Optical constants

Refractive index of Bi₁₂GeO₂₀ (Bismuth germanate, BGO)

Simon et al. 1997: n 0.45–0.70 µm

Data: formula 2
Range: 0.45–0.7 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.57032
Extinction coefficient k: 0

Permittivity ε₁: 6.60654
Permittivity ε₂: 0

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

Abbe number V_d: 11.119
Chromatic dispersion dn/dλ: -0.675058 µm⁻¹

Group index n_g: 2.96698
Group velocity dispersion: 1663.65 fs²/mm

Dispersion parameter D: -9076.07 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

# Bi12GeO20 (Bismuth germanate, BGO): Simon et al. 1997: n 0.45–0.70 µm
bi12geo20 = ls.fetch_refractiveindex("main", "Bi12GeO20", "Simon", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bi12geo20.range_nm)  # (450, 700) nm
eps = bi12geo20.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_bc83dbdc3936/lightsmith"
bi12geo20 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bi12geo20.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (bi12geo20/simon-1997).

# ... load bi12geo20 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bi12geo20)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=450, stop_nm=700, 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_bc83dbdc3936/lightsmith?model=drude_lorentz"
bi12geo20_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 = 2.165 + \frac{2.655 λ^{2}}{λ^{2} - 0.07891}

Valid from 0.45 to 0.7 µm.

Coefficients as stored

C_i	Value
C1	2.165
C2	2.655
C3	0.07891

Comments and conditions

21 °C

References

doi:10.1002/1521-396x(199702)159:2 Refractive indices of photorefractive bismuth titanate, barium-calcium titanate, bismuth germanium oxide, and lead germanate (1997)

Cite

M. Simon, F. Mersch, C. Kuper, S. Mendricks, S. Wevering, J. Imbrock, E. Krätzig. Refractive indices of photorefractive bismuth titanate, barium-calcium titanate, bismuth germanium oxide, and lead germanate. 3.0.CO;2-0">Phys. Stat. Sol. 159, 559-562 (1997); 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

