Optical constants
Refractive index of Be (Beryllium)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–62.0 µm
- Data
- tabulated nk
- Range
- 0.248–61.99 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.36133
- Extinction coefficient k
- 3.15172
- Permittivity ε1
- 1.36526
- Permittivity ε2
- 21.1879
- Absorption coefficient α
- 674024 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 29.6726 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 1.06125 µm⁻¹
- Group index ng
- 2.73774
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — 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
# Be (Beryllium): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–62.0 µm
be = ls.fetch_refractiveindex("main", "Be", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(be.range_nm) # (247.97, 61992) nm
eps = be.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_5ea2cda57f7d/lightsmith"
be = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(be.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (be/rakic-1998-bb).
# ... load be as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=be)],
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"]).
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.
Comments and conditions
References
[Calculation script (Python)]
- doi:10.1364/ao.37.005271 Optical properties of metallic films for vertical-cavity optoelectronic devices, Applied Optics (1998)
Cite
Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar and Marian L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics, 37, 5271 (1998), doi:10.1364/ao.37.005271; [Calculation script (Python)]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
200 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.24797 | 1.6444 | 2.9702 |
| 0.25494 | 1.7278 | 3.0024 |
| 0.26212 | 1.8112 | 3.0308 |
| 0.26949 | 1.8942 | 3.0554 |
| 0.27707 | 1.9763 | 3.0766 |
| 0.28487 | 2.0573 | 3.0944 |
| 0.29288 | 2.1368 | 3.1091 |
| 0.30112 | 2.2147 | 3.121 |
| 0.3096 | 2.2907 | 3.1302 |
| 0.31831 | 2.3646 | 3.1372 |
| 0.32726 | 2.4362 | 3.142 |
| 0.33647 | 2.5055 | 3.145 |
| 0.34594 | 2.5723 | 3.1464 |
| 0.35567 | 2.6366 | 3.1466 |
| 0.36568 | 2.6983 | 3.1456 |
| 0.37596 | 2.7574 | 3.1439 |
| 0.38654 | 2.8139 | 3.1415 |
| 0.39742 | 2.8678 | 3.1388 |
| 0.4086 | 2.919 | 3.1358 |
| 0.42009 | 2.9677 | 3.1328 |
| 0.43191 | 3.0138 | 3.13 |
| 0.44406 | 3.0574 | 3.1275 |
| 0.45656 | 3.0984 | 3.1255 |
| 0.4694 | 3.137 | 3.1241 |
| 0.48261 | 3.1731 | 3.1235 |
| 0.49619 | 3.2068 | 3.1238 |
| 0.51015 | 3.2381 | 3.125 |
