Optical constants

Refractive index of Bi₄Ge₃O₁₂ (Bismuth germanate, BGO)

Williams et al. 1996: n 0.305–1.0 µm

Data: formula 1
Range: 0.305–1 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.10901
Extinction coefficient k: 0

Permittivity ε₁: 4.44791
Permittivity ε₂: 0

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

Abbe number V_d: 19.251
Chromatic dispersion dn/dλ: -0.290599 µm⁻¹

Group index n_g: 2.27976
Group velocity dispersion: 592.884 fs²/mm

Dispersion parameter D: -3234.49 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

# Bi4Ge3O12 (Bismuth germanate, BGO): Williams et al. 1996: n 0.305–1.0 µm
bi4ge3o12 = ls.fetch_refractiveindex("main", "Bi4Ge3O12", "Williams", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bi4ge3o12.range_nm)  # (305, 1000) nm
eps = bi4ge3o12.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_e858f98d4ab6/lightsmith"
bi4ge3o12 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bi4ge3o12.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (bi4ge3o12/williams-1996).

# ... load bi4ge3o12 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bi4ge3o12)],
    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"]).

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_e858f98d4ab6/lightsmith?model=drude_lorentz"
bi4ge3o12_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 (formula 1), λ in µm

n^{2} - 1 = \frac{3.1218393 λ^{2}}{λ^{2} - {0.1807}^{2}}

Valid from 0.305 to 1.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	3.1218393
C3	0.1807

References

P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, P. D. Hale. Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate Bi₄Ge₃O₁₂. Appl. Opt. 35, 3562-3569 (1996)

doi:10.1364/ao.35.003562 Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi_4Ge_3O_12), Applied Optics (1996)

Cite

P. A. Williams et al.. Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi_4Ge_3O_12). Applied Optics, 35, 3562 (1996), doi:10.1364/ao.35.003562; 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

