Optical constants

Refractive index of Bi₄Ti₃O₁₂ (Bismuth titanate, BTO)

Simon et al. 1997: n(a); 0.45–0.70 µm

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

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.67245
Extinction coefficient k: 0

Permittivity ε₁: 7.14201
Permittivity ε₂: 0

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

Abbe number V_d: 13.397
Chromatic dispersion dn/dλ: -0.622241 µm⁻¹

Group index n_g: 3.03808
Group velocity dispersion: 1331.41 fs²/mm

Dispersion parameter D: -7263.55 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

# Bi4Ti3O12 (Bismuth titanate, BTO): Simon et al. 1997: n(a); 0.45–0.70 µm
bi4ti3o12 = ls.fetch_refractiveindex("main", "Bi4Ti3O12", "Simon-a", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bi4ti3o12.range_nm)  # (450, 700) nm
eps = bi4ti3o12.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_ebd362c012d9/lightsmith"
bi4ti3o12 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bi4ti3o12.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (bi4ti3o12/simon-1997-a).

# ... load bi4ti3o12 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bi4ti3o12)],
    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_ebd362c012d9/lightsmith?model=drude_lorentz"
bi4ti3o12_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{5.299 λ^{2}}{λ^{2} - 0.04739}

Valid from 0.45 to 0.7 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	5.299
C3	0.04739

Comments and conditions

Polarization parallel to a-axis. 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

