Optical constants

Refractive index of Ti (Titanium)

Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm

Data: tabulated nk
Range: 0.01759–2.48 µm
Points: 150
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 3.30108
Extinction coefficient k: 3.8784

Permittivity ε₁: -4.14481
Permittivity ε₂: 25.6058

Absorption coefficient α: 829431 cm⁻¹
Penetration depth δ = λ/(2πk): 24.1129 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 4.57027 µm⁻¹

Group index n_g: 0.615595
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): Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm
ti = ls.fetch_refractiveindex("main", "Ti", "Werner-DFT", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ti.range_nm)  # (17.586, 2479.68) 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_599285f0d6e0/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/werner-2009-dft).

# ... 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

Theoretical density function theory (DFT) calculations.

References

W. S. M. Werner, K. Glantschnig, C. Ambrosch-Draxl. Optical constants and inelastic electron-scattering data for 17 elemental metals. J. Phys Chem Ref. Data 38, 1013-1092 (2009)

doi:10.1063/1.3243762 Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals, Journal of Physical and Chemical Reference Data (2009)

Cite

Wolfgang S. M. Werner, Kathrin Glantschnig and Claudia Ambrosch-Draxl. Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals. Journal of Physical and Chemical Reference Data, 38, 1013-1092 (2009), doi:10.1063/1.3243762; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

150 rows as published

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

Ti (Titanium), Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm: n and k versus wavelength
λ (µm)	n	k
0.017586	0.922	0.0119
0.017712	0.9204	0.012
0.017839	0.9188	0.0125
0.017969	0.9172	0.0131
0.0181	0.915	0.0137
0.018233	0.9134	0.0153
0.018368	0.9123	0.0175
0.018505	0.914	0.0181
0.018644	0.9128	0.017
0.018785	0.9107	0.017
0.018929	0.9096	0.017
0.019074	0.9085	0.0176
0.019222	0.9079	0.0171
0.019373	0.9051	0.0155
0.019525	0.9013	0.0161
0.01968	0.8997	0.02
0.019837	0.9013	0.0194
0.019997	0.8996	0.0178
0.02016	0.8985	0.0156
0.020325	0.894	0.014
0.020493	0.8895	0.0141
0.020664	0.8856	0.0158
0.020838	0.8828	0.0159
0.021014	0.8782	0.0165
0.021194	0.8737	0.0189
0.021377	0.8709	0.0224
0.021562	0.8715	0.0241
0.021752	0.8703	0.0218
0.021944	0.8645	0.0197
0.02214	0.8582	0.0216
0.022339	0.8553	0.024
0.022543	0.8518	0.0235
0.022749	0.8454	0.0254
0.02296	0.8407	0.0291
0.023175	0.8407	0.0285
0.023393	0.8323	0.0282
0.023616	0.8252	0.0297
0.023843	0.8174	0.0349
0.024075	0.814	0.0393
0.024311	0.8146	0.0393
0.024551	0.8027	0.0374
0.024797	0.7928	0.0397
0.025047	0.7811	0.0461
0.025303	0.7765	0.0547
0.025564	0.7703	0.0578
0.02583	0.7603	0.0631
0.026102	0.7534	0.0677
0.02638	0.7406	0.0743
0.026663	0.7322	0.0847
0.026953	0.7256	0.0972
0.027249	0.7239	0.1002
0.027552	0.7112	0.0935
0.027862	0.6812	0.105
0.028178	0.6577	0.1285
0.028502	0.6419	0.1644
0.028834	0.6466	0.2026
0.029173	0.6677	0.2299
0.02952	0.6888	0.2439
0.029876	0.7724	0.1631
0.03024	0.6705	0.0925
0.030613	0.5624	0.1014
0.030996	0.4504	0.1543
0.031388	0.3793	0.2808
0.031791	0.3548	0.3833
0.032204	0.3275	0.4992
0.032627	0.3138	0.65
0.033062	0.3402	0.8347
0.033509	0.3903	1.1029
0.033968	0.8903	1.3877
0.03444	1.3113	1.039
0.034925	1.2239	0.7496
0.035424	1.1117	0.7475
0.035937	1.0767	0.9051
0.036466	1.3614	1.1547
0.03701	1.8029	0.893
0.037571	2.0422	0.3959
0.038149	1.6664	0.0762
0.038745	1.4855	0.0518
0.03936	1.3845	0.0444
0.039995	1.3118	0.0412
0.040651	1.2596	0.0405
0.041328	1.2167	0.0374
0.042029	1.1766	0.0361
0.042753	1.143	0.0389
0.043503	1.1148	0.0417
0.04428	1.0895	0.045
0.045085	1.0655	0.0483
0.04592	1.0453	0.0512
0.046786	1.0242	0.0547
0.047686	1.0057	0.0582
0.048621	0.9862	0.0603
0.049594	0.968	0.0635
0.050606	0.9499	0.0653
0.05166	0.9291	0.0651
0.052759	0.9048	0.0685
0.053906	0.88	0.0733
0.055104	0.8529	0.0797
0.056356	0.8234	0.0893
0.057667	0.7922	0.1029
0.05904	0.7663	0.1312
0.06048	0.7478	0.1458
0.061992	0.7303	0.1561
0.063582	0.6884	0.1729
0.065255	0.6527	0.1999
0.067018	0.6116	0.2281
0.06888	0.5787	0.2773
0.070848	0.537	0.3184
0.072932	0.5022	0.3863
0.075142	0.477	0.4685
0.07749	0.486	0.5659
0.07999	0.5411	0.6015
0.082656	0.5185	0.6587
0.085506	0.5306	0.7152
0.08856	0.5326	0.7782
0.09184	0.5463	0.8164
0.095372	0.5426	0.8902
0.099187	0.5256	1.0036
0.10332	0.579	1.1372
0.107812	0.6836	1.2551
0.112713	0.8645	1.3105
0.11808	0.9584	1.2568
0.123984	1.0406	1.2353
0.13051	1.0474	1.1748
0.13776	1.1538	0.8546
0.145864	0.638	0.9365
0.15498	0.4474	1.3904
0.165312	0.6539	1.7305
0.17712	0.8063	2.0241
0.190745	1.4833	2.0421
0.20664	1.2228	1.4287
0.225426	0.7446	1.9025
0.247968	0.7641	2.4833
0.261019	0.8706	2.7996
0.27552	1.082	3.1351
0.291728	1.4568	3.4203
0.30996	1.9913	3.5246
0.330625	2.2646	3.2838
0.354241	2.4208	3.2791
0.38149	2.6103	3.2021
0.413281	2.6809	3.1531
0.450852	2.662	3.2433
0.495937	2.7735	3.535
0.551041	3.134	3.8172
0.619921	3.4488	3.9325
0.708481	4.0011	4.1439
0.826561	4.6542	4.2412
0.991874	4.9433	3.8489
1.239842	4.9704	3.958
1.653123	5.3434	4.664
2.479684	5.3579	4.7848

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) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Ti/nk/Werner-DFT.yml
ID: ds_599285f0d6e0
API: /v1/datasets/ds_599285f0d6e0

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