Optical constants
Refractive index of Ti (Titanium)
Ordal et al. 1988: n,k 0.667–200 µm
- Data
- tabulated nk
- Range
- 0.667–200 µm
- Points
- 51
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 4.79248
- Extinction coefficient k
- 22.5299
- Permittivity ε1
- -484.627
- Permittivity ε2
- 215.948
- Absorption coefficient α
- 246190 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 81.238 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.500704 µm⁻¹
- Group index ng
- -0.965616
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.107812 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): Ordal et al. 1988: n,k 0.667–200 µm
ti = ls.fetch_refractiveindex("main", "Ti", "Ordal", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ti.range_nm) # (667, 200000) nm
eps = ti.eps([11500]) # 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_b7e23ebddc0d/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/ordal-1988).
# ... 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=667, 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.
References
- doi:10.1364/ao.27.001203 Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengths, Applied Optics (1988)
Cite
Mark A. Ordal, Robert J. Bell, Ralph W. Alexander, Lawrence A. Newquist and Marvin R. Querry. Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengths. Applied Optics, 27, 1203 (1988), doi:10.1364/ao.27.001203; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
51 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.667 | 2.370432 | 3.0317254 |
| 0.714 | 2.5658703 | 3.1836237 |
| 0.769 | 2.8061078 | 3.2717366 |
| 0.833 | 3.1079186 | 3.3007447 |
| 0.909 | 3.3065327 | 3.2405736 |
| 1.0 | 3.3957928 | 3.2418121 |
| 1.05 | 3.4440424 | 3.2989913 |
| 1.11 | 3.5179021 | 3.3609902 |
| 1.18 | 3.6009322 | 3.4342207 |
| 1.25 | 3.698148 | 3.5123265 |
| 1.33 | 3.8097162 | 3.5906589 |
| 1.43 | 3.9419174 | 3.7122171 |
| 1.54 | 4.0126191 | 3.8077018 |
| 1.67 | 4.2746437 | 3.8609249 |
| 1.82 | 4.4682212 | 3.8823682 |
| 2.0 | 4.6752372 | 3.8164244 |
| 2.11 | 4.7311251 | 3.7288987 |
| 2.22 | 4.7418094 | 3.6030774 |
| 2.35 | 4.6520327 | 3.3990496 |
| 2.5 | 4.364761 | 3.1898829 |
| 2.67 | 3.8144105 | 3.0741948 |
| 2.86 | 3.0649496 | 3.5829978 |
| 3.08 | 2.4004043 | 4.4865443 |
| 3.33 | 2.3943002 | 5.4204022 |
| 3.64 | 2.5809283 | 6.2578349 |
| 4.0 | 2.7313635 | 7.0189943 |
| 4.44 | 2.8327334 | 7.7291731 |
| 5.0 | 2.3660792 | 8.7896083 |
| 5.71 | 2.1867059 | 10.53627 |
| 6.67 | 2.4841185 | 12.895769 |
| 8.0 | 3.2048691 | 15.799043 |
| 10.0 | 4.0715739 | 19.664351 |
| 11.1 | 4.5921948 | 21.789718 |
| 12.5 | 5.29318 | 24.380236 |
| 14.3 | 6.2397504 | 27.621553 |
| 16.7 | 7.5817542 | 31.846917 |
| 20.0 | 9.6744916 | 37.605191 |
| 22.2 | 11.217047 | 41.326081 |
| 25.0 | 13.29969 | 45.839465 |
| 28.6 | 16.284041 | 51.475157 |
| 33.3 | 20.880752 | 58.046709 |
| 40.0 | 27.169229 | 65.925258 |
| 44.4 | 31.260311 | 70.562709 |
| 50.0 | 36.217641 | 75.809491 |
| 57.1 | 42.303853 | 81.834224 |
| 66.7 | 49.906684 | 88.904473 |
| 80.0 | 59.644857 | 97.484039 |
| 100.0 | 72.530316 | 108.42373 |
| 125.0 | 86.399911 | 120.07897 |
| 154.0 | 100.49717 | 131.88977 |
| 200.0 | 119.99544 | 148.43379 |
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
- —