Optical constants
Refractive index of Cr (Chromium)
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
- 3.05041
- Extinction coefficient k
- 4.25044
- Permittivity ε1
- -8.76125
- Permittivity ε2
- 25.9312
- Absorption coefficient α
- 908996 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 22.0023 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 6.50091 µm⁻¹
- Group index ng
- -0.769523
- 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
# Cr (Chromium): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–62.0 µm
cr = ls.fetch_refractiveindex("main", "Cr", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cr.range_nm) # (247.97, 61992) nm
eps = cr.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_46e3b10e7354/lightsmith"
cr = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(cr.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (cr/rakic-1998-bb).
# ... load cr as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=cr)],
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 | 0.73226 | 2.3139 |
| 0.25494 | 0.76518 | 2.3811 |
| 0.26212 | 0.79993 | 2.4494 |
| 0.26949 | 0.83662 | 2.5186 |
| 0.27707 | 0.87537 | 2.5888 |
| 0.28487 | 0.91629 | 2.66 |
| 0.29288 | 0.95952 | 2.732 |
| 0.30112 | 1.0052 | 2.8049 |
| 0.3096 | 1.0534 | 2.8786 |
| 0.31831 | 1.1044 | 2.9529 |
| 0.32726 | 1.1583 | 3.0279 |
| 0.33647 | 1.2152 | 3.1032 |
| 0.34594 | 1.2752 | 3.1788 |
| 0.35567 | 1.3387 | 3.2545 |
| 0.36568 | 1.4055 | 3.3301 |
| 0.37596 | 1.476 | 3.4052 |
| 0.38654 | 1.5502 | 3.4797 |
| 0.39742 | 1.6283 | 3.5531 |
| 0.4086 | 1.7101 | 3.6251 |
| 0.42009 | 1.7958 | 3.6954 |
| 0.43191 | 1.8853 | 3.7635 |
| 0.44406 | 1.9786 | 3.8289 |
| 0.45656 | 2.0753 | 3.8913 |
| 0.4694 | 2.1754 | 3.9501 |
| 0.48261 | 2.2784 | 4.0048 |
| 0.49619 | 2.3839 | 4.0552 |
| 0.51015 | 2.4916 | 4.1009 |
| 0.5245 | 2.6008 | 4.1414 |
| 0.53926 | 2.7109 | 4.1766 |
| 0.55443 | 2.8213 | 4.2063 |
| 0.57003 | 2.9314 | 4.2305 |
| 0.58606 | 3.0404 | 4.2492 |
| 0.60255 | 3.1476 | 4.2625 |
| 0.6195 | 3.2524 | 4.2706 |
| 0.63693 | 3.3541 | 4.2739 |
| 0.65485 | 3.4522 | 4.2727 |
| 0.67328 | 3.5462 | 4.2674 |
| 0.69222 | 3.6356 | 4.2586 |
| 0.7117 | 3.7199 | 4.2468 |
| 0.73172 | 3.7989 | 4.2326 |
| 0.75231 | 3.8724 | 4.2165 |
| 0.77347 | 3.9401 | 4.1991 |
| 0.79523 | 4.002 | 4.181 |
| 0.81761 | 4.0579 | 4.1628 |
| 0.84061 | 4.1079 | 4.145 |
| 0.86426 | 4.152 | 4.1281 |
| 0.88857 | 4.1902 | 4.1127 |
| 0.91357 | 4.2228 | 4.0992 |
| 0.93928 | 4.2497 | 4.088 |
| 0.9657 | 4.2712 | 4.0797 |
| 0.99287 | 4.2874 | 4.0745 |
| 1.0208 | 4.2985 | 4.0728 |
| 1.0495 | 4.3047 | 4.075 |
| 1.0791 | 4.3061 | 4.0815 |
| 1.1094 | 4.3029 | 4.0925 |
| 1.1406 | 4.2954 | 4.1083 |
| 1.1727 | 4.2838 | 4.1293 |
| 1.2057 | 4.2682 | 4.1557 |
| 1.2396 | 4.2488 | 4.1878 |
| 1.2745 | 4.2259 | 4.2259 |
| 1.3104 | 4.1997 | 4.2702 |
| 1.3472 | 4.1705 | 4.321 |
| 1.3851 | 4.1384 | 4.3785 |
| 1.4241 | 4.1037 | 4.443 |
| 1.4642 | 4.0667 | 4.5147 |
| 1.5054 | 4.0277 | 4.5939 |
| 1.5477 | 3.9869 | 4.6807 |
| 1.5913 | 3.9447 | 4.7754 |
| 1.636 | 3.9014 | 4.8781 |
| 1.6821 | 3.8573 | 4.989 |
| 1.7294 | 3.8128 | 5.1081 |
| 1.778 | 3.7682 | 5.2357 |
| 1.8281 | 3.7237 | 5.3717 |
| 1.8795 | 3.6799 | 5.5161 |
| 1.9324 | 3.6369 | 5.6691 |
| 1.9867 | 3.595 | 5.8307 |
| 2.0426 | 3.5546 | 6.0007 |
| 2.1001 | 3.5159 | 6.1791 |
| 2.1592 | 3.4792 | 6.3659 |
| 2.2199 | 3.4445 | 6.5611 |
| 2.2824 | 3.4122 | 6.7645 |
| 2.3466 | 3.3824 | 6.9761 |