Bi12GeO20 (Bismuth germanate, BGO), Simon et al. 1997: n 0.45–0.70 µm: n and k versus wavelength
λ (µm)	n
0.45	2.741381
0.450499	2.740262
0.450998	2.739147
0.451497	2.738038
0.451998	2.736934
0.452498	2.735836
0.453	2.734742
0.453502	2.733653
0.454004	2.732569
0.454507	2.73149
0.455011	2.730416
0.455515	2.729347
0.45602	2.728283
0.456525	2.727223
0.457031	2.726168
0.457537	2.725118
0.458044	2.724073
0.458551	2.723033
0.45906	2.721997
0.459568	2.720965
0.460077	2.719939
0.460587	2.718917
0.461097	2.717899
0.461608	2.716886
0.46212	2.715878
0.462632	2.714874
0.463144	2.713874
0.463657	2.712879
0.464171	2.711888
0.464685	2.710902
0.4652	2.70992
0.465716	2.708942
0.466232	2.707969
0.466748	2.706999
0.467265	2.706034
0.467783	2.705074
0.468301	2.704117
0.46882	2.703164
0.46934	2.702216
0.46986	2.701272
0.47038	2.700332
0.470902	2.699396
0.471423	2.698464
0.471946	2.697535
0.472468	2.696611
0.472992	2.695691
0.473516	2.694775
0.474041	2.693863
0.474566	2.692954
0.475092	2.69205
0.475618	2.691149
0.476145	2.690252
0.476673	2.689359
0.477201	2.68847
0.477729	2.687585
0.478259	2.686703
0.478789	2.685825
0.479319	2.68495
0.47985	2.68408
0.480382	2.683213
0.480914	2.682349
0.481447	2.681489
0.48198	2.680633
0.482514	2.679781
0.483049	2.678931
0.483584	2.678086
0.48412	2.677244
0.484656	2.676405
0.485193	2.67557
0.485731	2.674738
0.486269	2.67391
0.486808	2.673085
0.487347	2.672264
0.487887	2.671446
0.488428	2.670631
0.488969	2.66982
0.489511	2.669012
0.490053	2.668207
0.490596	2.667405
0.49114	2.666607
0.491684	2.665812
0.492228	2.66502
0.492774	2.664232
0.49332	2.663446
0.493866	2.662664
0.494414	2.661885
0.494961	2.661109
0.49551	2.660336
0.496059	2.659567
0.496608	2.6588
0.497159	2.658036
0.497709	2.657276
0.498261	2.656518
0.498813	2.655764
0.499366	2.655013
0.499919	2.654264
0.500473	2.653519
0.501027	2.652776
0.501582	2.652036
0.502138	2.6513
0.502694	2.650566
0.503251	2.649835
0.503809	2.649107
0.504367	2.648382
0.504926	2.64766
0.505486	2.64694
0.506046	2.646224
0.506606	2.64551
0.507168	2.644799
0.507729	2.644091
0.508292	2.643385
0.508855	2.642682
0.509419	2.641982
0.509983	2.641285
0.510548	2.64059
0.511114	2.639898
0.51168	2.639209
0.512247	2.638523
0.512815	2.637839
0.513383	2.637157
0.513952	2.636479
0.514521	2.635802
0.515091	2.635129
0.515662	2.634458
0.516233	2.63379
0.516805	2.633124
0.517378	2.632461
0.517951	2.6318
0.518525	2.631142
0.5191	2.630486
0.519675	2.629833
0.520251	2.629182
0.520827	2.628533
0.521404	2.627888
0.521982	2.627244
0.52256	2.626603
0.523139	2.625964
0.523719	2.625328
0.524299	2.624694
0.52488	2.624063
0.525461	2.623434
0.526044	2.622807
0.526626	2.622183
0.52721	2.621561
0.527794	2.620941
0.528379	2.620324
0.528964	2.619709
0.52955	2.619096
0.530137	2.618485
0.530724	2.617877
0.531312	2.617271
0.531901	2.616667
0.53249	2.616065
0.53308	2.615466
0.533671	2.614869
0.534262	2.614274
0.534854	2.613681
0.535447	2.613091
0.53604	2.612502
0.536634	2.611916
0.537229	2.611332
0.537824	2.61075
0.53842	2.61017
0.539016	2.609592
0.539613	2.609016
0.540211	2.608443
0.54081	2.607871
0.541409	2.607302
0.542009	2.606735
0.542609	2.606169
0.543211	2.605606
0.543812	2.605045
0.544415	2.604486
0.545018	2.603928
0.545622	2.603373
0.546227	2.60282
0.546832	2.602269
0.547438	2.60172
0.548044	2.601172
0.548651	2.600627
0.549259	2.600084
0.549868	2.599542
0.550477	2.599003
0.551087	2.598465
0.551698	2.597929
0.552309	2.597396
0.552921	2.596864
0.553533	2.596334
0.554147	2.595806
0.554761	2.595279
0.555375	2.594755
0.555991	2.594233
0.556607	2.593712
0.557223	2.593193
0.557841	2.592676
0.558459	2.592161
0.559078	2.591647
0.559697	2.591136
0.560317	2.590626
0.560938	2.590118
0.561559	2.589612
0.562182	2.589107
0.562805	2.588605
0.563428	2.588104
0.564052	2.587604
0.564677	2.587107
0.565303	2.586611
0.565929	2.586117
0.566556	2.585625
0.567184	2.585134
0.567812	2.584645
0.568442	2.584158
0.569071	2.583672
0.569702	2.583189
0.570333	2.582706
0.570965	2.582226
0.571598	2.581747
0.572231	2.58127
0.572865	2.580794
0.5735	2.58032
0.574135	2.579848
0.574771	2.579377
0.575408	2.578908
0.576046	2.57844
0.576684	2.577974
0.577323	2.57751
0.577962	2.577047
0.578603	2.576586
0.579244	2.576126
0.579886	2.575668
0.580528	2.575212
0.581171	2.574757
0.581815	2.574303
0.58246	2.573851
0.583105	2.573401
0.583751	2.572952
0.584398	2.572505
0.585045	2.572059
0.585694	2.571615
0.586343	2.571172
0.586992	2.57073
0.587643	2.57029
0.588294	2.569852
0.588946	2.569415
0.589598	2.56898
0.590251	2.568546
0.590905	2.568113
0.59156	2.567682
0.592215	2.567252
0.592872	2.566824
0.593528	2.566397
0.594186	2.565972
0.594844	2.565548
0.595503	2.565125
0.596163	2.564704
0.596824	2.564284
0.597485	2.563866
0.598147	2.563448
0.59881	2.563033
0.599473	2.562619
0.600137	2.562206
0.600802	2.561794
0.601468	2.561384
0.602134	2.560975
0.602802	2.560567
0.603469	2.560161
0.604138	2.559756
0.604807	2.559353
0.605478	2.558951
0.606148	2.55855
0.60682	2.55815
0.607492	2.557752
0.608165	2.557355
0.608839	2.556959
0.609514	2.556565
0.610189	2.556171
0.610865	2.55578
0.611542	2.555389
0.61222	2.555
0.612898	2.554612
0.613577	2.554225
0.614257	2.553839
0.614937	2.553455
0.615619	2.553072
0.616301	2.55269
0.616984	2.552309
0.617667	2.55193
0.618352	2.551552
0.619037	2.551175
0.619723	2.550799
0.620409	2.550425
0.621097	2.550051
0.621785	2.549679
0.622474	2.549308
0.623163	2.548938
0.623854	2.54857
0.624545	2.548203
0.625237	2.547836
0.62593	2.547471
0.626623	2.547107
0.627317	2.546745
0.628012	2.546383
0.628708	2.546023
0.629405	2.545663
0.630102	2.545305
0.6308	2.544948
0.631499	2.544592
0.632199	2.544237
0.632899	2.543884
0.633601	2.543531
0.634303	2.54318
0.635005	2.54283
0.635709	2.54248
0.636413	2.542132
0.637118	2.541785
0.637824	2.541439
0.638531	2.541094
0.639238	2.540751
0.639947	2.540408
0.640656	2.540066
0.641366	2.539726
0.642076	2.539386
0.642788	2.539048
0.6435	2.538711
0.644213	2.538374
0.644927	2.538039
0.645641	2.537705
0.646356	2.537372
0.647073	2.53704
0.64779	2.536708
0.648507	2.536378
0.649226	2.536049
0.649945	2.535721
0.650665	2.535394
0.651386	2.535068
0.652108	2.534743
0.65283	2.534419
0.653554	2.534096
0.654278	2.533774
0.655003	2.533453
0.655728	2.533133
0.656455	2.532814
0.657182	2.532496
0.65791	2.532179
0.658639	2.531863
0.659369	2.531548
0.6601	2.531234
0.660831	2.530921
0.661563	2.530609
0.662296	2.530297
0.66303	2.529987
0.663765	2.529678
0.6645	2.529369
0.665236	2.529062
0.665973	2.528755
0.666711	2.52845
0.66745	2.528145
0.668189	2.527841
0.66893	2.527538
0.669671	2.527236
0.670413	2.526935
0.671156	2.526635
0.671899	2.526336
0.672644	2.526038
0.673389	2.52574
0.674135	2.525444
0.674882	2.525148
0.67563	2.524854
0.676378	2.52456
0.677128	2.524267
0.677878	2.523975
0.678629	2.523684
0.679381	2.523394
0.680134	2.523104
0.680887	2.522816
0.681642	2.522528
0.682397	2.522241
0.683153	2.521955
0.68391	2.52167
0.684668	2.521386
0.685426	2.521103
0.686186	2.52082
0.686946	2.520539
0.687707	2.520258
0.688469	2.519978
0.689232	2.519699
0.689995	2.51942
0.69076	2.519143
0.691525	2.518866
0.692291	2.51859
0.693058	2.518315
0.693826	2.518041
0.694595	2.517768
0.695365	2.517495
0.696135	2.517223
0.696906	2.516953
0.697678	2.516682
0.698451	2.516413
0.699225	2.516144
0.7	2.515877

