Optical constants
Refractive index of Cu (Copper)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.207–12.4 µm
- Data
- tabulated nk
- Range
- 0.2066–12.4 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.460939
- Extinction coefficient k
- 2.97355
- Permittivity ε1
- -8.62953
- Permittivity ε2
- 2.74125
- Absorption coefficient α
- 635921 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 31.4504 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -4.7995 µm⁻¹
- Group index ng
- 3.28113
- 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
# Cu (Copper): Rakić et al. 1998: Brendel-Bormann model; n,k 0.207–12.4 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm) # (206.64, 12398) nm
eps = cu.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_157a517c1961/lightsmith"
cu = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(cu.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (cu/rakic-1998-bb).
# ... load cu as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=cu)],
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 |
|---|---|---|
| 0.20664 | 1.3031 | 1.6826 |
| 0.21094 | 1.322 | 1.7001 |
| 0.21532 | 1.3435 | 1.716 |
| 0.2198 | 1.3669 | 1.7294 |
| 0.22437 | 1.3916 | 1.7398 |
| 0.22903 | 1.4167 | 1.7469 |
| 0.23379 | 1.4414 | 1.7505 |
| 0.23865 | 1.4648 | 1.7507 |
| 0.24361 | 1.4861 | 1.7474 |
| 0.24868 | 1.5045 | 1.7411 |
| 0.25385 | 1.5194 | 1.7321 |
| 0.25912 | 1.5299 | 1.721 |
| 0.26451 | 1.5355 | 1.7083 |
| 0.27001 | 1.5356 | 1.695 |
| 0.27562 | 1.5297 | 1.6818 |
| 0.28135 | 1.5175 | 1.67 |
| 0.2872 | 1.4987 | 1.6607 |
| 0.29317 | 1.4736 | 1.6554 |
| 0.29926 | 1.4425 | 1.6557 |
| 0.30548 | 1.4064 | 1.6633 |
| 0.31183 | 1.3668 | 1.6796 |
| 0.31832 | 1.3258 | 1.7058 |
| 0.32493 | 1.2862 | 1.7422 |
| 0.33169 | 1.2507 | 1.7884 |
| 0.33858 | 1.222 | 1.8427 |
| 0.34562 | 1.202 | 1.9028 |
| 0.35281 | 1.1918 | 1.9658 |
| 0.36014 | 1.1915 | 2.0285 |
| 0.36763 | 1.2001 | 2.0881 |
| 0.37527 | 1.2161 | 2.1422 |
| 0.38307 | 1.2373 | 2.1891 |
| 0.39103 | 1.2613 | 2.2277 |
| 0.39916 | 1.2856 | 2.2575 |
| 0.40746 | 1.3077 | 2.2785 |
| 0.41593 | 1.3253 | 2.2916 |
| 0.42458 | 1.3363 | 2.2977 |
| 0.4334 | 1.3389 | 2.2984 |
| 0.44241 | 1.3316 | 2.2956 |
| 0.45161 | 1.3132 | 2.2913 |
| 0.461 | 1.2832 | 2.288 |
| 0.47058 | 1.2413 | 2.288 |
| 0.48036 | 1.1879 | 2.2941 |
| 0.49035 | 1.124 | 2.3088 |