| 0.5245 | 3.267 | 3.1275 |
| 0.53926 | 3.2937 | 3.1312 |
| 0.55443 | 3.318 | 3.1362 |
| 0.57003 | 3.34 | 3.1427 |
| 0.58606 | 3.3597 | 3.1508 |
| 0.60255 | 3.3772 | 3.1606 |
| 0.6195 | 3.3924 | 3.1723 |
| 0.63693 | 3.4054 | 3.1858 |
| 0.65485 | 3.4161 | 3.2013 |
| 0.67328 | 3.4246 | 3.2191 |
| 0.69222 | 3.4308 | 3.239 |
| 0.7117 | 3.4348 | 3.2614 |
| 0.73172 | 3.4366 | 3.2863 |
| 0.75231 | 3.436 | 3.3139 |
| 0.77347 | 3.4332 | 3.3443 |
| 0.79523 | 3.4282 | 3.3777 |
| 0.81761 | 3.4209 | 3.4142 |
| 0.84061 | 3.4113 | 3.454 |
| 0.86426 | 3.3994 | 3.4973 |
| 0.88857 | 3.3853 | 3.5442 |
| 0.91357 | 3.369 | 3.5951 |
| 0.93928 | 3.3505 | 3.6499 |
| 0.9657 | 3.3298 | 3.7091 |
| 0.99287 | 3.307 | 3.7728 |
| 1.0208 | 3.2822 | 3.8412 |
| 1.0495 | 3.2554 | 3.9145 |
| 1.0791 | 3.2268 | 3.9931 |
| 1.1094 | 3.1964 | 4.077 |
| 1.1406 | 3.1644 | 4.1666 |
| 1.1727 | 3.1309 | 4.262 |
| 1.2057 | 3.0961 | 4.3635 |
| 1.2396 | 3.0602 | 4.4712 |
| 1.2745 | 3.0233 | 4.5854 |
| 1.3104 | 2.9856 | 4.7062 |
| 1.3472 | 2.9474 | 4.8338 |
| 1.3851 | 2.9089 | 4.9683 |
| 1.4241 | 2.8702 | 5.1099 |
| 1.4642 | 2.8316 | 5.2586 |
| 1.5054 | 2.7933 | 5.4145 |
| 1.5477 | 2.7555 | 5.5777 |
| 1.5913 | 2.7183 | 5.7482 |
| 1.636 | 2.682 | 5.9262 |
| 1.6821 | 2.6466 | 6.1116 |
| 1.7294 | 2.6125 | 6.3045 |
| 1.778 | 2.5796 | 6.5049 |
| 1.8281 | 2.5481 | 6.7128 |
| 1.8795 | 2.518 | 6.9283 |
| 1.9324 | 2.4896 | 7.1515 |
| 1.9867 | 2.4629 | 7.3823 |
| 2.0426 | 2.4379 | 7.6208 |
| 2.1001 | 2.4147 | 7.8671 |
| 2.1592 | 2.3934 | 8.1213 |
| 2.2199 | 2.374 | 8.3835 |
| 2.2824 | 2.3565 | 8.6537 |
| 2.3466 | 2.341 | 8.932 |
| 2.4126 | 2.3276 | 9.2186 |
| 2.4805 | 2.3163 | 9.5136 |
| 2.5503 | 2.307 | 9.8172 |
| 2.6221 | 2.3 | 10.129 |
| 2.6958 | 2.2951 | 10.451 |
| 2.7717 | 2.2924 | 10.781 |
| 2.8497 | 2.2921 | 11.12 |
| 2.9298 | 2.294 | 11.469 |
| 3.0123 | 2.2984 | 11.827 |
| 3.097 | 2.3052 | 12.195 |
| 3.1841 | 2.3145 | 12.573 |
| 3.2737 | 2.3264 | 12.962 |
| 3.3658 | 2.3409 | 13.361 |
| 3.4605 | 2.3582 | 13.77 |
| 3.5579 | 2.3783 | 14.191 |
| 3.658 | 2.4013 | 14.623 |
| 3.7609 | 2.4273 | 15.067 |
| 3.8667 | 2.4564 | 15.522 |
| 3.9755 | 2.4888 | 15.99 |
| 4.0873 | 2.5246 | 16.47 |
| 4.2023 | 2.5638 | 16.963 |
| 4.3206 | 2.6068 | 17.468 |
| 4.4421 | 2.6535 | 17.988 |
| 4.5671 | 2.7041 | 18.521 |
| 4.6956 | 2.7589 | 19.068 |
| 4.8277 | 2.8181 | 19.629 |
| 4.9635 | 2.8817 | 20.205 |
| 5.1032 | 2.9501 | 20.796 |
| 5.2468 | 3.0234 | 21.403 |
| 5.3944 | 3.1019 | 22.026 |
| 5.5461 | 3.1858 | 22.665 |
| 5.7022 | 3.2754 | 23.32 |
| 5.8626 | 3.371 | 23.992 |
| 6.0275 | 3.4728 | 24.682 |
