Optical constants
Refractive index of Cu (Copper)
Rakić et al. 1998: Lorentz-Drude model; n,k 0.207–12.4 µm
- Data
- tabulated nk
- Range
- 0.2066–12.4 µm
- Points
- 200
- Licence
- CC0-1.0
- Lightsmith
- bundled
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.42725
- Extinction coefficient k
- 3.12106
- Permittivity ε1
- -9.55845
- Permittivity ε2
- 2.66694
- Absorption coefficient α
- 667467 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 29.964 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -2.62812 µm⁻¹
- Group index ng
- 1.97153
- 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: Lorentz-Drude model; n,k 0.207–12.4 µm
cu = ls.LibraryMaterial(name="Cu", dataset="Rakic-LD")
print(cu.range_nm) # (206.64, 12398) nm
eps = cu.eps([633]) # complex permittivity
Ships with the library: works offline.
import lightsmith as ls
# Cu (Copper): Rakić et al. 1998: Lorentz-Drude model; n,k 0.207–12.4 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Rakic-LD", 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_eb965425e780/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-ld).
# ... 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 | 1.1018 | 1.8654 |
| 0.21094 | 1.1579 | 1.8851 |
| 0.21532 | 1.2145 | 1.8982 |
| 0.2198 | 1.2707 | 1.9041 |
| 0.22437 | 1.325 | 1.9029 |
| 0.22903 | 1.3761 | 1.8947 |
| 0.23379 | 1.4225 | 1.88 |
| 0.23865 | 1.4632 | 1.8596 |
| 0.24361 | 1.4969 | 1.8346 |
| 0.24868 | 1.5229 | 1.8062 |
| 0.25385 | 1.5405 | 1.7759 |
| 0.25912 | 1.5496 | 1.7452 |
| 0.26451 | 1.5501 | 1.7155 |
| 0.27001 | 1.5424 | 1.6882 |
| 0.27562 | 1.527 | 1.6647 |
| 0.28135 | 1.5045 | 1.6461 |
| 0.2872 | 1.4758 | 1.6335 |
| 0.29317 | 1.4419 | 1.6279 |
| 0.29926 | 1.4041 | 1.63 |
| 0.30548 | 1.3636 | 1.6405 |
| 0.31183 | 1.3219 | 1.6598 |
| 0.31832 | 1.2807 | 1.688 |
| 0.32493 | 1.2418 | 1.725 |
| 0.33169 | 1.2068 | 1.7703 |
| 0.33858 | 1.1776 | 1.8227 |
| 0.34562 | 1.1556 | 1.8809 |
| 0.35281 | 1.1423 | 1.943 |
| 0.36014 | 1.1386 | 2.0067 |
| 0.36763 | 1.1448 | 2.0693 |
| 0.37527 | 1.1608 | 2.1277 |
| 0.38307 | 1.1854 | 2.1787 |
| 0.39103 | 1.2163 | 2.219 |
| 0.39916 | 1.2496 | 2.2459 |
| 0.40746 | 1.2805 | 2.258 |
| 0.41593 | 1.3033 | 2.2558 |
| 0.42458 | 1.3123 | 2.2423 |
| 0.4334 | 1.3036 | 2.2223 |
| 0.44241 | 1.2752 | 2.2022 |
| 0.45161 | 1.2279 | 2.1883 |
| 0.461 | 1.1644 | 2.1861 |
| 0.47058 | 1.0892 | 2.1995 |
