At one wavelength

Refractive index n: 0.419839
Extinction coefficient k: 2.95249

Permittivity ε₁: -8.54091
Permittivity ε₂: 2.47914

Absorption coefficient α: 631417 cm⁻¹
Penetration depth δ = λ/(2πk): 31.6748 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -2.0587 µm⁻¹

Group index n_g: 1.62953
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=11.4 nm; n,k 0.4–0.9 µm
au = ls.fetch_refractiveindex("main", "Au", "Klinavicius-11.4nm", 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_cac76b086b7e/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-2025-11-4nm).

# ... 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

11.4 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 informations)

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=11.4 nm; n,k 0.4–0.9 µm: n and k versus wavelength
λ (µm)	n	k
0.4	1.7188702	2.057943
0.401	1.7214904	2.0589575
0.402	1.7239512	2.0598412
0.403	1.726251	2.0605953
0.404	1.7283882	2.0612209
0.405	1.730361	2.0617193
0.406	1.732168	2.062092
0.407	1.7338075	2.0623404
0.408	1.735278	2.0624662
0.409	1.736578	2.062471
0.41	1.7377058	2.0623566
0.411	1.73866	2.062125
0.412	1.7394391	2.061778
0.413	1.7400417	2.0613178
0.414	1.7404662	2.0607466
0.415	1.7407112	2.0600666
0.416	1.7407754	2.0592801
0.417	1.7406572	2.0583896
0.418	1.7403554	2.0573978
0.419	1.7398686	2.0563072
0.42	1.7391954	2.0551206
0.421	1.7383346	2.0538408
0.422	1.7372849	2.0524707
0.423	1.736045	2.0510135
0.424	1.7346137	2.0494722
0.425	1.7329898	2.04785
0.426	1.7311722	2.0461503
0.427	1.7291596	2.0443765
0.428	1.726951	2.042532
0.429	1.7245454	2.0406204
0.43	1.7219416	2.0386455
0.431	1.7191388	2.036611
0.432	1.7161359	2.0345208
0.433	1.712932	2.0323788
0.434	1.7095262	2.0301891
0.435	1.7059178	2.0279557
0.436	1.702106	2.025683
0.437	1.69809	2.0233751
0.438	1.6938691	2.0210366
0.439	1.6894428	2.0186717
0.44	1.6848104	2.0162852
0.441	1.6799715	2.0138816
0.442	1.6749257	2.0114657
0.443	1.6696725	2.0090422
0.444	1.6642116	2.006616
0.445	1.658543	2.0041921
0.446	1.6526663	2.0017754
0.447	1.6465815	1.9993711
0.448	1.6402888	1.9969843
0.449	1.6337881	1.9946203
0.45	1.6270796	1.9922843
0.451	1.6201638	1.9899818
0.452	1.613041	1.9877181
0.453	1.6057117	1.9854987
0.454	1.5981765	1.9833292
0.455	1.5904363	1.9812152
0.456	1.5824918	1.9791623
0.457	1.5743442	1.9771761
0.458	1.5659944	1.9752626
0.459	1.5574439	1.9734273
0.46	1.548694	1.9716762
0.461	1.5397463	1.9700151
0.462	1.5306025	1.9684498
0.463	1.5212646	1.9669863
0.464	1.5117347	1.9656304
0.465	1.5020148	1.964388
0.466	1.4921076	1.9632651
0.467	1.4820156	1.9622675
0.468	1.4717416	1.9614013
0.469	1.4612887	1.9606721
0.47	1.45066	1.9600859
0.471	1.439859	1.9596485
0.472	1.4288892	1.9593655
0.473	1.4177547	1.9592428
0.474	1.4064594	1.9592859
