Optical constants
Refractive index of BN (Boron nitride)
Rah et al. 2019: h-BN; n(o) 0.4–1.6 µm
- Data
- formula 2
- Range
- 0.4–1.6 µm
- Optical axis
- o
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.14742
- Extinction coefficient k
- 0
- Permittivity ε1
- 4.61142
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 24.629
- Chromatic dispersion dn/dλ
- -0.236196 µm⁻¹
- Group index ng
- 2.28621
- Group velocity dispersion
- 471.586 fs²/mm
- Dispersion parameter D
- -2572.75 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(o) 0.4–1.6 µm
bn = ls.fetch_refractiveindex("main", "BN", "Rah-o", 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_221651e62fb4/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-o).
# ... 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_221651e62fb4/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 | 3.3361 |
| C3 | 0.026322 |
Comments and conditions
Conditions
- direction
- o
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 | 2.234502 |
| 0.401392 | 2.233285 |
| 0.402789 | 2.232079 |
| 0.404191 | 2.230884 |
| 0.405598 | 2.2297 |
| 0.40701 | 2.228526 |
| 0.408426 | 2.227363 |
| 0.409848 | 2.226211 |
| 0.411274 | 2.225069 |
| 0.412706 | 2.223937 |
| 0.414142 | 2.222815 |
| 0.415583 | 2.221703 |
| 0.41703 | 2.220601 |
| 0.418481 | 2.219509 |
| 0.419938 | 2.218427 |
| 0.421399 | 2.217354 |
| 0.422866 | 2.216291 |
| 0.424338 | 2.215237 |
| 0.425815 | 2.214193 |
| 0.427297 | 2.213157 |
| 0.428784 | 2.212131 |
| 0.430276 | 2.211114 |
| 0.431774 | 2.210105 |
| 0.433277 | 2.209106 |
| 0.434785 | 2.208115 |
| 0.436298 | 2.207132 |
| 0.437816 | 2.206159 |
| 0.43934 | 2.205194 |
| 0.440869 | 2.204237 |
| 0.442404 | 2.203288 |
| 0.443943 | 2.202348 |
| 0.445489 | 2.201415 |
| 0.447039 | 2.200491 |
| 0.448595 | 2.199575 |
| 0.450156 | 2.198667 |
| 0.451723 | 2.197766 |
| 0.453295 | 2.196873 |
| 0.454873 | 2.195988 |
| 0.456456 | 2.19511 |
| 0.458045 | 2.19424 |
| 0.459639 | 2.193377 |
| 0.461239 | 2.192521 |
| 0.462844 | 2.191673 |
| 0.464455 | 2.190832 |
| 0.466072 | 2.189998 |
| 0.467694 | 2.189171 |
| 0.469321 | 2.188351 |
| 0.470955 | 2.187538 |
| 0.472594 | 2.186732 |
| 0.474239 | 2.185933 |
| 0.475889 | 2.18514 |
| 0.477546 | 2.184354 |
| 0.479208 | 2.183575 |
| 0.480876 | 2.182802 |
| 0.482549 | 2.182035 |
| 0.484229 | 2.181275 |
| 0.485914 | 2.180521 |
| 0.487605 | 2.179774 |
| 0.489303 | 2.179033 |
| 0.491006 | 2.178297 |
| 0.492714 | 2.177568 |
| 0.494429 | 2.176845 |
| 0.49615 | 2.176128 |
| 0.497877 | 2.175417 |
| 0.49961 | 2.174712 |
| 0.501349 | 2.174012 |
| 0.503094 | 2.173319 |
| 0.504845 | 2.172631 |
