Optical constants

Refractive index of TiO2 (Titanium dioxide)

Zhukovsky et al. 2015: Thin film; n 0.211–1.69 µm

Data
tabulated nk
Range
0.211–1.69 µm
Points
700
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.211–1.69 µm
Refractive index n
2.41109
Extinction coefficient k
4.72562e-05
Permittivity ε1
5.81333
Permittivity ε2
0.000227877
Absorption coefficient α
10.1062 cm⁻¹
Penetration depth δ = λ/(2πk)
1.97899e+06 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.57432 µm⁻¹
Group index ng
2.74856
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

# TiO2 (Titanium dioxide): Zhukovsky et al. 2015: Thin film; n 0.211–1.69 µm
tio2 = ls.fetch_refractiveindex("main", "TiO2", "Zhukovsky", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tio2.range_nm)  # (211.002, 1689.84) nm
eps = tio2.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

20 nm thick films on Si substrate deposited by atomic layer deposition (ALD) at 120 °C deposition temperature.

Conditions

film thickness
20e-9
substrate
Si

References

S. V. Zhukovsky, A. Andryieuski, O. Takayama, E. Shkondin, R. Malureanu, F. Jensen, A. V. Lavrinenko. Experimental demonstration of effective medium approximation breakdown in deeply subwavelength all-dielectric multilayers. Phys. Rev. Lett. 115, 177402 (2015) (Numerical data kindly provided by Osamu Takayama)
  • doi:10.1103/physrevlett.115.177402 Experimental Demonstration of Effective Medium Approximation Breakdown in Deeply Subwavelength All-Dielectric Multilayers, Physical Review Letters (2015)

Cite

Sergei V. Zhukovsky et al.. Experimental Demonstration of Effective Medium Approximation Breakdown in Deeply Subwavelength All-Dielectric Multilayers. Physical Review Letters, 115, 177402 (2015), doi:10.1103/physrevlett.115.177402; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