0.475	1.3950077	1.9595004
0.476	1.3834041	1.9598917
0.477	1.3716533	1.9604651
0.478	1.3597605	1.9612259
0.479	1.3477308	1.9621791
0.48	1.3355698	1.9633298
0.481	1.323283	1.9646825
0.482	1.3108766	1.9662421
0.483	1.2983567	1.9680128
0.484	1.2857296	1.9699989
0.485	1.2730021	1.9722044
0.486	1.2601809	1.9746329
0.487	1.2472732	1.977288
0.488	1.2342862	1.980173
0.489	1.2212274	1.9832906
0.49	1.2081043	1.9866437
0.491	1.1949247	1.9902345
0.492	1.1816967	1.9940651
0.493	1.1684283	1.998137
0.494	1.1551276	2.0024517
0.495	1.141803	2.0070102
0.496	1.1284629	2.0118129
0.497	1.1151157	2.0168602
0.498	1.1017698	2.0221518
0.499	1.0884337	2.0276874
0.5	1.0751161	2.0334659
0.501	1.0618252	2.039486
0.502	1.0485695	2.0457462
0.503	1.0353573	2.0522442
0.504	1.022197	2.0589777
0.505	1.0090964	2.0659438
0.506	0.9960638	2.0731394
0.507	0.9831067	2.0805609
0.508	0.970233	2.0882045
0.509	0.9574498	2.096066
0.51	0.9447645	2.1041408
0.511	0.9321839	2.1124243
0.512	0.9197147	2.1209113
0.513	0.9073634	2.1295965
0.514	0.8951359	2.1384744
0.515	0.8830381	2.1475392
0.516	0.8710756	2.1567849
0.517	0.8592534	2.1662055
0.518	0.8475764	2.1757947
0.519	0.8360491	2.185546
0.52	0.8246757	2.195453
0.521	0.8134601	2.2055091
0.522	0.8024058	2.2157077
0.523	0.791516	2.2260421
0.524	0.7807935	2.2365056
0.525	0.7702409	2.2470916
0.526	0.7598605	2.2577933
0.527	0.749654	2.2686042
0.528	0.7396232	2.2795176
0.529	0.7297694	2.2905271
0.53	0.7200936	2.3016263
0.531	0.7105966	2.3128089
0.532	0.7012789	2.3240686
0.533	0.6921408	2.3353993
0.534	0.6831823	2.3467952
0.535	0.6744032	2.3582503
0.536	0.6658031	2.3697591
0.537	0.6573814	2.381316
0.538	0.6491372	2.3929156
0.539	0.6410697	2.4045529
0.54	0.6331776	2.4162227
0.541	0.6254596	2.4279203
0.542	0.6179143	2.4396409
0.543	0.6105401	2.4513801
0.544	0.6033353	2.4631336
0.545	0.5962981	2.4748971
0.546	0.5894265	2.4866669
0.547	0.5827186	2.498439
0.548	0.5761723	2.5102099
0.549	0.5697853	2.5219761
0.55	0.5635555	2.5337343
0.551	0.5574804	2.5454815
0.552	0.5515579	2.5572147
0.553	0.5457854	2.5689312
0.554	0.5401606	2.5806283
0.555	0.534681	2.5923036
0.556	0.529344	2.6039547
0.557	0.5241472	2.6155796
0.558	0.519088	2.6271761
0.559	0.5141639	2.6387424
0.56	0.5093722	2.6502768
0.561	0.5047106	2.6617777
0.562	0.5001763	2.6732435
0.563	0.4957669	2.6846729
0.564	0.4914798	2.6960647
0.565	0.4873125	2.7074177
0.566	0.4832624	2.718731
0.567	0.479327	2.7300035
0.568	0.4755039	2.7412345
0.569	0.4717906	2.7524234
0.57	0.4681846	2.7635693
0.571	0.4646836	2.774672
0.572	0.4612851	2.7857308
0.573	0.4579867	2.7967454
0.574	0.4547862	2.8077155
0.575	0.4516811	2.818641
0.576	0.4486693	2.8295217
0.577	0.4457485	2.8403576
0.578	0.4429165	2.8511485
0.579	0.4401711	2.8618946
0.58	0.43751	2.8725961
0.581	0.4349314	2.8832529
