Optical constants

Refractive index of Pb₅Ge₃O₁₁ (Lead germanate, PGO)

Simon et al. 1997: n(e) 0.45–0.70 µm

Data: formula 4
Range: 0.45–0.7 µm
Temperature: 294 K
Optical axis: e
Licence: CC0-1.0

Uniaxial crystal, axes: oe

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.16214
Extinction coefficient k: 0

Permittivity ε₁: 4.67485
Permittivity ε₂: 0

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

Abbe number V_d: 15.557
Chromatic dispersion dn/dλ: -0.366658 µm⁻¹

Group index n_g: 2.37759
Group velocity dispersion: 830.511 fs²/mm

Dispersion parameter D: -4530.88 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

# Pb5Ge3O11 (Lead germanate, PGO): Simon et al. 1997: n(e) 0.45–0.70 µm
pb5ge3o11 = ls.fetch_refractiveindex("main", "Pb5Ge3O11", "Simon-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pb5ge3o11.range_nm)  # (450, 700) nm
eps = pb5ge3o11.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_8f8cc982497e/lightsmith"
pb5ge3o11 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pb5ge3o11.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (pb5ge3o11/simon-1997-e).

# ... load pb5ge3o11 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=pb5ge3o11)],
    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"]).

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

RefractiveIndex.INFO (formula 4), λ in µm

n^{2} = 2.358 + \frac{1.929 λ^{2.0}}{λ^{2} - {0.0578}^{1.0}}

Valid from 0.45 to 0.7 µm.

Coefficients as stored

C_i	Value
C1	2.358
C2	1.929
C3	2.0
C4	0.0578
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	1.0

Comments and conditions

Extraordinary ray (e). 21 °C.