700 rows as published
TiO2 (Titanium dioxide), Zhukovsky et al. 2015: Thin film; n 0.211–1.69 µm: n and k versus wavelength
λ (µm)nk
0.2110021.7168481.305756
0.2125761.7361341.322382
0.214151.7560031.3385
0.2157241.776441.354101
0.2172991.7974321.369177
0.2188731.8189651.383719
0.2204471.8410271.397717
0.2220221.8636061.411162
0.2235961.8866891.424044
0.2251711.9102641.436353
0.2267461.934321.448076
0.2283211.9588451.459205
0.2298961.9838271.469726
0.2314712.0092551.479628
0.2330462.0351171.488898
0.2346212.0614021.497524
0.2361962.0880961.505493
0.2377712.1151871.512791
0.2393472.1426641.519404
0.2409222.1705131.525319
0.2424982.198721.530519
0.2440732.2272711.53499
0.2456492.2561531.538718
0.2472252.2853491.541685
0.24882.3148461.543877
0.2503762.3446251.545277
0.2519522.374671.545867
0.2535282.4049641.545632
0.2551052.4354871.544554
0.2566812.4662211.542615
0.2582572.4971441.539799
0.2598332.5282351.536088
0.261412.5594731.531463
0.2629862.5908321.525906
0.2645632.6222881.519401
0.2661392.6538141.511929
0.2677162.6853851.503471
0.2692932.7169691.494012
0.270872.7485391.483531
0.2724472.7800611.472014
0.2740242.8115021.459442
0.2756012.8428281.445799
0.2771782.8740021.43107
0.2787552.9049851.415239
0.2803322.9357391.398292
0.2819092.966221.380216
0.2834872.9963871.360997
0.2850643.0261951.340626
0.2866423.0555971.319093
0.2882193.0845461.296389
0.2897973.1129931.27251
0.2913753.1408891.247451
0.2929523.1681861.221211
0.294533.1948361.193791
0.2961083.2207921.165193
0.2976863.2460131.135426
0.2992643.2704641.104499
0.3008423.294121.072421
0.302423.3169731.039208
0.3039983.3390461.004873
0.3055763.3604060.969427
0.3071553.3812090.932871
0.3087333.4017790.895181
0.3103113.4228220.856268
0.311893.4462120.815812
0.3134683.4842070.769207
0.3150473.4976630.686527
0.3166263.4902550.617094
0.3182043.4748720.556571
0.3197833.4550540.503183
0.3213623.4325820.45577
0.3229413.4085190.413468
0.324523.3835590.375601
0.3260993.3581750.341612
0.3276783.3326980.311038
0.3292573.3073680.283485
0.3308363.2823560.258616
0.3324153.2577850.236138
0.3339943.2337440.215796
0.3355733.2102940.197365
0.3371533.1874750.180649
0.3387323.1653160.165474
0.3403113.1438290.151684
0.3418913.1230190.139143
0.343473.1028850.127729
0.345053.083420.117331
0.346633.0646120.107852
0.3482093.0464470.099205
0.3497893.0289090.091311
0.3513693.011980.0841
0.3529482.9956410.077508
0.3545282.9798730.071477
0.3561082.9646540.065957
0.3576882.9499670.060901
0.3592682.9357890.056267
0.3608482.9221010.052017
0.3624282.9088850.048117
0.3640082.8961210.044536
0.3655882.883790.041247
0.3671692.8718760.038222
0.3687492.8603590.03544
0.3703292.8492250.032879
0.3719092.8384560.030521
0.373492.8280380.028348
0.375072.8179560.026345
0.376652.8081960.024497
0.3782312.7987430.022791
0.3798112.7895860.021216
0.3813922.7807110.01976
0.3829722.7721080.018414
0.3845532.7637640.017169
0.3861342.7556690.016017
0.3877142.7478130.01495
0.3892952.7401860.013961
0.3908762.7327790.013045
0.3924572.7255830.012195
0.3940372.7185890.011406
0.3956182.711790.010673
0.3971992.7051770.009993
0.398782.6987440.00936
0.4003612.6924840.008772
0.4019422.6863890.008225
0.4035232.6804540.007716
0.4051042.6746720.007241
0.4066852.6690380.006799
0.4082662.6635460.006387
0.4098472.6581920.006003
0.4114282.6529690.005645
0.413012.6478740.00531
0.4145912.6429010.004998
0.4161722.6380470.004705
0.4177532.6333070.004432
0.4193352.6286770.004177
0.4209162.6241540.003938
0.4224972.6197340.003714
0.4240792.6154130.003505
0.425662.6111880.003309
0.4272412.6070560.003125
0.4288232.6030140.002952
0.4304042.5990590.00279
0.4319862.5951890.002638
0.4335672.5913990.002496
0.4351492.5876890.002362
0.436732.5840550.002236
0.4383122.5804960.002118
0.4398942.5770080.002006
0.4414752.573590.001902
0.4430572.570240.001803
0.4446382.5669550.00171
0.446222.5637340.001623
0.4478022.5605750.00154
0.4493842.5574750.001463
0.4509652.5544350.001389
0.4525472.5514510.00132
0.4541292.5485220.001255
0.4557112.5456470.001193
0.4572922.5428240.001135
