At one wavelength

Refractive index n: 5.725
Extinction coefficient k: 1.681

Permittivity ε₁: 29.9499
Permittivity ε₂: 19.2475

Absorption coefficient α: 359497 cm⁻¹
Penetration depth δ = λ/(2πk): 55.6332 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 13.9286 µm⁻¹

Group index n_g: -2.45943
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

# Ge (Germanium): Nunley et al, 2016: n,k 0.188–2.48 µm
ge = ls.fetch_refractiveindex("main", "Ge", "Nunley", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ge.range_nm)  # (187.9, 2480) nm
eps = ge.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_7fe723a18081/lightsmith"
ge = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ge.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ge/nunley-2016).

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

300 K

References

T. N. Nunley, N. S. Fernando, N. Samarasingha, J. M. Moya, C. M. Nelson, A. A. Medina, S. Zollner. Optical constants of germanium and thermally grown germanium dioxide from 0.5 to 6.6 eV via a multi-sample ellipsometry investigation. J. Vac. Sci. Technol. B 34, 061205 (2016) (See supplemental materials)

doi:10.1116/1.4963075 Optical constants of germanium and thermally grown germanium dioxide from 0.5 to 6.6eV via a multisample ellipsometry investigation, Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena (2016)

Cite

Timothy Nathan Nunley et al.. Optical constants of germanium and thermally grown germanium dioxide from 0.5 to 6.6eV via a multisample ellipsometry investigation. Journal of Vacuum Science & Technology B, Nanotechnology and Microelectronics: Materials, Processing, Measurement, and Phenomena, 34, 061205 (2016), doi:10.1116/1.4963075; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

