Optical constants
Refractive index of GaN (Gallium nitride)
Barker and Ilegems 1973: n(e) 0.35–10 µm
- Data
- formula 1
- Range
- 0.35–10 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
- 2.31193
- Extinction coefficient k
- 0
- Permittivity ε1
- 5.34501
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- 2158.1
- Chromatic dispersion dn/dλ
- -0.00367585 µm⁻¹
- Group index ng
- 2.31409
- Group velocity dispersion
- -2.25843 fs²/mm
- Dispersion parameter D
- 12.3209 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
# GaN (Gallium nitride): Barker and Ilegems 1973: n(e) 0.35–10 µm
gan = ls.fetch_refractiveindex("main", "GaN", "Barker-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(gan.range_nm) # (350, 10000) nm
eps = gan.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_7f366f9fb055/lightsmith"
gan = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(gan.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (gan/barker-ilegems-1973-e).
# ... load gan as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=gan)],
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_7f366f9fb055/lightsmith?model=drude_lorentz"
gan_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 0.35 to 10.0 µm.
Coefficients as stored
| Ci | Value |
|---|---|
| C1 | 4.35 |
| C2 | 5.08 |
| C3 | 18.76 |
Comments and conditions
References
- doi:10.1103/physrevb.7.743 Infrared Lattice Vibrations and Free-Electron Dispersion in GaN, Physical Review B (1973)
Cite
A. S. Barker and M. Ilegems. Infrared Lattice Vibrations and Free-Electron Dispersion in GaN. Physical Review B, 7, 743-750 (1973), doi:10.1103/physrevb.7.743; 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 |
|---|---|
| 0.35 | 2.312624 |
| 0.352953 | 2.312618 |
| 0.355931 | 2.312611 |
| 0.358934 | 2.312605 |
| 0.361963 | 2.312598 |
| 0.365017 | 2.312591 |
| 0.368097 | 2.312584 |
| 0.371202 | 2.312577 |
| 0.374334 | 2.312569 |
| 0.377493 | 2.312562 |
| 0.380678 | 2.312554 |
| 0.38389 | 2.312547 |
| 0.387129 | 2.312539 |
| 0.390395 | 2.312531 |
| 0.393689 | 2.312523 |
| 0.397011 | 2.312515 |
| 0.400361 | 2.312506 |
| 0.403739 | 2.312498 |
| 0.407145 | 2.312489 |
| 0.41058 | 2.31248 |
| 0.414045 | 2.312471 |
| 0.417538 | 2.312462 |
| 0.421061 | 2.312453 |
| 0.424614 | 2.312444 |
| 0.428196 | 2.312434 |
| 0.431809 | 2.312425 |
| 0.435453 | 2.312415 |
| 0.439127 | 2.312405 |
| 0.442832 | 2.312394 |
| 0.446568 | 2.312384 |
| 0.450336 | 2.312373 |
| 0.454136 | 2.312363 |
| 0.457967 | 2.312352 |
| 0.461831 | 2.312341 |
| 0.465728 | 2.312329 |
| 0.469658 | 2.312318 |
| 0.47362 | 2.312306 |
| 0.477616 | 2.312294 |
| 0.481646 | 2.312282 |
| 0.48571 | 2.31227 |
| 0.489808 | 2.312257 |
| 0.493941 | 2.312245 |
| 0.498109 | 2.312232 |
| 0.502311 | 2.312219 |
