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

Range 0.248–31 µm
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.

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

Fit of experimental data from several sources to Brendel-Bormann (BB) model

References

A. D. Rakić, A. B. Djurišic, J. M. Elazar, M. L. Majewski. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 37, 5271-5283 (1998)
[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
Ti (Titanium), Rakić et al. 1998: Brendel-Bormann model; n,k 0.248–31.0 µm: n and k versus wavelength
λ (µm)nk
0.247970.188851.4035
0.254060.196181.4617
0.26030.20411.5216
0.266690.212691.5835
0.273240.222141.6477
0.279950.232751.7146
0.286830.244921.7846
0.293870.259281.8581
0.301090.276641.9353
0.308480.297982.0161
0.316060.324412.1005
0.323820.357072.1878
0.331770.397012.277
0.339920.445042.3668
0.348270.501642.4557
0.356820.566842.5419
0.365590.640242.6237
0.374570.720992.6994
0.383770.807822.7678
0.393190.89922.8277
0.402850.993372.8785
0.412741.08852.9201
0.422881.18282.9525
0.433261.27452.9764
0.44391.36222.9928
0.454811.44483.0028
0.465981.52133.0078
0.477421.59113.0093
0.489151.65423.0088
0.501161.71053.0077
0.513471.76063.0074
0.526081.8053.009
0.5391.84453.0134
0.552241.88023.0214
0.56581.91293.0334
0.57971.94383.0495
0.593931.97373.0699
0.608522.00353.0943
0.623462.03393.1224
0.638782.06563.1537
0.654462.09893.1878
0.670542.13433.2241
0.687012.17183.2621
0.703882.21153.3014
0.721172.25353.3414
0.738882.29763.3818
0.757022.34373.4223
0.775622.39153.4625
0.794662.4413.5023
0.814182.49193.5415
0.834182.54393.58
0.854662.59693.6176
0.875652.65073.6544
0.897162.7053.6903
0.919192.75973.7253
0.941772.81463.7595
0.96492.86963.7929
0.98862.92453.8256
1.01292.97923.8576
1.03783.03363.889
1.06323.08763.9198
1.08943.14123.9502
1.11613.19423.9803
1.14353.24654.01
1.17163.29824.0396
1.20043.34914.0691
1.22993.39934.0985
1.26013.44864.128
1.2913.4974.1576
1.32273.54454.1874
1.35523.59114.2176
1.38853.63674.2481
1.42263.68134.2791
1.45753.72484.3106
1.49333.76734.3428
1.533.80884.3756
1.56763.84914.4092
1.60613.88834.4437
1.64553.92634.4792
1.68593.96324.5157
1.72733.99884.5533
1.76984.03334.5922
1.81324.06654.6324
1.85774.09854.6739
1.90344.12914.717
1.95014.15854.7617
1.9984.18664.8082
2.04714.21334.8564
2.09744.23874.9067
2.14894.26284.959
2.20164.28555.0134
2.25574.30695.0702
2.31114.32695.1295
2.36794.34565.1914
2.4264.36295.256
2.48564.37895.3235
2.54674.39375.394
2.60924.40715.4678
2.67334.41945.5449
2.73894.43055.6255
2.80624.44045.7097
2.87514.44935.7979
2.94574.45725.89
3.01814.46425.9864
3.09224.47046.0871
3.16824.47596.1923
3.2464.48076.3022
3.32574.48516.4169
3.40744.48926.5366
3.4914.4936.6616
3.57684.49686.7918
3.66464.50076.9274
3.75464.50497.0687
3.84684.50957.2156
3.94134.51487.3684
4.03814.52097.5272
4.13734.5287.6919
4.23894.53637.8628
4.3434.5468.04
4.44974.55738.2234
4.55894.57058.4131
4.67094.58568.6092
4.78564.6038.8118
4.90324.62289.0209
5.02364.64529.2365
5.1474.67049.4586
5.27344.69879.6873
5.40294.73019.9225
5.53564.76510.164
5.67154.803510.413
5.81084.845710.668
5.95354.891910.929
6.09974.942311.197
6.24954.99711.472
6.4035.056211.753
6.56035.120212.04
6.72145.188912.334
6.88655.262812.634
7.05565.341812.941
7.22895.426213.254
7.40645.516213.573
7.58835.611913.899
7.77475.713514.23
7.96565.821214.568
8.16135.935114.912
8.36176.055315.262
8.56716.182215.618
8.77756.315715.98
8.99316.456216.347
9.21396.603616.72
9.44026.758317.099
9.67216.920317.484
9.90967.089717.873
10.1537.266918.269
10.4027.451818.669
10.6587.644619.074
10.927.845419.485
11.1888.054419.9
11.4638.271820.32
11.7448.497520.744
12.0328.731721.173
12.3288.974621.607
12.6319.226122.044
12.9419.486422.485
13.2599.755622.93
13.58410.03423.379
13.91810.32123.832
14.2610.61724.287
14.6110.92224.746
14.96911.23625.208
15.33711.5625.673
15.71311.89226.14
16.09912.23426.61
16.49412.58527.083
16.912.94427.557
17.31513.31328.034
17.7413.69128.513
18.17614.07828.993
18.62214.47329.475
19.07914.87829.959
19.54815.29130.444
20.02815.71330.93
20.5216.14331.418
21.02416.58231.907
21.5417.02932.396
22.06917.48432.887
22.61117.94833.379
23.16618.41933.872
23.73518.89834.365
24.31819.38534.859
24.91619.8835.355
25.52820.38235.85
26.15420.89236.347
26.79721.40836.845
27.45521.93237.343
28.12922.46337.842
28.8223.038.343
29.52823.54538.844
30.25324.09639.346
30.99624.65339.849

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—