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

Range 0.2066–12.4 µm
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.

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

Fit of experimental data from several sources to Lorentz-Drude (LD) model

References

A. D. Rakić, A. B. Djurišic, J. M. Elazar, and M. L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 37, 5271-5283 (1998)
[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
Cu (Copper), Rakić et al. 1998: Lorentz-Drude model; n,k 0.207–12.4 µm: n and k versus wavelength
λ (µm)nk
0.206641.10181.8654
0.210941.15791.8851
0.215321.21451.8982
0.21981.27071.9041
0.224371.3251.9029
0.229031.37611.8947
0.233791.42251.88
0.238651.46321.8596
0.243611.49691.8346
0.248681.52291.8062
0.253851.54051.7759
0.259121.54961.7452
0.264511.55011.7155
0.270011.54241.6882
0.275621.5271.6647
0.281351.50451.6461
0.28721.47581.6335
0.293171.44191.6279
0.299261.40411.63
0.305481.36361.6405
0.311831.32191.6598
0.318321.28071.688
0.324931.24181.725
0.331691.20681.7703
0.338581.17761.8227
0.345621.15561.8809
0.352811.14231.943
0.360141.13862.0067
0.367631.14482.0693
0.375271.16082.1277
0.383071.18542.1787
0.391031.21632.219
0.399161.24962.2459
0.407461.28052.258
0.415931.30332.2558
0.424581.31232.2423
0.43341.30362.2223
0.442411.27522.2022
0.451611.22792.1883
0.4611.16442.1861
0.470581.08922.1995
0.480361.00732.2301
0.490350.923562.2781
0.500540.842042.3418
0.510940.76562.4188
0.521570.69592.5066
0.532410.633582.6025
0.543480.578612.7044
0.554770.530522.8106
0.566310.488652.9199
0.578080.452273.0314
0.59010.420683.1446
0.602360.393263.259
0.614880.369433.3746
0.627670.348723.491
0.640710.330723.6084
0.654030.315073.7266
0.667630.301493.8457
0.681510.289713.9658
0.695670.279554.0869
0.710140.270814.2092
0.72490.263364.3326
0.739970.257064.4573
0.755350.25184.5834
0.771050.247514.7109
0.787080.244094.8399
0.803440.241494.9706
0.820140.239655.1029
0.837190.238535.2371
0.854590.238075.373
0.872360.238255.511
0.890490.239045.6509
0.9090.240425.793
0.92790.242375.9372
0.947190.244876.0836
0.966880.247916.2324
0.986980.251486.3836
1.00750.255576.5372
1.02840.260196.6934
1.04980.265326.8523
1.07160.270967.0138
1.09390.277137.1781
1.11670.283827.3452
1.13990.291047.5152
1.16360.29887.6883
1.18780.307097.8643
1.21240.315958.0436
1.23760.325378.226
1.26340.335368.4118
1.28960.345958.6009
1.31640.357148.7934
1.34380.368968.9895
1.37170.381429.1891
1.40030.394549.3925
1.42940.408349.5995
1.45910.422849.8104
1.48940.4380610.025
1.52040.4540310.244
1.5520.4707710.467
1.58420.488310.694
1.61720.5066610.925
1.65080.5258711.161
1.68510.5459611.4
1.72010.5669611.645
1.75590.588911.894
1.79240.611812.147
1.82970.635712.405
1.86770.6606412.668
1.90650.6866412.936
1.94620.7137313.209
1.98660.7419513.486
2.02790.7713413.769
2.07010.8019114.057
2.11310.833714.35
2.1570.8667414.649
2.20190.9010614.952
2.24760.9366915.262
2.29440.9736415.576
2.34211.011915.897
2.39071.051616.223
2.44041.092616.554
2.49121.135116.892
2.5431.178917.235
2.59581.224117.584
2.64981.270717.939
2.70491.318618.3
2.76111.367918.668
2.81851.418519.041
2.87711.470419.421
2.93691.523519.808
2.99791.577820.2
3.06021.633220.6
3.12391.689621.006
3.18881.74721.419
3.25511.805321.839
3.32281.864322.266
3.39181.924122.7
3.46231.984423.143
3.53432.045223.592
3.60782.106424.05
3.68282.167924.517
3.75932.229624.991
3.83752.291425.475
3.91732.353425.968
3.99872.415426.471
4.08182.477526.983
4.16672.539627.507
4.25332.601828.04
4.34172.664128.585
4.43192.726729.142
4.52412.789529.711
4.61812.852930.292
4.71412.916830.886
4.81212.981631.494
4.91223.047432.115
5.01433.114532.751
5.11853.183233.401
5.22493.253634.066
5.33353.326134.746
5.44443.401135.442
5.55763.478736.154
5.67313.559336.882
5.7913.643237.626
5.91143.730838.388
6.03433.822339.166
6.15973.918239.962
6.28784.018640.775
6.41854.123941.606
6.55194.234442.456
6.68814.350443.323
6.82714.472244.209
6.96914.600245.114
7.11394.734646.038
7.26184.875846.981
7.41285.023947.944
7.56695.179448.926
7.72425.342549.928
7.88475.513650.95
8.04865.692951.993
8.21595.880853.056
8.38676.077654.14
8.56116.283555.245
8.7396.49956.372
8.92076.724457.52
9.10616.9658.691
9.29547.206159.883
9.48877.463261.098
9.68597.731662.335
9.88738.011763.596
10.0938.303964.879
10.3038.608666.186
10.5178.926167.517
10.7359.25768.872
10.9599.601770.251
11.1869.960671.655
11.41910.33473.083
11.65610.72374.536
11.89911.12776.015
12.14611.54877.519
12.39811.98579.048

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—