611 rows as published

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

Ge (Germanium), Nunley et al, 2016: n,k 0.188–2.48 µm: n and k versus wavelength
λ (µm)	n	k
0.1879	0.8351	2.567
0.1881	0.8394	2.57
0.1884	0.8434	2.573
0.1887	0.8475	2.576
0.189	0.8518	2.579
0.1893	0.8558	2.582
0.1896	0.8598	2.585
0.1899	0.864	2.588
0.1902	0.8679	2.592
0.1905	0.872	2.595
0.1907	0.876	2.598
0.191	0.88	2.601
0.1913	0.884	2.604
0.1916	0.888	2.607
0.1919	0.8918	2.611
0.1922	0.8958	2.614
0.1925	0.8998	2.617
0.1928	0.9035	2.621
0.1931	0.9074	2.624
0.1934	0.9113	2.628
0.1937	0.9152	2.631
0.194	0.9189	2.635
0.1943	0.9228	2.638
0.1946	0.9265	2.642
0.1949	0.9302	2.646
0.1953	0.934	2.649
0.1956	0.9377	2.653
0.1959	0.9414	2.657
0.1962	0.945	2.661
0.1965	0.9487	2.665
0.1968	0.9523	2.669
0.1971	0.956	2.673
0.1974	0.9598	2.676
0.1977	0.9633	2.681
0.1981	0.9668	2.686
0.1984	0.9705	2.69
0.1987	0.9741	2.695
0.199	0.9779	2.699
0.1993	0.9814	2.704
0.1997	0.9851	2.708
0.2	0.9888	2.713
0.2003	0.9925	2.719
0.2006	0.9964	2.724
0.2009	1.0	2.729
0.2013	1.004	2.734
0.2016	1.008	2.74
0.2019	1.012	2.746
0.2023	1.016	2.752
0.2026	1.021	2.757
0.2029	1.025	2.763
0.2033	1.03	2.77
0.2036	1.034	2.777
0.2039	1.039	2.783
0.2043	1.045	2.789
0.2046	1.05	2.796
0.2049	1.056	2.802
0.2053	1.061	2.809
0.2056	1.067	2.816
0.206	1.074	2.823
0.2063	1.08	2.83
0.2066	1.087	2.837
0.207	1.094	2.843
0.2073	1.102	2.85
0.2077	1.109	2.857
0.208	1.117	2.863
0.2084	1.125	2.87
0.2087	1.134	2.876
0.2091	1.143	2.882
0.2094	1.152	2.888
0.2098	1.161	2.893
0.2101	1.17	2.899
0.2105	1.18	2.904
0.2109	1.19	2.908
0.2112	1.2	2.913
0.2116	1.21	2.917
0.2119	1.22	2.921
0.2123	1.231	2.924
0.2127	1.241	2.927
0.213	1.251	2.93
0.2134	1.262	2.932
0.2138	1.272	2.934
0.2141	1.283	2.936
0.2145	1.293	2.936
0.2149	1.303	2.937
0.2153	1.312	2.938
0.2156	1.322	2.937
0.216	1.332	2.937
0.2164	1.341	2.937
0.2168	1.35	2.936
0.2171	1.358	2.934
0.2175	1.366	2.933
0.2179	1.375	2.931
0.2183	1.382	2.93
0.2187	1.389	2.928
0.2191	1.396	2.926
0.2194	1.402	2.924
0.2198	1.408	2.922
0.2202	1.414	2.919
0.2206	1.42	2.917
0.221	1.425	2.915
0.2214	1.429	2.913
0.2218	1.433	2.91
0.2222	1.437	2.908
0.2226	1.44	2.907
0.223	1.444	2.905
0.2234	1.446	2.903
0.2238	1.449	2.902
0.2242	1.451	2.901
0.2246	1.453	2.899
0.225	1.455	2.899
0.2254	1.456	2.898
0.2258	1.457	2.898
0.2262	1.458	2.898
0.2267	1.459	2.898
0.2271	1.459	2.898
0.2275	1.46	2.899
0.2279	1.46	2.9
0.2283	1.46	2.901
0.2288	1.46	2.903
0.2292	1.46	2.905
0.2296	1.459	2.907
0.23	1.459	2.909
0.2305	1.459	2.912
0.2309	1.458	2.915
0.2313	1.457	2.919
0.2317	1.457	2.923
0.2322	1.456	2.927
0.2326	1.456	2.931
0.2331	1.455	2.935
0.2335	1.455	2.94
0.2339	1.454	2.945
0.2344	1.453	2.95
0.2348	1.453	2.956
0.2353	1.452	2.962
0.2357	1.452	2.968
0.2362	1.451	2.975
0.2366	1.451	2.982
0.2371	1.45	2.989
0.2375	1.45	2.996
0.238	1.45	3.004
0.2384	1.45	3.012
0.2389	1.45	3.02
0.2394	1.45	3.028
0.2398	1.45	3.037
0.2403	1.45	3.046
0.2407	1.451	3.055
0.2412	1.451	3.065
0.2417	1.452	3.075