| 0.50054 | 1.0512 | 2.3343 |
| 0.51094 | 0.97185 | 2.3725 |
| 0.52157 | 0.88859 | 2.4247 |
| 0.53241 | 0.80438 | 2.4911 |
| 0.54348 | 0.72204 | 2.5713 |
| 0.55477 | 0.64392 | 2.6639 |
| 0.56631 | 0.57177 | 2.7672 |
| 0.57808 | 0.50663 | 2.8793 |
| 0.5901 | 0.44894 | 2.9983 |
| 0.60236 | 0.39868 | 3.1227 |
| 0.61488 | 0.35554 | 3.2509 |
| 0.62767 | 0.31902 | 3.3821 |
| 0.64071 | 0.28853 | 3.5153 |
| 0.65403 | 0.26347 | 3.65 |
| 0.66763 | 0.24324 | 3.7857 |
| 0.68151 | 0.22732 | 3.9221 |
| 0.69567 | 0.2152 | 4.0592 |
| 0.71014 | 0.20645 | 4.1967 |
| 0.7249 | 0.20067 | 4.3347 |
| 0.73997 | 0.19753 | 4.4732 |
| 0.75535 | 0.19675 | 4.6121 |
| 0.77105 | 0.19806 | 4.7516 |
| 0.78708 | 0.20124 | 4.8917 |
| 0.80344 | 0.2061 | 5.0325 |
| 0.82014 | 0.21249 | 5.174 |
| 0.83719 | 0.22024 | 5.3164 |
| 0.85459 | 0.22924 | 5.4597 |
| 0.87236 | 0.23937 | 5.604 |
| 0.89049 | 0.25052 | 5.7494 |
| 0.909 | 0.26262 | 5.896 |
| 0.9279 | 0.27557 | 6.0439 |
| 0.94719 | 0.28931 | 6.1931 |
| 0.96688 | 0.30376 | 6.3438 |
| 0.98698 | 0.31885 | 6.4959 |
| 1.0075 | 0.33454 | 6.6497 |
| 1.0284 | 0.35076 | 6.8052 |
| 1.0498 | 0.36747 | 6.9624 |
| 1.0716 | 0.38461 | 7.1215 |
| 1.0939 | 0.40215 | 7.2825 |
| 1.1167 | 0.42004 | 7.4456 |
| 1.1399 | 0.43824 | 7.6108 |
| 1.1636 | 0.45673 | 7.7782 |
| 1.1878 | 0.47546 | 7.948 |
| 1.2124 | 0.4944 | 8.1202 |
| 1.2376 | 0.51354 | 8.2949 |
| 1.2634 | 0.53284 | 8.4722 |
| 1.2896 | 0.55229 | 8.6522 |
| 1.3164 | 0.57187 | 8.835 |
| 1.3438 | 0.59155 | 9.0208 |
| 1.3717 | 0.61134 | 9.2095 |
| 1.4003 | 0.63121 | 9.4014 |
| 1.4294 | 0.65116 | 9.5966 |
| 1.4591 | 0.67118 | 9.7951 |
| 1.4894 | 0.69127 | 9.997 |
| 1.5204 | 0.71142 | 10.203 |
| 1.552 | 0.73165 | 10.412 |
| 1.5842 | 0.75195 | 10.625 |
| 1.6172 | 0.77232 | 10.842 |
| 1.6508 | 0.79277 | 11.063 |
| 1.6851 | 0.81332 | 11.288 |
| 1.7201 | 0.83397 | 11.517 |
| 1.7559 | 0.85474 | 11.751 |
| 1.7924 | 0.87563 | 11.989 |
| 1.8297 | 0.89667 | 12.232 |
| 1.8677 | 0.91787 | 12.479 |
| 1.9065 | 0.93926 | 12.732 |
| 1.9462 | 0.96085 | 12.989 |
| 1.9866 | 0.98266 | 13.252 |
| 2.0279 | 1.0047 | 13.52 |
| 2.0701 | 1.0271 | 13.793 |
| 2.1131 | 1.0497 | 14.072 |
| 2.157 | 1.0726 | 14.356 |
| 2.2019 | 1.096 | 14.646 |
| 2.2476 | 1.1197 | 14.942 |
| 2.2944 | 1.1438 | 15.244 |
| 2.3421 | 1.1684 | 15.552 |
| 2.3907 | 1.1934 | 15.866 |
| 2.4404 | 1.219 | 16.187 |
