At one wavelength

Refractive index n: 0.404812
Extinction coefficient k: 3.01594

Permittivity ε₁: -8.93201
Permittivity ε₂: 2.44177

Absorption coefficient α: 644986 cm⁻¹
Penetration depth δ = λ/(2πk): 31.0084 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -2.8369 µm⁻¹

Group index n_g: 2.07177
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

# Au (Gold): Klinavičius 2025: R=40.0 nm; n,k 0.4–0.9 µm
au = ls.fetch_refractiveindex("main", "Au", "Klinavicius-40.0nm", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(au.range_nm)  # (400, 900) nm
eps = au.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_3fc306b8f026/lightsmith"
au = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(au.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (au/klinavicius-2025-40-0nm).

# ... load au as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=au)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=900, 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

40.0 nm average radius chemically synthesized spherical gold nanoparticles. Colloid solution in water.

References

T. Klinavičius, A. Tamulevičienė, T. Tamulevičius. How to select the proper gold permittivity for generating training data for deep neural networks for analysis of the nanoparticle colloid size distributions from their UV–Vis–NIR extinction spectra? J. Phys. Chem. C 129, 17616-17631 (2025) (See Supporting information)

doi:10.1021/acs.jpcc.5c03973 How to Select the Proper Gold Permittivity for Generating Training Data for Deep Neural Networks for Analysis of the Nanoparticle Colloid Size Distributions from Their UV–Vis–NIR Extinction Spectra?, The Journal of Physical Chemistry C (2025)

Cite

Tomas Klinavičius, Asta Tamulevičienė and Tomas Tamulevičius. How to Select the Proper Gold Permittivity for Generating Training Data for Deep Neural Networks for Analysis of the Nanoparticle Colloid Size Distributions from Their UV–Vis–NIR Extinction Spectra?. The Journal of Physical Chemistry C, acs.jpcc.5c03973 (2025), doi:10.1021/acs.jpcc.5c03973; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