Bi4Ge3O12 (Bismuth germanate, BGO), Williams et al. 1996: n 0.305–1.0 µm: n and k versus wavelength
λ (µm)	n
0.305	2.410454
0.305909	2.407259
0.306821	2.4041
0.307735	2.400975
0.308652	2.397884
0.309572	2.394826
0.310495	2.391802
0.311421	2.388809
0.312349	2.385849
0.31328	2.38292
0.314213	2.380023
0.31515	2.377156
0.316089	2.374319
0.317031	2.371512
0.317976	2.368734
0.318924	2.365986
0.319874	2.363265
0.320828	2.360573
0.321784	2.357909
0.322743	2.355271
0.323705	2.352661
0.32467	2.350078
0.325638	2.34752
0.326608	2.344989
0.327582	2.342483
0.328558	2.340002
0.329537	2.337546
0.330519	2.335114
0.331504	2.332707
0.332492	2.330323
0.333483	2.327964
0.334477	2.325627
0.335474	2.323313
0.336474	2.321022
0.337477	2.318753
0.338483	2.316506
0.339492	2.314281
0.340504	2.312078
0.341518	2.309895
0.342536	2.307734
0.343557	2.305593
0.344581	2.303473
0.345608	2.301373
0.346638	2.299292
0.347671	2.297232
0.348708	2.295191
0.349747	2.293169
0.350789	2.291165
0.351835	2.289181
0.352884	2.287215
0.353935	2.285267
0.35499	2.283338
0.356048	2.281426
0.357109	2.279532
0.358174	2.277655
0.359241	2.275795
0.360312	2.273953
0.361386	2.272127
0.362463	2.270317
0.363543	2.268525
0.364627	2.266748
0.365714	2.264987
0.366804	2.263242
0.367897	2.261513
0.368993	2.259799
0.370093	2.2581
0.371196	2.256417
0.372303	2.254748
0.373412	2.253095
0.374525	2.251455
0.375641	2.249831
0.376761	2.24822
0.377884	2.246624
0.37901	2.245041
0.38014	2.243473
0.381273	2.241918
0.382409	2.240376
0.383549	2.238848
0.384692	2.237333
0.385839	2.235831
0.386989	2.234342
0.388142	2.232866
0.389299	2.231402
0.390459	2.229951
0.391623	2.228512
0.39279	2.227085
0.393961	2.225671
0.395135	2.224268
0.396313	2.222877
0.397494	2.221498
0.398679	2.220131
0.399867	2.218775
0.401059	2.21743
0.402254	2.216097
0.403453	2.214775
0.404656	2.213463
0.405862	2.212163
0.407071	2.210873
0.408285	2.209594
0.409502	2.208325
0.410722	2.207067
0.411946	2.20582
0.413174	2.204582
0.414405	2.203355
0.415641	2.202137
0.416879	2.20093
0.418122	2.199732
0.419368	2.198544
0.420618	2.197366
0.421872	2.196197
0.423129	2.195038
0.42439	2.193888
0.425655	2.192747
0.426924	2.191615
0.428196	2.190492
0.429472	2.189379
0.430752	2.188274
0.432036	2.187178
0.433324	2.186091
0.434615	2.185012
0.435911	2.183942
0.43721	2.18288
0.438513	2.181827
0.43982	2.180782
0.441131	2.179745
0.442446	2.178717
0.443764	2.177696
0.445087	2.176684
0.446414	2.175679
0.447744	2.174682
0.449079	2.173693
0.450417	2.172712
0.45176	2.171738
0.453106	2.170772
0.454457	2.169813
0.455811	2.168861
0.45717	2.167917
0.458532	2.166981
0.459899	2.166051
0.46127	2.165128
0.462644	2.164213
0.464023	2.163305
0.465406	2.162403
0.466793	2.161509
0.468185	2.160621
0.46958	2.15974
0.47098	2.158865
0.472383	2.157998
0.473791	2.157136
0.475203	2.156282
0.47662	2.155433
0.47804	2.154592
0.479465	2.153756
0.480894	2.152927
0.482327	2.152104
0.483765	2.151287
0.485207	2.150476
0.486653	2.149671
0.488104	2.148873
0.489558	2.14808
0.491017	2.147293
0.492481	2.146512
0.493949	2.145737
0.495421	2.144967
0.496898	2.144204
0.498379	2.143445
0.499864	2.142693
0.501354	2.141946
0.502848	2.141204
0.504347	2.140468
0.50585	2.139737
0.507358	2.139012
0.50887	2.138292
0.510386	2.137577
0.511908	2.136868
0.513433	2.136163
0.514964	2.135464
0.516499	2.13477
0.518038	2.134081
0.519582	2.133397
0.521131	2.132717
0.522684	2.132043
0.524242	2.131374
0.525804	2.130709
0.527371	2.130049
0.528943	2.129394
0.53052	2.128744
0.532101	2.128099
0.533687	2.127458
0.535277	2.126821
0.536873	2.126189
0.538473	2.125562
0.540078	2.124939
0.541687	2.124321
0.543302	2.123707
0.544921	2.123097
0.546545	2.122492
0.548174	2.121891
0.549808	2.121294
0.551447	2.120702
0.55309	2.120113
0.554739	2.119529
0.556392	2.118949
0.558051	2.118373
0.559714	2.117801
0.561382	2.117233
0.563055	2.11667
0.564733	2.11611
0.566417	2.115554
0.568105	2.115002
0.569798	2.114454
0.571496	2.113909
0.5732	2.113369
0.574908	2.112832
0.576622	2.112299
0.57834	2.11177
0.580064	2.111244
0.581793	2.110722
0.583527	2.110204
0.585266	2.109689
0.58701	2.109178
0.58876	2.10867
0.590515	2.108166
0.592275	2.107666
0.59404	2.107168
0.595811	2.106675
0.597586	2.106184
0.599367	2.105698
0.601154	2.105214
0.602946	2.104734
0.604743	2.104257
0.606545	2.103783
0.608353	2.103313
0.610166	2.102846
0.611985	2.102382
0.613809	2.101921
0.615638	2.101463
0.617473	2.101009
0.619313	2.100557
0.621159	2.100109
0.623011	2.099664
0.624867	2.099221
0.62673	2.098782
0.628598	2.098346
0.630471	2.097912
0.63235	2.097482
0.634235	2.097055
0.636125	2.09663
0.638021	2.096208
0.639923	2.09579
0.64183	2.095374
0.643743	2.094961
0.645662	2.09455
0.647586	2.094143
0.649516	2.093738
0.651452	2.093336
0.653394	2.092936
0.655341	2.092539
0.657295	2.092145
0.659254	2.091754
0.661219	2.091365
0.663189	2.090979
0.665166	2.090595
0.667148	2.090214
0.669137	2.089836
0.671131	2.08946
0.673132	2.089086
0.675138	2.088715
0.67715	2.088347
0.679168	2.087981
0.681193	2.087617
0.683223	2.087256
0.685259	2.086897
0.687302	2.086541
0.68935	2.086187
0.691405	2.085835
0.693465	2.085486
0.695532	2.085139
0.697605	2.084794
0.699684	2.084452
0.70177	2.084112
0.703861	2.083774
0.705959	2.083438
0.708063	2.083105
0.710174	2.082773
0.71229	2.082444
0.714413	2.082117
0.716543	2.081793
0.718678	2.08147
0.72082	2.08115
0.722969	2.080831
0.725124	2.080515
0.727285	2.080201
0.729452	2.079888
0.731627	2.079578
0.733807	2.07927
0.735994	2.078964
0.738188	2.07866
0.740388	2.078358
0.742595	2.078058
0.744808	2.07776
0.747028	2.077464
0.749254	2.07717
0.751488	2.076877
0.753727	2.076587
0.755974	2.076298
0.758227	2.076012
0.760487	2.075727
0.762753	2.075444
0.765027	2.075163
0.767307	2.074884
0.769594	2.074606
0.771888	2.07433
0.774188	2.074057
0.776496	2.073785
0.77881	2.073514
0.781131	2.073246
0.783459	2.072979
0.785795	2.072714
0.788137	2.07245
0.790486	2.072189
0.792842	2.071929
0.795205	2.07167
0.797575	2.071414
0.799952	2.071159
0.802336	2.070905
0.804728	2.070654
0.807126	2.070404
0.809532	2.070155
0.811944	2.069908
0.814364	2.069663
0.816792	2.069419
0.819226	2.069177
0.821668	2.068936
0.824117	2.068697
0.826573	2.06846
0.829037	2.068224
0.831507	2.067989
0.833986	2.067756
0.836471	2.067525
0.838965	2.067295
0.841465	2.067066
0.843973	2.066839
0.846488	2.066614
0.849011	2.06639
0.851542	2.066167
0.85408	2.065945
0.856625	2.065726
0.859179	2.065507
0.861739	2.06529
0.864308	2.065074
0.866884	2.06486
0.869468	2.064647
0.872059	2.064435
0.874658	2.064225
0.877265	2.064016
0.87988	2.063808
0.882502	2.063602
0.885132	2.063397
0.887771	2.063193
0.890417	2.062991
0.89307	2.06279
0.895732	2.06259
0.898402	2.062392
0.90108	2.062194
0.903765	2.061998
0.906459	2.061803
0.909161	2.06161
0.91187	2.061417
0.914588	2.061226
0.917314	2.061036
0.920048	2.060848
0.92279	2.06066
0.925541	2.060474
0.928299	2.060289
0.931066	2.060105
0.933841	2.059922
0.936624	2.05974
0.939416	2.059559
0.942216	2.05938
0.945024	2.059202
0.947841	2.059025
0.950666	2.058849
0.953499	2.058674
0.956341	2.0585
0.959191	2.058327
0.96205	2.058155
0.964918	2.057985
0.967794	2.057815
0.970678	2.057647
0.973571	2.057479
0.976473	2.057313
0.979383	2.057148
0.982302	2.056984
0.98523	2.05682
0.988166	2.056658
0.991112	2.056497
0.994066	2.056337
0.997028	2.056178
1	2.056019

