Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.0141
Extinction coefficient k: 0

Permittivity ε₁: 16.113
Permittivity ε₂: 0

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

Abbe number V_d: —
Chromatic dispersion dn/dλ: -0.00530599 µm⁻¹

Group index n_g: 4.04217
Group velocity dispersion: 801.282 fs²/mm

Dispersion parameter D: -53.9355 ps/(nm·km)
Photon energy: 0.234375 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): Burnett et al. 2016: n 2.00–14.0 µm
ge = ls.fetch_refractiveindex("main", "Ge", "Burnett", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ge.range_nm)  # (2000, 14000) nm
eps = ge.eps([5290])  # 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_15abda6aa164/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/burnett-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=2000, stop_nm=14000, 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"]).

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_15abda6aa164/lightsmith?model=drude_lorentz"
ge_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

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

Sellmeier (C in µm²) (formula 2), λ in µm

n^{2} - 1 = \frac{0.4886331 λ^{2}}{λ^{2} - 1.393959} + \frac{14.5142535 λ^{2}}{λ^{2} - 0.1626427} + \frac{0.0091224 λ^{2}}{λ^{2} - 752.19}

Valid from 2.0 to 14.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.4886331
C3	1.393959
C4	14.5142535
C5	0.1626427
C6	0.0091224
C7	752.19

Comments and conditions

Standard uncertainties ranging from 2×10^-5 near 2 µm to 8×10^-5 near 14 µm

Conditions

temperature: 295 K

References

J. H. Burnett, S. G. Kaplan, E. Stover, A. Phenis. Refractive index measurements of Ge. Proc. SPIE 9974, 99740X (2016)

doi:10.1117/12.2237978 Refractive index measurements of Ge, SPIE Proceedings (2016)

Cite

John H. Burnett, Simon G. Kaplan, Eric Stover and Adam Phenis. Refractive index measurements of Ge. SPIE Proceedings, 9974, 99740X (2016), doi:10.1117/12.2237978; 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

