Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.78589
Extinction coefficient k: 0

Permittivity ε₁: 3.18941
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.273456 µm⁻¹

Group index n_g: 1.94658
Group velocity dispersion: 690.125 fs²/mm

Dispersion parameter D: -3765 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

# E44: Li et al. 2005: n(e) 0.450–0.656 µm
e44 = ls.fetch_refractiveindex("other", "E44", "Li-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(e44.range_nm)  # (450, 656) nm
eps = e44.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_3f8335e4cc19/lightsmith"
e44 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(e44.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (e44/li-2005-e).

# ... load e44 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=e44)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=450, stop_nm=656, 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.

Dispersion formula

Cauchy (formula 5), λ in µm

n = 1.7282 + 0.0121 λ^{- 2.0} + 0.0027 λ^{- 4.0}

Valid from 0.45 to 0.656 µm.

Coefficients as stored

C_i	Value
C1	1.7282
C2	0.0121
C3	-2.0
C4	0.0027
C5	-4.0

Comments and conditions

25 °C. Extraordinary ray (e).

Conditions

temperature: 298 K
direction: e

References

J. Li, C. H. Wen, S. Gauza, R. Lu, S. T. Wu. Refractive indices of liquid crystals for display applications. J. Disp. Technol. 1, 51-61, 2005

doi:10.1109/jdt.2005.853357 Refractive Indices of Liquid Crystals for Display Applications, Journal of Display Technology (2005)

Cite

J. Li, C.-H. Wen, S. Gauza, R. Lu and S.-T. Wu. Refractive Indices of Liquid Crystals for Display Applications. Journal of Display Technology, 1, 51-61 (2005), doi:10.1109/jdt.2005.853357; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library

