817221 |
| 1.26332 | 1.817145 |
| 1.26772 | 1.81707 |
| 1.27213 | 1.816995 |
| 1.27656 | 1.816921 |
| 1.281 | 1.816847 |
| 1.28546 | 1.816774 |
| 1.28993 | 1.816701 |
| 1.29442 | 1.816629 |
| 1.29893 | 1.816557 |
| 1.30345 | 1.816486 |
| 1.30798 | 1.816415 |
| 1.31254 | 1.816345 |
| 1.3171 | 1.816275 |
| 1.32169 | 1.816206 |
| 1.32629 | 1.816137 |
| 1.33091 | 1.816069 |
| 1.33554 | 1.816001 |
| 1.34019 | 1.815934 |
| 1.34485 | 1.815867 |
| 1.34953 | 1.8158 |
| 1.35423 | 1.815735 |
| 1.35894 | 1.815669 |
| 1.36367 | 1.815604 |
| 1.36842 | 1.81554 |
| 1.37318 | 1.815476 |
| 1.37796 | 1.815412 |
| 1.38276 | 1.815349 |
| 1.38757 | 1.815286 |
| 1.3924 | 1.815224 |
| 1.39724 | 1.815162 |
| 1.40211 | 1.815101 |
| 1.40699 | 1.81504 |
| 1.41188 | 1.81498 |
| 1.4168 | 1.81492 |
| 1.42173 | 1.81486 |
| 1.42668 | 1.814801 |
| 1.43164 | 1.814742 |
| 1.43662 | 1.814684 |
| 1.44163 | 1.814626 |
| 1.44664 | 1.814568 |
| 1.45168 | 1.814511 |
| 1.45673 | 1.814454 |
| 1.4618 | 1.814398 |
| 1.46689 | 1.814342 |
| 1.47199 | 1.814287 |
| 1.47712 | 1.814231 |
| 1.48226 | 1.814177 |
| 1.48742 | 1.814122 |
| 1.49259 | 1.814068 |
| 1.49779 | 1.814015 |
| 1.503 | 1.813962 |
| 1.50823 | 1.813909 |
| 1.51348 | 1.813856 |
| 1.51875 | 1.813804 |
| 1.52404 | 1.813752 |
| 1.52934 | 1.813701 |
| 1.53466 | 1.81365 |
| 1.54 | 1.813599 |
| 1.54536 | 1.813549 |
| 1.55074 | 1.813499 |
| 1.55614 | 1.81345 |
| 1.56156 | 1.8134 |
| 1.56699 | 1.813351 |
| 1.57244 | 1.813303 |
| 1.57792 | 1.813255 |
| 1.58341 | 1.813207 |
| 1.58892 | 1.813159 |
| 1.59445 | 1.813112 |
| 1.6 | 1.813065 |
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
- —
Hexagonal boron nitride (hBN). Mechanically exfoliated, few-hundred-nm-thick h-BN flakes on a Si substrate. Extraordinary ray (e).