Optical constants

Refractive index of WSe₂ (Tungsten diselenide)

Gu et al. 2019: 4-layer (4L) film; n,k 0.193–1.69 µm

Data: tabulated nk
Range: 0.193–1.69 µm
Points: 1084
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.88402
Extinction coefficient k: 1.35168

Permittivity ε₁: 22.0267
Permittivity ε₂: 13.2032

Absorption coefficient α: 289068 cm⁻¹
Penetration depth δ = λ/(2πk): 69.1878 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 2.933 µm⁻¹

Group index n_g: 3.16059
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

# WSe2 (Tungsten diselenide): Gu et al. 2019: 4-layer (4L) film; n,k 0.193–1.69 µm
wse2 = ls.fetch_refractiveindex("main", "WSe2", "Gu-4L", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(wse2.range_nm)  # (193, 1690) nm
eps = wse2.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_e3214c7e265a/lightsmith"
wse2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(wse2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (wse2/gu-2019-4l).

# ... load wse2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=wse2)],
    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

4-layer, 4L

Conditions

film thickness: 4L
substrate: sapphire

References

H. Gu, B. Song, M. Fang, Y. Hong, X. Chen, H. Jiang, W. Ren, S. Liu. Layer-dependent dielectric and optical properties of centimeter-scale 2D WSe₂: evolution from a single layer to few layers. Nanoscale 11, 22762-22771 (2019) (Numerical data kindly provided by Baokun Song)

doi:10.1039/c9nr04270a Layer-dependent dielectric and optical properties of centimeter-scale 2D WSe <sub>2</sub> : evolution from a single layer to few layers, Nanoscale (2019)

Cite

Honggang Gu et al.. Layer-dependent dielectric and optical properties of centimeter-scale 2D WSe <sub>2</sub> : evolution from a single layer to few layers. Nanoscale, 11, 22762-22771 (2019), doi:10.1039/c9nr04270a; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