Ge (Germanium), Burnett et al. 2016: n 2.00–14.0 µm: n and k versus wavelength
λ (µm)	n
2	4.108452
2.00978	4.107223
2.0196	4.106011
2.02948	4.104816
2.0394	4.103637
2.04937	4.102474
2.05939	4.101327
2.06946	4.100195
2.07957	4.099078
2.08974	4.097976
2.09996	4.096889
2.11022	4.095816
2.12054	4.094757
2.13091	4.093711
2.14132	4.09268
2.15179	4.091661
2.16231	4.090656
2.17288	4.089664
2.18351	4.088684
2.19418	4.087717
2.20491	4.086762
2.21569	4.085819
2.22652	4.084888
2.23741	4.083968
2.24835	4.08306
2.25934	4.082163
2.27038	4.081278
2.28148	4.080403
2.29264	4.079539
2.30384	4.078685
2.31511	4.077842
2.32643	4.07701
2.3378	4.076187
2.34923	4.075374
2.36071	4.074571
2.37226	4.073778
2.38385	4.072994
2.39551	4.072219
2.40722	4.071454
2.41899	4.070698
2.43081	4.06995
2.4427	4.069212
2.45464	4.068482
2.46664	4.067761
2.4787	4.067048
2.49082	4.066343
2.50299	4.065647
2.51523	4.064959
2.52753	4.064279
2.53988	4.063606
2.5523	4.062942
2.56478	4.062285
2.57732	4.061635
2.58992	4.060993
2.60258	4.060358
2.6153	4.059731
2.62809	4.059111
2.64094	4.058497
2.65385	4.057891
2.66682	4.057292
2.67986	4.056699
2.69296	4.056113
2.70613	4.055533
2.71936	4.05496
2.73265	4.054394
2.74601	4.053834
2.75944	4.05328
2.77293	4.052732
2.78649	4.05219
2.80011	4.051654
2.8138	4.051125
2.82755	4.050601
2.84138	4.050083
2.85527	4.04957
2.86923	4.049063
2.88325	4.048562
2.89735	4.048067
2.91152	4.047576
2.92575	4.047091
2.94005	4.046612
2.95443	4.046137
2.96887	4.045668
2.98338	4.045204
2.99797	4.044745
3.01263	4.044291
3.02736	4.043841
3.04216	4.043397
3.05703	4.042958
3.07197	4.042523
3.08699	4.042093
3.10208	4.041667
3.11725	4.041246
3.13249	4.04083
3.1478	4.040418
3.16319	4.04001
3.17866	4.039607
3.1942	4.039208
3.20981	4.038813
3.22551	4.038423
3.24128	4.038037
3.25712	4.037654
3.27305	4.037276
3.28905	4.036902
3.30513	4.036532
3.32129	4.036166
3.33752	4.035803
3.35384	4.035445
3.37024	4.03509
3.38671	4.034739
3.40327	4.034392
3.41991	4.034048
3.43663	4.033708
3.45343	4.033371
3.47031	4.033039
3.48728	4.032709
3.50433	4.032383
3.52146	4.03206
3.53868	4.031741
3.55598	4.031425
3.57336	4.031113
3.59083	4.030803
3.60838	4.030497
3.62603	4.030194
3.64375	4.029894
3.66157	4.029598
3.67947	4.029304
3.69746	4.029013
3.71553	4.028726
3.7337	4.028441
3.75195	4.02816
3.77029	4.027881
3.78873	4.027605
3.80725	4.027332
3.82586	4.027062
3.84457	4.026794
3.86336	4.02653
3.88225	4.026268
3.90123	4.026009
3.9203	4.025752
3.93947	4.025498
3.95873	4.025247
3.97808	4.024998
3.99753	4.024752
4.01707	4.024508
4.03671	4.024267
4.05645	4.024028
4.07628	4.023792
4.09621	4.023558
4.11623	4.023327
4.13636	4.023097
4.15658	4.022871
4.1769	4.022646
4.19732	4.022424
4.21784	4.022204
4.23846	4.021986
4.25918	4.021771
4.28	4.021558
4.30093	4.021346
4.32196	4.021138
4.34309	4.020931
4.36432	4.020726
4.38566	4.020523
4.4071	4.020323
4.42864	4.020124
4.45029	4.019927
4.47205	4.019733
4.49391	4.01954
4.51588	4.019349
4.53796	4.019161
4.56015	4.018974
4.58244	4.018789
4.60484	4.018606
4.62736	4.018424
4.64998	4.018245
4.67271	4.018067
4.69556	4.017891
4.71851	4.017717
4.74158	4.017545
4.76476	4.017374
4.78806	4.017205
4.81146	4.017038
4.83499	4.016873
4.85862	4.016709
4.88238	4.016547
4.90625	4.016386
4.93023	4.016227
4.95434	4.01607
4.97856	4.015914
5.0029	4.01576
5.02736	4.015607
5.05193	4.015456
5.07663	4.015306
5.10145	4.015158
5.12639	4.015011
5.15145	4.014866
5.17664	4.014722
5.20195	4.014579
5.22738	4.014438
5.25293	4.014299