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: —

Bi₁₂GeO₂₀ (Bismuth germanate, BGO): all datasets

Simon et al. 1997: n 0.45–0.70 µm n 0.45–0.7 µm default

About Bi12GeO20 (Bismuth germanate, BGO)

Bi₁₂GeO₂₀, also abbreviated as BGO but distinct from bismuth germanate, is a bismuth germanium oxide compound known for its fascinating electro-optic and acousto-optic properties. It is primarily used in applications requiring high-speed modulation and deflection of light, such as in Q-switching of lasers, optical data storage, and light modulation for telecommunications. The crystal structure of Bi₁₂GeO₂₀ contributes to its large electro-optic and acousto-optic coefficients, making it one of the preferred materials for devices that require fast and efficient control of optical signals. It is also used in piezoelectric applications and has been explored for its potential as a photorefractive material. The crystal can be grown using techniques like the Czochralski method, and its optical properties can be fine-tuned through doping or altering growth conditions. Although it is less common than other electro-optic materials like lithium niobate, its unique combination of properties, such as high optical damage threshold and good thermal stability, make it a valuable material for specialized optical applications.

More about Bi12GeO20 (Bismuth germanate, BGO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Bi12GeO20/nk/Simon.yml
ID: ds_bc83dbdc3936
API: /v1/datasets/ds_bc83dbdc3936

Plot