0.2422	1.453	3.085
0.2426	1.454	3.095
0.2431	1.455	3.106
0.2436	1.456	3.116
0.2441	1.457	3.127
0.2445	1.459	3.139
0.245	1.461	3.151
0.2455	1.463	3.162
0.246	1.465	3.174
0.2465	1.467	3.187
0.247	1.47	3.199
0.2475	1.472	3.212
0.248	1.475	3.225
0.2485	1.478	3.238
0.249	1.481	3.252
0.2495	1.485	3.265
0.25	1.489	3.279
0.2505	1.493	3.294
0.251	1.497	3.308
0.2515	1.502	3.323
0.252	1.506	3.337
0.2525	1.511	3.353
0.253	1.516	3.368
0.2535	1.522	3.383
0.2541	1.527	3.399
0.2546	1.534	3.415
0.2551	1.54	3.431
0.2556	1.546	3.448
0.2562	1.553	3.464
0.2567	1.56	3.481
0.2572	1.568	3.498
0.2578	1.575	3.516
0.2583	1.583	3.533
0.2588	1.592	3.551
0.2594	1.6	3.569
0.2599	1.609	3.587
0.2605	1.618	3.606
0.261	1.627	3.625
0.2616	1.637	3.644
0.2621	1.647	3.663
0.2627	1.657	3.683
0.2632	1.667	3.703
0.2638	1.678	3.724
0.2644	1.689	3.745
0.2649	1.701	3.766
0.2655	1.712	3.788
0.2661	1.724	3.81
0.2666	1.737	3.833
0.2672	1.749	3.857
0.2678	1.762	3.882
0.2684	1.776	3.907
0.2689	1.791	3.933
0.2695	1.806	3.961
0.2701	1.822	3.989
0.2707	1.839	4.019
0.2713	1.857	4.05
0.2719	1.876	4.082
0.2725	1.898	4.116
0.2731	1.921	4.151
0.2737	1.947	4.187
0.2743	1.975	4.224
0.2749	2.006	4.262
0.2755	2.041	4.3
0.2761	2.079	4.339
0.2768	2.12	4.378
0.2774	2.166	4.416
0.278	2.216	4.454
0.2786	2.27	4.489
0.2792	2.329	4.523
0.2799	2.391	4.554
0.2805	2.457	4.581
0.2811	2.527	4.604
0.2818	2.6	4.624
0.2824	2.676	4.638
0.2831	2.754	4.647
0.2837	2.833	4.651
0.2844	2.913	4.648
0.285	2.993	4.64
0.2857	3.073	4.626
0.2863	3.152	4.606
0.287	3.228	4.58
0.2877	3.302	4.549
0.2883	3.372	4.513
0.289	3.439	4.473
0.2897	3.501	4.429
0.2904	3.559	4.381
0.291	3.613	4.331
0.2917	3.661	4.279
0.2924	3.704	4.226
0.2931	3.742	4.172
0.2938	3.776	4.118
0.2945	3.805	4.064
0.2952	3.829	4.012
0.2959	3.85	3.961
0.2966	3.867	3.911
0.2973	3.882	3.863
0.298	3.893	3.818
0.2988	3.903	3.774
0.2995	3.91	3.733
0.3002	3.916	3.694
0.3009	3.921	3.658
0.3017	3.925	3.623
0.3024	3.929	3.59
0.3031	3.932	3.559
0.3039	3.935	3.53
0.3046	3.938	3.502
0.3054	3.941	3.475
0.3061	3.944	3.449
0.3069	3.947	3.425
0.3077	3.95	3.401
0.3084	3.953	3.377
0.3092	3.957	3.355
0.31	3.96	3.333
0.3107	3.963	3.311
0.3115	3.967	3.29
0.3123	3.97	3.27
0.3131	3.973	3.249
0.3139	3.977	3.229
0.3147	3.98	3.21
0.3155	3.983	3.191
0.3163	3.986	3.172
0.3171	3.989	3.153
0.3179	3.992	3.135
0.3187	3.994	3.117
0.3195	3.997	3.099
0.3204	3.999	3.082
0.3212	4.002	3.065
0.322	4.004	3.048
0.3229	4.006	3.031
0.3237	4.008	3.015
0.3246	4.01	2.999
0.3254	4.011	2.984
0.3263	4.013	2.969
0.3271	4.015	2.954
0.328	4.016	2.939
0.3289	4.018	2.925
0.3297	4.019	2.911
0.3306	4.02	2.897
0.3315	4.022	2.884
0.3324	4.023	2.871
0.3333	4.024	2.858
0.3342	4.025	2.845
0.3351	4.026	2.833
0.336	4.028	2.821
0.3369	4.029	2.81
0.3378	4.03	2.798
0.3388	4.031	2.787
0.3397	4.033	2.777
0.3406	4.034	2.766
0.3416	4.036	2.756
0.3425	4.037	2.746
0.3434	4.039	2.736
0.3444	4.041	2.727
0.3454	4.043	2.718
0.3463	4.045	2.709
0.3473	4.047	2.7
0.3483	4.05	2.692
0.3493	4.053	2.684