| 2.4126 | 3.3552 | 7.1959 |
| 2.4805 | 3.3307 | 7.4238 |
| 2.5503 | 3.3091 | 7.6597 |
| 2.6221 | 3.2904 | 7.9037 |
| 2.6958 | 3.2747 | 8.1557 |
| 2.7717 | 3.2621 | 8.4158 |
| 2.8497 | 3.2525 | 8.6839 |
| 2.9298 | 3.2461 | 8.9601 |
| 3.0123 | 3.2429 | 9.2444 |
| 3.097 | 3.243 | 9.537 |
| 3.1841 | 3.2463 | 9.8379 |
| 3.2737 | 3.253 | 10.147 |
| 3.3658 | 3.263 | 10.465 |
| 3.4605 | 3.2765 | 10.791 |
| 3.5579 | 3.2935 | 11.127 |
| 3.658 | 3.3141 | 11.471 |
| 3.7609 | 3.3383 | 11.824 |
| 3.8667 | 3.3662 | 12.187 |
| 3.9755 | 3.398 | 12.559 |
| 4.0873 | 3.4337 | 12.94 |
| 4.2023 | 3.4734 | 13.332 |
| 4.3206 | 3.5172 | 13.733 |
| 4.4421 | 3.5654 | 14.145 |
| 4.5671 | 3.618 | 14.567 |
| 4.6956 | 3.6751 | 15.0 |
| 4.8277 | 3.7371 | 15.444 |
| 4.9635 | 3.8039 | 15.899 |
| 5.1032 | 3.8759 | 16.365 |
| 5.2468 | 3.9532 | 16.843 |
| 5.3944 | 4.0361 | 17.333 |
| 5.5461 | 4.1247 | 17.835 |
| 5.7022 | 4.2194 | 18.349 |
| 5.8626 | 4.3203 | 18.876 |
| 6.0275 | 4.4277 | 19.415 |
| 6.1971 | 4.542 | 19.968 |
| 6.3715 | 4.6634 | 20.534 |
| 6.5507 | 4.7923 | 21.113 |
| 6.735 | 4.9289 | 21.707 |
| 6.9245 | 5.0736 | 22.314 |
| 7.1193 | 5.2269 | 22.935 |
| 7.3196 | 5.3889 | 23.571 |
| 7.5256 | 5.5602 | 24.221 |
| 7.7373 | 5.741 | 24.886 |
| 7.955 | 5.932 | 25.567 |
| 8.1788 | 6.1334 | 26.262 |
| 8.4089 | 6.3457 | 26.973 |
| 8.6455 | 6.5694 | 27.699 |
| 8.8887 | 6.805 | 28.44 |
| 9.1388 | 7.0528 | 29.198 |
| 9.3959 | 7.3135 | 29.971 |
| 9.6603 | 7.5876 | 30.761 |
| 9.9321 | 7.8755 | 31.566 |
| 10.212 | 8.1777 | 32.388 |
| 10.499 | 8.4949 | 33.225 |
| 10.794 | 8.8276 | 34.079 |
| 11.098 | 9.1762 | 34.949 |
| 11.41 | 9.5415 | 35.835 |
| 11.731 | 9.9238 | 36.737 |
| 12.061 | 10.324 | 37.654 |
| 12.401 | 10.742 | 38.588 |
| 12.749 | 11.179 | 39.537 |
| 13.108 | 11.636 | 40.502 |
| 13.477 | 12.112 | 41.482 |
| 13.856 | 12.609 | 42.477 |
| 14.246 | 13.127 | 43.487 |
| 14.647 | 13.666 | 44.512 |
| 15.059 | 14.227 | 45.55 |
| 15.482 | 14.811 | 46.603 |
| 15.918 | 15.417 | 47.669 |
| 16.366 | 16.047 | 48.748 |
| 16.826 | 16.701 | 49.84 |
| 17.3 | 17.378 | 50.944 |
| 17.786 | 18.08 | 52.06 |
| 18.287 | 18.807 | 53.187 |
| 18.801 | 19.559 | 54.325 |
| 19.33 | 20.337 | 55.474 |
| 19.874 | 21.139 | 56.632 |
| 20.433 | 21.968 | 57.8 |
| 21.008 | 22.822 | 58.976 |
| 21.599 | 23.702 | 60.161 |
| 22.207 | 24.609 | 61.354 |
| 22.832 | 25.541 | 62.554 |
| 23.474 | 26.499 | 63.761 |
| 24.134 | 27.482 | 64.974 |
| 24.813 | 28.492 | 66.193 |
| 25.512 | 29.527 | 67.418 |
| 26.229 | 30.588 | 68.647 |
| 26.967 | 31.673 | 69.881 |
| 27.726 | 32.784 | 71.119 |
| 28.506 | 33.919 | 72.362 |
| 29.308 | 35.078 | 73.607 |
| 30.133 | 36.262 | 74.857 |
| 30.98 | 37.469 | 76.109 |
| 31.852 | 38.699 | 77.364 |
| 32.748 | 39.952 | 78.622 |
| 33.67 | 41.228 | 79.883 |
| 34.617 | 42.526 | 81.146 |
| 35.591 | 43.845 | 82.412 |
| 36.592 | 45.186 | 83.681 |
| 37.622 | 46.547 | 84.952 |
| 38.68 | 47.929 | 86.226 |
| 39.768 | 49.331 | 87.503 |
| 40.887 | 50.752 | 88.783 |
| 42.038 | 52.193 | 90.067 |
| 43.22 | 53.652 | 91.354 |
| 44.436 | 55.13 | 92.645 |
| 45.686 | 56.626 | 93.94 |
| 46.972 | 58.14 | 95.24 |
| 48.293 | 59.672 | 96.544 |
| 49.652 | 61.221 | 97.854 |
| 51.049 | 62.787 | 99.17 |
| 52.485 | 64.37 | 100.49 |
| 53.962 | 65.97 | 101.82 |
| 55.48 | 67.586 | 103.16 |
| 57.041 | 69.219 | 104.5 |
| 58.646 | 70.868 | 105.85 |
| 60.296 | 72.533 | 107.21 |
| 61.992 | 74.214 | 108.58 |
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