Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 0.61504
Extinction coefficient k: 2.38164

Permittivity ε₁: -5.29393
Permittivity ε₂: 2.92961

Absorption coefficient α: 509336 cm⁻¹
Penetration depth δ = λ/(2πk): 39.2668 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -2.1 µm⁻¹

Group index n_g: 1.849
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): Yakubovsky et al. 2019: 4-nm film; n,k 0.30–3.3 µm
au = ls.fetch_refractiveindex("main", "Au", "Yakubovsky-4nm", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(au.range_nm)  # (300, 3300) 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_e71e661a4ef4/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/yakubovsky-2019-4nm).

# ... 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=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

Au thickness = 4.1 nm, e-beam evaporated at 5 Å/s with a base pressure of 5e-7 Torr on MoS₂ CVD monolayer on SiO₂ substrate at T = 20 °C. Thickness was determined by AFM.

Conditions

film thickness: 4.1e-9
substrate: MoS2/SiO2

References

D. I. Yakubovsky, Y. V. Stebunov, R. V. Kirtaev, G. A. Ermolaev, M. S. Mironov, S. M. Novikov, A. V. Arsenin, V. S. Volkov. Ultrathin and ultrasmooth gold films on monolayer MoS₂. Adv. Mater. Interfaces 6, 1900196 (2019) (Numerical data kindly provided by Georgy Ermolaev)

doi:10.1002/admi.201900196 Ultrathin and Ultrasmooth Gold Films on Monolayer MoS <sub>2</sub>, Advanced Materials Interfaces (2019)

Cite

Dmitry I. Yakubovsky et al.. Ultrathin and Ultrasmooth Gold Films on Monolayer MoS <sub>2</sub>. Advanced Materials Interfaces, 6, 1900196 (2019), doi:10.1002/admi.201900196; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