0.582	0.4324329	2.8938655
0.583	0.4300127	2.904434
0.584	0.4276686	2.9149587
0.585	0.4253988	2.9254401
0.586	0.4232012	2.9358785
0.587	0.4210741	2.9462743
0.588	0.4190154	2.956628
0.589	0.4170234	2.9669401
0.59	0.4150963	2.9772111
0.591	0.4132323	2.9874416
0.592	0.4114297	2.9976322
0.593	0.4096868	3.0077835
0.594	0.408002	3.0178961
0.595	0.4063736	3.0279706
0.596	0.4048	3.0380077
0.597	0.4032798	3.0480081
0.598	0.4018113	3.0579725
0.599	0.4003931	3.0679016
0.6	0.3990238	3.077796
0.601	0.3977019	3.0876565
0.602	0.3964261	3.0974839
0.603	0.395195	3.1072789
0.604	0.3940073	3.1170421
0.605	0.3928617	3.1267744
0.606	0.3917569	3.1364765
0.607	0.3906917	3.1461491
0.608	0.389665	3.155793
0.609	0.3886755	3.1654089
0.61	0.3877222	3.1749976
0.611	0.3868039	3.1845597
0.612	0.3859195	3.1940961
0.613	0.385068	3.2036074
0.614	0.3842484	3.2130943
0.615	0.3834597	3.2225576
0.616	0.3827009	3.231998
0.617	0.381971	3.2414162
0.618	0.3812692	3.2508128
0.619	0.3805946	3.2601886
0.62	0.3799463	3.2695441
0.621	0.3793234	3.2788801
0.622	0.3787251	3.2881972
0.623	0.3781508	3.2974961
0.624	0.3775994	3.3067773
0.625	0.3770704	3.3160415
0.626	0.376563	3.3252893
0.627	0.3760765	3.3345212
0.628	0.3756102	3.3437379
0.629	0.3751635	3.3529398
0.63	0.3747356	3.3621277
0.631	0.3743261	3.3713018
0.632	0.3739341	3.3804629
0.633	0.3735593	3.3896114
0.634	0.373201	3.3987479
0.635	0.3728587	3.4078727
0.636	0.3725318	3.4169863
0.637	0.3722199	3.4260893
0.638	0.3719224	3.435182
0.639	0.3716388	3.4442649
0.64	0.3713687	3.4533384
0.641	0.3711116	3.4624029
0.642	0.3708672	3.4714588
0.643	0.3706349	3.4805064
0.644	0.3704143	3.4895461
0.645	0.3702052	3.4985783
0.646	0.370007	3.5076034
0.647	0.3698195	3.5166215
0.648	0.3696423	3.5256331
0.649	0.369475	3.5346384
0.65	0.3693173	3.5436377
0.651	0.3691689	3.5526313
0.652	0.3690295	3.5616195
0.653	0.3688988	3.5706025
0.654	0.3687766	3.5795805
0.655	0.3686624	3.5885539
0.656	0.3685561	3.5975227
0.657	0.3684575	3.6064872
0.658	0.3683663	3.6154476
0.659	0.3682822	3.6244041
0.66	0.368205	3.6333568
0.661	0.3681345	3.642306
0.662	0.3680705	3.6512518
0.663	0.3680129	3.6601942
0.664	0.3679613	3.6691336
0.665	0.3679157	3.67807
0.666	0.3678758	3.6870034
0.667	0.3678415	3.6959341
0.668	0.3678125	3.7048622
0.669	0.3677889	3.7137876
0.67	0.3677704	3.7227106
0.671	0.3677568	3.7316312
0.672	0.367748	3.7405495
0.673	0.367744	3.7494655
0.674	0.3677445	3.7583793
0.675	0.3677495	3.767291
0.676	0.3677587	3.7762005
0.677	0.3677722	3.785108
0.678	0.3677899	3.7940135
0.679	0.3678115	3.802917
0.68	0.367837	3.8118185
0.681	0.3678664	3.8207181
0.682	0.3678995	3.8296157
0.683	0.3679362	3.8385113
0.684	0.3679765	3.847405
0.685	0.3680203	3.8562968
0.686	0.3680675	3.8651867
0.687	0.368118	3.8740745
0.688	0.3681719	3.8829604
