Optical constants
Refractive index of Metamaterials
Valentine et al. 2008: Metamaterial; n 1.200–1.775 µm
- Data
- tabulated n
- Range
- 1.2–1.775 µm
- Points
- 24
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 0.238
- Extinction coefficient k
- 0
- Permittivity ε1
- 0.056644
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1.2 µm⁻¹
- Group index ng
- 1.99
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.849207 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
# Metamaterials: Valentine et al. 2008: Metamaterial; n 1.200–1.775 µm
metamaterials = ls.fetch_refractiveindex("other", "metamaterials", "Valentine", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(metamaterials.range_nm) # (1200, 1775) nm
eps = metamaterials.eps([1460]) # complex permittivityDownloads 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_24315ee35c57/lightsmith"
metamaterials = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(metamaterials.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (metamaterials/valentine-2008).
# ... load metamaterials as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=metamaterials)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=1200, stop_nm=1775, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelengthSame 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
- n <= 0 at some wavelengths in the source data
References
- doi:10.1038/nature07247 Three-dimensional optical metamaterial with a negative refractive index, Nature (2008)
Cite
Jason Valentine et al.. Three-dimensional optical metamaterial with a negative refractive index. Nature, 455, 376-379 (2008), doi:10.1038/nature07247; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
24 rows as published| λ (µm) | n |
|---|---|
| 1.2 | 0.63 |
| 1.225 | 0.66 |
| 1.25 | 0.66 |
| 1.275 | 0.6 |
| 1.3 | 0.56 |
| 1.325 | 0.56 |
| 1.35 | 0.5 |
| 1.375 | 0.45 |
| 1.4 | 0.41 |
| 1.425 | 0.32 |
| 1.45 | 0.25 |
| 1.475 | 0.22 |
| 1.5 | 0.13 |
| 1.525 | 0.06 |
| 1.55 | -0.04 |
| 1.575 | -0.17 |
| 1.6 | -0.21 |
| 1.625 | -0.34 |
| 1.65 | -0.47 |
| 1.675 | -0.57 |
| 1.7 | -0.63 |
| 1.725 | -0.8 |
| 1.75 | -1.03 |
| 1.775 | -1.24 |
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
- —