Optical constants

Refractive index of TiO₂ (Titanium dioxide)

Kischkat et al. 2012: Thin film; n,k 1.54–14.29 µm

Data: tabulated nk
Range: 1.538–14.29 µm
Points: 1451
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.26484
Extinction coefficient k: 0.00251902

Permittivity ε₁: 5.12951
Permittivity ε₂: 0.0114104

Absorption coefficient α: 67.4946 cm⁻¹
Penetration depth δ = λ/(2πk): 296320 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.0762954 µm⁻¹

Group index n_g: 2.62267
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 0.264359 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

# TiO2 (Titanium dioxide): Kischkat et al. 2012: Thin film; n,k 1.54–14.29 µm
tio2 = ls.fetch_refractiveindex("main", "TiO2", "Kischkat", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(tio2.range_nm)  # (1538.46, 14285.7) nm
eps = tio2.eps([4690])  # 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_4eb8af1a738c/lightsmith"
tio2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(tio2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (tio2/kischkat-2012).

# ... load tio2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=tio2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=1539, stop_nm=14280, 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

352-nm single layer on Si substrate. Prepared by room temperature reactive sputter deposition using TiO₂ target.
Data on the influence of deposition conditions on the optical properties of the film can be found in the original publication.
Data on the refractive index (n) in the visible can be found in the original publication.

References

J. Kischkat, S. Peters, B. Gruska, M. Semtsiv, M. Chashnikova, M. Klinkmüller, O. Fedosenko, S. Machulik, A. Aleksandrova, G. Monastyrskyi, Y. Flores, W. T. Masselink. Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride. Appl. Opt. 51, 6789-6798 (2012) (Numerical data kindly provided by Jan Kischkat)

doi:10.1364/ao.51.006789 Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride, Applied Optics (2012)

Cite

Jan Kischkat et al.. Mid-infrared optical properties of thin films of aluminum oxide, titanium dioxide, silicon dioxide, aluminum nitride, and silicon nitride. Applied Optics, 51, 6789 (2012), doi:10.1364/ao.51.006789; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1451 rows as published

