At one wavelength

Refractive index n: 0.505403
Extinction coefficient k: 2.78806

Permittivity ε₁: -7.51784
Permittivity ε₂: 2.81819

Absorption coefficient α: 596252 cm⁻¹
Penetration depth δ = λ/(2πk): 33.5428 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -13.3582 µm⁻¹

Group index n_g: 8.35469
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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): Hagemann et al. 1974: n,k 0.0000248–248 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Hagemann", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm)  # (0.0248, 248000) 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_b2c5a3c0ff79/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/hagemann-1974).

# ... 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"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

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.

References

1) H.-J. Hagemann, W. Gudat, C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al₂O₃. J. Opt. Soc. Am. 65, 742-744 (1975)
2) H.-J. Hagemann, W. Gudat, C. Kunz. DESY report SR-74/7 (1974)

doi:10.1364/josa.65.000742 Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3, Journal of the Optical Society of America (1975)

Cite

H.-J. Hagemann, W. Gudat and C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3. Journal of the Optical Society of America, 65, 742 (1975), doi:10.1364/josa.65.000742; H.-J. Hagemann, W. Gudat, C. Kunz. DESY report SR-74/7 (1974); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

149 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Cu (Copper), Hagemann et al. 1974: n,k 0.0000248–248 µm: n and k versus wavelength
λ (µm)	n	k
2.48e-05	1.0	4.45e-09
4.133e-05	1.0	3.09e-08
8.266e-05	1.0	4.06e-07
0.0001378	1.001	3.65e-07
0.0001393	1.001	3.56e-07
0.000155	1.001	5.38e-07
0.00031	1.0	6.62e-06
0.0006199	1.0	9.49e-05
0.0008266	1.0	0.000273
0.001033	0.999	0.000624
0.001127	0.999	0.000823
0.00124	0.999	0.000851
0.001378	1.0	0.000174
0.00155	0.999	0.000263
0.001771	0.998	0.000395
0.002066	0.997	0.000651
0.00248	0.997	0.00111
0.0031	0.993	0.00245
0.004133	0.988	0.00513
0.006199	0.978	0.0159
0.008266	0.969	0.031
0.01033	0.965	0.054
0.01127	0.968	0.0599
0.01181	0.968	0.0625
0.0124	0.967	0.0653
0.01305	0.965	0.0693
0.01348	0.963	0.0744
0.01378	0.963	0.0788
0.01409	0.963	0.0834
0.01442	0.966	0.0877
0.01476	0.969	0.0911
0.01494	0.971	0.0923
0.01512	0.973	0.0934
0.01531	0.974	0.0943
0.0155	0.977	0.0946
0.01569	0.979	0.0941
0.0159	0.98	0.0936
0.0161	0.982	0.0921
0.01631	0.984	0.091
0.01653	0.983	0.0872
0.01675	0.979	0.085
0.01698	0.977	0.0857
0.01722	0.975	0.0868
0.01746	0.974	0.0881
0.01771	0.972	0.0893
0.01797	0.97	0.0908
0.01823	0.968	0.0927
0.01851	0.968	0.0945
0.01879	0.967	0.0963
0.01907	0.966	0.099
0.01937	0.965	0.102
0.01968	0.965	0.104
0.02	0.965	0.107
0.02033	0.966	0.108
0.02066	0.966	0.109
0.02101	0.966	0.109
0.02138	0.964	0.11
0.02175	0.962	0.112
0.02214	0.96	0.114
0.02254	0.958	0.117
0.02296	0.957	0.12
0.02339	0.956	0.123
0.02384	0.954	0.126
0.02431	0.953	0.13
0.0248	0.953	0.134
0.0253	0.952	0.137
0.02583	0.952	0.14
0.02638	0.951	0.143
0.02695	0.951	0.146
0.02755	0.949	0.148
0.02818	0.948	0.151
0.02883	0.945	0.154
0.02952	0.942	0.157
0.03024	0.938	0.161
0.031	0.934	0.167
0.03179	0.93	0.174
0.03263	0.927	0.18
0.03351	0.925	0.187
0.03444	0.922	0.193
0.03542	0.917	0.198
0.03647	0.91	0.205
0.03757	0.901	0.214
0.03875	0.891	0.223
0.03999	0.876	0.239
0.04133	0.856	0.262
0.04275	0.849	0.302
0.04428	0.862	0.346
0.04592	0.884	0.382
0.04769	0.921	0.403
0.04959	0.96	0.396
0.05166	0.961	0.373
0.05391	0.943	0.366
0.05636	0.917	0.381
0.05904	0.897	0.411
0.06199	0.882	0.455
0.06525	0.883	0.507
0.06888	0.89	0.561
0.07293	0.913	0.62
0.07749	0.954	0.673
0.07999	0.981	0.695
0.08266	1.009	0.707
0.08551	1.034	0.717
0.08856	1.055	0.724
0.09537	1.084	0.724
0.1033	1.091	0.713
0.1127	1.074	0.754
0.124	1.038	0.818
0.1305	1.029	0.867
0.1378	1.027	0.921
0.1459	1.029	0.979
0.155	1.029	1.03
0.1653	1.005	1.09
0.1771	0.972	1.2
0.1907	0.958	1.37
0.2066	1.036	1.59
0.2138	1.102	1.67
0.2214	1.183	1.74
0.2296	1.276	1.78
0.2384	1.378	1.8
0.248	1.47	1.78
0.2583	1.533	1.71
0.2695	1.52	1.67
0.2818	1.487	1.64
0.2952	1.419	1.64
0.31	1.344	1.72
0.3263	1.336	1.81
0.3444	1.31	1.87
0.3647	1.27	1.95
0.3875	1.232	2.07
0.4133	1.184	2.21
0.4428	1.169	2.36
0.4769	1.152	2.5
0.5166	1.121	2.6
0.5391	1.037	2.59
0.5636	0.826	2.6
0.5904	0.468	2.81
0.6199	0.272	3.24
0.6525	0.214	3.67
0.6702	0.215	3.86
0.6888	0.213	4.05
0.7085	0.214	4.24
0.7293	0.223	4.43
0.8266	0.26	5.26
1.24	0.433	8.46
2.48	1.692	17.6
12.4	29.1	71.1
24.8	62.8	103.0
124.0	186.0	213.0
248.0	270.0	294.0

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Plot