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

E44, Li et al. 2005: n(e) 0.450–0.656 µm: n and k versus wavelength
λ (µm)	n
0.45	1.853797
0.450425	1.853436
0.450851	1.853076
0.451277	1.852717
0.451704	1.852359
0.45213	1.852003
0.452558	1.851647
0.452985	1.851293
0.453414	1.85094
0.453842	1.850588
0.454271	1.850237
0.4547	1.849887
0.45513	1.849538
0.45556	1.849191
0.455991	1.848844
0.456422	1.848499
0.456853	1.848155
0.457285	1.847812
0.457717	1.847469
0.45815	1.847128
0.458583	1.846788
0.459016	1.84645
0.45945	1.846112
0.459884	1.845775
0.460319	1.845439
0.460754	1.845105
0.461189	1.844771
0.461625	1.844439
0.462061	1.844108
0.462498	1.843777
0.462935	1.843448
0.463373	1.84312
0.463811	1.842792
0.464249	1.842466
0.464688	1.842141
0.465127	1.841817
0.465566	1.841494
0.466006	1.841171
0.466447	1.84085
0.466888	1.84053
0.467329	1.840211
0.467771	1.839893
0.468213	1.839576
0.468655	1.83926
0.469098	1.838945
0.469541	1.838631
0.469985	1.838318
0.470429	1.838006
0.470874	1.837695
0.471319	1.837384
0.471764	1.837075
0.47221	1.836767
0.472657	1.83646
0.473103	1.836154
0.47355	1.835848
0.473998	1.835544
0.474446	1.835241
0.474894	1.834938
0.475343	1.834637
0.475792	1.834336
0.476242	1.834037
0.476692	1.833738
0.477143	1.83344
0.477594	1.833143
0.478045	1.832848
0.478497	1.832553
0.478949	1.832259
0.479402	1.831966
0.479855	1.831673
0.480308	1.831382
0.480762	1.831092
0.481217	1.830802
0.481671	1.830514
0.482127	1.830226
0.482582	1.82994
0.483038	1.829654
0.483495	1.829369
0.483952	1.829085
0.484409	1.828802
0.484867	1.828519
0.485325	1.828238
0.485784	1.827957
0.486243	1.827678
0.486703	1.827399
0.487162	1.827121
0.487623	1.826844
0.488084	1.826568
0.488545	1.826293
0.489007	1.826018
0.489469	1.825745
0.489932	1.825472
0.490395	1.8252
0.490858	1.824929
0.491322	1.824659
0.491786	1.824389
0.492251	1.824121
0.492716	1.823853
0.493182	1.823586
0.493648	1.82332
0.494115	1.823055
0.494582	1.822791
0.495049	1.822527
0.495517	1.822264
0.495985	1.822003
0.496454	1.821741
0.496923	1.821481
0.497393	1.821222
0.497863	1.820963
0.498333	1.820705
0.498804	1.820448
0.499276	1.820192
0.499748	1.819936
0.50022	1.819682
0.500693	1.819428
0.501166	1.819175
0.501639	1.818922
0.502114	1.818671
0.502588	1.81842
0.503063	1.81817
0.503539	1.817921
0.504014	1.817672
0.504491	1.817424
0.504968	1.817177
0.505445	1.816931
0.505923	1.816686
0.506401	1.816441
0.506879	1.816197
0.507358	1.815954
0.507838	1.815712
0.508318	1.81547
0.508798	1.815229
0.509279	1.814989
0.50976	1.81475
0.510242	1.814511
0.510724	1.814273
0.511207	1.814036
0.51169	1.813799
0.512174	1.813563
0.512658	1.813328
0.513142	1.813094
0.513627	1.81286
0.514113	1.812628
0.514599	1.812395
0.515085	1.812164
0.515572	1.811933
0.516059	1.811703
0.516547	1.811474
0.517035	1.811245
0.517524	1.811017
0.518013	1.81079
0.518502	1.810564
0.518992	1.810338
0.519483	1.810113
0.519974	1.809888
0.520465	1.809664
0.520957	1.809441
0.521449	1.809219
0.521942	1.808997
0.522435	1.808776
0.522929	1.808556
0.523423	1.808336
0.523918	1.808117
0.524413	1.807899
0.524909	1.807681
0.525405	1.807464
0.525902	1.807248
0.526399	1.807032
0.526896	1.806817
0.527394	1.806602
0.527892	1.806389
0.528391	1.806176
0.528891	1.805963
0.529391	1.805751
0.529891	1.80554
0.530392	1.80533
0.530893	1.80512
0.531395	1.804911
0.531897	1.804702
0.5324	1.804494
0.532903	1.804287
0.533406	1.80408
0.533911	1.803874
0.534415	1.803669
0.53492	1.803464
0.535426	1.80326
0.535932	1.803056
0.536438	1.802853
0.536945	1.802651
0.537453	1.802449
0.537961	1.802248
0.538469	1.802047
0.538978	1.801848
0.539487	1.801648
0.539997	1.80145
0.540508	1.801251
0.541018	1.801054
0.54153	1.800857
0.542042	1.800661
