Optical constants
Refractive index of Ge - Germanium (CRYSTRAN)
Ge - Germanium: n,k 2.058–13.02 µm
- Data
- tabulated n + tabulated k
- Range
- 2.058–13.02 µm
- Points
- 16
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 4.01526
- Extinction coefficient k
- 0
- Permittivity ε1
- 16.1223
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -0.00553936 µm⁻¹
- Group index ng
- 4.04395
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.239352 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
# Ge - Germanium (CRYSTRAN): Ge - Germanium
crystran_ge = ls.fetch_refractiveindex("specs", "CRYSTRAN-optical", "Ge", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(crystran_ge.range_nm) # (2058, 13020) nm
eps = crystran_ge.eps([5180]) # 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_6f540a28946c/lightsmith"
crystran_ge = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(crystran_ge.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (crystran-ge/crystran).
# ... load crystran_ge as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=crystran_ge)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=2058, stop_nm=13020, 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
Properties
- density
- value: 5330
- thermal dispersion
- type: constant, value: 396e-06
- thermal expansion
- value: 6.1e-06, temperature: 298
- hardness
- type: Knoop, value: 7.65e9
- melting point
- value: 1209
- thermal conductivity
- value: 58.62, temperature: 293
- youngs modulus
- value: 102.7e9
- poissons ratio
- value: 0.28
- solubility
- value: 0
Thermo-optic coefficient
- dn/dT = 0.000396 K⁻¹
References
See also Crystran Ge online data sheet
Cite
Crystran Ltd. The Crystran handbook of infra-red and ultra-violet optical materials (5th edition, 2023); See also Crystran Ge online data sheet; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
Computed on 16 wavelengths, the same grid as the API and the library| λ (µm) | n | k |
|---|---|---|
| 2.058 | 4.102 | 0 |
| 2.153 | 4.0919 | 0 |
| 2.313 | 4.0786 | 0 |
| 2.437 | 4.0708 | 0 |
| 2.577 | 4.0609 | 0 |
| 2.714 | 4.0562 | 0 |
| 2.998 | 4.0452 | 0 |
| 3.303 | 4.0369 | 0 |
| 4.258 | 4.0216 | 0 |
| 4.866 | 4.017 | 0 |
| 6.238 | 4.0094 | 0 |
| 8.66 | 4.0043 | 1.442000e-06 |
| 9.72 | 4.0034 | 1.404000e-06 |
| 11.04 | 4.0026 | 2.446000e-06 |
| 12 | 4.0023 | 3.380000e-05 |
| 13.02 | 4.0021 | 3.136000e-05 |
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
- —
Germanium is a high index material that is used to manufacture Attenuated Total Reflection (ATR) prisms for spectroscopy. Its refractive index is such that Germanium makes an effective natural 50% beamsplitter without the need for coatings. Germanium is also used extensively as a substrate for production of optical filters. Germanium covers the whole of the 8-14 micron thermal band and is used in lens systems for thermal imaging. Germanium can be AR coated with Diamond producing an extremely tough front optic.
Germanium is grown using the Czochralski technique by a small number of manufacturers in Belgium, USA, China and Russia. The refractive index of Germanium changes rapidly with temperature and the material becomes opaque at all wavelengths a little above 350K as the band gap floods with thermal electrons.
REFERENCES:
(1) Handbook Optical Constants, ed Palik, V1, ISBN 0-12-544420-6
(2) Li, Refractive Index of Germanium etc, J.Phys Chem, V9, p561, 1980
(3) Pearson & Brattain, Proc. Inst. Radio Eng. V43, p1794, 1955 (4) Fine, J.App.Phys, V24, p338, 1953
(5) Wortman & Evans, V36, (1), P153 (1965)
(6) Hawkins, Sherwood, Djotni: Mid IR Filters for astronomical and remote sensing instrumentation. Invited Paper SPIE Conference Glasgow 2008
(7) Manufactures Published Data