Optical constants
Refractive index of Ti (Titanium)
Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–31.0 µm
- Data
- tabulated nk
- Range
- 0.248–31 µm
- Points
- 200
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 1.9604
- Extinction coefficient k
- 3.06083
- Permittivity ε1
- -5.52549
- Permittivity ε2
- 12.0009
- Absorption coefficient α
- 654586 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 30.5537 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 2.10119 µm⁻¹
- Group index ng
- 0.725737
- 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): Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–31.0 µm
ti = ls.fetch_refractiveindex("main", "Ti", "Rakic-BB", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ti.range_nm) # (247.97, 30996) 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_4c33f8ef0371/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/rakic-1998-bb).
# ... 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"]).
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
[Calculation script (Python)]
- doi:10.1364/ao.37.005271 Optical properties of metallic films for vertical-cavity optoelectronic devices, Applied Optics (1998)
Cite
Aleksandar D. Rakić, Aleksandra B. Djurišić, Jovan M. Elazar and Marian L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Applied Optics, 37, 5271 (1998), doi:10.1364/ao.37.005271; [Calculation script (Python)]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
200 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.24797 | 0.18885 | 1.4035 |
| 0.25406 | 0.19618 | 1.4617 |
| 0.2603 | 0.2041 | 1.5216 |
| 0.26669 | 0.21269 | 1.5835 |
| 0.27324 | 0.22214 | 1.6477 |
| 0.27995 | 0.23275 | 1.7146 |
| 0.28683 | 0.24492 | 1.7846 |
| 0.29387 | 0.25928 | 1.8581 |
| 0.30109 | 0.27664 | 1.9353 |
| 0.30848 | 0.29798 | 2.0161 |
| 0.31606 | 0.32441 | 2.1005 |
| 0.32382 | 0.35707 | 2.1878 |
| 0.33177 | 0.39701 | 2.277 |
| 0.33992 | 0.44504 | 2.3668 |
| 0.34827 | 0.50164 | 2.4557 |
| 0.35682 | 0.56684 | 2.5419 |
| 0.36559 | 0.64024 | 2.6237 |
| 0.37457 | 0.72099 | 2.6994 |
| 0.38377 | 0.80782 | 2.7678 |
| 0.39319 | 0.8992 | 2.8277 |
| 0.40285 | 0.99337 | 2.8785 |
| 0.41274 | 1.0885 | 2.9201 |
| 0.42288 | 1.1828 | 2.9525 |
| 0.43326 | 1.2745 | 2.9764 |
| 0.4439 | 1.3622 | 2.9928 |
| 0.45481 | 1.4448 | 3.0028 |
| 0.46598 | 1.5213 | 3.0078 |
| 0.47742 | 1.5911 | 3.0093 |
| 0.48915 | 1.6542 | 3.0088 |
| 0.50116 | 1.7105 | 3.0077 |
| 0.51347 | 1.7606 | 3.0074 |
| 0.52608 | 1.805 | 3.009 |