501 rows as published

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

Au (Gold), Klinavičius 2025: R=40.0 nm; n,k 0.4–0.9 µm: n and k versus wavelength
λ (µm)	n	k
0.4	1.5745904	1.891451
0.401	1.5756918	1.8908777
0.402	1.5767368	1.8901944
0.403	1.5777243	1.8894027
0.404	1.5786531	1.8885046
0.405	1.5795218	1.8875019
0.406	1.5803289	1.8863968
0.407	1.581073	1.8851916
0.408	1.5817523	1.8838887
0.409	1.5823652	1.8824906
0.41	1.5829099	1.881
0.411	1.5833844	1.8794196
0.412	1.5837867	1.8777526
0.413	1.5841149	1.8760019
0.414	1.5843665	1.8741708
0.415	1.5845394	1.8722627
0.416	1.5846312	1.8702811
0.417	1.5846393	1.8682296
0.418	1.5845613	1.8661121
0.419	1.5843943	1.8639325
0.42	1.5841357	1.8616948
0.421	1.5837825	1.8594032
0.422	1.5833319	1.857062
0.423	1.5827808	1.8546756
0.424	1.582126	1.8522487
0.425	1.5813644	1.8497858
0.426	1.5804927	1.8472917
0.427	1.5795076	1.8447714
0.428	1.5784056	1.8422299
0.429	1.5771833	1.8396722
0.43	1.5758371	1.8371037
0.431	1.5743634	1.8345295
0.432	1.5727587	1.8319551
0.433	1.5710192	1.8293861
0.434	1.5691412	1.8268279
0.435	1.567121	1.8242862
0.436	1.5649549	1.8217668
0.437	1.5626391	1.8192755
0.438	1.5601698	1.8168181
0.439	1.5575434	1.8144006
0.44	1.554756	1.812029
0.441	1.551804	1.8097094
0.442	1.5486837	1.8074477
0.443	1.5453915	1.8052502
0.444	1.5419239	1.803123
0.445	1.5382773	1.8010724
0.446	1.5344483	1.7991045
0.447	1.5304337	1.7972257
0.448	1.5262302	1.7954422
0.449	1.5218348	1.7937603
0.45	1.5172445	1.7921863
0.451	1.5124564	1.7907265
0.452	1.5074679	1.7893872
0.453	1.5022766	1.7881748
0.454	1.4968801	1.7870953
0.455	1.4912763	1.7861552
0.456	1.4854633	1.7853607
0.457	1.4794395	1.7847178
0.458	1.4732033	1.7842329
0.459	1.4667536	1.7839119
0.46	1.4600894	1.7837609
0.461	1.4532102	1.7837859
0.462	1.4461154	1.7839928
0.463	1.4388051	1.7843874
0.464	1.4312794	1.7849754
0.465	1.4235389	1.7857625
0.466	1.4155846	1.7867542
0.467	1.4074176	1.7879559
0.468	1.3990395	1.7893728
0.469	1.3904522	1.79101
0.47	1.381658	1.7928726
0.471	1.3726597	1.7949653
0.472	1.3634603	1.7972927
0.473	1.3540632	1.7998591
0.474	1.3444722	1.8026689
0.475	1.3346915	1.8057259
0.476	1.3247258	1.8090339
0.477	1.31458	1.8125962
0.478	1.3042594	1.8164162
0.479	1.2937699	1.8204966
0.48	1.2831174	1.82484
0.481	1.2723085	1.8294487
0.482	1.26135	1.8343246
0.483	1.250249	1.8394693
0.484	1.2390129	1.8448838
0.485	1.2276496	1.8505691
0.486	1.216167	1.8565256
0.487	1.2045735	1.8627531
0.488	1.1928776	1.8692514
0.489	1.181088	1.8760195
0.49	1.1692138	1.8830562
0.491	1.1572639	1.8903597
0.492	1.1452477	1.8979279
0.493	1.1331744	1.9057582
0.494	1.1210535	1.9138475
0.495	1.1088943	1.9221924
0.496	1.0967064	1.9307889
0.497	1.0844991	1.9396326
0.498	1.0722818	1.948719
0.499	1.0600637	1.9580427
0.5	1.047854	1.9675982
0.501	1.0356617	1.9773797
0.502	1.0234956	1.987381
0.503	1.0113643	1.9975954
0.504	0.9992761	2.008016
0.505	0.9872393	2.0186358
0.506	0.9752615	2.0294474
0.507	0.9633505	2.0404431
0.508	0.9515134	2.0516152
0.509	0.9397571	2.0629556
0.51	0.9280883	2.0744564
0.511	0.9165131	2.0861093
0.512	0.9050373	2.097906
0.513	0.8936667	2.1098383
0.514	0.8824061	2.1218978
0.515	0.8712605	2.1340762
0.516	0.8602343	2.1463652
0.517	0.8493315	2.1587566
0.518	0.8385558	2.1712423
0.519	0.8279106	2.1838144
0.52	0.8173989	2.1964648