| 0.506602 | 2.171948 |
| 0.508365 | 2.171271 |
| 0.510134 | 2.1706 |
| 0.51191 | 2.169934 |
| 0.513692 | 2.169274 |
| 0.515479 | 2.168619 |
| 0.517274 | 2.167969 |
| 0.519074 | 2.167325 |
| 0.52088 | 2.166686 |
| 0.522693 | 2.166052 |
| 0.524513 | 2.165423 |
| 0.526338 | 2.164799 |
| 0.52817 | 2.164181 |
| 0.530008 | 2.163567 |
| 0.531853 | 2.162958 |
| 0.533704 | 2.162355 |
| 0.535562 | 2.161756 |
| 0.537426 | 2.161162 |
| 0.539296 | 2.160572 |
| 0.541173 | 2.159988 |
| 0.543057 | 2.159408 |
| 0.544947 | 2.158832 |
| 0.546843 | 2.158262 |
| 0.548747 | 2.157696 |
| 0.550657 | 2.157134 |
| 0.552573 | 2.156577 |
| 0.554496 | 2.156024 |
| 0.556426 | 2.155476 |
| 0.558363 | 2.154932 |
| 0.560306 | 2.154393 |
| 0.562256 | 2.153857 |
| 0.564213 | 2.153326 |
| 0.566177 | 2.152799 |
| 0.568148 | 2.152277 |
| 0.570125 | 2.151758 |
| 0.572109 | 2.151244 |
| 0.5741 | 2.150733 |
| 0.576099 | 2.150227 |
| 0.578104 | 2.149725 |
| 0.580116 | 2.149226 |
| 0.582135 | 2.148732 |
| 0.584161 | 2.148241 |
| 0.586194 | 2.147754 |
| 0.588234 | 2.147271 |
| 0.590282 | 2.146792 |
| 0.592336 | 2.146317 |
| 0.594398 | 2.145845 |
| 0.596466 | 2.145377 |
| 0.598542 | 2.144913 |
| 0.600626 | 2.144452 |
| 0.602716 | 2.143995 |
| 0.604814 | 2.143542 |
| 0.606919 | 2.143092 |
| 0.609031 | 2.142645 |
| 0.611151 | 2.142202 |
| 0.613278 | 2.141762 |
| 0.615413 | 2.141326 |
| 0.617554 | 2.140893 |
| 0.619704 | 2.140464 |
| 0.621861 | 2.140038 |
| 0.624025 | 2.139615 |
| 0.626197 | 2.139195 |
| 0.628376 | 2.138779 |
| 0.630563 | 2.138366 |
| 0.632758 | 2.137956 |
| 0.63496 | 2.137549 |
| 0.63717 | 2.137145 |
| 0.639388 | 2.136745 |
| 0.641613 | 2.136347 |
| 0.643847 | 2.135953 |
| 0.646087 | 2.135562 |
| 0.648336 | 2.135173 |
| 0.650593 | 2.134788 |
| 0.652857 | 2.134406 |
| 0.655129 | 2.134026 |
| 0.657409 | 2.133649 |
| 0.659697 | 2.133276 |
| 0.661993 | 2.132905 |
| 0.664298 | 2.132537 |
| 0.66661 | 2.132171 |
| 0.66893 | 2.131809 |
| 0.671258 | 2.131449 |
| 0.673594 | 2.131092 |
| 0.675939 | 2.130738 |
| 0.678291 | 2.130387 |
| 0.680652 | 2.130038 |
| 0.683021 | 2.129692 |
| 0.685398 | 2.129348 |
| 0.687784 | 2.129007 |
| 0.690177 | 2.128669 |
| 0.69258 | 2.128333 |
| 0.69499 | 2.127999 |
| 0.697409 | 2.127669 |
| 0.699836 | 2.12734 |
| 0.702272 | 2.127015 |
| 0.704716 | 2.126691 |
| 0.707169 | 2.12637 |
| 0.70963 | 2.126052 |
| 0.7121 | 2.125736 |
| 0.714579 | 2.125422 |
| 0.717066 | 2.125111 |
| 0.719561 | 2.124802 |
| 0.722066 | 2.124495 |
| 0.724579 | 2.124191 |
| 0.727101 | 2.123889 |
| 0.729631 | 2.123589 |
| 0.732171 | 2.123291 |
| 0.734719 | 2.122996 |
| 0.737276 | 2.122703 |