| 0.539 | 1.8445 | 3.0134 |
| 0.55224 | 1.8802 | 3.0214 |
| 0.5658 | 1.9129 | 3.0334 |
| 0.5797 | 1.9438 | 3.0495 |
| 0.59393 | 1.9737 | 3.0699 |
| 0.60852 | 2.0035 | 3.0943 |
| 0.62346 | 2.0339 | 3.1224 |
| 0.63878 | 2.0656 | 3.1537 |
| 0.65446 | 2.0989 | 3.1878 |
| 0.67054 | 2.1343 | 3.2241 |
| 0.68701 | 2.1718 | 3.2621 |
| 0.70388 | 2.2115 | 3.3014 |
| 0.72117 | 2.2535 | 3.3414 |
| 0.73888 | 2.2976 | 3.3818 |
| 0.75702 | 2.3437 | 3.4223 |
| 0.77562 | 2.3915 | 3.4625 |
| 0.79466 | 2.441 | 3.5023 |
| 0.81418 | 2.4919 | 3.5415 |
| 0.83418 | 2.5439 | 3.58 |
| 0.85466 | 2.5969 | 3.6176 |
| 0.87565 | 2.6507 | 3.6544 |
| 0.89716 | 2.705 | 3.6903 |
| 0.91919 | 2.7597 | 3.7253 |
| 0.94177 | 2.8146 | 3.7595 |
| 0.9649 | 2.8696 | 3.7929 |
| 0.9886 | 2.9245 | 3.8256 |
| 1.0129 | 2.9792 | 3.8576 |
| 1.0378 | 3.0336 | 3.889 |
| 1.0632 | 3.0876 | 3.9198 |
| 1.0894 | 3.1412 | 3.9502 |
| 1.1161 | 3.1942 | 3.9803 |
| 1.1435 | 3.2465 | 4.01 |
| 1.1716 | 3.2982 | 4.0396 |
| 1.2004 | 3.3491 | 4.0691 |
| 1.2299 | 3.3993 | 4.0985 |
| 1.2601 | 3.4486 | 4.128 |
| 1.291 | 3.497 | 4.1576 |
| 1.3227 | 3.5445 | 4.1874 |
| 1.3552 | 3.5911 | 4.2176 |
| 1.3885 | 3.6367 | 4.2481 |
| 1.4226 | 3.6813 | 4.2791 |
| 1.4575 | 3.7248 | 4.3106 |
| 1.4933 | 3.7673 | 4.3428 |
| 1.53 | 3.8088 | 4.3756 |
| 1.5676 | 3.8491 | 4.4092 |
| 1.6061 | 3.8883 | 4.4437 |
| 1.6455 | 3.9263 | 4.4792 |
| 1.6859 | 3.9632 | 4.5157 |
| 1.7273 | 3.9988 | 4.5533 |
| 1.7698 | 4.0333 | 4.5922 |
| 1.8132 | 4.0665 | 4.6324 |
| 1.8577 | 4.0985 | 4.6739 |
| 1.9034 | 4.1291 | 4.717 |
| 1.9501 | 4.1585 | 4.7617 |
| 1.998 | 4.1866 | 4.8082 |
| 2.0471 | 4.2133 | 4.8564 |
| 2.0974 | 4.2387 | 4.9067 |
| 2.1489 | 4.2628 | 4.959 |
| 2.2016 | 4.2855 | 5.0134 |
| 2.2557 | 4.3069 | 5.0702 |
| 2.3111 | 4.3269 | 5.1295 |
| 2.3679 | 4.3456 | 5.1914 |
| 2.426 | 4.3629 | 5.256 |
| 2.4856 | 4.3789 | 5.3235 |
| 2.5467 | 4.3937 | 5.394 |
| 2.6092 | 4.4071 | 5.4678 |
| 2.6733 | 4.4194 | 5.5449 |
| 2.7389 | 4.4305 | 5.6255 |
| 2.8062 | 4.4404 | 5.7097 |
| 2.8751 | 4.4493 | 5.7979 |
| 2.9457 | 4.4572 | 5.89 |
| 3.0181 | 4.4642 | 5.9864 |
| 3.0922 | 4.4704 | 6.0871 |
| 3.1682 | 4.4759 | 6.1923 |
| 3.246 | 4.4807 | 6.3022 |
| 3.3257 | 4.4851 | 6.4169 |
| 3.4074 | 4.4892 | 6.5366 |
| 3.491 | 4.493 | 6.6616 |
| 3.5768 | 4.4968 | 6.7918 |
| 3.6646 | 4.5007 | 6.9274 |
| 3.7546 | 4.5049 | 7.0687 |
| 3.8468 | 4.5095 | 7.2156 |
| 3.9413 | 4.5148 | 7.3684 |
| 4.0381 | 4.5209 | 7.5272 |
| 4.1373 | 4.528 | 7.6919 |
| 4.2389 | 4.5363 | 7.8628 |