1084 rows as published

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

WSe2 (Tungsten diselenide), Gu et al. 2019: 4-layer (4L) film; n,k 0.193–1.69 µm: n and k versus wavelength
λ (µm)	n	k
0.193	1.39271	2.138145
0.194	1.392163	2.18944
0.195	1.396797	2.231995
0.196	1.405026	2.26786
0.197	1.415805	2.298452
0.198	1.42841	2.324784
0.199	1.442322	2.347598
0.2	1.457155	2.36746
0.201	1.47261	2.384805
0.202	1.488451	2.399985
0.203	1.504491	2.413283
0.204	1.520573	2.42494
0.205	1.536569	2.435161
0.206	1.552372	2.444124
0.207	1.567891	2.451992
0.208	1.583053	2.45891
0.209	1.597796	2.465011
0.21	1.61207	2.470423
0.211	1.625839	2.475264
0.212	1.639072	2.479645
0.213	1.651754	2.483672
0.214	1.663874	2.487449
0.215	1.675432	2.491071
0.216	1.686438	2.494631
0.217	1.696908	2.498216
0.218	1.706866	2.501908
0.219	1.716345	2.505786
0.22	1.725384	2.509921
0.221	1.734028	2.514378
0.222	1.74233	2.519219
0.223	1.750348	2.524497
0.224	1.758144	2.530257
0.225	1.765788	2.53654
0.226	1.773352	2.543377
0.227	1.780911	2.550792
0.228	1.788547	2.558799
0.229	1.796339	2.567404
0.23	1.804373	2.576604
0.231	1.812732	2.586387
0.232	1.821501	2.596728
0.233	1.830763	2.607594
0.234	1.8406	2.618942
0.235	1.851089	2.630716
0.236	1.862304	2.642849
0.237	1.874311	2.655267
0.238	1.88717	2.66788
0.239	1.90093	2.680592
0.24	1.91563	2.693296
0.241	1.931295	2.705877
0.242	1.947935	2.718213
0.243	1.965543	2.730178
0.244	1.984095	2.741642
0.245	2.003545	2.752477
0.246	2.02383	2.762558
0.247	2.044864	2.771767
0.248	2.066542	2.779997
0.249	2.088738	2.787156
0.25	2.111314	2.793173
0.251	2.134114	2.797998
0.252	2.156976	2.801607
0.253	2.179733	2.804003
0.254	2.202221	2.805219
0.255	2.22428	2.805317
0.256	2.245766	2.804384
0.257	2.266552	2.802532
0.258	2.286534	2.799892
0.259	2.305634	2.796611
0.26	2.323802	2.792843
0.261	2.341018	2.788746
0.262	2.357288	2.784475
0.263	2.372647	2.780178
0.264	2.387153	2.775987
0.265	2.400882	2.772022
0.266	2.413929	2.76838
0.267	2.426396	2.765139
0.268	2.438397	2.762357
0.269	2.450044	2.760067
0.27	2.461452	2.758285
0.271	2.47273	2.757007
0.272	2.48398	2.756214
0.273	2.495297	2.75587
0.274	2.506765	2.755928
0.275	2.518456	2.75633
0.276	2.530431	2.757011
0.277	2.542737	2.757901
0.278	2.555411	2.758925
0.279	2.568475	2.760007
0.28	2.581945	2.761072
0.281	2.59582	2.762043
0.282	2.610092	2.762847
0.283	2.624744	2.763416
0.284	2.63975	2.763684
0.285	2.655076	2.763591
0.286	2.670682	2.763084
0.287	2.686522	2.762113
0.288	2.702546	2.760637
0.289	2.718698	2.758622
0.29	2.73492	2.756039
0.291	2.751154	2.752868
0.292	2.767336	2.749095
0.293	2.783406	2.744712
0.294	2.7993	2.739721
0.295	2.814957	2.734127
0.296	2.830317	2.727943
0.297	2.845322	2.72119
0.298	2.859916	2.713891
0.299	2.874047	2.706077
0.3	2.887664	2.697783
0.301	2.900724	2.689048
0.302	2.913185	2.679916
0.303	2.925009	2.670434
0.304	2.936167	2.660652
0.305	2.946629	2.650623
0.306	2.956374	2.6404
0.307	2.965384	2.630039
