Optical constants
Refractive index of Ti (Titanium)
Mash and Motulevich 1973: n,k 0.4–10 µm
- Data
- tabulated nk
- Range
- 0.4–10 µm
- Points
- 46
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.354
- Extinction coefficient k
- 2.9976
- Permittivity ε1
- -3.44429
- Permittivity ε2
- 14.1127
- Absorption coefficient α
- 641065 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 31.1981 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 2.5 µm⁻¹
- Group index ng
- 0.885
- 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
# Ti (Titanium): Mash and Motulevich 1973: n,k 0.4–10 µm
ti = ls.fetch_refractiveindex("main", "Ti", "Mash", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ti.range_nm) # (400, 10000) nm
eps = ti.eps([633]) # 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_af26a73e9eba/lightsmith"
ti = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ti.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (ti/mash-motulevich-1973).
# ... load ti as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ti)],
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 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
References
Cite
I. D. Mash and G.P. Motulevich. Optical constants and electronic characteristics of titanium, Sov. Phys. JETP 36, 516-520 (1973); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
46 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.4 | 1.71 | 2.23 |
| 0.42 | 1.73 | 2.44 |
| 0.44 | 1.89 | 2.59 |
| 0.46 | 1.92 | 2.67 |
| 0.48 | 2.03 | 2.77 |
| 0.5 | 2.1 | 2.82 |
| 0.52 | 2.19 | 2.88 |
| 0.54 | 2.22 | 2.91 |
| 0.56 | 2.27 | 2.94 |
| 0.57 | 2.31 | 2.98 |
| 0.59 | 2.36 | 3.0 |
| 0.61 | 2.42 | 3.04 |
| 0.635 | 2.49 | 3.11 |
| 0.655 | 2.55 | 3.15 |
| 0.675 | 2.6 | 3.17 |
| 0.7 | 2.67 | 3.2 |
| 0.72 | 2.73 | 3.22 |
| 0.74 | 2.78 | 3.23 |
| 0.765 | 2.83 | 3.3 |
| 0.785 | 2.91 | 3.34 |
| 0.81 | 2.98 | 3.4 |
| 0.83 | 3.06 | 3.44 |
| 0.855 | 3.13 | 3.49 |
| 0.875 | 3.18 | 3.51 |
| 0.895 | 3.24 | 3.51 |
| 0.92 | 3.3 | 3.54 |
| 0.94 | 3.34 | 3.55 |
| 0.96 | 3.4 | 3.55 |
| 0.98 | 3.42 | 3.58 |
| 1.2 | 3.3 | 3.7 |
| 1.5 | 3.54 | 4.0 |
| 1.8 | 3.89 | 4.29 |
| 2.0 | 4.03 | 4.47 |
| 2.25 | 4.02 | 4.52 |
| 2.5 | 3.96 | 4.6 |
| 3.0 | 3.65 | 5.36 |
| 3.5 | 3.35 | 6.4 |
| 4.0 | 3.31 | 7.33 |
| 4.5 | 3.36 | 8.3 |
| 5.0 | 3.44 | 9.37 |
| 5.5 | 3.57 | 10.1 |
| 6.0 | 3.8 | 10.9 |
| 7.0 | 4.56 | 12.7 |
| 8.0 | 5.81 | 14.9 |
| 9.0 | 7.27 | 16.1 |
| 10.0 | 9.09 | 18.6 |
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
- —
Room temperature