0.4588742.5400520.00108
0.4604562.5373290.001028
0.4620382.5346540.000979
0.463622.5320260.000933
0.4652022.5294440.000889
0.4667842.5269060.000847
0.4683652.5244110.000808
0.4699472.5219590.00077
0.4715292.5195470.000735
0.4731112.5171760.000701
0.4746932.5148440.00067
0.4762752.5125490.00064
0.4778572.5102930.000611
0.4794392.5080720.000584
0.4810212.5058870.000558
0.4826032.5037360.000534
0.4841852.5016190.00051
0.4857672.4995360.000488
0.4873492.4974840.000467
0.4889312.4954640.000447
0.4905132.4934740.000428
0.4920952.4915150.00041
0.4936772.4895850.000393
0.4952592.4876840.000377
0.4968412.4858110.000361
0.4984232.4839660.000346
0.5000052.4821470.000332
0.5015872.4803560.000319
0.5031692.4785890.000306
0.5047522.4768480.000293
0.5063342.4751310.000282
0.5079162.4734390.000271
0.5094982.4717710.00026
0.511082.4701250.00025
0.5126622.4685030.00024
0.5142442.4669020.000231
0.5158262.4653230.000222
0.5174082.4637660.000213
0.518992.462230.000205
0.5205722.4607140.000198
0.5221542.4592190.00019
0.5237362.4577430.000183
0.5253182.4562870.000176
0.5269012.4548490.00017
0.5284832.453430.000164
0.5300652.452030.000158
0.5316472.4506470.000152
0.5332292.4492820.000147
0.5348112.4479350.000141
0.5363932.4466040.000136
0.5379752.445290.000131
0.5395572.4439920.000127
0.5411392.4427110.000122
0.5427212.4414450.000118
0.5443032.4401950.000114
0.5458852.438960.00011
0.5474672.4377390.000106
0.5490492.4365340.000103
0.5506312.4353439.9e-05
0.5522132.4341669.6e-05
0.5537942.4330039.3e-05
0.5553762.4318549e-05
0.5569582.4307188.7e-05
0.558542.4295958.4e-05
0.5601222.4284868.1e-05
0.5617042.4273897.9e-05
0.5632862.4263057.6e-05
0.5648682.4252337.4e-05
0.5664492.4241747.1e-05
0.5680312.4231266.9e-05
0.5696132.422096.7e-05
0.5711952.4210666.5e-05
0.5727762.4200536.3e-05
0.5743582.4190526.1e-05
0.575942.4180615.9e-05
0.5775222.4170825.7e-05
0.5791032.4161135.5e-05
0.5806852.4151545.4e-05
0.5822672.4142065.2e-05
0.5838482.4132695.1e-05
0.585432.4123414.9e-05
0.5870122.4114234.8e-05
0.5885932.4105154.6e-05
0.5901752.4096164.5e-05
0.5917562.4087274.4e-05
0.5933382.4078474.2e-05
0.5949192.4069774.1e-05
0.5965012.4061164e-05
0.5980822.4052633.9e-05
0.5996632.4044193.8e-05
0.6012452.4035843.7e-05
0.6028262.4027573.6e-05
0.6044072.4019393.5e-05
0.6059892.4011293.4e-05
0.607572.4003273.3e-05
0.6091512.3995343.2e-05
0.6107332.3987483.1e-05
0.6123142.397973e-05
0.6138952.3971992.9e-05
0.6154762.3964372.9e-05
0.6170572.3956822.8e-05
0.6186382.3949342.7e-05
0.6202192.3941932.6e-05
0.62182.393462.6e-05
0.6233812.3927342.5e-05
0.6249622.3920142.4e-05
0.6265432.3913022.4e-05
0.6281242.3905962.3e-05
0.6297052.3898982.2e-05
0.6312862.3892052.2e-05
0.6328672.388522.1e-05
0.6344472.3878412.1e-05
0.6360282.3871672e-05
0.6376092.3865012e-05
0.6391892.3858411.9e-05
0.640772.3851861.9e-05
0.6423512.3845381.8e-05
0.6439312.3838961.8e-05
0.6455122.3832591.7e-05
0.6470922.3826291.7e-05
0.6486722.3820041.7e-05
0.6502532.3813851.6e-05
0.6518332.3807711.6e-05
0.6534142.3801631.5e-05
0.6549942.379561.5e-05
0.6565742.3789631.5e-05
0.6581542.3783711.4e-05
0.6597342.3777841.4e-05
0.6613152.3772031.4e-05
0.6628952.3766261.3e-05
0.6644752.3760551.3e-05
0.6660552.3754881.3e-05
0.6676352.3749271.3e-05
0.6692142.374371.2e-05
0.6707942.3738181.2e-05
0.6723742.3732711.2e-05
0.6739542.3727291.1e-05
0.6755342.3721911.1e-05
0.6771132.3716581.1e-05
0.6786932.371131.1e-05
0.6802732.3706051e-05
0.6818522.3700861e-05
0.6834322.369571e-05
0.6850112.3690591e-05
0.686592.3685521e-05
0.688172.368059e-06
0.6897492.3675529e-06
0.6913282.3670579e-06
0.6929072.3665679e-06
0.6944872.3660819e-06
0.6960662.3655998e-06
0.6976452.3651218e-06
0.6992242.3646468e-06
0.7008032.3641768e-06
0.7023812.3637098e-06
0.703962.3632468e-06
0.7055392.3627877e-06
0.7071182.3623327e-06
0.7086962.361887e-06
0.7102752.3614327e-06
0.7118542.3609877e-06
0.7134322.3605467e-06
0.715012.3601087e-06
0.7165892.3596746e-06
0.7181672.3592436e-06
0.7197452.3588156e-06
0.7213242.3583916e-06
0.7229022.357976e-06
0.724482.3575536e-06