| 2.4912 | 1.2451 | 16.515 |
| 2.543 | 1.2719 | 16.849 |
| 2.5958 | 1.2993 | 17.19 |
| 2.6498 | 1.3273 | 17.539 |
| 2.7049 | 1.3561 | 17.894 |
| 2.7611 | 1.3856 | 18.257 |
| 2.8185 | 1.416 | 18.627 |
| 2.8771 | 1.4472 | 19.005 |
| 2.9369 | 1.4793 | 19.39 |
| 2.9979 | 1.5124 | 19.784 |
| 3.0602 | 1.5465 | 20.186 |
| 3.1239 | 1.5817 | 20.596 |
| 3.1888 | 1.6179 | 21.014 |
| 3.2551 | 1.6554 | 21.442 |
| 3.3228 | 1.6941 | 21.878 |
| 3.3918 | 1.7341 | 22.323 |
| 3.4623 | 1.7755 | 22.777 |
| 3.5343 | 1.8183 | 23.241 |
| 3.6078 | 1.8627 | 23.714 |
| 3.6828 | 1.9086 | 24.197 |
| 3.7593 | 1.9561 | 24.69 |
| 3.8375 | 2.0054 | 25.193 |
| 3.9173 | 2.0565 | 25.706 |
| 3.9987 | 2.1095 | 26.23 |
| 4.0818 | 2.1645 | 26.765 |
| 4.1667 | 2.2215 | 27.311 |
| 4.2533 | 2.2807 | 27.868 |
| 4.3417 | 2.3422 | 28.436 |
| 4.4319 | 2.406 | 29.016 |
| 4.5241 | 2.4723 | 29.608 |
| 4.6181 | 2.5412 | 30.211 |
| 4.7141 | 2.6127 | 30.828 |
| 4.8121 | 2.687 | 31.456 |
| 4.9122 | 2.7643 | 32.098 |
| 5.0143 | 2.8446 | 32.752 |
| 5.1185 | 2.928 | 33.42 |
| 5.2249 | 3.0148 | 34.101 |
| 5.3335 | 3.105 | 34.796 |
| 5.4444 | 3.1988 | 35.505 |
| 5.5576 | 3.2963 | 36.228 |
| 5.6731 | 3.3977 | 36.966 |
| 5.791 | 3.5031 | 37.718 |
| 5.9114 | 3.6128 | 38.486 |
| 6.0343 | 3.7269 | 39.269 |
| 6.1597 | 3.8455 | 40.067 |
| 6.2878 | 3.9689 | 40.881 |
| 6.4185 | 4.0972 | 41.712 |
| 6.5519 | 4.2306 | 42.559 |
| 6.6881 | 4.3695 | 43.423 |
| 6.8271 | 4.5138 | 44.303 |
| 6.9691 | 4.664 | 45.201 |
| 7.1139 | 4.8202 | 46.117 |
| 7.2618 | 4.9826 | 47.05 |
| 7.4128 | 5.1515 | 48.002 |
| 7.5669 | 5.3272 | 48.972 |
| 7.7242 | 5.5099 | 49.961 |
| 7.8847 | 5.6999 | 50.969 |
| 8.0486 | 5.8974 | 51.996 |
| 8.2159 | 6.1028 | 53.043 |
| 8.3867 | 6.3164 | 54.11 |
| 8.5611 | 6.5385 | 55.198 |
| 8.739 | 6.7693 | 56.306 |
| 8.9207 | 7.0093 | 57.434 |
| 9.1061 | 7.2588 | 58.584 |
| 9.2954 | 7.5181 | 59.756 |
| 9.4887 | 7.7876 | 60.949 |
| 9.6859 | 8.0676 | 62.165 |
| 9.8873 | 8.3586 | 63.403 |
| 10.093 | 8.661 | 64.663 |
| 10.303 | 8.9752 | 65.947 |
| 10.517 | 9.3015 | 67.254 |
| 10.735 | 9.6405 | 68.584 |
| 10.959 | 9.9926 | 69.938 |
| 11.186 | 10.358 | 71.317 |
| 11.419 | 10.738 | 72.719 |
| 11.656 | 11.132 | 74.147 |
| 11.899 | 11.541 | 75.599 |
| 12.146 | 11.966 | 77.077 |
| 12.398 | 12.406 | 78.579 |
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