0.308	2.973648	2.619597
0.309	2.981158	2.609132
0.31	2.987912	2.598701
0.311	2.993912	2.588361
0.312	2.999164	2.578167
0.313	3.00368	2.568177
0.314	3.007476	2.558443
0.315	3.010571	2.549018
0.316	3.012988	2.539952
0.317	3.014755	2.531294
0.318	3.015902	2.52309
0.319	3.016463	2.515383
0.32	3.016473	2.508213
0.321	3.015972	2.50162
0.322	3.015002	2.495638
0.323	3.013607	2.490298
0.324	3.011832	2.485631
0.325	3.009726	2.481661
0.326	3.007339	2.478411
0.327	3.00472	2.4759
0.328	3.001923	2.474144
0.329	2.999001	2.473153
0.33	2.996009	2.472937
0.331	2.993002	2.473501
0.332	2.990036	2.474844
0.333	2.987166	2.476964
0.334	2.984448	2.479854
0.335	2.98194	2.483502
0.336	2.979695	2.487894
0.337	2.97777	2.49301
0.338	2.976217	2.498827
0.339	2.97509	2.505318
0.34	2.974438	2.51245
0.341	2.974313	2.520187
0.342	2.974759	2.528489
0.343	2.975821	2.537313
0.344	2.97754	2.546609
0.345	2.979953	2.556326
0.346	2.983093	2.566409
0.347	2.98699	2.576798
0.348	2.991667	2.587431
0.349	2.997144	2.598244
0.35	3.003435	2.609169
0.351	3.010547	2.620138
0.352	3.018481	2.631081
0.353	3.027234	2.641926
0.354	3.036793	2.652603
0.355	3.047139	2.66304
0.356	3.058247	2.673169
0.357	3.070085	2.682923
0.358	3.082613	2.692236
0.359	3.095785	2.701049
0.36	3.109548	2.709304
0.361	3.123845	2.71695
0.362	3.13861	2.723943
0.363	3.153775	2.730244
0.364	3.169266	2.735822
0.365	3.185005	2.740653
0.366	3.200915	2.744723
0.367	3.216913	2.748026
0.368	3.232919	2.750564
0.369	3.248852	2.75235
0.37	3.264632	2.753405
0.371	3.280182	2.753758
0.372	3.29543	2.753448
0.373	3.310309	2.752522
0.374	3.324756	2.751034
0.375	3.338715	2.749043
0.376	3.352138	2.746615
0.377	3.364985	2.743822
0.378	3.377223	2.740739
0.379	3.38883	2.737443
0.38	3.399791	2.734014
0.381	3.410101	2.730532
0.382	3.419762	2.727076
0.383	3.428788	2.723726
0.384	3.437197	2.720558
0.385	3.445019	2.717645
0.386	3.452288	2.715057
0.387	3.459048	2.71286
0.388	3.465348	2.711113
0.389	3.471241	2.709872
0.39	3.476788	2.709184
0.391	3.482052	2.709094
0.392	3.4871	2.709635
0.393	3.492003	2.710839
0.394	3.496834	2.712725
0.395	3.501667	2.715311
0.396	3.506577	2.718603
0.397	3.511641	2.722604
0.398	3.516932	2.727307
0.399	3.522528	2.7327
0.4	3.528502	2.738764
0.401	3.534925	2.745474
0.402	3.541866	2.752797
0.403	3.549394	2.760696
0.404	3.557572	2.769128
0.405	3.56646	2.778042
0.406	3.576114	2.787385
0.407	3.586587	2.797097
0.408	3.597925	2.807115
0.409	3.61017	2.81737
0.41	3.623359	2.82779
0.411	3.637523	2.838301
0.412	3.652686	2.848823
0.413	3.668868	2.859277
0.414	3.686079	2.869578
0.415	3.704325	2.879642
0.416	3.723604	2.889385
0.417	3.743908	2.89872
0.418	3.765221	2.907561
0.419	3.787519	2.915822
0.42	3.810771	2.923421
0.421	3.834941	2.930274
0.422	3.859984	2.936303
0.423	3.885848	2.941431
0.424	3.912474	2.945586
0.425	3.939797	2.9487
0.426	3.967747	2.95071
0.427	3.996247	2.951559
0.428	4.025215	2.951196
0.429	4.054564	2.949578
0.43	4.084203	2.946667
0.431	4.11404	2.942435