| 0.739842 | 2.122412 |
| 0.742417 | 2.122123 |
| 0.745001 | 2.121837 |
| 0.747594 | 2.121552 |
| 0.750196 | 2.12127 |
| 0.752807 | 2.12099 |
| 0.755427 | 2.120711 |
| 0.758057 | 2.120435 |
| 0.760695 | 2.120161 |
| 0.763343 | 2.11989 |
| 0.765999 | 2.11962 |
| 0.768665 | 2.119352 |
| 0.771341 | 2.119086 |
| 0.774025 | 2.118822 |
| 0.776719 | 2.11856 |
| 0.779423 | 2.1183 |
| 0.782135 | 2.118042 |
| 0.784858 | 2.117786 |
| 0.787589 | 2.117531 |
| 0.790331 | 2.117279 |
| 0.793081 | 2.117029 |
| 0.795842 | 2.11678 |
| 0.798611 | 2.116533 |
| 0.801391 | 2.116288 |
| 0.80418 | 2.116045 |
| 0.806979 | 2.115804 |
| 0.809788 | 2.115564 |
| 0.812606 | 2.115326 |
| 0.815434 | 2.11509 |
| 0.818273 | 2.114856 |
| 0.821121 | 2.114623 |
| 0.823978 | 2.114392 |
| 0.826846 | 2.114163 |
| 0.829724 | 2.113936 |
| 0.832612 | 2.11371 |
| 0.83551 | 2.113486 |
| 0.838418 | 2.113263 |
| 0.841336 | 2.113042 |
| 0.844264 | 2.112823 |
| 0.847202 | 2.112605 |
| 0.850151 | 2.112389 |
| 0.85311 | 2.112175 |
| 0.856079 | 2.111962 |
| 0.859059 | 2.111751 |
| 0.862049 | 2.111541 |
| 0.865049 | 2.111333 |
| 0.86806 | 2.111126 |
| 0.871081 | 2.110921 |
| 0.874113 | 2.110717 |
| 0.877155 | 2.110515 |
| 0.880208 | 2.110314 |
| 0.883272 | 2.110115 |
| 0.886346 | 2.109917 |
| 0.889431 | 2.109721 |
| 0.892526 | 2.109526 |
| 0.895633 | 2.109333 |
| 0.89875 | 2.109141 |
| 0.901878 | 2.10895 |
| 0.905017 | 2.108761 |
| 0.908167 | 2.108573 |
| 0.911328 | 2.108386 |
| 0.9145 | 2.108201 |
| 0.917682 | 2.108017 |
| 0.920876 | 2.107835 |
| 0.924081 | 2.107654 |
| 0.927298 | 2.107474 |
| 0.930525 | 2.107296 |
| 0.933764 | 2.107118 |
| 0.937014 | 2.106942 |
| 0.940275 | 2.106768 |
| 0.943548 | 2.106594 |
| 0.946832 | 2.106422 |
| 0.950127 | 2.106251 |
| 0.953434 | 2.106082 |
| 0.956752 | 2.105913 |
| 0.960082 | 2.105746 |
| 0.963424 | 2.10558 |
| 0.966777 | 2.105416 |
| 0.970142 | 2.105252 |
| 0.973518 | 2.10509 |
| 0.976907 | 2.104928 |
| 0.980307 | 2.104768 |
| 0.983719 | 2.104609 |
| 0.987142 | 2.104452 |
| 0.990578 | 2.104295 |
| 0.994026 | 2.10414 |
| 0.997485 | 2.103985 |
| 1.00096 | 2.103832 |
| 1.00444 | 2.10368 |
| 1.00794 | 2.103529 |
| 1.01144 | 2.103379 |
| 1.01497 | 2.10323 |
| 1.0185 | 2.103083 |
| 1.02204 | 2.102936 |
| 1.0256 | 2.10279 |
| 1.02917 | 2.102646 |
| 1.03275 | 2.102502 |
| 1.03635 | 2.10236 |
| 1.03995 | 2.102218 |
| 1.04357 | 2.102078 |
| 1.0472 | 2.101938 |
| 1.05085 | 2.1018 |
| 1.05451 | 2.101662 |
| 1.05818 | 2.101526 |
| 1.06186 | 2.10139 |
| 1.06556 | 2.101256 |
| 1.06926 | 2.101122 |
| 1.07299 | 2.10099 |
| 1.07672 | 2.100858 |
| 1.08047 | 2.100727 |
| 1.08423 | 2.100598 |