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

TiO2 (Titanium dioxide), Kischkat et al. 2012: Thin film; n,k 1.54–14.29 µm: n and k versus wavelength
λ (µm)	n	k
1.53846	2.43346	0.0001
1.53941	2.4334	0.0001
1.54036	2.43334	0.0001
1.54131	2.43329	0.0001
1.54226	2.43323	0.0001
1.54321	2.43317	0.0001
1.54416	2.43312	0.0001
1.54512	2.43306	0.0001
1.54607	2.433	0.0001
1.54703	2.43295	0.0001
1.54799	2.43289	0.0001
1.54895	2.43283	0.0001
1.54991	2.43277	0.0001
1.55087	2.43272	0.0001
1.55183	2.43266	0.0001
1.5528	2.4326	0.0001
1.55376	2.43255	0.0001
1.55473	2.43249	0.0001
1.55569	2.43243	0.0001
1.55666	2.43238	0.0001
1.55763	2.43232	0.0001
1.5586	2.43226	0.0001
1.55958	2.43221	0.0001
1.56055	2.43215	0.0001
1.56152	2.43209	0.0001
1.5625	2.43204	0.0001
1.56348	2.43198	0.0001
1.56446	2.43192	0.0001
1.56544	2.43187	0.0001
1.56642	2.43181	0.0001
1.5674	2.43175	0.0001
1.56838	2.4317	0.0001
1.56937	2.43164	0.0001
1.57035	2.43158	0.0001
1.57134	2.43153	0.0001
1.57233	2.43147	0.0001
1.57332	2.43141	0.0001
1.57431	2.43136	0.0001
1.5753	2.4313	0.0001
1.57629	2.43124	0.0001
1.57729	2.43119	0.0001
1.57828	2.43113	0.0001
1.57928	2.43107	0.0001
1.58028	2.43102	0.0001
1.58128	2.43096	0.0001
1.58228	2.4309	0.0001
1.58328	2.43085	0.0001
1.58428	2.43079	0.0001
1.58529	2.43073	0.0001
1.58629	2.43068	0.0001
1.5873	2.43062	0.0001
1.58831	2.43056	0.0001
1.58932	2.43051	0.0001
1.59033	2.43045	0.0001
1.59134	2.43039	0.0001
1.59236	2.43034	0.0001
1.59337	2.43028	0.0001
1.59439	2.43022	0.0001
1.59541	2.43017	0.0001
1.59642	2.43011	0.0001
1.59744	2.43005	0.0001
1.59847	2.43	0.0001
1.59949	2.42994	0.0001
1.60051	2.42988	0.0001
1.60154	2.42983	0.0001
1.60256	2.42977	0.0001
1.60359	2.42971	0.0001
1.60462	2.42966	0.0001
1.60565	2.4296	0.0001
1.60668	2.42954	0.0001
1.60772	2.42949	0.0001
1.60875	2.42943	0.00011
1.60979	2.42937	0.00011
1.61082	2.42932	0.00011
1.61186	2.42926	0.00011
1.6129	2.4292	0.00011
1.61394	2.42915	0.00011
1.61499	2.42909	0.00011
1.61603	2.42903	0.00011
1.61708	2.42897	0.00011
1.61812	2.42892	0.00011
1.61917	2.42886	0.00011
1.62022	2.4288	0.00011
1.62127	2.42875	0.00011
1.62232	2.42869	0.00011
1.62338	2.42863	0.00011
1.62443	2.42858	0.00011
1.62549	2.42852	0.00011
1.62655	2.42846	0.00011
1.6276	2.42841	0.00011
1.62866	2.42835	0.00011
1.62973	2.42829	0.00011
1.63079	2.42824	0.00011
1.63185	2.42818	0.00011
1.63292	2.42812	0.00011
1.63399	2.42807	0.00011
1.63506	2.42801	0.00011
1.63613	2.42795	0.00011
1.6372	2.4279	0.00011
1.63827	2.42784	0.00011
1.63934	2.42778	0.00011
1.64042	2.42772	0.00011
1.6415	2.42767	0.00011
1.64258	2.42761	0.00011
1.64366	2.42755	0.00011
1.64474	2.4275	0.00011
1.64582	2.42744	0.00011
1.6469	2.42738	0.00011
1.64799	2.42733	0.00011
1.64908	2.42727	0.00011
1.65017	2.42721	0.00011
1.65125	2.42715	0.00011
1.65235	2.4271	0.00011
1.65344	2.42704	0.00011
1.65453	2.42698	0.00011
1.65563	2.42693	0.00011
1.65673	2.42687	0.00011
1.65782	2.42681	0.00011
1.65893	2.42675	0.00011
1.66003	2.4267	0.00011
1.66113	2.42664	0.00011
1.66223	2.42658	0.00011
1.66334	2.42653	0.00011
1.66445	2.42647	0.00011
1.66556	2.42641	0.00011
1.66667	2.42635	0.00011
1.66778	2.4263	0.00011
1.66889	2.42624	0.00011
1.67001	2.42618	0.00011
1.67112	2.42613	0.00011
1.67224	2.42607	0.00011
1.67336	2.42601	0.00011
1.67448	2.42595	0.00011
1.6756	2.4259	0.00011
1.67673	2.42584	0.00011
1.67785	2.42578	0.00011
1.67898	2.42572	0.00011
1.68011	2.42567	0.00011
1.68124	2.42561	0.00011
1.68237	2.42555	0.00011
1.6835	2.42549	0.00011
1.68464	2.42544	0.00012
1.68577	2.42538	0.00012
1.68691	2.42532	0.00012
1.68805	2.42526	0.00012
1.68919	2.42521	0.00012
1.69033	2.42515	0.00012
1.69147	2.42509	0.00012
1.69262	2.42503	0.00012
1.69377	2.42498	0.00012
1.69492	2.42492	0.00012
1.69607	2.42486	0.00012