0.521	0.8070233	2.2091859
0.522	0.7967863	2.2219702
0.523	0.7866899	2.2348102
0.524	0.7767358	2.2476989
0.525	0.7669256	2.2606292
0.526	0.7572603	2.2735944
0.527	0.747741	2.2865882
0.528	0.7383683	2.2996041
0.529	0.7291427	2.3126364
0.53	0.7200644	2.3256791
0.531	0.7111335	2.3387269
0.532	0.7023498	2.3517745
0.533	0.6937129	2.3648171
0.534	0.6852225	2.37785
0.535	0.6768777	2.3908687
0.536	0.6686778	2.4038691
0.537	0.6606219	2.4168475
0.538	0.652709	2.4298
0.539	0.6449379	2.4427235
0.54	0.6373073	2.4556147
0.541	0.6298159	2.4684709
0.542	0.6224624	2.4812894
0.543	0.6152451	2.4940678
0.544	0.6081626	2.5068039
0.545	0.6012133	2.5194959
0.546	0.5943955	2.5321419
0.547	0.5877075	2.5447405
0.548	0.5811476	2.5572904
0.549	0.574714	2.5697903
0.55	0.5684051	2.5822394
0.551	0.5622189	2.5946368
0.552	0.5561537	2.606982
0.553	0.5502076	2.6192745
0.554	0.5443788	2.631514
0.555	0.5386656	2.6437003
0.556	0.533066	2.6558334
0.557	0.5275782	2.6679134
0.558	0.5222005	2.6799405
0.559	0.516931	2.691915
0.56	0.511768	2.7038374
0.561	0.5067095	2.7157082
0.562	0.501754	2.7275281
0.563	0.4968995	2.7392977
0.564	0.4921444	2.7510177
0.565	0.4874869	2.7626892
0.566	0.4829254	2.7743129
0.567	0.4784582	2.7858899
0.568	0.4740835	2.7974211
0.569	0.4697998	2.8089078
0.57	0.4656055	2.8203509
0.571	0.4614989	2.8317516
0.572	0.4574784	2.8431111
0.573	0.4535426	2.8544307
0.574	0.4496899	2.8657116
0.575	0.4459188	2.8769549
0.576	0.4422278	2.888162
0.577	0.4386155	2.8993342
0.578	0.4350803	2.9104728
0.579	0.431621	2.9215789
0.58	0.4282361	2.932654
0.581	0.4249243	2.9436992
0.582	0.4216841	2.9547159
0.583	0.4185144	2.9657054
0.584	0.4154137	2.9766688
0.585	0.4123809	2.9876075
0.586	0.4094146	2.9985226
0.587	0.4065137	3.0094154
0.588	0.4036768	3.020287
0.589	0.4009029	3.0311387
0.59	0.3981908	3.0419715
0.591	0.3955392	3.0527866
0.592	0.3929471	3.0635851
0.593	0.3904134	3.074368
0.594	0.3879369	3.0851365
0.595	0.3855166	3.0958914
0.596	0.3831515	3.1066338
0.597	0.3808404	3.1173646
0.598	0.3785824	3.1280848
0.599	0.3763765	3.1387953
0.6	0.3742217	3.1494968
0.601	0.372117	3.1601904
0.602	0.3700614	3.1708766
0.603	0.3680541	3.1815564
0.604	0.3660941	3.1922305
0.605	0.3641805	3.2028996
0.606	0.3623124	3.2135643
0.607	0.3604889	3.2242253
0.608	0.3587093	3.2348832
0.609	0.3569725	3.2455386
0.61	0.3552779	3.2561921
0.611	0.3536246	3.2668442
0.612	0.3520117	3.2774954
0.613	0.3504386	3.2881462
0.614	0.3489044	3.2987971
0.615	0.3474083	3.3094484
0.616	0.3459497	3.3201005
0.617	0.3445277	3.3307538
0.618	0.3431417	3.3414088
0.619	0.3417909	3.3520656
0.62	0.3404747	3.3627246
0.621	0.3391924	3.373386
0.622	0.3379432	3.3840502
0.623	0.3367265	3.3947173
0.624	0.3355418	3.4053876
0.625	0.3343882	3.4160612
0.626	0.3332652	3.4267384
0.627	0.3321722	3.4374193
0.628	0.3311086	3.4481039
0.629	0.3300738	3.4587925
0.63	0.3290671	3.4694852
0.631	0.3280881	3.480182
0.632	0.3271361	3.490883
0.633	0.3262106	3.5015882
0.634	0.325311	3.5122977
0.635	0.3244369	3.5230116
0.636	0.3235876	3.5337298
0.637	0.3227627	3.5444524
0.638	0.3219616	3.5551793
0.639	0.3211839	3.5659106
0.64	0.320429	3.5766461
0.641	0.3196966	3.5873859
0.642	0.318986	3.5981299
0.643	0.318297	3.6088781
0.644	0.3176289	3.6196303
0.645	0.3169814	3.6303866
0.646	0.316354	3.6411468
0.647	0.3157462	3.6519108