| 0.48036 | 1.0073 | 2.2301 |
| 0.49035 | 0.92356 | 2.2781 |
| 0.50054 | 0.84204 | 2.3418 |
| 0.51094 | 0.7656 | 2.4188 |
| 0.52157 | 0.6959 | 2.5066 |
| 0.53241 | 0.63358 | 2.6025 |
| 0.54348 | 0.57861 | 2.7044 |
| 0.55477 | 0.53052 | 2.8106 |
| 0.56631 | 0.48865 | 2.9199 |
| 0.57808 | 0.45227 | 3.0314 |
| 0.5901 | 0.42068 | 3.1446 |
| 0.60236 | 0.39326 | 3.259 |
| 0.61488 | 0.36943 | 3.3746 |
| 0.62767 | 0.34872 | 3.491 |
| 0.64071 | 0.33072 | 3.6084 |
| 0.65403 | 0.31507 | 3.7266 |
| 0.66763 | 0.30149 | 3.8457 |
| 0.68151 | 0.28971 | 3.9658 |
| 0.69567 | 0.27955 | 4.0869 |
| 0.71014 | 0.27081 | 4.2092 |
| 0.7249 | 0.26336 | 4.3326 |
| 0.73997 | 0.25706 | 4.4573 |
| 0.75535 | 0.2518 | 4.5834 |
| 0.77105 | 0.24751 | 4.7109 |
| 0.78708 | 0.24409 | 4.8399 |
| 0.80344 | 0.24149 | 4.9706 |
| 0.82014 | 0.23965 | 5.1029 |
| 0.83719 | 0.23853 | 5.2371 |
| 0.85459 | 0.23807 | 5.373 |
| 0.87236 | 0.23825 | 5.511 |
| 0.89049 | 0.23904 | 5.6509 |
| 0.909 | 0.24042 | 5.793 |
| 0.9279 | 0.24237 | 5.9372 |
| 0.94719 | 0.24487 | 6.0836 |
| 0.96688 | 0.24791 | 6.2324 |
| 0.98698 | 0.25148 | 6.3836 |
| 1.0075 | 0.25557 | 6.5372 |
| 1.0284 | 0.26019 | 6.6934 |
| 1.0498 | 0.26532 | 6.8523 |
| 1.0716 | 0.27096 | 7.0138 |
| 1.0939 | 0.27713 | 7.1781 |
| 1.1167 | 0.28382 | 7.3452 |
| 1.1399 | 0.29104 | 7.5152 |
| 1.1636 | 0.2988 | 7.6883 |
| 1.1878 | 0.30709 | 7.8643 |
| 1.2124 | 0.31595 | 8.0436 |
| 1.2376 | 0.32537 | 8.226 |
| 1.2634 | 0.33536 | 8.4118 |
| 1.2896 | 0.34595 | 8.6009 |
| 1.3164 | 0.35714 | 8.7934 |
| 1.3438 | 0.36896 | 8.9895 |
| 1.3717 | 0.38142 | 9.1891 |
| 1.4003 | 0.39454 | 9.3925 |
| 1.4294 | 0.40834 | 9.5995 |
| 1.4591 | 0.42284 | 9.8104 |
| 1.4894 | 0.43806 | 10.025 |
| 1.5204 | 0.45403 | 10.244 |
| 1.552 | 0.47077 | 10.467 |
| 1.5842 | 0.4883 | 10.694 |
| 1.6172 | 0.50666 | 10.925 |
| 1.6508 | 0.52587 | 11.161 |
| 1.6851 | 0.54596 | 11.4 |
| 1.7201 | 0.56696 | 11.645 |
| 1.7559 | 0.5889 | 11.894 |
| 1.7924 | 0.6118 | 12.147 |
| 1.8297 | 0.6357 | 12.405 |
| 1.8677 | 0.66064 | 12.668 |
| 1.9065 | 0.68664 | 12.936 |
| 1.9462 | 0.71373 | 13.209 |
| 1.9866 | 0.74195 | 13.486 |
| 2.0279 | 0.77134 | 13.769 |
| 2.0701 | 0.80191 | 14.057 |
| 2.1131 | 0.8337 | 14.35 |
| 2.157 | 0.86674 | 14.649 |
| 2.2019 | 0.90106 | 14.952 |
| 2.2476 | 0.93669 | 15.262 |
| 2.2944 | 0.97364 | 15.576 |
| 2.3421 | 1.0119 | 15.897 |
| 2.3907 | 1.0516 | 16.223 |