301 rows as published

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

Au (Gold), Yakubovsky et al. 2019: 4-nm film; n,k 0.30–3.3 µm: n and k versus wavelength
λ (µm)	n	k
0.3	1.469	1.596
0.31	1.621	1.537
0.32	1.739	1.499
0.33	1.823	1.396
0.34	1.823	1.313
0.35	1.872	1.216
0.36	1.791	1.175
0.37	1.685	1.139
0.38	1.645	1.126
0.39	1.602	1.168
0.4	1.534	1.187
0.41	1.474	1.209
0.42	1.403	1.222
0.43	1.318	1.259
0.44	1.242	1.309
0.45	1.176	1.371
0.46	1.109	1.436
0.47	1.034	1.514
0.48	0.934	1.614
0.49	0.89	1.692
0.5	0.85	1.781
0.51	0.821	1.881
0.52	0.799	1.977
0.53	0.768	2.064
0.54	0.74	2.146
0.55	0.735	2.162
0.56	0.687	2.208
0.57	0.653	2.268
0.58	0.631	2.333
0.59	0.61	2.397
0.6	0.581	2.459
0.61	0.553	2.531
0.62	0.534	2.608
0.63	0.523	2.686
0.64	0.514	2.763
0.65	0.51	2.84
0.66	0.507	2.915
0.67	0.51	2.984
0.68	0.523	3.043
0.69	0.544	3.049
0.7	0.529	3.175
0.71	0.556	3.27
0.72	0.575	3.353
0.73	0.588	3.432
0.74	0.603	3.51
0.75	0.628	3.586
0.76	0.657	3.649
0.77	0.678	3.705
0.78	0.696	3.756
0.79	0.716	3.806
0.8	0.738	3.852
0.81	0.764	3.89
0.82	0.798	3.915
0.83	0.835	3.929
0.84	0.874	3.932
0.85	0.924	3.916
0.86	0.934	4.007
0.87	0.943	4.094
0.88	0.952	4.179
0.89	0.962	4.262
0.9	0.97	4.344
0.91	0.976	4.425
0.92	0.981	4.509
0.93	0.986	4.591
0.94	0.988	4.677
0.95	0.989	4.767
0.96	0.987	4.863
0.97	0.979	4.968
0.98	0.968	5.083
0.99	0.953	5.205
1.0	0.927	5.345
1.01	0.943	5.375
1.02	0.957	5.406
1.03	0.97	5.439
1.04	0.981	5.474
1.05	0.992	5.508
1.06	1.0	5.546
1.07	1.009	5.582
1.08	1.016	5.621
1.09	1.023	5.656
1.1	1.029	5.695
1.11	1.034	5.734
1.12	1.038	5.775
1.13	1.042	5.812
1.14	1.045	5.853
1.15	1.046	5.898
1.16	1.049	5.937
1.17	1.05	5.982
1.18	1.051	6.028
1.19	1.052	6.079
1.2	1.052	6.128
1.21	1.052	6.182
1.22	1.055	6.228
1.23	1.055	6.285
1.24	1.054	6.348
1.25	1.055	6.41
1.26	1.058	6.451
1.27	1.063	6.491
1.28	1.066	6.545
1.29	1.07	6.601
1.3	1.075	6.655
1.31	1.078	6.714
1.32	1.083	6.768
1.33	1.09	6.812
1.34	1.097	6.862
1.35	1.105	6.915
1.36	1.114	6.961
1.37	1.121	7.015
1.38	1.131	7.059
1.39	1.141	7.097
1.4	1.152	7.137
1.41	1.16	7.196
1.42	1.167	7.256
1.43	1.177	7.305
1.44	1.186	7.346
1.45	1.197	7.389
1.46	1.208	7.432
1.47	1.218	7.478
1.48	1.227	7.527
1.49	1.237	7.57
1.5	1.247	7.607
1.51	1.257	7.65
1.52	1.267	7.693
1.53	1.277	7.734
1.54	1.286	7.778
1.55	1.296	7.82
1.56	1.305	7.863
1.57	1.314	7.903
1.58	1.324	7.942
1.59	1.333	7.989
1.6	1.342	8.033
1.61	1.351	8.075
1.62	1.359	8.119
1.63	1.367	8.165
1.64	1.376	8.207
1.65	1.384	8.256
1.66	1.391	8.3
1.67	1.398	8.344
1.68	1.406	8.384
1.69	1.412	8.426
1.7	1.419	8.467
1.71	1.426	8.507
1.72	1.433	8.554
1.73	1.439	8.597
1.74	1.445	8.64
1.75	1.45	8.683
1.76	1.456	8.725
1.77	1.462	8.765
1.78	1.468	8.809
1.79	1.474	8.855
1.8	1.479	8.894
1.81	1.484	8.937
1.82	1.49	8.982
1.83	1.496	9.032
1.84	1.502	9.078
1.85	1.508	9.125
1.86	1.515	9.173
1.87	1.52	9.219
1.88	1.525	9.265
1.89	1.531	9.308
1.9	1.537	9.355
1.91	1.543	9.407
1.92	1.549	9.457
1.93	1.555	9.505
1.94	1.563	9.553
1.95	1.558	9.566
1.96	1.569	9.601
1.97	1.581	9.721
1.98	1.587	9.767
1.99	1.596	9.818
2.0	1.594	9.852
2.01	1.6	9.896
2.02	1.601	9.947
2.03	1.6	9.972
2.04	1.608	10.035
2.05	1.612	10.079
2.06	1.621	10.127
2.07	1.629	10.184
2.08	1.63	10.235
2.09	1.635	10.271
2.1	1.637	10.31
2.11	1.65	10.385
2.12	1.659	10.442
2.13	1.674	10.507
2.14	1.678	10.551
2.15	1.679	10.596
2.16	1.68	10.639
2.17	1.691	10.689
2.18	1.695	10.739
2.19	1.694	10.777
2.2	1.694	10.82
2.21	1.7	10.875
2.22	1.715	10.942
2.23	1.725	10.99
2.24	1.734	11.042
2.25	1.743	11.094
2.26	1.744	11.138
2.27	1.749	11.192
2.28	1.761	11.251
2.29	1.769	11.305
2.3	1.781	11.359
2.31	1.786	11.394
2.32	1.786	11.431
2.33	1.791	11.47
2.34	1.801	11.524
2.35	1.808	11.574
2.36	1.817	11.619
2.37	1.819	11.662
2.38	1.834	11.716
2.39	1.836	11.774
2.4	1.85	11.834
2.41	1.897	11.874
2.42	1.91	11.924
2.43	1.923	11.99
2.44	1.935	12.057
2.45	1.943	12.107
2.46	1.948	12.149
2.47	1.96	12.2
2.48	1.967	12.25
2.49	1.966	12.293
2.5	1.98	12.346
2.51	1.987	12.403
2.52	2.006	12.463
2.53	2.013	12.53
2.54	2.037	12.595
2.55	2.033	12.664
2.56	2.053	12.691
2.57	2.061	12.719
2.58	2.073	12.769
2.59	2.084	12.833
2.6	2.093	12.88
2.61	2.104	12.935
2.62	2.116	12.976
2.63	2.126	13.006
2.64	2.132	13.073
2.65	2.139	13.138
2.66	2.146	13.16
2.67	2.169	13.214
2.68	2.189	13.282
2.69	2.184	13.331
2.7	2.204	13.369
2.71	2.206	13.442
2.72	2.256	13.533
2.73	2.263	13.538
2.74	2.281	13.579
2.75	2.298	13.666
2.76	2.305	13.726
2.77	2.323	13.783
2.78	2.328	13.827
2.79	2.339	13.85
2.8	2.356	13.919
2.81	2.361	13.96
2.82	2.369	14.007
2.83	2.389	14.05
2.84	2.417	14.125
2.85	2.427	14.192
2.86	2.446	14.254
2.87	2.457	14.284
2.88	2.461	14.289
2.89	2.463	14.342
2.9	2.474	14.366
2.91	2.493	14.464
2.92	2.506	14.517
2.93	2.525	14.542
2.94	2.536	14.588
2.95	2.567	14.653
2.96	2.566	14.72
2.97	2.577	14.771
2.98	2.587	14.804
2.99	2.621	14.826
3.0	2.633	14.86
3.01	2.657	14.927
3.02	2.669	15.012
3.03	2.685	15.09
3.04	2.7	15.142
3.05	2.721	15.196
3.06	2.734	15.242
3.07	2.758	15.28
3.08	2.767	15.317
3.09	2.784	15.381
3.1	2.791	15.445
3.11	2.802	15.486
3.12	2.83	15.526
3.13	2.842	15.55
3.14	2.857	15.59
3.15	2.893	15.685
3.16	2.898	15.759
3.17	2.909	15.797
3.18	2.92	15.815
3.19	2.942	15.884
3.2	2.963	15.932
3.21	2.976	16.028
3.22	2.995	16.067
3.23	2.982	16.119
3.24	3.002	16.128
3.25	3.007	16.186
3.26	3.033	16.234
3.27	3.056	16.318
3.28	3.075	16.394
3.29	3.131	16.346
3.3	3.141	16.498

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