1.69722	2.4248	0.00012
1.69837	2.42475	0.00012
1.69952	2.42469	0.00012
1.70068	2.42463	0.00012
1.70184	2.42457	0.00012
1.703	2.42452	0.00012
1.70416	2.42446	0.00012
1.70532	2.4244	0.00012
1.70648	2.42434	0.00012
1.70765	2.42428	0.00012
1.70882	2.42423	0.00012
1.70999	2.42417	0.00012
1.71116	2.42411	0.00012
1.71233	2.42405	0.00012
1.7135	2.42399	0.00012
1.71468	2.42394	0.00012
1.71585	2.42388	0.00012
1.71703	2.42382	0.00012
1.71821	2.42376	0.00012
1.71939	2.4237	0.00012
1.72058	2.42365	0.00012
1.72176	2.42359	0.00012
1.72295	2.42353	0.00012
1.72414	2.42347	0.00012
1.72533	2.42341	0.00012
1.72652	2.42336	0.00012
1.72771	2.4233	0.00012
1.72891	2.42324	0.00012
1.7301	2.42318	0.00012
1.7313	2.42312	0.00012
1.7325	2.42306	0.00012
1.7337	2.42301	0.00012
1.73491	2.42295	0.00012
1.73611	2.42289	0.00012
1.73732	2.42283	0.00012
1.73853	2.42277	0.00012
1.73974	2.42271	0.00012
1.74095	2.42266	0.00012
1.74216	2.4226	0.00012
1.74338	2.42254	0.00012
1.74459	2.42248	0.00012
1.74581	2.42242	0.00012
1.74703	2.42236	0.00012
1.74825	2.4223	0.00012
1.74948	2.42224	0.00012
1.7507	2.42219	0.00012
1.75193	2.42213	0.00012
1.75316	2.42207	0.00013
1.75439	2.42201	0.00013
1.75562	2.42195	0.00013
1.75685	2.42189	0.00013
1.75809	2.42183	0.00013
1.75932	2.42177	0.00013
1.76056	2.42171	0.00013
1.7618	2.42166	0.00013
1.76305	2.4216	0.00013
1.76429	2.42154	0.00013
1.76554	2.42148	0.00013
1.76678	2.42142	0.00013
1.76803	2.42136	0.00013
1.76929	2.4213	0.00013
1.77054	2.42124	0.00013
1.77179	2.42118	0.00013
1.77305	2.42112	0.00013
1.77431	2.42106	0.00013
1.77557	2.421	0.00013
1.77683	2.42095	0.00013
1.77809	2.42089	0.00013
1.77936	2.42083	0.00013
1.78063	2.42077	0.00013
1.7819	2.42071	0.00013
1.78317	2.42065	0.00013
1.78444	2.42059	0.00013
1.78571	2.42053	0.00013
1.78699	2.42047	0.00013
1.78827	2.42041	0.00013
1.78955	2.42035	0.00013
1.79083	2.42029	0.00013
1.79211	2.42023	0.00013
1.7934	2.42017	0.00013
1.79469	2.42011	0.00013
1.79598	2.42005	0.00013
1.79727	2.41999	0.00013
1.79856	2.41993	0.00013
1.79986	2.41987	0.00013
1.80115	2.41981	0.00013
1.80245	2.41975	0.00013
1.80375	2.41969	0.00013
1.80505	2.41963	0.00013
1.80636	2.41957	0.00013
1.80766	2.41951	0.00013
1.80897	2.41945	0.00013
1.81028	2.41939	0.00013
1.81159	2.41933	0.00013
1.81291	2.41927	0.00013
1.81422	2.41921	0.00014
1.81554	2.41915	0.00014
1.81686	2.41908	0.00014
1.81818	2.41902	0.00014
1.81951	2.41896	0.00014
1.82083	2.4189	0.00014
1.82216	2.41884	0.00014
1.82349	2.41878	0.00014
1.82482	2.41872	0.00014
1.82615	2.41866	0.00014
1.82749	2.4186	0.00014
1.82882	2.41854	0.00014
1.83016	2.41848	0.00014
1.8315	2.41842	0.00014
1.83284	2.41835	0.00014
1.83419	2.41829	0.00014
1.83554	2.41823	0.00014
1.83688	2.41817	0.00014
1.83824	2.41811	0.00014
1.83959	2.41805	0.00014
1.84094	2.41799	0.00014
1.8423	2.41793	0.00014
1.84366	2.41786	0.00014
1.84502	2.4178	0.00014
1.84638	2.41774	0.00014
1.84775	2.41768	0.00014
1.84911	2.41762	0.00014
1.85048	2.41756	0.00014
1.85185	2.41749	0.00014
1.85322	2.41743	0.00014
1.8546	2.41737	0.00014
1.85598	2.41731	0.00014
1.85736	2.41725	0.00014
1.85874	2.41718	0.00014
1.86012	2.41712	0.00014
1.8615	2.41706	0.00014
1.86289	2.417	0.00014
1.86428	2.41694	0.00014
1.86567	2.41687	0.00014
1.86706	2.41681	0.00014
1.86846	2.41675	0.00014
1.86986	2.41669	0.00014
1.87126	2.41662	0.00015
1.87266	2.41656	0.00015
1.87406	2.4165	0.00015
1.87547	2.41644	0.00015
1.87688	2.41637	0.00015
1.87829	2.41631	0.00015
1.8797	2.41625	0.00015
1.88111	2.41618	0.00015
1.88253	2.41612	0.00015
1.88395	2.41606	0.00015
1.88537	2.416	0.00015
1.88679	2.41593	0.00015
1.88822	2.41587	0.00015
1.88964	2.41581	0.00015
1.89107	2.41574	0.00015
1.89251	2.41568	0.00015
1.89394	2.41562	0.00015
1.89538	2.41555	0.00015
1.89681	2.41549	0.00015