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: —

Bi₄Ge₃O₁₂ (Bismuth germanate, BGO): all datasets

Williams et al. 1996: n 0.305–1.0 µm n 0.305–1 µm default

About Bi4Ge3O12 (Bismuth germanate, BGO)

Bi₄Ge₃O₁₂, commonly known as bismuth germanate (BGO), is a scintillation material that has found extensive use in medical imaging, high-energy physics, and radiation detection. Composed of bismuth, germanium, and oxygen, this compound is valued for its high atomic number, high density, and effective Z-value, which result in strong stopping power for high-energy radiation. In optical applications, BGO is often employed as a scintillator in positron emission tomography (PET) scanners and in various types of detectors for gamma and X-ray radiation. The crystal exhibits excellent scintillation properties, including good energy resolution and fast decay times. One of the key advantages of BGO over other scintillators is its non-hygroscopic nature, which makes it easier to handle and less sensitive to moisture. The material can be grown using techniques like the Bridgman or Czochralski methods, and can be doped with various activators to tailor its scintillation properties. Overall, BGO stands as a material of choice for high-performance radiation detection and imaging applications due to its robust scintillation performance and ease of handling.

Bismuth germanate - Wikipedia

More about Bi4Ge3O12 (Bismuth germanate, BGO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Bi4Ge3O12/nk/Williams.yml
ID: ds_e858f98d4ab6
API: /v1/datasets/ds_e858f98d4ab6

Plot