0.689	0.3682289	3.8918443
0.69	0.3682891	3.9007262
0.691	0.3683524	3.909606
0.692	0.3684187	3.9184838
0.693	0.368488	3.9273594
0.694	0.3685602	3.9362329
0.695	0.3686353	3.9451042
0.696	0.3687133	3.9539732
0.697	0.3687941	3.9628399
0.698	0.3688776	3.9717043
0.699	0.3689638	3.9805663
0.7	0.3690528	3.9894259
0.701	0.3691443	3.9982829
0.702	0.3692385	4.0071374
0.703	0.3693353	4.0159892
0.704	0.3694346	4.0248383
0.705	0.3695364	4.0336846
0.706	0.3696408	4.0425281
0.707	0.3697476	4.0513687
0.708	0.3698569	4.0602063
0.709	0.3699685	4.0690408
0.71	0.3700826	4.0778722
0.711	0.3701991	4.0867004
0.712	0.3703179	4.0955252
0.713	0.3704391	4.1043467
0.714	0.3705627	4.1131647
0.715	0.3706885	4.1219791
0.716	0.3708166	4.1307899
0.717	0.370947	4.139597
0.718	0.3710797	4.1484003
0.719	0.3712147	4.1571996
0.72	0.3713519	4.165995
0.721	0.3714913	4.1747862
0.722	0.371633	4.1835733
0.723	0.3717769	4.1923561
0.724	0.371923	4.2011345
0.725	0.3720713	4.2099084
0.726	0.3722218	4.2186778
0.727	0.3723745	4.2274425
0.728	0.3725294	4.2362025
0.729	0.3726864	4.2449575
0.73	0.3728457	4.2537077
0.731	0.3730071	4.2624527
0.732	0.3731706	4.2711926
0.733	0.3733364	4.2799272
0.734	0.3735042	4.2886565
0.735	0.3736743	4.2973803
0.736	0.3738464	4.3060985
0.737	0.3740208	4.3148111
0.738	0.3741973	4.3235178
0.739	0.3743759	4.3322187
0.74	0.3745566	4.3409136
0.741	0.3747396	4.3496024
0.742	0.3749246	4.358285
0.743	0.3751118	4.3669613
0.744	0.3753011	4.3756311
0.745	0.3754926	4.3842945
0.746	0.3756862	4.3929512
0.747	0.375882	4.4016012
0.748	0.3760799	4.4102444
0.749	0.3762799	4.4188806
0.75	0.3764821	4.4275097
0.751	0.3766865	4.4361317
0.752	0.376893	4.4447464
0.753	0.3771016	4.4533537
0.754	0.3773124	4.4619536
0.755	0.3775253	4.4705458
0.756	0.3777404	4.4791303
0.757	0.3779576	4.487707
0.758	0.378177	4.4962758
0.759	0.3783986	4.5048366
0.76	0.3786223	4.5133892
0.761	0.3788482	4.5219335
0.762	0.3790763	4.5304695
0.763	0.3793065	4.5389969
0.764	0.3795389	4.5475158
0.765	0.3797735	4.556026
0.766	0.3800103	4.5645274
0.767	0.3802492	4.5730199
0.768	0.3804903	4.5815033
0.769	0.3807337	4.5899776
0.77	0.3809792	4.5984427
0.771	0.3812269	4.6068983
0.772	0.3814768	4.6153445
0.773	0.3817289	4.6237812
0.774	0.3819833	4.6322081
0.775	0.3822398	4.6406252
0.776	0.3824986	4.6490324
0.777	0.3827596	4.6574295
0.778	0.3830228	4.6658165
0.779	0.3832882	4.6741933
0.78	0.3835559	4.6825597
0.781	0.3838258	4.6909156
0.782	0.3840979	4.6992609
0.783	0.3843723	4.7075955
0.784	0.384649	4.7159193
0.785	0.3849279	4.7242322
0.786	0.385209	4.7325341
0.787	0.3854924	4.7408248
0.788	0.3857781	4.7491042
0.789	0.3860661	4.7573723
0.79	0.3863563	4.7656289
0.791	0.3866489	4.7738739
0.792	0.3869437	4.7821071
0.793	0.3872408	4.7903286
0.794	0.3875402	4.7985381
0.795	0.3878419	4.8067356