| 1.088 | 2.100469 |
| 1.09179 | 2.100341 |
| 1.09559 | 2.100214 |
| 1.0994 | 2.100088 |
| 1.10323 | 2.099963 |
| 1.10707 | 2.099838 |
| 1.11092 | 2.099715 |
| 1.11479 | 2.099593 |
| 1.11867 | 2.099471 |
| 1.12256 | 2.09935 |
| 1.12647 | 2.09923 |
| 1.13039 | 2.099111 |
| 1.13432 | 2.098993 |
| 1.13827 | 2.098876 |
| 1.14223 | 2.098759 |
| 1.14621 | 2.098644 |
| 1.1502 | 2.098529 |
| 1.1542 | 2.098415 |
| 1.15822 | 2.098302 |
| 1.16225 | 2.098189 |
| 1.16629 | 2.098078 |
| 1.17035 | 2.097967 |
| 1.17443 | 2.097857 |
| 1.17851 | 2.097748 |
| 1.18262 | 2.097639 |
| 1.18673 | 2.097532 |
| 1.19086 | 2.097425 |
| 1.19501 | 2.097319 |
| 1.19917 | 2.097214 |
| 1.20334 | 2.097109 |
| 1.20753 | 2.097005 |
| 1.21173 | 2.096902 |
| 1.21595 | 2.0968 |
| 1.22018 | 2.096698 |
| 1.22443 | 2.096597 |
| 1.22869 | 2.096497 |
| 1.23297 | 2.096397 |
| 1.23726 | 2.096299 |
| 1.24156 | 2.0962 |
| 1.24588 | 2.096103 |
| 1.25022 | 2.096006 |
| 1.25457 | 2.09591 |
| 1.25894 | 2.095815 |
| 1.26332 | 2.09572 |
| 1.26772 | 2.095626 |
| 1.27213 | 2.095533 |
| 1.27656 | 2.095441 |
| 1.281 | 2.095349 |
| 1.28546 | 2.095257 |
| 1.28993 | 2.095167 |
| 1.29442 | 2.095077 |
| 1.29893 | 2.094987 |
| 1.30345 | 2.094898 |
| 1.30798 | 2.09481 |
| 1.31254 | 2.094723 |
| 1.3171 | 2.094636 |
| 1.32169 | 2.09455 |
| 1.32629 | 2.094464 |
| 1.33091 | 2.094379 |
| 1.33554 | 2.094294 |
| 1.34019 | 2.094211 |
| 1.34485 | 2.094127 |
| 1.34953 | 2.094045 |
| 1.35423 | 2.093963 |
| 1.35894 | 2.093881 |
| 1.36367 | 2.0938 |
| 1.36842 | 2.09372 |
| 1.37318 | 2.09364 |
| 1.37796 | 2.093561 |
| 1.38276 | 2.093482 |
| 1.38757 | 2.093404 |
| 1.3924 | 2.093327 |
| 1.39724 | 2.09325 |
| 1.40211 | 2.093173 |
| 1.40699 | 2.093097 |
| 1.41188 | 2.093022 |
| 1.4168 | 2.092947 |
| 1.42173 | 2.092873 |
| 1.42668 | 2.092799 |
| 1.43164 | 2.092726 |
| 1.43662 | 2.092653 |
| 1.44163 | 2.092581 |
| 1.44664 | 2.092509 |
| 1.45168 | 2.092438 |
| 1.45673 | 2.092367 |
| 1.4618 | 2.092297 |
| 1.46689 | 2.092227 |
| 1.47199 | 2.092158 |
| 1.47712 | 2.092089 |
| 1.48226 | 2.092021 |
| 1.48742 | 2.091953 |
| 1.49259 | 2.091886 |
| 1.49779 | 2.091819 |
| 1.503 | 2.091753 |
| 1.50823 | 2.091687 |
| 1.51348 | 2.091622 |
| 1.51875 | 2.091557 |
| 1.52404 | 2.091492 |
| 1.52934 | 2.091428 |
| 1.53466 | 2.091365 |
| 1.54 | 2.091302 |
| 1.54536 | 2.091239 |
| 1.55074 | 2.091177 |
| 1.55614 | 2.091115 |
| 1.56156 | 2.091053 |
| 1.56699 | 2.090993 |
| 1.57244 | 2.090932 |
| 1.57792 | 2.090872 |
| 1.58341 | 2.090812 |
| 1.58892 | 2.090753 |
| 1.59445 | 2.090694 |
| 1.6 | 2.090636 |
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. Ordinary ray (o).