0.432	4.143977	2.936862
0.433	4.173915	2.929933
0.434	4.203756	2.921647
0.435	4.233401	2.912006
0.436	4.26275	2.901026
0.437	4.291706	2.888726
0.438	4.320175	2.875138
0.439	4.348065	2.860299
0.44	4.375289	2.844255
0.441	4.401764	2.827059
0.442	4.427413	2.808769
0.443	4.452164	2.78945
0.444	4.475952	2.769173
0.445	4.498719	2.748011
0.446	4.520413	2.726044
0.447	4.54099	2.703352
0.448	4.560415	2.680017
0.449	4.578657	2.656126
0.45	4.595694	2.631761
0.451	4.611511	2.60701
0.452	4.626101	2.581955
0.453	4.63946	2.556681
0.454	4.651594	2.531268
0.455	4.662513	2.505795
0.456	4.672233	2.480338
0.457	4.680774	2.454971
0.458	4.688161	2.429763
0.459	4.694424	2.404781
0.46	4.699594	2.380088
0.461	4.703709	2.355742
0.462	4.706807	2.331799
0.463	4.708927	2.30831
0.464	4.710114	2.285323
0.465	4.710413	2.262881
0.466	4.709867	2.241025
0.467	4.708525	2.219791
0.468	4.706434	2.199213
0.469	4.703643	2.179321
0.47	4.7002	2.160141
0.471	4.696153	2.141697
0.472	4.691553	2.12401
0.473	4.686448	2.1071
0.474	4.680886	2.090981
0.475	4.674918	2.075667
0.476	4.668591	2.061168
0.477	4.661955	2.047495
0.478	4.655056	2.034653
0.479	4.647945	2.022647
0.48	4.640668	2.01148
0.481	4.633274	2.001151
0.482	4.625809	1.99166
0.483	4.618322	1.983003
0.484	4.61086	1.975175
0.485	4.60347	1.968167
0.486	4.5962	1.961971
0.487	4.589096	1.956575
0.488	4.582205	1.951964
0.489	4.575574	1.948122
0.49	4.56925	1.945029
0.491	4.563277	1.942665
0.492	4.557703	1.941005
0.493	4.55257	1.940022
0.494	4.547924	1.939685
0.495	4.543808	1.939962
0.496	4.540262	1.940816
0.497	4.537328	1.942208
0.498	4.535043	1.944094
0.499	4.533445	1.946428
0.5	4.532566	1.94916
0.501	4.532436	1.952238
0.502	4.533085	1.955605
0.503	4.534536	1.959203
0.504	4.536808	1.962968
0.505	4.539916	1.966836
0.506	4.54387	1.97074
0.507	4.548676	1.974611
0.508	4.554332	1.978379
0.509	4.560831	1.981973
0.51	4.56816	1.985321
0.511	4.576299	1.988353
0.512	4.585223	1.990997
0.513	4.594897	1.993185
0.514	4.605282	1.994853
0.515	4.616333	1.995937
0.516	4.627996	1.996379
0.517	4.640215	1.996124
0.518	4.652925	1.995126
0.519	4.666059	1.993342
0.52	4.679545	1.990736
0.521	4.693308	1.98728
0.522	4.70727	1.982955
0.523	4.721351	1.977746
0.524	4.735471	1.971649
0.525	4.749551	1.964668
0.526	4.763512	1.956813
0.527	4.777277	1.948103
0.528	4.790774	1.938564
0.529	4.803933	1.92823
0.53	4.816687	1.917139
0.531	4.828977	1.905336
0.532	4.840747	1.892871
0.533	4.85195	1.879799
0.534	4.862542	1.866176
0.535	4.872488	1.852063
0.536	4.881757	1.837522
0.537	4.890326	1.822617
0.538	4.89818	1.80741
0.539	4.905308	1.791966
0.54	4.911705	1.776346
0.541	4.917371	1.760613
0.542	4.922314	1.744825
0.543	4.926545	1.72904
0.544	4.930079	1.713312
0.545	4.932937	1.697692
0.546	4.935142	1.68223
0.547	4.936719	1.666969
0.548	4.937699	1.651951
0.549	4.938114	1.637215
0.55	4.937996	1.622796
0.551	4.937382	1.608724
0.552	4.936307	1.595028
0.553	4.934812	1.581731
0.554	4.932932	1.568855