0.7260582.3571386e-06
0.7276362.3567276e-06
0.7292142.3563196e-06
0.7307922.3559145e-06
0.7323692.3555125e-06
0.7339472.3551135e-06
0.7355252.3547175e-06
0.7371022.3543255e-06
0.738682.3539355e-06
0.7402572.3535485e-06
0.7418352.3531645e-06
0.7434122.3527835e-06
0.7449892.3524055e-06
0.7465662.3520295e-06
0.7481442.3516574e-06
0.7497212.3512874e-06
0.7512982.3509194e-06
0.7528752.3505554e-06
0.7544512.3501934e-06
0.7560282.3498344e-06
0.7576052.3494784e-06
0.7591822.3491234e-06
0.7607582.3487724e-06
0.7623352.3484234e-06
0.7639112.3480774e-06
0.7654882.3477334e-06
0.7670642.3473924e-06
0.768642.3470534e-06
0.7702162.3467163e-06
0.7717922.3463823e-06
0.7733682.346053e-06
0.7749442.3457213e-06
0.776522.3453943e-06
0.7780962.3450693e-06
0.7796722.3447463e-06
0.7812472.3444263e-06
0.7828232.3441083e-06
0.7843982.3437923e-06
0.7859742.3434793e-06
0.7875492.3431673e-06
0.7891242.3428583e-06
0.79072.3425513e-06
0.7922752.3422463e-06
0.793852.3419433e-06
0.7954252.3416423e-06
0.7972.3413433e-06
0.7985742.3410463e-06
0.8001492.3407513e-06
0.8017242.3404593e-06
0.8032982.3401682e-06
0.8048732.3398792e-06
0.8064472.3395922e-06
0.8080212.3393072e-06
0.8095962.3390242e-06
0.811172.3387422e-06
0.8127442.3384632e-06
0.8143182.3381862e-06
0.8158912.337912e-06
0.8174652.3376362e-06
0.8190392.3373642e-06
0.8206132.3370942e-06
0.8221862.3368252e-06
0.823762.3365592e-06
0.8253332.3362942e-06
0.8269062.336032e-06
0.8284792.3357692e-06
0.8300522.3355092e-06
0.8316252.3352512e-06
0.8331982.3349942e-06
0.8347712.3347392e-06
0.8363442.3344862e-06
0.8379162.3342342e-06
0.8394892.3339852e-06
0.8410612.3337362e-06
0.8426342.3334892e-06
0.8442062.3332442e-06
0.8457782.3332e-06
0.847352.3327582e-06
0.8489222.3325172e-06
0.8504942.3322782e-06
0.8520662.3320412e-06
0.8536382.3318042e-06
0.8552092.331572e-06
0.8567812.3313362e-06
0.8583522.3311052e-06
0.8599232.3308741e-06
0.8614952.3306451e-06
0.8630662.3304181e-06
0.8646372.3301921e-06
0.8662082.3299671e-06
0.8677782.3297431e-06
0.8693492.3295211e-06
0.870922.3293011e-06
0.872492.3290811e-06
0.8740612.3288631e-06
0.8756312.3286471e-06
0.8772012.3284311e-06
0.8787712.3282171e-06
0.8803412.3280051e-06
0.8819112.3277931e-06
0.8834812.3275831e-06
0.885052.3273741e-06
0.886622.3271661e-06
0.8881892.326961e-06
0.8897592.3267541e-06
0.8913282.326551e-06
0.8928972.3263471e-06
0.8944662.3261461e-06
0.8960352.3259451e-06
0.8976042.3257461e-06
0.8991732.3255481e-06
0.9007412.3253511e-06
0.902312.3251551e-06
0.9038782.324961e-06
0.9054462.3247671e-06
0.9070142.3245741e-06
0.9085832.3243831e-06
0.9101512.3241931e-06
0.9117182.3240041e-06
0.9132862.3238161e-06
0.9148542.3236291e-06
0.9164212.3234431e-06
0.9179882.3232581e-06
0.9195562.3230751e-06
0.9211232.3228921e-06
0.922692.322711e-06
0.9242572.322531e-06
0.9258232.322351e-06
0.927392.3221711e-06
0.9289572.3219941e-06
0.9305232.3218171e-06
0.9320892.3216411e-06
0.9336562.3214671e-06
0.9352222.3212931e-06
0.9367882.3211211e-06
0.9383542.3209491e-06
0.9399192.3207781e-06
0.9414852.3206081e-06
0.943052.3204391e-06
0.9446162.3202711e-06
0.9461812.3201041e-06
0.9477462.3199381e-06
0.9493112.3197731e-06
0.9508762.3196091e-06
0.9524412.3194451e-06
0.9540052.3192831e-06
0.955572.3191211e-06
0.9571342.318961e-06
0.9586982.3188011e-06
0.9602622.3186421e-06
0.9618262.3184841e-06
0.963392.3183261e-06
0.9649542.318171e-06
0.9665172.3180141e-06
0.9680812.3178591e-06
0.9696442.3177051e-06
0.9712072.3175521e-06
0.9727712.31741e-06
0.9743332.3172491e-06
0.9758962.3170981e-06
0.9774592.3169481e-06
0.9790212.3167991e-06
0.9805842.3166511e-06
0.9821462.3165031e-06
0.9837082.3163561e-06
0.985272.316211e-06
0.9868322.3160651e-06
0.9883942.3159211e-06
0.9899562.3157771e-06
0.9915172.3156341e-06
0.9930782.3154921e-06
0.994642.315351e-06
0.9962012.315211e-06
0.9977622.315071e-06
0.9993222.314931e-06
1.0113462.3138811e-06
1.0147112.3135940.0
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1.6863532.2871970.0
1.6898422.2871370.0

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
—