1.89825	2.41543	0.00015
1.8997	2.41536	0.00015
1.90114	2.4153	0.00015
1.90259	2.41523	0.00015
1.90404	2.41517	0.00015
1.90549	2.41511	0.00015
1.90694	2.41504	0.00015
1.9084	2.41498	0.00015
1.90985	2.41492	0.00015
1.91131	2.41485	0.00015
1.91278	2.41479	0.00015
1.91424	2.41472	0.00015
1.91571	2.41466	0.00015
1.91718	2.41459	0.00015
1.91865	2.41453	0.00015
1.92012	2.41447	0.00015
1.9216	2.4144	0.00015
1.92308	2.41434	0.00015
1.92456	2.41427	0.00016
1.92604	2.41421	0.00016
1.92753	2.41414	0.00016
1.92901	2.41408	0.00016
1.9305	2.41401	0.00016
1.93199	2.41395	0.00016
1.93349	2.41388	0.00016
1.93498	2.41382	0.00016
1.93648	2.41375	0.00016
1.93798	2.41369	0.00016
1.93949	2.41362	0.00016
1.94099	2.41356	0.00016
1.9425	2.41349	0.00016
1.94401	2.41342	0.00016
1.94553	2.41336	0.00016
1.94704	2.41329	0.00016
1.94856	2.41323	0.00016
1.95008	2.41316	0.00016
1.9516	2.4131	0.00016
1.95313	2.41303	0.00016
1.95465	2.41296	0.00016
1.95618	2.4129	0.00016
1.95771	2.41283	0.00016
1.95925	2.41277	0.00016
1.96078	2.4127	0.00016
1.96232	2.41263	0.00016
1.96386	2.41257	0.00016
1.96541	2.4125	0.00016
1.96696	2.41243	0.00016
1.9685	2.41237	0.00016
1.97006	2.4123	0.00016
1.97161	2.41223	0.00016
1.97316	2.41217	0.00017
1.97472	2.4121	0.00017
1.97628	2.41203	0.00017
1.97785	2.41197	0.00017
1.97941	2.4119	0.00017
1.98098	2.41183	0.00017
1.98255	2.41176	0.00017
1.98413	2.4117	0.00017
1.9857	2.41163	0.00017
1.98728	2.41156	0.00017
1.98886	2.41149	0.00017
1.99045	2.41143	0.00017
1.99203	2.41136	0.00017
1.99362	2.41129	0.00017
1.99521	2.41122	0.00017
1.99681	2.41115	0.00017
1.9984	2.41109	0.00017
2.0	2.41102	0.00017
2.0016	2.41095	0.00017
2.00321	2.41088	0.00017
2.00481	2.41081	0.00017
2.00642	2.41074	0.00017
2.00803	2.41067	0.00017
2.00965	2.41061	0.00017
2.01126	2.41054	0.00017
2.01288	2.41047	0.00017
2.0145	2.4104	0.00017
2.01613	2.41033	0.00017
2.01776	2.41026	0.00017
2.01939	2.41019	0.00017
2.02102	2.41012	0.00018
2.02265	2.41005	0.00018
2.02429	2.40998	0.00018
2.02593	2.40991	0.00018
2.02758	2.40984	0.00018
2.02922	2.40977	0.00018
2.03087	2.4097	0.00018
2.03252	2.40963	0.00018
2.03417	2.40956	0.00018
2.03583	2.40949	0.00018
2.03749	2.40942	0.00018
2.03915	2.40935	0.00018
2.04082	2.40928	0.00018
2.04248	2.40921	0.00018
2.04415	2.40914	0.00018
2.04583	2.40907	0.00018
2.0475	2.409	0.00018
2.04918	2.40893	0.00018
2.05086	2.40886	0.00018
2.05255	2.40879	0.00018
2.05423	2.40872	0.00018
2.05592	2.40864	0.00018
2.05761	2.40857	0.00018
2.05931	2.4085	0.00018
2.06101	2.40843	0.00018
2.06271	2.40836	0.00018
2.06441	2.40829	0.00019
2.06612	2.40821	0.00019
2.06782	2.40814	0.00019
2.06954	2.40807	0.00019
2.07125	2.408	0.00019
2.07297	2.40793	0.00019
2.07469	2.40785	0.00019
2.07641	2.40778	0.00019
2.07814	2.40771	0.00019
2.07987	2.40764	0.00019
2.0816	2.40756	0.00019
2.08333	2.40749	0.00019
2.08507	2.40742	0.00019
2.08681	2.40734	0.00019
2.08855	2.40727	0.00019
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3.66032	2.33304	0.00103
3.66569	2.33274	0.00104
3.67107	2.33243	0.00104
3.67647	2.33212	0.00105
3.68189	2.33181	0.00105
3.68732	2.33149	0.00106
3.69276	2.33118	0.00106
3.69822	2.33086	0.00107
3.7037	2.33055	0.00107
3.7092	2.33023	0.00108
3.71471	2.32991	0.00108
3.72024	2.32959	0.00109
3.72578	2.32926	0.0011
3.73134	2.32894	0.0011
3.73692	2.32861	0.00111
3.74251	2.32829	0.00111
3.74813	2.32796	0.00112
3.75375	2.32763	0.00112
3.7594	2.3273	0.00113
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3.78215	2.32595	0.00115
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3.79363	2.32527	0.00117
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3.80518	2.32459	0.00118
3.81098	2.32424	0.00118
3.81679	2.32389	0.00119
3.82263	2.32354	0.0012
3.82848	2.32319	0.0012
3.83436	2.32284	0.00121