| 0.50655 | 2.312205 |
| 0.510824 | 2.312192 |
| 0.515134 | 2.312178 |
| 0.51948 | 2.312164 |
| 0.523863 | 2.31215 |
| 0.528283 | 2.312135 |
| 0.53274 | 2.31212 |
| 0.537235 | 2.312105 |
| 0.541768 | 2.31209 |
| 0.546339 | 2.312074 |
| 0.550949 | 2.312059 |
| 0.555598 | 2.312042 |
| 0.560285 | 2.312026 |
| 0.565013 | 2.312009 |
| 0.56978 | 2.311993 |
| 0.574588 | 2.311975 |
| 0.579436 | 2.311958 |
| 0.584325 | 2.31194 |
| 0.589255 | 2.311922 |
| 0.594227 | 2.311904 |
| 0.59924 | 2.311885 |
| 0.604296 | 2.311866 |
| 0.609395 | 2.311846 |
| 0.614537 | 2.311827 |
| 0.619722 | 2.311807 |
| 0.624951 | 2.311786 |
| 0.630224 | 2.311766 |
| 0.635541 | 2.311745 |
| 0.640903 | 2.311723 |
| 0.646311 | 2.311701 |
| 0.651764 | 2.311679 |
| 0.657263 | 2.311657 |
| 0.662809 | 2.311634 |
| 0.668401 | 2.31161 |
| 0.674041 | 2.311587 |
| 0.679728 | 2.311563 |
| 0.685463 | 2.311538 |
| 0.691247 | 2.311513 |
| 0.697079 | 2.311488 |
| 0.702961 | 2.311462 |
| 0.708892 | 2.311436 |
| 0.714873 | 2.311409 |
| 0.720905 | 2.311382 |
| 0.726987 | 2.311355 |
| 0.733121 | 2.311326 |
| 0.739307 | 2.311298 |
| 0.745545 | 2.311269 |
| 0.751835 | 2.311239 |
| 0.758179 | 2.311209 |
| 0.764576 | 2.311179 |
| 0.771027 | 2.311148 |
| 0.777532 | 2.311116 |
| 0.784093 | 2.311084 |
| 0.790709 | 2.311052 |
| 0.79738 | 2.311018 |
| 0.804108 | 2.310985 |
| 0.810892 | 2.31095 |
| 0.817734 | 2.310915 |
| 0.824634 | 2.31088 |
| 0.831592 | 2.310844 |
| 0.838608 | 2.310807 |
| 0.845684 | 2.31077 |
| 0.852819 | 2.310732 |
| 0.860015 | 2.310693 |
| 0.867271 | 2.310654 |
| 0.874589 | 2.310614 |
| 0.881968 | 2.310573 |
| 0.889409 | 2.310532 |
| 0.896914 | 2.310489 |
| 0.904481 | 2.310447 |
| 0.912113 | 2.310403 |
| 0.919809 | 2.310359 |
| 0.92757 | 2.310314 |
| 0.935396 | 2.310268 |
| 0.943288 | 2.310222 |
| 0.951247 | 2.310174 |
| 0.959273 | 2.310126 |
| 0.967367 | 2.310077 |
| 0.975529 | 2.310027 |
| 0.98376 | 2.309977 |
| 0.99206 | 2.309925 |
| 1.00043 | 2.309873 |
| 1.00887 | 2.309819 |
| 1.01738 | 2.309765 |
| 1.02597 | 2.30971 |
| 1.03462 | 2.309654 |
| 1.04335 | 2.309597 |
| 1.05216 | 2.309539 |
| 1.06104 | 2.30948 |
| 1.06999 | 2.30942 |
| 1.07902 | 2.309359 |
| 1.08812 | 2.309297 |
| 1.0973 | 2.309234 |
| 1.10656 | 2.30917 |
| 1.1159 | 2.309104 |
| 1.12531 | 2.309038 |
| 1.13481 | 2.30897 |
| 1.14438 | 2.308901 |
| 1.15404 | 2.308832 |
| 1.16377 | 2.30876 |
| 1.17359 | 2.308688 |
| 1.18349 | 2.308615 |
| 1.19348 | 2.30854 |
| 1.20355 | 2.308464 |
| 1.2137 | 2.308386 |
| 1.22395 | 2.308308 |
| 1.23427 | 2.308228 |
| 1.24469 | 2.308146 |
| 1.25519 | 2.308063 |
| 1.26578 | 2.307979 |
| 1.27646 | 2.307893 |
| 1.28723 | 2.307806 |
| 1.29809 | 2.307718 |
| 1.30904 | 2.307627 |
| 1.32009 | 2.307536 |
| 1.33122 | 2.307442 |
| 1.34246 | 2.307348 |
| 1.35378 | 2.307251 |
