Optical constants

Refractive index of Cu (Copper)

Brimhall et al. 2009: n,k 0.0101–0.0421 µm

Data
tabulated nk
Range
0.0101–0.0421 µm
Points
31
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.0101–0.0421 µm
Refractive index n
0.969909
Extinction coefficient k
0.0502727
Permittivity ε1
0.938196
Permittivity ε2
0.09752
Absorption coefficient α
306673 cm⁻¹
Penetration depth δ = λ/(2πk)
65.2161 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.909091 µm⁻¹
Group index ng
0.988636
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
60.1865 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): Brimhall et al. 2009: n,k 0.0101–0.0421 µm
cu = ls.fetch_refractiveindex("main", "Cu", "Brimhall", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cu.range_nm)  # (10.1, 42.1) nm
eps = cu.eps([20.6])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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

N. Brimhall, N. Herrick, D. D. Allred, R. S. Turley, M. Ware, J. Peatross. Measured optical constants of copper from 10 nm to 35 nm. Opt. Express 17, 23873-23879 (2009)

Cite

Nicole Brimhall et al.. Measured optical constants of copper from 10 nm to 35 nm. Optics Express, 17, 23873 (2009), doi:10.1364/oe.17.023873; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

34 rows as published
Cu (Copper), Brimhall et al. 2009: n,k 0.0101–0.0421 µm: n and k versus wavelength
λ (µm)nk
0.01010.9910.017
0.01040.9850.025
0.01070.9920.017
0.0110.9870.008
0.01130.9820.016
0.01160.9830.017
0.01190.9850.01
0.01230.9820.011
0.01270.9780.022
0.01310.9720.031
0.01360.9710.039
0.01360.9690.042
0.0140.9780.038
0.0140.9720.03
0.01450.9760.044
0.01450.9740.042
0.01510.9740.051
0.01570.9730.055
0.01630.9760.047
0.0170.9750.041
0.01780.9680.044
0.01860.9670.044
0.01950.9670.05
0.02050.970.05
0.02160.9690.053
0.02290.9610.063
0.02420.9580.066
0.02580.9490.068
0.02760.940.084
0.02960.9270.093
0.0320.9120.107
0.03480.8910.14
0.03810.880.184
0.04210.8740.236

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
—