0.3502	4.056	2.675
0.3512	4.059	2.667
0.3522	4.063	2.659
0.3532	4.067	2.652
0.3542	4.071	2.644
0.3553	4.076	2.636
0.3563	4.081	2.628
0.3573	4.086	2.62
0.3583	4.092	2.612
0.3594	4.098	2.604
0.3604	4.104	2.595
0.3615	4.111	2.586
0.3625	4.117	2.577
0.3636	4.124	2.567
0.3647	4.131	2.557
0.3657	4.138	2.546
0.3668	4.144	2.535
0.3679	4.151	2.523
0.369	4.157	2.511
0.3701	4.163	2.499
0.3712	4.168	2.486
0.3723	4.173	2.473
0.3734	4.177	2.459
0.3746	4.181	2.446
0.3757	4.184	2.433
0.3769	4.187	2.421
0.378	4.189	2.408
0.3792	4.191	2.396
0.3803	4.194	2.384
0.3815	4.196	2.372
0.3827	4.199	2.36
0.3839	4.202	2.348
0.385	4.204	2.336
0.3862	4.206	2.323
0.3875	4.208	2.31
0.3887	4.21	2.297
0.3899	4.211	2.283
0.3911	4.211	2.269
0.3924	4.211	2.256
0.3936	4.209	2.242
0.3949	4.207	2.228
0.3961	4.205	2.215
0.3974	4.201	2.202
0.3987	4.197	2.19
0.3999	4.192	2.178
0.4012	4.187	2.167
0.4025	4.181	2.157
0.4039	4.175	2.147
0.4052	4.168	2.138
0.4065	4.161	2.131
0.4078	4.154	2.124
0.4092	4.147	2.117
0.4105	4.14	2.112
0.4119	4.133	2.107
0.4133	4.126	2.104
0.4147	4.119	2.101
0.4161	4.113	2.099
0.4175	4.107	2.097
0.4189	4.101	2.097
0.4203	4.096	2.097
0.4217	4.091	2.097
0.4232	4.086	2.098
0.4246	4.082	2.1
0.4261	4.079	2.102
0.4275	4.076	2.105
0.429	4.073	2.107
0.4305	4.071	2.111
0.432	4.07	2.115
0.4335	4.069	2.119
0.435	4.068	2.123
0.4366	4.069	2.127
0.4381	4.069	2.132
0.4397	4.071	2.137
0.4412	4.072	2.142
0.4428	4.075	2.147
0.4444	4.077	2.152
0.446	4.081	2.158
0.4476	4.084	2.164
0.4492	4.089	2.169
0.4509	4.094	2.175
0.4525	4.099	2.181
0.4542	4.105	2.187
0.4558	4.111	2.193
0.4575	4.117	2.199
0.4592	4.125	2.204
0.4609	4.132	2.211
0.4626	4.14	2.217
0.4644	4.149	2.223
0.4661	4.158	2.229
0.4679	4.167	2.235
0.4696	4.177	2.242
0.4714	4.188	2.248
0.4732	4.199	2.254
0.475	4.21	2.261
0.4769	4.222	2.267
0.4787	4.235	2.274
0.4806	4.248	2.28
0.4824	4.261	2.287
0.4843	4.276	2.294
0.4862	4.29	2.3
0.4881	4.306	2.307
0.4901	4.322	2.314
0.492	4.339	2.322
0.494	4.357	2.329
0.4959	4.376	2.337
0.4979	4.395	2.345
0.4999	4.416	2.353
0.502	4.439	2.361
0.504	4.463	2.369
0.5061	4.488	2.378
0.5081	4.516	2.386
0.5102	4.546	2.394
0.5123	4.578	2.4
0.5145	4.613	2.406
0.5166	4.65	2.41
0.5188	4.69	2.411
0.5209	4.731	2.41
0.5231	4.775	2.405
0.5254	4.82	2.397
0.5276	4.865	2.385
0.5298	4.91	2.368
0.5321	4.953	2.348
0.5344	4.996	2.323
0.5367	5.035	2.296
0.5391	5.072	2.265
0.5414	5.105	2.233
0.5438	5.134	2.2
0.5462	5.16	2.167
0.5486	5.183	2.134
0.551	5.202	2.104
0.5535	5.219	2.076
0.556	5.236	2.051
0.5585	5.252	2.031
0.561	5.27	2.014
0.5636	5.292	2.0
0.5661	5.319	1.989
0.5687	5.353	1.979
0.5714	5.396	1.966
0.574	5.446	1.948
0.5767	5.504	1.92
0.5794	5.564	1.88
0.5821	5.625	1.826
0.5848	5.68	1.759
0.5876	5.725	1.681
0.5904	5.758	1.595
0.5932	5.778	1.505
0.5961	5.785	1.416
0.599	5.78	1.329
0.6019	5.766	1.249
0.6048	5.745	1.175
0.6078	5.719	1.108
0.6108	5.69	1.047
0.6138	5.66	0.9913
0.6168	5.628	0.9408
0.6199	5.596	0.8947
0.623	5.564	0.8524
0.6262	5.532	0.8137