| 2.4404 | 1.0926 | 16.554 |
| 2.4912 | 1.1351 | 16.892 |
| 2.543 | 1.1789 | 17.235 |
| 2.5958 | 1.2241 | 17.584 |
| 2.6498 | 1.2707 | 17.939 |
| 2.7049 | 1.3186 | 18.3 |
| 2.7611 | 1.3679 | 18.668 |
| 2.8185 | 1.4185 | 19.041 |
| 2.8771 | 1.4704 | 19.421 |
| 2.9369 | 1.5235 | 19.808 |
| 2.9979 | 1.5778 | 20.2 |
| 3.0602 | 1.6332 | 20.6 |
| 3.1239 | 1.6896 | 21.006 |
| 3.1888 | 1.747 | 21.419 |
| 3.2551 | 1.8053 | 21.839 |
| 3.3228 | 1.8643 | 22.266 |
| 3.3918 | 1.9241 | 22.7 |
| 3.4623 | 1.9844 | 23.143 |
| 3.5343 | 2.0452 | 23.592 |
| 3.6078 | 2.1064 | 24.05 |
| 3.6828 | 2.1679 | 24.517 |
| 3.7593 | 2.2296 | 24.991 |
| 3.8375 | 2.2914 | 25.475 |
| 3.9173 | 2.3534 | 25.968 |
| 3.9987 | 2.4154 | 26.471 |
| 4.0818 | 2.4775 | 26.983 |
| 4.1667 | 2.5396 | 27.507 |
| 4.2533 | 2.6018 | 28.04 |
| 4.3417 | 2.6641 | 28.585 |
| 4.4319 | 2.7267 | 29.142 |
| 4.5241 | 2.7895 | 29.711 |
| 4.6181 | 2.8529 | 30.292 |
| 4.7141 | 2.9168 | 30.886 |
| 4.8121 | 2.9816 | 31.494 |
| 4.9122 | 3.0474 | 32.115 |
| 5.0143 | 3.1145 | 32.751 |
| 5.1185 | 3.1832 | 33.401 |
| 5.2249 | 3.2536 | 34.066 |
| 5.3335 | 3.3261 | 34.746 |
| 5.4444 | 3.4011 | 35.442 |
| 5.5576 | 3.4787 | 36.154 |
| 5.6731 | 3.5593 | 36.882 |
| 5.791 | 3.6432 | 37.626 |
| 5.9114 | 3.7308 | 38.388 |
| 6.0343 | 3.8223 | 39.166 |
| 6.1597 | 3.9182 | 39.962 |
| 6.2878 | 4.0186 | 40.775 |
| 6.4185 | 4.1239 | 41.606 |
| 6.5519 | 4.2344 | 42.456 |
| 6.6881 | 4.3504 | 43.323 |
| 6.8271 | 4.4722 | 44.209 |
| 6.9691 | 4.6002 | 45.114 |
| 7.1139 | 4.7346 | 46.038 |
| 7.2618 | 4.8758 | 46.981 |
| 7.4128 | 5.0239 | 47.944 |
| 7.5669 | 5.1794 | 48.926 |
| 7.7242 | 5.3425 | 49.928 |
| 7.8847 | 5.5136 | 50.95 |
| 8.0486 | 5.6929 | 51.993 |
| 8.2159 | 5.8808 | 53.056 |
| 8.3867 | 6.0776 | 54.14 |
| 8.5611 | 6.2835 | 55.245 |
| 8.739 | 6.499 | 56.372 |
| 8.9207 | 6.7244 | 57.52 |
| 9.1061 | 6.96 | 58.691 |
| 9.2954 | 7.2061 | 59.883 |
| 9.4887 | 7.4632 | 61.098 |
| 9.6859 | 7.7316 | 62.335 |
| 9.8873 | 8.0117 | 63.596 |
| 10.093 | 8.3039 | 64.879 |
| 10.303 | 8.6086 | 66.186 |
| 10.517 | 8.9261 | 67.517 |
| 10.735 | 9.257 | 68.872 |
| 10.959 | 9.6017 | 70.251 |
| 11.186 | 9.9606 | 71.655 |
| 11.419 | 10.334 | 73.083 |
| 11.656 | 10.723 | 74.536 |
| 11.899 | 11.127 | 76.015 |
| 12.146 | 11.548 | 77.519 |
| 12.398 | 11.985 | 79.048 |
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 Lorentz-Drude (LD) model