0.796	0.3881459	4.814921
0.797	0.3884522	4.8230941
0.798	0.3887609	4.8312548
0.799	0.3890719	4.839403
0.8	0.3893852	4.8475386
0.801	0.3897008	4.8556615
0.802	0.3900188	4.8637716
0.803	0.3903391	4.8718687
0.804	0.3906617	4.8799529
0.805	0.3909867	4.8880238
0.806	0.3913141	4.8960815
0.807	0.3916439	4.9041258
0.808	0.391976	4.9121566
0.809	0.3923105	4.9201738
0.81	0.3926474	4.9281773
0.811	0.3929866	4.936167
0.812	0.3933283	4.9441427
0.813	0.3936724	4.9521044
0.814	0.3940188	4.960052
0.815	0.3943677	4.9679853
0.816	0.394719	4.9759042
0.817	0.3950727	4.9838086
0.818	0.3954289	4.9916984
0.819	0.3957875	4.9995735
0.82	0.3961485	5.0074338
0.821	0.396512	5.0152792
0.822	0.3968779	5.0231095
0.823	0.3972463	5.0309246
0.824	0.3976172	5.0387246
0.825	0.3979905	5.0465091
0.826	0.3983664	5.0542782
0.827	0.3987447	5.0620316
0.828	0.3991255	5.0697694
0.829	0.3995088	5.0774914
0.83	0.3998946	5.0851974
0.831	0.4002829	5.0928875
0.832	0.4006737	5.1005613
0.833	0.4010671	5.108219
0.834	0.401463	5.1158603
0.835	0.4018614	5.1234851
0.836	0.4022624	5.1310934
0.837	0.402666	5.138685
0.838	0.4030721	5.1462597
0.839	0.4034807	5.1538176
0.84	0.403892	5.1613585
0.841	0.4043058	5.1688823
0.842	0.4047222	5.1763889
0.843	0.4051412	5.1838781
0.844	0.4055628	5.1913499
0.845	0.405987	5.1988041
0.846	0.4064139	5.2062408
0.847	0.4068434	5.2136596
0.848	0.4072755	5.2210606
0.849	0.4077102	5.2284436
0.85	0.4081476	5.2358085
0.851	0.4085876	5.2431553
0.852	0.4090303	5.2504837
0.853	0.4094757	5.2577938
0.854	0.4099238	5.2650854
0.855	0.4103745	5.2723583
0.856	0.4108279	5.2796126
0.857	0.4112841	5.286848
0.858	0.4117429	5.2940645
0.859	0.4122045	5.301262
0.86	0.4126688	5.3084403
0.861	0.4131358	5.3155994
0.862	0.4136056	5.3227392
0.863	0.4140781	5.3298595
0.864	0.4145534	5.3369602
0.865	0.4150314	5.3440413
0.866	0.4155122	5.3511027
0.867	0.4159958	5.3581441
0.868	0.4164822	5.3651657
0.869	0.4169714	5.3721671
0.87	0.4174634	5.3791484
0.871	0.4179582	5.3861094
0.872	0.4184559	5.39305
0.873	0.4189563	5.3999702
0.874	0.4194597	5.4068697
0.875	0.4199658	5.4137486
0.876	0.4204749	5.4206067
0.877	0.4209868	5.4274439
0.878	0.4215016	5.4342602
0.879	0.4220193	5.4410553
0.88	0.4225398	5.4478293
0.881	0.4230633	5.4545819
0.882	0.4235897	5.4613132
0.883	0.424119	5.468023
0.884	0.4246513	5.4747112
0.885	0.4251865	5.4813778
0.886	0.4257246	5.4880225
0.887	0.4262657	5.4946453
0.888	0.4268098	5.5012462
0.889	0.4273569	5.507825
0.89	0.427907	5.5143816
0.891	0.42846	5.520916
0.892	0.4290161	5.5274279
0.893	0.4295752	5.5339174
0.894	0.4301373	5.5403844
0.895	0.4307025	5.5468286
0.896	0.4312707	5.5532501
0.897	0.431842	5.5596488
0.898	0.4324163	5.5660245
0.899	0.4329937	5.5723771
0.9	0.4335743	5.5787066

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