Conditions

temperature: 294 K
direction: e

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

Pb5Ge3O11 (Lead germanate, PGO), Simon et al. 1997: n(e) 0.45–0.70 µm: n and k versus wavelength
λ (µm)	n
0.45	2.248896
0.450499	2.248366
0.450998	2.247838
0.451497	2.247312
0.451998	2.246788
0.452498	2.246266
0.453	2.245746
0.453502	2.245228
0.454004	2.244711
0.454507	2.244197
0.455011	2.243684
0.455515	2.243174
0.45602	2.242665
0.456525	2.242158
0.457031	2.241653
0.457537	2.24115
0.458044	2.240649
0.458551	2.240149
0.45906	2.239652
0.459568	2.239156
0.460077	2.238662
0.460587	2.23817
0.461097	2.237679
0.461608	2.237191
0.46212	2.236704
0.462632	2.236219
0.463144	2.235736
0.463657	2.235254
0.464171	2.234774
0.464685	2.234296
0.4652	2.23382
0.465716	2.233346
0.466232	2.232873
0.466748	2.232401
0.467265	2.231932
0.467783	2.231464
0.468301	2.230998
0.46882	2.230534
0.46934	2.230071
0.46986	2.22961
0.47038	2.22915
0.470902	2.228692
0.471423	2.228236
0.471946	2.227782
0.472468	2.227329
0.472992	2.226877
0.473516	2.226427
0.474041	2.225979
0.474566	2.225533
0.475092	2.225088
0.475618	2.224644
0.476145	2.224202
0.476673	2.223762
0.477201	2.223323
0.477729	2.222886
0.478259	2.22245
0.478789	2.222016
0.479319	2.221584
0.47985	2.221153
0.480382	2.220723
0.480914	2.220295
0.481447	2.219868
0.48198	2.219443
0.482514	2.21902
0.483049	2.218597
0.483584	2.218177
0.48412	2.217758
0.484656	2.21734
0.485193	2.216923
0.485731	2.216509
0.486269	2.216095
0.486808	2.215683
0.487347	2.215273
0.487887	2.214863
0.488428	2.214456
0.488969	2.214049
0.489511	2.213644
0.490053	2.213241
0.490596	2.212838
0.49114	2.212438
0.491684	2.212038
0.492228	2.21164
0.492774	2.211243
0.49332	2.210848
0.493866	2.210454
0.494414	2.210061
0.494961	2.20967
0.49551	2.20928
0.496059	2.208891
0.496608	2.208504
0.497159	2.208118
0.497709	2.207733
0.498261	2.20735
0.498813	2.206968
0.499366	2.206587
0.499919	2.206207
0.500473	2.205829
0.501027	2.205452
0.501582	2.205076
0.502138	2.204702
0.502694	2.204328
0.503251	2.203956
0.503809	2.203586
0.504367	2.203216
0.504926	2.202848
0.505486	2.202481
0.506046	2.202115
0.506606	2.201751
0.507168	2.201387
0.507729	2.201025
0.508292	2.200664
0.508855	2.200304
0.509419	2.199946
0.509983	2.199588
0.510548	2.199232
0.511114	2.198877
0.51168	2.198523
0.512247	2.198171
0.512815	2.197819
0.513383	2.197469
0.513952	2.19712
0.514521	2.196772
0.515091	2.196425
0.515662	2.196079
0.516233	2.195734
0.516805	2.195391
0.517378	2.195048
0.517951	2.194707
0.518525	2.194367
0.5191	2.194028
0.519675	2.19369
0.520251	2.193353
0.520827	2.193018
0.521404	2.192683
0.521982	2.19235
0.52256	2.192017
0.523139	2.191686
0.523719	2.191355
0.524299	2.191026
0.52488	2.190698
0.525461	2.190371
0.526044	2.190045
0.526626	2.18972
0.52721	2.189396
0.527794	2.189073
0.528379	2.188751
0.528964	2.188431
0.52955	2.188111
0.530137	2.187792
0.530724	2.187474
0.531312	2.187158
0.531901	2.186842
0.53249	2.186527
0.53308	2.186214
0.533671	2.185901
0.534262	2.185589
0.534854	2.185278
0.535447	2.184969
0.53604	2.18466
0.536634	2.184352
0.537229	2.184046
0.537824	2.18374
0.53842	2.183435
0.539016	2.183131
0.539613	2.182828
0.540211	2.182527
0.54081	2.182226
0.541409	2.181926
0.542009	2.181627
0.542609	2.181328
0.543211	2.181031
0.543812	2.180735
0.544415	2.18044
0.545018	2.180145
0.545622	2.179852
0.546227	2.179559
0.546832	2.179268
0.547438	2.178977
0.548044	2.178687
0.548651	2.178399
0.549259	2.178111
0.549868	2.177824
0.550477	2.177537
0.551087	2.177252
0.551698	2.176968
0.552309	2.176684
0.552921	2.176402
0.553533	2.17612
0.554147	2.175839
0.554761	2.175559
0.555375	2.17528
0.555991	2.175002
0.556607	2.174724
0.557223	2.174448
0.557841	2.174172
0.558459	2.173897
0.559078	2.173623
0.559697	2.17335
0.560317	2.173078
0.560938	2.172807
0.561559	2.172536
0.562182	2.172266
0.562805	2.171997
0.563428	2.171729
0.564052	2.171462
0.564677	2.171195
0.565303	2.17093
0.565929	2.170665
0.566556	2.170401
0.567184	2.170138
0.567812	2.169875
0.568442	2.169614
0.569071	2.169353
0.569702	2.169093
0.570333	2.168834
0.570965	2.168575
0.571598	2.168318
0.572231	2.168061
0.572865	2.167805
0.5735	2.167549
0.574135	2.167295
0.574771	2.167041
0.575408	2.166788