0.6294	5.5	0.778
0.6326	5.468	0.7453
0.6358	5.437	0.7151
0.6391	5.407	0.6874
0.6424	5.377	0.6618
0.6458	5.348	0.6382
0.6491	5.319	0.6164
0.6525	5.292	0.5961
0.656	5.265	0.5774
0.6595	5.239	0.5599
0.663	5.214	0.5435
0.6666	5.19	0.5282
0.6702	5.167	0.5137
0.6738	5.144	0.5001
0.6775	5.122	0.4871
0.6812	5.101	0.4748
0.685	5.081	0.463
0.6888	5.061	0.4517
0.6926	5.041	0.4409
0.6965	5.022	0.4305
0.7005	5.004	0.4204
0.7045	4.986	0.4108
0.7085	4.969	0.4015
0.7126	4.951	0.3925
0.7167	4.935	0.3838
0.7208	4.918	0.3755
0.7251	4.902	0.3674
0.7293	4.887	0.3597
0.7336	4.871	0.3522
0.738	4.856	0.3449
0.7424	4.841	0.338
0.7469	4.827	0.3313
0.7514	4.812	0.3248
0.756	4.798	0.3186
0.7606	4.785	0.3126
0.7653	4.771	0.3068
0.7701	4.758	0.3012
0.7749	4.745	0.2958
0.7798	4.733	0.2906
0.7847	4.721	0.2855
0.7897	4.708	0.2807
0.7948	4.697	0.276
0.7999	4.685	0.2714
0.8051	4.674	0.267
0.8104	4.663	0.2628
0.8157	4.652	0.2587
0.8211	4.641	0.2547
0.8266	4.631	0.2508
0.8321	4.621	0.247
0.8377	4.611	0.2433
0.8434	4.601	0.2397
0.8492	4.591	0.2362
0.8551	4.582	0.2328
0.861	4.573	0.2295
0.867	4.564	0.2262
0.8731	4.555	0.223
0.8793	4.546	0.2199
0.8856	4.538	0.2168
0.892	4.53	0.2137
0.8984	4.522	0.2108
0.905	4.514	0.2078
0.9116	4.506	0.2049
0.9184	4.499	0.202
0.9253	4.492	0.1991
0.9322	4.484	0.1963
0.9393	4.477	0.1935
0.9464	4.47	0.1907
0.9537	4.464	0.188
0.9611	4.457	0.1852
0.9686	4.45	0.1825
0.9763	4.444	0.1797
0.984	4.438	0.177
0.9919	4.432	0.1743
0.9999	4.426	0.1716
1.008	4.42	0.1689
1.016	4.414	0.1661
1.025	4.408	0.1634
1.033	4.403	0.1607
1.042	4.397	0.158
1.051	4.392	0.1553
1.06	4.387	0.1525
1.069	4.382	0.1498
1.078	4.377	0.147
1.088	4.372	0.1442
1.097	4.368	0.1412
1.107	4.364	0.1378
1.117	4.36	0.1338
1.127	4.355	0.1292
1.137	4.35	0.1245
1.148	4.344	0.1204
1.159	4.337	0.1171
1.17	4.331	0.1143
1.181	4.326	0.1118
1.192	4.32	0.1093
1.204	4.315	0.1068
1.216	4.31	0.1044
1.228	4.306	0.1019
1.24	4.301	0.09945
1.252	4.296	0.09698
1.265	4.292	0.09449
1.278	4.287	0.092
1.292	4.283	0.0895
1.305	4.279	0.08699
1.319	4.275	0.08447
1.333	4.271	0.08194
1.348	4.267	0.07941
1.362	4.263	0.07687
1.378	4.259	0.07433
1.393	4.256	0.0718
1.409	4.253	0.06928
1.425	4.249	0.06677
1.442	4.246	0.06429
1.459	4.244	0.06183
1.476	4.242	0.05941
1.494	4.241	0.057
1.512	4.243	0.05406
1.531	4.249	0.04564
1.55	4.25	0.02519
1.569	4.234	0.007651
1.59	4.216	0.002758
1.61	4.204	0.001915
1.631	4.194	0.001465
1.653	4.186	0.001106
1.675	4.178	0.0008197
1.698	4.171	0.0005967
1.722	4.164	0.0004261
1.746	4.158	0.0002984
1.771	4.152	0.0002048
1.797	4.146	0.0001376
1.823	4.141	9.06e-05
1.851	4.136	5.835e-05
1.879	4.131	3.677e-05
1.907	4.126	2.267e-05
1.937	4.122	1.366e-05
1.968	4.117	8.048e-06
2.0	4.113	4.634e-06
2.033	4.109	2.607e-06
2.066	4.105	1.433e-06
2.101	4.101	7.691e-07
2.138	4.097	4.043e-07
2.175	4.094	2.065e-07
2.214	4.09	0.0
2.254	4.087	0.0
2.296	4.083	0.0
2.339	4.08	0.0
2.384	4.077	0.0
2.431	4.074	0.0
2.48	4.071	0.0

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