| 6.1971 | 3.5811 | 25.39 |
| 6.3715 | 3.6963 | 26.116 |
| 6.5507 | 3.8187 | 26.86 |
| 6.735 | 3.9487 | 27.624 |
| 6.9245 | 4.0866 | 28.406 |
| 7.1193 | 4.2328 | 29.209 |
| 7.3196 | 4.3877 | 30.032 |
| 7.5256 | 4.5517 | 30.876 |
| 7.7373 | 4.7254 | 31.74 |
| 7.955 | 4.9091 | 32.627 |
| 8.1788 | 5.1034 | 33.535 |
| 8.4089 | 5.3087 | 34.465 |
| 8.6455 | 5.5256 | 35.418 |
| 8.8887 | 5.7546 | 36.395 |
| 9.1388 | 5.9964 | 37.394 |
| 9.3959 | 6.2515 | 38.418 |
| 9.6603 | 6.5205 | 39.466 |
| 9.9321 | 6.8041 | 40.539 |
| 10.212 | 7.1029 | 41.636 |
| 10.499 | 7.4177 | 42.759 |
| 10.794 | 7.7492 | 43.908 |
| 11.098 | 8.098 | 45.083 |
| 11.41 | 8.4651 | 46.283 |
| 11.731 | 8.851 | 47.511 |
| 12.061 | 9.2568 | 48.765 |
| 12.401 | 9.6831 | 50.046 |
| 12.749 | 10.131 | 51.355 |
| 13.108 | 10.601 | 52.69 |
| 13.477 | 11.094 | 54.053 |
| 13.856 | 11.611 | 55.444 |
| 14.246 | 12.154 | 56.862 |
| 14.647 | 12.722 | 58.308 |
| 15.059 | 13.317 | 59.782 |
| 15.482 | 13.94 | 61.283 |
| 15.918 | 14.592 | 62.812 |
| 16.366 | 15.274 | 64.368 |
| 16.826 | 15.986 | 65.952 |
| 17.3 | 16.73 | 67.562 |
| 17.786 | 17.506 | 69.199 |
| 18.287 | 18.316 | 70.863 |
| 18.801 | 19.161 | 72.552 |
| 19.33 | 20.041 | 74.267 |
| 19.874 | 20.957 | 76.007 |
| 20.433 | 21.91 | 77.772 |
| 21.008 | 22.902 | 79.561 |
| 21.599 | 23.932 | 81.373 |
| 22.207 | 25.001 | 83.208 |
| 22.832 | 26.111 | 85.066 |
| 23.474 | 27.261 | 86.944 |
| 24.134 | 28.454 | 88.844 |
| 24.813 | 29.688 | 90.763 |
| 25.512 | 30.965 | 92.701 |
| 26.229 | 32.284 | 94.658 |
| 26.967 | 33.648 | 96.631 |
| 27.726 | 35.054 | 98.622 |
| 28.506 | 36.505 | 100.63 |
| 29.308 | 38.0 | 102.65 |
| 30.133 | 39.54 | 104.68 |
| 30.98 | 41.123 | 106.73 |
| 31.852 | 42.751 | 108.79 |
| 32.748 | 44.423 | 110.86 |
| 33.67 | 46.139 | 112.94 |
| 34.617 | 47.899 | 115.03 |
| 35.591 | 49.702 | 117.13 |
| 36.592 | 51.548 | 119.24 |
| 37.622 | 53.437 | 121.36 |
| 38.68 | 55.369 | 123.48 |
| 39.768 | 57.342 | 125.61 |
| 40.887 | 59.356 | 127.75 |
| 42.038 | 61.411 | 129.89 |
| 43.22 | 63.506 | 132.04 |
| 44.436 | 65.641 | 134.19 |
| 45.686 | 67.814 | 136.35 |
| 46.972 | 70.025 | 138.51 |
| 48.293 | 72.273 | 140.68 |
| 49.652 | 74.558 | 142.85 |
| 51.049 | 76.879 | 145.03 |
| 52.485 | 79.235 | 147.21 |
| 53.962 | 81.626 | 149.39 |
| 55.48 | 84.05 | 151.59 |
| 57.041 | 86.508 | 153.78 |
| 58.646 | 88.998 | 155.99 |
| 60.296 | 91.521 | 158.2 |
| 61.992 | 94.075 | 160.42 |
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
- —
Fit of experimental data from several sources to Brendel-Bormann (BB) model