Optical constants

Refractive index of Ti (Titanium)

Johnson and Christy 1974: n,k 0.188–1.94 µm

Data: tabulated nk
Range: 0.188–1.937 µm
Points: 49
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.6112
Extinction coefficient k: 3.6024

Permittivity ε₁: -6.15892
Permittivity ε₂: 18.8132

Absorption coefficient α: 770407 cm⁻¹
Penetration depth δ = λ/(2πk): 25.9603 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 2 µm⁻¹

Group index n_g: 1.436
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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): Johnson and Christy 1974: n,k 0.188–1.94 µm
ti = ls.fetch_refractiveindex("main", "Ti", "Johnson", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ti.range_nm)  # (188, 1937) nm
eps = ti.eps([633])  # complex permittivity

Downloads 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_b05e2598cd9d/lightsmith"
ti = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ti.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ti/johnson-christy-1974).

# ... 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 wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

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

Room temperature

References

P. B. Johnson and R. W. Christy. Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd. Phys. Rev. B 9, 5056-5070 (1974)

doi:10.1103/physrevb.9.5056 Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd, Physical Review B (1974)

Cite

P. Johnson and R. Christy. Optical constants of transition metals: Ti, V, Cr, Mn, Fe, Co, Ni, and Pd. Physical Review B, 9, 5056-5070 (1974), doi:10.1103/physrevb.9.5056; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

49 rows as published

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Ti (Titanium), Johnson and Christy 1974: n,k 0.188–1.94 µm: n and k versus wavelength
λ (µm)	n	k
0.188	1.1	1.62
0.192	1.16	1.64
0.195	1.22	1.66
0.199	1.25	1.68
0.203	1.27	1.69
0.207	1.31	1.69
0.212	1.31	1.68
0.216	1.32	1.67
0.221	1.32	1.66
0.226	1.32	1.66
0.231	1.31	1.68
0.237	1.3	1.72
0.243	1.28	1.77
0.249	1.27	1.83
0.255	1.26	1.91
0.262	1.27	1.99
0.269	1.27	2.07
0.276	1.3	2.17
0.284	1.35	2.26
0.292	1.4	2.36
0.301	1.45	2.46
0.311	1.5	2.57
0.32	1.55	2.66
0.332	1.61	2.74
0.342	1.72	2.82
0.354	1.82	2.87
0.368	1.9	2.9
0.381	1.99	2.93
0.397	2.08	2.95
0.413	2.14	2.98
0.431	2.21	3.01
0.451	2.27	3.04
0.471	2.32	3.1
0.496	2.36	3.19
0.521	2.44	3.3
0.549	2.54	3.43
0.582	2.6	3.58
0.617	2.67	3.72
0.659	2.76	3.84
0.704	2.86	3.96
0.756	3.0	4.01
0.821	3.21	4.01
0.892	3.29	3.96
0.984	3.35	3.97
1.088	3.5	4.02
1.216	3.62	4.15
1.393	3.67	4.37
1.61	3.69	4.7
1.937	3.51	5.19

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Ti (Titanium): all datasets

Experimental data

Models and simulations

About Ti (Titanium)

Titanium (Ti) is a transition metal with the atomic number 22. It is recognized for its high strength-to-weight ratio and excellent corrosion resistance. With a silver color and low density, titanium is as strong as some steels but significantly less dense. This makes it highly valued in aerospace applications where weight savings are crucial. Titanium is also biocompatible, which makes it a critical material for medical implants such as hip replacements and dental implants. The metal is also found in everyday products like tennis rackets, eyeglass frames, and even some laptops. Titanium can be alloyed with elements like aluminum and vanadium to further enhance its properties. Titanium dioxide (TiO₂), one of its compounds, is widely used as a white pigment in paints and is an active ingredient in sunscreens due to its UV-blocking properties.

More about Ti (Titanium) →

Listed in

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Ti/nk/Johnson.yml
ID: ds_b05e2598cd9d
API: /v1/datasets/ds_b05e2598cd9d

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