0.555	4.930708	1.556417
0.556	4.928179	1.544432
0.557	4.925386	1.532911
0.558	4.922368	1.521863
0.559	4.919163	1.511293
0.56	4.915812	1.501204
0.561	4.912354	1.491597
0.562	4.908827	1.482468
0.563	4.905269	1.473812
0.564	4.901715	1.465621
0.565	4.898203	1.457884
0.566	4.894767	1.45059
0.567	4.891441	1.443722
0.568	4.888258	1.437262
0.569	4.885248	1.431192
0.57	4.88244	1.425488
0.571	4.879863	1.420125
0.572	4.877542	1.415078
0.573	4.875501	1.410316
0.574	4.873761	1.405811
0.575	4.87234	1.401528
0.576	4.871253	1.397434
0.577	4.870515	1.393493
0.578	4.870134	1.389668
0.579	4.870117	1.385922
0.58	4.870466	1.382216
0.581	4.871179	1.37851
0.582	4.87225	1.374767
0.583	4.873668	1.370948
0.584	4.875418	1.367017
0.585	4.877474	1.362938
0.586	4.879796	1.358682
0.587	4.882264	1.35432
0.588	4.885197	1.349912
0.589	4.888478	1.345186
0.59	4.892025	1.340127
0.591	4.895791	1.33472
0.592	4.89973	1.328945
0.593	4.903803	1.32279
0.594	4.907968	1.316243
0.595	4.912181	1.309297
0.596	4.916404	1.301949
0.597	4.920596	1.294201
0.598	4.924717	1.286056
0.599	4.928729	1.277524
0.6	4.932596	1.268616
0.601	4.936284	1.259347
0.602	4.939761	1.249735
0.603	4.942997	1.239801
0.604	4.945965	1.229568
0.605	4.948642	1.21906
0.606	4.951008	1.208304
0.607	4.953044	1.197327
0.608	4.954737	1.186156
0.609	4.956074	1.174821
0.61	4.957047	1.16335
0.611	4.957649	1.151772
0.612	4.957878	1.140112
0.613	4.957733	1.1284
0.614	4.957215	1.11666
0.615	4.956327	1.104918
0.616	4.955076	1.093197
0.617	4.953467	1.08152
0.618	4.95151	1.069907
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0.73	4.256879	1.068855
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0.744	4.476462	1.337119
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1.2	4.139429	0.272708
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1.2775	4.101704	0.27137
1.28	4.100598	0.271359
1.2825	4.099498	0.271349
1.285	4.098404	0.27134
1.2875	4.097316	0.271334
1.29	4.096235	0.271329
1.2925	4.095159	0.271326
1.295	4.094088	0.271325
1.2975	4.093024	0.271326
1.3	4.091965	0.271328
1.3025	4.090911	0.271331
1.305	4.089863	0.271337
1.3075	4.088821	0.271344
1.31	4.087784	0.271352
1.3125	4.086752	0.271363
1.315	4.085725	0.271374
1.3175	4.084704	0.271388
1.32	4.083688	0.271403
1.3225	4.082677	0.271419
1.325	4.081671	0.271437
1.3275	4.08067	0.271457
1.33	4.079674	0.271478
1.3325	4.078683	0.2715
1.335	4.077696	0.271524
1.3375	4.076715	0.27155
1.34	4.075738	0.271577
1.3425	4.074766	0.271605
1.345	4.073798	0.271635
1.3475	4.072835	0.271666
1.35	4.071877	0.271699
1.3525	4.070923	0.271733
1.355	4.069973	0.271769
1.3575	4.069028	0.271805
1.36	4.068088	0.271844
1.3625	4.067151	0.271883
1.365	4.066219	0.271924
1.3675	4.06529	0.271966
1.37	4.064367	0.27201
1.3725	4.063447	0.272055
1.375	4.062531	0.272101
1.3775	4.06162	0.272148
1.38	4.060712	0.272197
1.3825	4.059808	0.272247
1.385	4.058908	0.272298
1.3875	4.058013	0.272351
1.39	4.057121	0.272405
1.3925	4.056232	0.27246