| 1.36521 | 2.307153 |
| 1.37673 | 2.307053 |
| 1.38834 | 2.306951 |
| 1.40006 | 2.306848 |
| 1.41187 | 2.306743 |
| 1.42378 | 2.306636 |
| 1.43579 | 2.306527 |
| 1.44791 | 2.306417 |
| 1.46012 | 2.306304 |
| 1.47244 | 2.30619 |
| 1.48487 | 2.306073 |
| 1.4974 | 2.305955 |
| 1.51003 | 2.305834 |
| 1.52277 | 2.305712 |
| 1.53562 | 2.305587 |
| 1.54858 | 2.30546 |
| 1.56164 | 2.305331 |
| 1.57482 | 2.3052 |
| 1.58811 | 2.305067 |
| 1.60151 | 2.304931 |
| 1.61502 | 2.304793 |
| 1.62864 | 2.304652 |
| 1.64239 | 2.304509 |
| 1.65624 | 2.304364 |
| 1.67022 | 2.304216 |
| 1.68431 | 2.304066 |
| 1.69852 | 2.303913 |
| 1.71285 | 2.303757 |
| 1.7273 | 2.303598 |
| 1.74188 | 2.303437 |
| 1.75658 | 2.303273 |
| 1.7714 | 2.303107 |
| 1.78634 | 2.302937 |
| 1.80141 | 2.302764 |
| 1.81661 | 2.302589 |
| 1.83194 | 2.30241 |
| 1.8474 | 2.302228 |
| 1.86299 | 2.302043 |
| 1.8787 | 2.301855 |
| 1.89456 | 2.301664 |
| 1.91054 | 2.301469 |
| 1.92666 | 2.301271 |
| 1.94292 | 2.301069 |
| 1.95931 | 2.300864 |
| 1.97584 | 2.300656 |
| 1.99251 | 2.300443 |
| 2.00932 | 2.300227 |
| 2.02628 | 2.300008 |
| 2.04337 | 2.299784 |
| 2.06062 | 2.299557 |
| 2.078 | 2.299325 |
| 2.09553 | 2.29909 |
| 2.11322 | 2.29885 |
| 2.13105 | 2.298606 |
| 2.14903 | 2.298358 |
| 2.16716 | 2.298106 |
| 2.18544 | 2.297849 |
| 2.20388 | 2.297588 |
| 2.22248 | 2.297322 |
| 2.24123 | 2.297051 |
| 2.26014 | 2.296776 |
| 2.27921 | 2.296496 |
| 2.29844 | 2.296211 |
| 2.31783 | 2.295921 |
| 2.33739 | 2.295625 |
| 2.35711 | 2.295325 |
| 2.377 | 2.295019 |
| 2.39706 | 2.294708 |
| 2.41728 | 2.294392 |
| 2.43768 | 2.294069 |
| 2.45824 | 2.293741 |
| 2.47899 | 2.293408 |
| 2.4999 | 2.293068 |
| 2.52099 | 2.292723 |
| 2.54226 | 2.292371 |
| 2.56371 | 2.292013 |
| 2.58535 | 2.291648 |
| 2.60716 | 2.291278 |
| 2.62916 | 2.2909 |
| 2.65134 | 2.290516 |
| 2.67371 | 2.290125 |
| 2.69627 | 2.289727 |
| 2.71902 | 2.289322 |
| 2.74196 | 2.28891 |
| 2.7651 | 2.28849 |
| 2.78843 | 2.288063 |
| 2.81195 | 2.287628 |
| 2.83568 | 2.287186 |
| 2.85961 | 2.286735 |
| 2.88373 | 2.286276 |
| 2.90806 | 2.28581 |
| 2.9326 | 2.285334 |
| 2.95734 | 2.28485 |
| 2.9823 | 2.284358 |
| 3.00746 | 2.283856 |
| 3.03283 | 2.283346 |
| 3.05842 | 2.282826 |
| 3.08423 | 2.282297 |
| 3.11025 | 2.281758 |
| 3.13649 | 2.28121 |
| 3.16296 | 2.280651 |
| 3.18965 | 2.280082 |
| 3.21656 | 2.279503 |
| 3.2437 | 2.278914 |
| 3.27107 | 2.278313 |
| 3.29867 | 2.277702 |
| 3.3265 | 2.277079 |
| 3.35456 | 2.276445 |
| 3.38287 | 2.2758 |
| 3.41141 | 2.275142 |
| 3.4402 | 2.274473 |
| 3.46922 | 2.273791 |
| 3.49849 | 2.273096 |
| 3.52801 | 2.272389 |
| 3.55778 | 2.271668 |
| 3.5878 | 2.270934 |
| 3.61807 | 2.270187 |
| 3.6486 | 2.269425 |
| 3.67938 | 2.26865 |
| 3.71042 | 2.26786 |
| 3.74173 | 2.267055 |