0.542554	1.800465
0.543067	1.80027
0.54358	1.800076
0.544094	1.799882
0.544608	1.799688
0.545122	1.799495
0.545638	1.799303
0.546153	1.799112
0.546669	1.798921
0.547186	1.79873
0.547703	1.79854
0.548221	1.798351
0.548739	1.798162
0.549258	1.797974
0.549777	1.797787
0.550296	1.7976
0.550816	1.797413
0.551337	1.797227
0.551858	1.797042
0.55238	1.796857
0.552902	1.796673
0.553424	1.796489
0.553947	1.796306
0.554471	1.796124
0.554995	1.795942
0.555519	1.79576
0.556044	1.795579
0.55657	1.795399
0.557096	1.795219
0.557622	1.79504
0.558149	1.794861
0.558677	1.794683
0.559205	1.794505
0.559733	1.794328
0.560262	1.794151
0.560792	1.793975
0.561322	1.793799
0.561852	1.793624
0.562383	1.79345
0.562915	1.793276
0.563447	1.793102
0.563979	1.792929
0.564512	1.792757
0.565046	1.792585
0.56558	1.792413
0.566114	1.792243
0.566649	1.792072
0.567185	1.791902
0.567721	1.791733
0.568258	1.791564
0.568795	1.791396
0.569332	1.791228
0.56987	1.79106
0.570409	1.790893
0.570948	1.790727
0.571488	1.790561
0.572028	1.790396
0.572568	1.790231
0.573109	1.790066
0.573651	1.789903
0.574193	1.789739
0.574736	1.789576
0.575279	1.789414
0.575823	1.789252
0.576367	1.78909
0.576912	1.788929
0.577457	1.788769
0.578003	1.788609
0.578549	1.788449
0.579096	1.78829
0.579643	1.788131
0.580191	1.787973
0.580739	1.787815
0.581288	1.787658
0.581837	1.787501
0.582387	1.787345
0.582938	1.787189
0.583489	1.787034
0.58404	1.786879
0.584592	1.786724
0.585144	1.78657
0.585697	1.786417
0.586251	1.786264
0.586805	1.786111
0.58736	1.785959
0.587915	1.785807
0.58847	1.785656
0.589027	1.785505
0.589583	1.785354
0.59014	1.785204
0.590698	1.785055
0.591256	1.784906
0.591815	1.784757
0.592375	1.784609
0.592934	1.784461
0.593495	1.784314
0.594056	1.784167
0.594617	1.78402
0.595179	1.783874
0.595742	1.783729
0.596305	1.783584
0.596868	1.783439
0.597432	1.783294
0.597997	1.783151
0.598562	1.783007
0.599128	1.782864
0.599694	1.782721
0.600261	1.782579
0.600828	1.782437
0.601396	1.782296
0.601964	1.782155
0.602533	1.782014
0.603103	1.781874
0.603673	1.781734
0.604243	1.781595
0.604814	1.781456
0.605386	1.781318
0.605958	1.781179
0.606531	1.781042
0.607104	1.780904
0.607678	1.780767
0.608252	1.780631
0.608827	1.780495
0.609402	1.780359
0.609978	1.780224
0.610555	1.780089
0.611132	1.779954
0.611709	1.77982
0.612287	1.779686
0.612866	1.779553
0.613445	1.77942
0.614025	1.779287
0.614605	1.779155
0.615186	1.779023
0.615768	1.778892
0.61635	1.778761
0.616932	1.77863
0.617515	1.7785
0.618099	1.77837
0.618683	1.77824
0.619268	1.778111
0.619853	1.777982
0.620439	1.777854
0.621025	1.777726
0.621612	1.777598
0.622199	1.777471
0.622787	1.777344
0.623376	1.777217
0.623965	1.777091
0.624555	1.776965
0.625145	1.77684
0.625736	1.776715
0.626327	1.77659
0.626919	1.776466
0.627512	1.776342
0.628105	1.776218
0.628698	1.776095
0.629293	1.775972
0.629887	1.775849
0.630483	1.775727
0.631079	1.775605
0.631675	1.775483
0.632272	1.775362
0.63287	1.775241
0.633468	1.775121
0.634066	1.775001
0.634666	1.774881
0.635265	1.774761
0.635866	1.774642
0.636467	1.774524
0.637068	1.774405
0.63767	1.774287
0.638273	1.774169
0.638876	1.774052
0.63948	1.773935
0.640084	1.773818
0.640689	1.773702
0.641295	1.773586
0.641901	1.77347
0.642508	1.773354
0.643115	1.773239
0.643723	1.773125
0.644331	1.77301
0.64494	1.772896
0.645549	1.772782
0.64616	1.772669
0.64677	1.772556
0.647381	1.772443
0.647993	1.77233
0.648606	1.772218
0.649219	1.772106
0.649832	1.771995
0.650446	1.771884
0.651061	1.771773
0.651677	1.771662
0.652292	1.771552
0.652909	1.771442
0.653526	1.771333
0.654144	1.771223
0.654762	1.771114
0.655381	1.771006
0.656	1.770897

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