Optical constants
Refractive index of TiO2 (Titanium dioxide)
Bond 1965: n(e) 0.45–2.4 µm
- Data
- tabulated n
- Range
- 0.45–2.4 µm
- Points
- 14
- Optical axis
- e
- State
- crystalline
- Licence
- CC0-1.0
Uniaxial crystal, axes: oe
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 2.90352
- Extinction coefficient k
- 0
- Permittivity ε1
- 8.43041
- Permittivity ε2
- 0
- Absorption coefficient α
- 0 cm⁻¹
- Penetration depth δ = λ/(2πk)
- — nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- -1.09 µm⁻¹
- Group index ng
- 3.544
- 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
# TiO2 (Titanium dioxide): Bond 1965: n(e) 0.45–2.4 µm
tio2 = ls.fetch_refractiveindex("main", "TiO2", "Bond-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tio2.range_nm) # (450, 2400) nm
eps = tio2.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_e1c5e6cb9839/lightsmith"
tio2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(tio2.source) # citation and provenance travel with the dataAny dataset here, as the library's Tabulated material (tio2/bond-1965-e).
# ... load tio2 as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=tio2)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=450, 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
Conditions
- direction
- e
References
- doi:10.1063/1.1703106 Measurement of the Refractive Indices of Several Crystals, Journal of Applied Physics (1965)
Cite
W. L. Bond. Measurement of the Refractive Indices of Several Crystals. Journal of Applied Physics, 36, 1674-1677 (1965), doi:10.1063/1.1703106; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
14 rows as published| λ (µm) | n |
|---|---|
| 0.45 | 3.1465 |
| 0.5 | 2.999 |
| 0.6 | 2.89 |
| 0.7 | 2.8255 |
| 0.8 | 2.7866 |
| 0.9 | 2.7612 |
| 1.0 | 2.743 |
| 1.2 | 2.7193 |
| 1.4 | 2.7024 |
| 1.6 | 2.6902 |
| 1.8 | 2.6793 |
| 2.0 | 2.6698 |
| 2.2 | 2.66 |
| 2.4 | 2.6501 |
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
- —
Extraordinary ray (e); Room temperature.