| 3.7733 | 2.266235 |
| 3.80514 | 2.2654 |
| 3.83724 | 2.264549 |
| 3.86962 | 2.263682 |
| 3.90227 | 2.262798 |
| 3.9352 | 2.261898 |
| 3.9684 | 2.260981 |
| 4.00188 | 2.260047 |
| 4.03565 | 2.259095 |
| 4.0697 | 2.258124 |
| 4.10404 | 2.257135 |
| 4.13866 | 2.256128 |
| 4.17358 | 2.255101 |
| 4.2088 | 2.254054 |
| 4.24431 | 2.252987 |
| 4.28012 | 2.251899 |
| 4.31623 | 2.250791 |
| 4.35265 | 2.249661 |
| 4.38937 | 2.248509 |
| 4.42641 | 2.247335 |
| 4.46376 | 2.246137 |
| 4.50142 | 2.244917 |
| 4.5394 | 2.243672 |
| 4.5777 | 2.242403 |
| 4.61633 | 2.241109 |
| 4.65528 | 2.23979 |
| 4.69455 | 2.238444 |
| 4.73416 | 2.237072 |
| 4.77411 | 2.235672 |
| 4.81439 | 2.234244 |
| 4.85501 | 2.232788 |
| 4.89597 | 2.231303 |
| 4.93728 | 2.229787 |
| 4.97894 | 2.228241 |
| 5.02095 | 2.226664 |
| 5.06331 | 2.225055 |
| 5.10604 | 2.223413 |
| 5.14912 | 2.221737 |
| 5.19256 | 2.220027 |
| 5.23637 | 2.218282 |
| 5.28056 | 2.2165 |
| 5.32511 | 2.214682 |
| 5.37004 | 2.212826 |
| 5.41535 | 2.210932 |
| 5.46104 | 2.208997 |
| 5.50712 | 2.207022 |
| 5.55358 | 2.205005 |
| 5.60044 | 2.202946 |
| 5.6477 | 2.200843 |
| 5.69535 | 2.198695 |
| 5.7434 | 2.196501 |
| 5.79186 | 2.194259 |
| 5.84073 | 2.191969 |
| 5.89001 | 2.18963 |
| 5.93971 | 2.187239 |
| 5.98982 | 2.184797 |
| 6.04036 | 2.1823 |
| 6.09133 | 2.179749 |
| 6.14272 | 2.17714 |
| 6.19455 | 2.174474 |
| 6.24682 | 2.171748 |
| 6.29952 | 2.16896 |
| 6.35267 | 2.16611 |
| 6.40627 | 2.163194 |
| 6.46033 | 2.160212 |
| 6.51484 | 2.157161 |
| 6.5698 | 2.15404 |
| 6.62524 | 2.150847 |
| 6.68114 | 2.147578 |
| 6.73751 | 2.144233 |
| 6.79435 | 2.140809 |
| 6.85168 | 2.137304 |
| 6.90949 | 2.133714 |
| 6.96779 | 2.130039 |
| 7.02658 | 2.126274 |
| 7.08587 | 2.122417 |
| 7.14565 | 2.118466 |
| 7.20594 | 2.114417 |
| 7.26674 | 2.110268 |
| 7.32806 | 2.106015 |
| 7.38989 | 2.101654 |
| 7.45224 | 2.097183 |
| 7.51511 | 2.092597 |
| 7.57852 | 2.087894 |
| 7.64247 | 2.083068 |
| 7.70695 | 2.078115 |
| 7.77198 | 2.073032 |
| 7.83755 | 2.067814 |
| 7.90368 | 2.062456 |
| 7.97037 | 2.056953 |
| 8.03762 | 2.0513 |
| 8.10543 | 2.045491 |
| 8.17382 | 2.039521 |
| 8.24279 | 2.033383 |
| 8.31234 | 2.027072 |
| 8.38247 | 2.02058 |
| 8.4532 | 2.013901 |
| 8.52452 | 2.007028 |
| 8.59644 | 1.999952 |
| 8.66898 | 1.992665 |
| 8.74212 | 1.985159 |
| 8.81588 | 1.977425 |
| 8.89026 | 1.969453 |
| 8.96528 | 1.961232 |
| 9.04092 | 1.952753 |
| 9.1172 | 1.944004 |
| 9.19413 | 1.934972 |
| 9.2717 | 1.925645 |
| 9.34993 | 1.916008 |
| 9.42882 | 1.906049 |
| 9.50837 | 1.89575 |
| 9.5886 | 1.885095 |
| 9.6695 | 1.874067 |
| 9.75109 | 1.862647 |
| 9.83336 | 1.850814 |
| 9.91633 | 1.838547 |
| 10 | 1.825822 |
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
- —
α-GaN (wurtzite); Extrardinary ray (e); 300 K (27 °C).