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3.90625	2.31848	0.00129
3.91236	2.3181	0.0013
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3.94945	2.31581	0.00134
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3.96197	2.31503	0.00136
3.96825	2.31464	0.00136
3.97456	2.31425	0.00137
3.98089	2.31385	0.00138
3.98724	2.31345	0.00139
3.99361	2.31305	0.00139
4.0	2.31265	0.0014
4.00641	2.31225	0.00141
4.01284	2.31184	0.00142
4.01929	2.31144	0.00143
4.02576	2.31103	0.00143
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4.03877	2.3102	0.00145
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4.05186	2.30937	0.00147
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4.06504	2.30852	0.00148
4.07166	2.3081	0.00149
4.0783	2.30767	0.0015
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4.13907	2.30373	0.00158
4.14594	2.30328	0.00159
4.15282	2.30283	0.0016
4.15973	2.30238	0.00161
4.16667	2.30192	0.00162
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4.19463	2.30007	0.00166
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4.21585	2.29866	0.00169
4.22297	2.29818	0.0017
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4.24448	2.29674	0.00173
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4.25894	2.29576	0.00175
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4.2735	2.29477	0.00178
4.28082	2.29428	0.00179
4.28816	2.29378	0.0018
4.29553	2.29327	0.00181
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4.34783	2.28968	0.00189
4.3554	2.28915	0.0019
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4.47227	2.28091	0.0021
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4.48833	2.27976	0.00213
4.4964	2.27918	0.00214
4.5045	2.27859	0.00216
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4.52899	2.27682	0.0022
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4.54545	2.27562	0.00223
4.55373	2.27501	0.00225
4.56204	2.2744	0.00226
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4.57875	2.27317	0.0023
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4.68165	2.26548	0.0025
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4.74383	2.26073	0.00263
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4.77099	2.25862	0.00269
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4.82625	2.2543	0.00281
4.83559	2.25357	0.00283
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4.85437	2.25208	0.00288
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4.97018	2.24275	0.00316
4.98008	2.24193	0.00318
4.99002	2.24112	0.00321
5.0	2.2403	0.00323
5.01002	2.23947	0.00326
5.02008	2.23863	0.00329
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5.06073	2.23525	0.0034
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5.13347	2.22909	0.0036
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10.0	1.38799	0.14239
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11.11111	0.98133	0.36642
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12.31527	0.67024	0.95191
12.37624	0.66615	0.98374
12.43781	0.66286	1.0155
12.5	0.66033	1.04716
12.56281	0.65851	1.07869
12.62626	0.65735	1.11007
12.69036	0.65684	1.1413
12.7551	0.65692	1.17237
12.82051	0.65757	1.20327
12.8866	0.65875	1.23399
12.95337	0.66045	1.26455
13.02083	0.66263	1.29493
13.08901	0.66528	1.32514
13.15789	0.66836	1.35518
13.22751	0.67187	1.38506
13.29787	0.67578	1.41478
13.36898	0.68008	1.44434
13.44086	0.68476	1.47374
13.51351	0.6898	1.503
13.58696	0.69519	1.53211
13.6612	0.70092	1.56108
13.73626	0.70697	1.58992
13.81215	0.71335	1.61863
13.88889	0.72004	1.64721
13.96648	0.72703	1.67567
14.04494	0.73431	1.70401
14.12429	0.74188	1.73223
14.20455	0.74974	1.76035
14.28571	0.75787	1.78836

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: —

Plot