| 4.343 | 4.546 | 8.04 |
| 4.4497 | 4.5573 | 8.2234 |
| 4.5589 | 4.5705 | 8.4131 |
| 4.6709 | 4.5856 | 8.6092 |
| 4.7856 | 4.603 | 8.8118 |
| 4.9032 | 4.6228 | 9.0209 |
| 5.0236 | 4.6452 | 9.2365 |
| 5.147 | 4.6704 | 9.4586 |
| 5.2734 | 4.6987 | 9.6873 |
| 5.4029 | 4.7301 | 9.9225 |
| 5.5356 | 4.765 | 10.164 |
| 5.6715 | 4.8035 | 10.413 |
| 5.8108 | 4.8457 | 10.668 |
| 5.9535 | 4.8919 | 10.929 |
| 6.0997 | 4.9423 | 11.197 |
| 6.2495 | 4.997 | 11.472 |
| 6.403 | 5.0562 | 11.753 |
| 6.5603 | 5.1202 | 12.04 |
| 6.7214 | 5.1889 | 12.334 |
| 6.8865 | 5.2628 | 12.634 |
| 7.0556 | 5.3418 | 12.941 |
| 7.2289 | 5.4262 | 13.254 |
| 7.4064 | 5.5162 | 13.573 |
| 7.5883 | 5.6119 | 13.899 |
| 7.7747 | 5.7135 | 14.23 |
| 7.9656 | 5.8212 | 14.568 |
| 8.1613 | 5.9351 | 14.912 |
| 8.3617 | 6.0553 | 15.262 |
| 8.5671 | 6.1822 | 15.618 |
| 8.7775 | 6.3157 | 15.98 |
| 8.9931 | 6.4562 | 16.347 |
| 9.2139 | 6.6036 | 16.72 |
| 9.4402 | 6.7583 | 17.099 |
| 9.6721 | 6.9203 | 17.484 |
| 9.9096 | 7.0897 | 17.873 |
| 10.153 | 7.2669 | 18.269 |
| 10.402 | 7.4518 | 18.669 |
| 10.658 | 7.6446 | 19.074 |
| 10.92 | 7.8454 | 19.485 |
| 11.188 | 8.0544 | 19.9 |
| 11.463 | 8.2718 | 20.32 |
| 11.744 | 8.4975 | 20.744 |
| 12.032 | 8.7317 | 21.173 |
| 12.328 | 8.9746 | 21.607 |
| 12.631 | 9.2261 | 22.044 |
| 12.941 | 9.4864 | 22.485 |
| 13.259 | 9.7556 | 22.93 |
| 13.584 | 10.034 | 23.379 |
| 13.918 | 10.321 | 23.832 |
| 14.26 | 10.617 | 24.287 |
| 14.61 | 10.922 | 24.746 |
| 14.969 | 11.236 | 25.208 |
| 15.337 | 11.56 | 25.673 |
| 15.713 | 11.892 | 26.14 |
| 16.099 | 12.234 | 26.61 |
| 16.494 | 12.585 | 27.083 |
| 16.9 | 12.944 | 27.557 |
| 17.315 | 13.313 | 28.034 |
| 17.74 | 13.691 | 28.513 |
| 18.176 | 14.078 | 28.993 |
| 18.622 | 14.473 | 29.475 |
| 19.079 | 14.878 | 29.959 |
| 19.548 | 15.291 | 30.444 |
| 20.028 | 15.713 | 30.93 |
| 20.52 | 16.143 | 31.418 |
| 21.024 | 16.582 | 31.907 |
| 21.54 | 17.029 | 32.396 |
| 22.069 | 17.484 | 32.887 |
| 22.611 | 17.948 | 33.379 |
| 23.166 | 18.419 | 33.872 |
| 23.735 | 18.898 | 34.365 |
| 24.318 | 19.385 | 34.859 |
| 24.916 | 19.88 | 35.355 |
| 25.528 | 20.382 | 35.85 |
| 26.154 | 20.892 | 36.347 |
| 26.797 | 21.408 | 36.845 |
| 27.455 | 21.932 | 37.343 |
| 28.129 | 22.463 | 37.842 |
| 28.82 | 23.0 | 38.343 |
| 29.528 | 23.545 | 38.844 |
| 30.253 | 24.096 | 39.346 |
| 30.996 | 24.653 | 39.849 |
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
- —
Fit of experimental data from several sources to Brendel-Bormann (BB) model