5.27862	4.014161
5.30442	4.014024
5.33035	4.013888
5.35641	4.013754
5.3826	4.013622
5.40892	4.01349
5.43536	4.01336
5.46193	4.013231
5.48863	4.013103
5.51547	4.012977
5.54243	4.012852
5.56953	4.012728
5.59676	4.012606
5.62412	4.012484
5.65161	4.012364
5.67924	4.012245
5.70701	4.012127
5.73491	4.01201
5.76295	4.011895
5.79112	4.011781
5.81943	4.011667
5.84789	4.011555
5.87647	4.011444
5.9052	4.011334
5.93407	4.011225
5.96309	4.011118
5.99224	4.011011
6.02153	4.010905
6.05097	4.0108
6.08055	4.010697
6.11028	4.010594
6.14015	4.010493
6.17017	4.010392
6.20034	4.010292
6.23065	4.010194
6.26111	4.010096
6.29172	4.009999
6.32248	4.009903
6.35339	4.009809
6.38445	4.009715
6.41566	4.009622
6.44703	4.00953
6.47855	4.009438
6.51022	4.009348
6.54205	4.009259
6.57403	4.00917
6.60617	4.009082
6.63847	4.008995
6.67092	4.008909
6.70354	4.008824
6.73631	4.00874
6.76924	4.008656
6.80234	4.008574
6.83559	4.008492
6.86901	4.008411
6.90259	4.00833
6.93634	4.008251
6.97025	4.008172
7.00433	4.008094
7.03857	4.008017
7.07298	4.00794
7.10756	4.007864
7.14231	4.007789
7.17722	4.007715
7.21231	4.007641
7.24757	4.007568
7.28301	4.007496
7.31861	4.007424
7.35439	4.007354
7.39035	4.007283
7.42648	4.007214
7.46278	4.007145
7.49927	4.007077
7.53593	4.007009
7.57277	4.006943
7.6098	4.006876
7.647	4.006811
7.68438	4.006746
7.72195	4.006681
7.7597	4.006618
7.79764	4.006554
7.83576	4.006492
7.87407	4.00643
7.91257	4.006368
7.95125	4.006308
7.99012	4.006247
8.02918	4.006188
8.06844	4.006129
8.10788	4.00607
8.14752	4.006012
8.18735	4.005955
8.22738	4.005898
8.2676	4.005841
8.30802	4.005786
8.34864	4.00573
8.38946	4.005675
8.43047	4.005621
8.47169	4.005567
8.5131	4.005514
8.55472	4.005461
8.59655	4.005409
8.63857	4.005357
8.68081	4.005306
8.72325	4.005255
8.76589	4.005204
8.80875	4.005155
8.85181	4.005105
8.89509	4.005056
8.93858	4.005007
8.98228	4.004959
9.02619	4.004912
9.07032	4.004864
9.11466	4.004818
9.15922	4.004771
9.204	4.004725
9.249	4.00468
9.29421	4.004634
9.33965	4.00459
9.38531	4.004545
9.4312	4.004501
9.4773	4.004458
9.52364	4.004415
9.5702	4.004372
9.61699	4.004329
9.664	4.004287
9.71125	4.004246
9.75872	4.004204
9.80643	4.004164
9.85438	4.004123
9.90255	4.004083
9.95097	4.004043
9.99961	4.004003
10.0485	4.003964
10.0976	4.003925
10.147	4.003887
10.1966	4.003849
10.2465	4.003811
10.2965	4.003773
10.3469	4.003736
10.3975	4.003699
10.4483	4.003663
10.4994	4.003626
10.5507	4.00359
10.6023	4.003555
10.6541	4.003519
10.7062	4.003484
10.7586	4.003449
10.8112	4.003415
10.864	4.003381
10.9171	4.003347
10.9705	4.003313
11.0241	4.00328
11.078	4.003247
11.1322	4.003214
11.1866	4.003181
11.2413	4.003149
11.2962	4.003117
11.3515	4.003085
11.407	4.003053
11.4627	4.003022
11.5188	4.002991
11.5751	4.00296
11.6317	4.002929
11.6885	4.002899
11.7457	4.002869
11.8031	4.002839
11.8608	4.002809
11.9188	4.002779
11.9771	4.00275
12.0356	4.002721
12.0945	4.002692
12.1536	4.002663
12.213	4.002635
12.2727	4.002606
12.3327	4.002578
12.393	4.00255
12.4536	4.002522
12.5145	4.002495
12.5757	4.002467
12.6372	4.00244
12.6989	4.002413
12.761	4.002386
12.8234	4.00236
12.8861	4.002333
12.9491	4.002307
13.0124	4.00228
13.076	4.002254
13.1399	4.002228
13.2042	4.002202
13.2687	4.002177
13.3336	4.002151
13.3988	4.002126
13.4643	4.002101
13.5301	4.002075
13.5963	4.00205
13.6627	4.002026
13.7295	4.002001
13.7967	4.001976
13.8641	4.001952
13.9319	4.001927
14	4.001903

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