0.648	0.3151578	3.6626786
0.649	0.3145882	3.67345
0.65	0.3140371	3.6842249
0.651	0.3135041	3.6950033
0.652	0.3129887	3.7057849
0.653	0.3124906	3.7165697
0.654	0.3120094	3.7273576
0.655	0.3115448	3.7381483
0.656	0.3110964	3.7489418
0.657	0.3106639	3.7597379
0.658	0.3102469	3.7705365
0.659	0.309845	3.7813374
0.66	0.309458	3.7921405
0.661	0.3090855	3.8029455
0.662	0.3087272	3.8137524
0.663	0.3083828	3.824561
0.664	0.308052	3.8353711
0.665	0.3077345	3.8461825
0.666	0.3074301	3.8569951
0.667	0.3071383	3.8678087
0.668	0.306859	3.8786231
0.669	0.3065919	3.8894381
0.67	0.3063368	3.9002536
0.671	0.3060933	3.9110694
0.672	0.3058612	3.9218853
0.673	0.3056403	3.9327011
0.674	0.3054303	3.9435166
0.675	0.305231	3.9543317
0.676	0.3050422	3.9651462
0.677	0.3048636	3.9759598
0.678	0.304695	3.9867724
0.679	0.3045362	3.9975838
0.68	0.3043871	4.0083938
0.681	0.3042473	4.0192022
0.682	0.3041167	4.0300089
0.683	0.3039951	4.0408135
0.684	0.3038824	4.0516161
0.685	0.3037783	4.0624162
0.686	0.3036826	4.0732138
0.687	0.3035952	4.0840087
0.688	0.3035159	4.0948006
0.689	0.3034445	4.1055894
0.69	0.303381	4.1163748
0.691	0.303325	4.1271568
0.692	0.3032765	4.137935
0.693	0.3032354	4.1487093
0.694	0.3032014	4.1594795
0.695	0.3031744	4.1702453
0.696	0.3031543	4.1810067
0.697	0.303141	4.1917634
0.698	0.3031343	4.2025151
0.699	0.3031341	4.2132618
0.7	0.3031403	4.2240032
0.701	0.3031527	4.234739
0.702	0.3031713	4.2454692
0.703	0.3031959	4.2561935
0.704	0.3032264	4.2669117
0.705	0.3032627	4.2776236
0.706	0.3033048	4.2883291
0.707	0.3033524	4.2990278
0.708	0.3034055	4.3097197
0.709	0.3034641	4.3204045
0.71	0.3035279	4.331082
0.711	0.303597	4.341752
0.712	0.3036713	4.3524144
0.713	0.3037506	4.3630689
0.714	0.3038348	4.3737153
0.715	0.303924	4.3843535
0.716	0.304018	4.3949831
0.717	0.3041167	4.4056042
0.718	0.3042201	4.4162163
0.719	0.3043281	4.4268194
0.72	0.3044406	4.4374132
0.721	0.3045576	4.4479975
0.722	0.304679	4.4585722
0.723	0.3048047	4.469137
0.724	0.3049348	4.4796918
0.725	0.305069	4.4902363
0.726	0.3052074	4.5007703
0.727	0.30535	4.5112936
0.728	0.3054966	4.5218062
0.729	0.3056472	4.5323076
0.73	0.3058018	4.5427978
0.731	0.3059604	4.5532765
0.732	0.3061228	4.5637436
0.733	0.306289	4.5741988
0.734	0.306459	4.584642
0.735	0.3066328	4.5950729
0.736	0.3068103	4.6054913
0.737	0.3069915	4.6158971
0.738	0.3071763	4.62629
0.739	0.3073647	4.6366699
0.74	0.3075567	4.6470365
0.741	0.3077522	4.6573897
0.742	0.3079513	4.6677292
0.743	0.3081538	4.6780549
0.744	0.3083598	4.6883665
0.745	0.3085692	4.6986639
0.746	0.308782	4.7089468
0.747	0.3089982	4.7192151
0.748	0.3092177	4.7294685
0.749	0.3094406	4.7397069
0.75	0.3096668	4.74993
0.751	0.3098963	4.7601377
0.752	0.310129	4.7703297
0.753	0.310365	4.7805059
0.754	0.3106042	4.790666
0.755	0.3108466	4.8008099
0.756	0.3110922	4.8109374
0.757	0.311341	4.8210482
0.758	0.311593	4.8311422
0.759	0.3118482	4.8412191
0.76	0.3121064	4.8512788
0.761	0.3123678	4.8613211
0.762	0.3126324	4.8713457
0.763	0.3129	4.8813525
0.764	0.3131707	4.8913413
0.765	0.3134446	4.9013118
0.766	0.3137215	4.9112639
0.767	0.3140015	4.9211974
0.768	0.3142845	4.931112
0.769	0.3145706	4.9410077
0.77	0.3148597	4.9508841
0.771	0.3151519	4.9607411
0.772	0.3154472	4.9705784
0.773	0.3157454	4.980396
0.774	0.3160468	4.9901935
0.775	0.3163511	4.9999709