0.576046	2.166536
0.576684	2.166285
0.577323	2.166034
0.577962	2.165784
0.578603	2.165535
0.579244	2.165286
0.579886	2.165039
0.580528	2.164792
0.581171	2.164546
0.581815	2.1643
0.58246	2.164055
0.583105	2.163811
0.583751	2.163568
0.584398	2.163326
0.585045	2.163084
0.585694	2.162843
0.586343	2.162603
0.586992	2.162363
0.587643	2.162124
0.588294	2.161886
0.588946	2.161648
0.589598	2.161412
0.590251	2.161176
0.590905	2.16094
0.59156	2.160706
0.592215	2.160472
0.592872	2.160239
0.593528	2.160006
0.594186	2.159774
0.594844	2.159543
0.595503	2.159312
0.596163	2.159083
0.596824	2.158854
0.597485	2.158625
0.598147	2.158397
0.59881	2.15817
0.599473	2.157944
0.600137	2.157718
0.600802	2.157493
0.601468	2.157269
0.602134	2.157045
0.602802	2.156822
0.603469	2.156599
0.604138	2.156377
0.604807	2.156156
0.605478	2.155936
0.606148	2.155716
0.60682	2.155497
0.607492	2.155278
0.608165	2.15506
0.608839	2.154843
0.609514	2.154626
0.610189	2.15441
0.610865	2.154195
0.611542	2.15398
0.61222	2.153766
0.612898	2.153553
0.613577	2.15334
0.614257	2.153128
0.614937	2.152916
0.615619	2.152705
0.616301	2.152495
0.616984	2.152285
0.617667	2.152076
0.618352	2.151867
0.619037	2.151659
0.619723	2.151452
0.620409	2.151245
0.621097	2.151039
0.621785	2.150833
0.622474	2.150628
0.623163	2.150424
0.623854	2.15022
0.624545	2.150017
0.625237	2.149814
0.62593	2.149612
0.626623	2.149411
0.627317	2.14921
0.628012	2.14901
0.628708	2.14881
0.629405	2.148611
0.630102	2.148412
0.6308	2.148214
0.631499	2.148017
0.632199	2.14782
0.632899	2.147624
0.633601	2.147428
0.634303	2.147233
0.635005	2.147038
0.635709	2.146844
0.636413	2.146651
0.637118	2.146458
0.637824	2.146265
0.638531	2.146074
0.639238	2.145882
0.639947	2.145692
0.640656	2.145501
0.641366	2.145312
0.642076	2.145123
0.642788	2.144934
0.6435	2.144746
0.644213	2.144558
0.644927	2.144371
0.645641	2.144185
0.646356	2.143999
0.647073	2.143814
0.64779	2.143629
0.648507	2.143444
0.649226	2.143261
0.649945	2.143077
0.650665	2.142894
0.651386	2.142712
0.652108	2.14253
0.65283	2.142349
0.653554	2.142168
0.654278	2.141988
0.655003	2.141809
0.655728	2.141629
0.656455	2.141451
0.657182	2.141272
0.65791	2.141095
0.658639	2.140918
0.659369	2.140741
0.6601	2.140565
0.660831	2.140389
0.661563	2.140214
0.662296	2.140039
0.66303	2.139865
0.663765	2.139691
0.6645	2.139518
0.665236	2.139345
0.665973	2.139173
0.666711	2.139001
0.66745	2.138829
0.668189	2.138659
0.66893	2.138488
0.669671	2.138318
0.670413	2.138149
0.671156	2.13798
0.671899	2.137811
0.672644	2.137643
0.673389	2.137476
0.674135	2.137309
0.674882	2.137142
0.67563	2.136976
0.676378	2.13681
0.677128	2.136645
0.677878	2.13648
0.678629	2.136316
0.679381	2.136152
0.680134	2.135989
0.680887	2.135826
0.681642	2.135663
0.682397	2.135501
0.683153	2.13534
0.68391	2.135178
0.684668	2.135018
0.685426	2.134857
0.686186	2.134698
0.686946	2.134538
0.687707	2.134379
0.688469	2.134221
0.689232	2.134063
0.689995	2.133905
0.69076	2.133748
0.691525	2.133591
0.692291	2.133435
0.693058	2.133279
0.693826	2.133123
0.694595	2.132968
0.695365	2.132813
0.696135	2.132659
0.696906	2.132505
0.697678	2.132352
0.698451	2.132199
0.699225	2.132046
0.7	2.131894

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: —

Pb₅Ge₃O₁₁ (Lead germanate, PGO): all datasets

About Pb5Ge3O11 (Lead germanate, PGO)

Lead germanate (Pb₅Ge₃O₁₁), often referred to as PGO, is a crystalline compound with unique optical properties. Its high density and high atomic number make it particularly suitable as a scintillation material for radiation detection, especially gamma rays. PGO scintillators are characterized by their fast response times and relatively high light yield. Moreover, in the realm of nonlinear optics, PGO has been studied for frequency conversion processes. Due to its specific material properties, lead germanate has been considered for various photonics and optoelectronics applications. However, handling and usage of PGO, like other lead compounds, require precautions due to the toxic nature of lead.

More about Pb5Ge3O11 (Lead germanate, PGO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Pb5Ge3O11/nk/Simon-e.yml
ID: ds_8f8cc982497e
API: /v1/datasets/ds_8f8cc982497e

Plot