1.395	4.055348	0.272516
1.3975	4.054467	0.272573
1.4	4.05359	0.272632
1.4025	4.052717	0.272692
1.405	4.051847	0.272753
1.4075	4.050981	0.272815
1.41	4.050118	0.272878
1.4125	4.049259	0.272943
1.415	4.048403	0.273009
1.4175	4.047551	0.273075
1.42	4.046702	0.273143
1.4225	4.045856	0.273212
1.425	4.045014	0.273283
1.4275	4.044175	0.273354
1.43	4.043339	0.273426
1.4325	4.042507	0.2735
1.435	4.041678	0.273574
1.4375	4.040852	0.27365
1.44	4.040029	0.273727
1.4425	4.039209	0.273805
1.445	4.038392	0.273883
1.4475	4.037579	0.273963
1.45	4.036768	0.274044
1.4525	4.03596	0.274126
1.455	4.035155	0.274209
1.4575	4.034354	0.274293
1.46	4.033555	0.274378
1.4625	4.032759	0.274464
1.465	4.031965	0.274551
1.4675	4.031175	0.274639
1.47	4.030387	0.274728
1.4725	4.029603	0.274818
1.475	4.028821	0.274909
1.4775	4.028041	0.275001
1.48	4.027265	0.275094
1.4825	4.02649	0.275187
1.485	4.025719	0.275282
1.4875	4.02495	0.275378
1.49	4.024184	0.275474
1.4925	4.02342	0.275572
1.495	4.022659	0.27567
1.4975	4.021901	0.27577
1.5	4.021144	0.27587
1.5025	4.020391	0.275971
1.505	4.019639	0.276073
1.5075	4.01889	0.276176
1.51	4.018144	0.276279
1.5125	4.0174	0.276384
1.515	4.016658	0.27649
1.5175	4.015919	0.276596
1.52	4.015182	0.276703
1.5225	4.014447	0.276811
1.525	4.013714	0.27692
1.5275	4.012984	0.27703
1.53	4.012256	0.27714
1.5325	4.01153	0.277252
1.535	4.010806	0.277364
1.5375	4.010084	0.277477
1.54	4.009365	0.277591
1.5425	4.008647	0.277706
1.545	4.007932	0.277821
1.5475	4.007219	0.277937
1.55	4.006508	0.278054
1.5525	4.005799	0.278172
1.555	4.005092	0.278291
1.5575	4.004386	0.27841
1.56	4.003683	0.27853
1.5625	4.002982	0.278651
1.565	4.002283	0.278773
1.5675	4.001585	0.278895
1.57	4.00089	0.279019
1.5725	4.000196	0.279143
1.575	3.999505	0.279267
1.5775	3.998815	0.279393
1.58	3.998127	0.279519
1.5825	3.99744	0.279646
1.585	3.996756	0.279773
1.5875	3.996073	0.279902
1.59	3.995392	0.280031
1.5925	3.994713	0.28016
1.595	3.994036	0.280291
1.5975	3.99336	0.280422
1.6	3.992686	0.280554
1.6025	3.992014	0.280686
1.605	3.991343	0.28082
1.6075	3.990674	0.280953
1.61	3.990007	0.281088
1.6125	3.989341	0.281223
1.615	3.988677	0.281359
1.6175	3.988014	0.281496
1.62	3.987353	0.281633
1.6225	3.986694	0.281771
1.625	3.986036	0.28191
1.6275	3.985379	0.282049
1.63	3.984725	0.282189
1.6325	3.984071	0.282329
1.635	3.983419	0.282471
1.6375	3.982769	0.282612
1.64	3.98212	0.282755
1.6425	3.981472	0.282898
1.645	3.980826	0.283042
1.6475	3.980182	0.283186
1.65	3.979538	0.283331
1.6525	3.978896	0.283476
1.655	3.978256	0.283623
1.6575	3.977617	0.283769
1.66	3.976979	0.283917
1.6625	3.976343	0.284065
1.665	3.975708	0.284213
1.6675	3.975074	0.284363
1.67	3.974441	0.284512
1.6725	3.97381	0.284663
1.675	3.97318	0.284814
1.6775	3.972551	0.284965
1.68	3.971924	0.285117
1.6825	3.971298	0.28527
1.685	3.970673	0.285423
1.6875	3.970049	0.285577
1.69	3.969426	0.285732

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