0.776	0.3166584	5.0097278
0.777	0.3169688	5.0194642
0.778	0.3172822	5.0291797
0.779	0.3175986	5.0388743
0.78	0.3179181	5.0485476
0.781	0.3182405	5.0581996
0.782	0.318566	5.06783
0.783	0.3188945	5.0774386
0.784	0.319226	5.0870252
0.785	0.3195605	5.0965897
0.786	0.319898	5.1061318
0.787	0.3202386	5.1156513
0.788	0.3205821	5.1251481
0.789	0.3209287	5.134622
0.79	0.3212783	5.1440727
0.791	0.321631	5.1535
0.792	0.3219866	5.1629039
0.793	0.3223453	5.172284
0.794	0.3227071	5.1816402
0.795	0.3230719	5.1909723
0.796	0.3234397	5.20028
0.797	0.3238106	5.2095633
0.798	0.3241845	5.2188219
0.799	0.3245615	5.2280556
0.8	0.3249415	5.2372643
0.801	0.3253247	5.2464477
0.802	0.3257109	5.2556056
0.803	0.3261001	5.2647379
0.804	0.3264925	5.2738443
0.805	0.326888	5.2829248
0.806	0.3272865	5.291979
0.807	0.3276882	5.3010068
0.808	0.328093	5.310008
0.809	0.3285009	5.3189825
0.81	0.3289119	5.3279299
0.811	0.3293261	5.3368502
0.812	0.3297434	5.3457432
0.813	0.3301639	5.3546086
0.814	0.3305875	5.3634463
0.815	0.3310143	5.3722561
0.816	0.3314442	5.3810378
0.817	0.3318774	5.3897913
0.818	0.3323137	5.3985162
0.819	0.3327533	5.4072126
0.82	0.3331961	5.41588
0.821	0.3336421	5.4245185
0.822	0.3340913	5.4331278
0.823	0.3345438	5.4417077
0.824	0.3349995	5.450258
0.825	0.3354585	5.4587786
0.826	0.3359207	5.4672692
0.827	0.3363862	5.4757297
0.828	0.3368551	5.4841599
0.829	0.3373272	5.4925597
0.83	0.3378026	5.5009288
0.831	0.3382814	5.5092671
0.832	0.3387635	5.5175743
0.833	0.339249	5.5258504
0.834	0.3397378	5.5340951
0.835	0.34023	5.5423082
0.836	0.3407256	5.5504897
0.837	0.3412245	5.5586392
0.838	0.3417269	5.5667566
0.839	0.3422327	5.5748418
0.84	0.3427419	5.5828946
0.841	0.3432546	5.5909148
0.842	0.3437707	5.5989022
0.843	0.3442902	5.6068566
0.844	0.3448133	5.6147779
0.845	0.3453399	5.622666
0.846	0.3458699	5.6305205
0.847	0.3464035	5.6383415
0.848	0.3469406	5.6461286
0.849	0.3474813	5.6538818
0.85	0.3480255	5.6616008
0.851	0.3485733	5.6692855
0.852	0.3491247	5.6769357
0.853	0.3496796	5.6845513
0.854	0.3502382	5.692132
0.855	0.3508004	5.6996778
0.856	0.3513663	5.7071884
0.857	0.3519358	5.7146638
0.858	0.352509	5.7221036
0.859	0.3530859	5.7295078
0.86	0.3536664	5.7368762
0.861	0.3542507	5.7442087
0.862	0.3548387	5.751505
0.863	0.3554305	5.7587651
0.864	0.356026	5.7659887
0.865	0.3566253	5.7731757
0.866	0.3572284	5.7803259
0.867	0.3578353	5.7874392
0.868	0.358446	5.7945155
0.869	0.3590605	5.8015545
0.87	0.3596789	5.8085561
0.871	0.3603012	5.8155202
0.872	0.3609274	5.8224466
0.873	0.3615574	5.8293351
0.874	0.3621914	5.8361856
0.875	0.3628293	5.842998
0.876	0.3634712	5.8497721
0.877	0.364117	5.8565077
0.878	0.3647668	5.8632047
0.879	0.3654207	5.869863
0.88	0.3660785	5.8764823
0.881	0.3667404	5.8830626
0.882	0.3674063	5.8896037
0.883	0.3680763	5.8961055
0.884	0.3687504	5.9025678
0.885	0.3694286	5.9089904
0.886	0.3701109	5.9153733
0.887	0.3707974	5.9217163
0.888	0.371488	5.9280192
0.889	0.3721828	5.9342819
0.89	0.3728818	5.9405043
0.891	0.373585	5.9466862
0.892	0.3742925	5.9528274
0.893	0.3750042	5.958928
0.894	0.3757202	5.9649876
0.895	0.3764405	5.9710062
0.896	0.377165	5.9769837
0.897	0.3778939	5.9829199
0.898	0.3786272	5.9888147
0.899	0.3793648	5.9946679
0.9	0.3801069	6.0004794

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