Bi4Ti3O12 (Bismuth titanate, BTO), Simon et al. 1997: n(a); 0.45–0.70 µm: n and k versus wavelength
λ (µm)	n
0.45	2.81389
0.450499	2.81306
0.450998	2.812232
0.451497	2.811407
0.451998	2.810585
0.452498	2.809765
0.453	2.808948
0.453502	2.808134
0.454004	2.807322
0.454507	2.806513
0.455011	2.805707
0.455515	2.804903
0.45602	2.804102
0.456525	2.803303
0.457031	2.802507
0.457537	2.801713
0.458044	2.800923
0.458551	2.800134
0.45906	2.799348
0.459568	2.798565
0.460077	2.797784
0.460587	2.797006
0.461097	2.79623
0.461608	2.795457
0.46212	2.794686
0.462632	2.793918
0.463144	2.793152
0.463657	2.792388
0.464171	2.791627
0.464685	2.790869
0.4652	2.790112
0.465716	2.789359
0.466232	2.788607
0.466748	2.787858
0.467265	2.787112
0.467783	2.786367
0.468301	2.785625
0.46882	2.784886
0.46934	2.784149
0.46986	2.783414
0.47038	2.782681
0.470902	2.781951
0.471423	2.781223
0.471946	2.780497
0.472468	2.779774
0.472992	2.779053
0.473516	2.778334
0.474041	2.777617
0.474566	2.776903
0.475092	2.776191
0.475618	2.775481
0.476145	2.774773
0.476673	2.774068
0.477201	2.773365
0.477729	2.772664
0.478259	2.771965
0.478789	2.771268
0.479319	2.770574
0.47985	2.769881
0.480382	2.769191
0.480914	2.768503
0.481447	2.767817
0.48198	2.767133
0.482514	2.766452
0.483049	2.765772
0.483584	2.765095
0.48412	2.764419
0.484656	2.763746
0.485193	2.763075
0.485731	2.762406
0.486269	2.761739
0.486808	2.761074
0.487347	2.760411
0.487887	2.75975
0.488428	2.759091
0.488969	2.758434
0.489511	2.757779
0.490053	2.757126
0.490596	2.756475
0.49114	2.755826
0.491684	2.75518
0.492228	2.754535
0.492774	2.753892
0.49332	2.753251
0.493866	2.752612
0.494414	2.751975
0.494961	2.75134
0.49551	2.750706
0.496059	2.750075
0.496608	2.749446
0.497159	2.748818
0.497709	2.748193
0.498261	2.747569
0.498813	2.746947
0.499366	2.746327
0.499919	2.745709
0.500473	2.745093
0.501027	2.744479
0.501582	2.743867
0.502138	2.743256
0.502694	2.742647
0.503251	2.74204
0.503809	2.741435
0.504367	2.740832
0.504926	2.740231
0.505486	2.739631
0.506046	2.739033
0.506606	2.738437
0.507168	2.737843
0.507729	2.73725
0.508292	2.73666
0.508855	2.736071
0.509419	2.735483
0.509983	2.734898
0.510548	2.734314
0.511114	2.733732
0.51168	2.733152
0.512247	2.732574
0.512815	2.731997
0.513383	2.731422
0.513952	2.730848
0.514521	2.730277
0.515091	2.729707
0.515662	2.729139
0.516233	2.728572
0.516805	2.728007
0.517378	2.727444
0.517951	2.726882
0.518525	2.726322
0.5191	2.725764
0.519675	2.725208
0.520251	2.724653
0.520827	2.724099
0.521404	2.723548
0.521982	2.722998
0.52256	2.722449
0.523139	2.721902
0.523719	2.721357
0.524299	2.720813
0.52488	2.720271
0.525461	2.719731
0.526044	2.719192
0.526626	2.718655
0.52721	2.718119
0.527794	2.717585
0.528379	2.717052
0.528964	2.716521
0.52955	2.715992
0.530137	2.715464
0.530724	2.714938
0.531312	2.714413
0.531901	2.713889
0.53249	2.713368
0.53308	2.712847
0.533671	2.712328
0.534262	2.711811
0.534854	2.711295
0.535447	2.710781
0.53604	2.710268
0.536634	2.709757
0.537229	2.709247
0.537824	2.708739
0.53842	2.708232
0.539016	2.707727
0.539613	2.707223
0.540211	2.70672
0.54081	2.706219
0.541409	2.705719
0.542009	2.705221
0.542609	2.704724
0.543211	2.704229
0.543812	2.703735
0.544415	2.703243
0.545018	2.702752
0.545622	2.702262
0.546227	2.701774
0.546832	2.701287
0.547438	2.700802
0.548044	2.700318
0.548651	2.699835
0.549259	2.699354
0.549868	2.698874
0.550477	2.698395
0.551087	2.697918
0.551698	2.697442
0.552309	2.696968
0.552921	2.696495
0.553533	2.696023
0.554147	2.695552
0.554761	2.695083
0.555375	2.694616
0.555991	2.694149
0.556607	2.693684
0.557223	2.69322
0.557841	2.692758
0.558459	2.692297
0.559078	2.691837
0.559697	2.691378
0.560317	2.690921
0.560938	2.690465
0.561559	2.690011
0.562182	2.689557
0.562805	2.689105
0.563428	2.688654
0.564052	2.688205
0.564677	2.687756
0.565303	2.687309
0.565929	2.686864
0.566556	2.686419
0.567184	2.685976
0.567812	2.685534
0.568442	2.685093
0.569071	2.684654
0.569702	2.684215
0.570333	2.683778
0.570965	2.683342
0.571598	2.682908
0.572231	2.682474
0.572865	2.682042
0.5735	2.681611
0.574135	2.681182
0.574771	2.680753
0.575408	2.680326
0.576046	2.679899
0.576684	2.679474
0.577323	2.679051
0.577962	2.678628
0.578603	2.678207
0.579244	2.677786
0.579886	2.677367
0.580528	2.676949
0.581171	2.676532
0.581815	2.676117
0.58246	2.675702
0.583105	2.675289
0.583751	2.674877
0.584398	2.674466
0.585045	2.674056
0.585694	2.673647
0.586343	2.67324
0.586992	2.672833
0.587643	2.672428
0.588294	2.672024
0.588946	2.67162
0.589598	2.671218
0.590251	2.670817
0.590905	2.670418
0.59156	2.670019
0.592215	2.669621
0.592872	2.669225
0.593528	2.668829
0.594186	2.668435
0.594844	2.668042
0.595503	2.66765
0.596163	2.667259
0.596824	2.666869
0.597485	2.66648
0.598147	2.666092
0.59881	2.665705
0.599473	2.665319
0.600137	2.664935
0.600802	2.664551
0.601468	2.664168
0.602134	2.663787
0.602802	2.663406
0.603469	2.663027
0.604138	2.662648
0.604807	2.662271
0.605478	2.661895
0.606148	2.661519
0.60682	2.661145
0.607492	2.660772
0.608165	2.6604
0.608839	2.660028
0.609514	2.659658
0.610189	2.659289
0.610865	2.658921
0.611542	2.658553
0.61222	2.658187
0.612898	2.657822
0.613577	2.657458
0.614257	2.657094
0.614937	2.656732
0.615619	2.656371
0.616301	2.65601
0.616984	2.655651
0.617667	2.655293
0.618352	2.654935
0.619037	2.654579
0.619723	2.654223
0.620409	2.653869
0.621097	2.653515
0.621785	2.653163
0.622474	2.652811
0.623163	2.65246
0.623854	2.65211
0.624545	2.651762
0.625237	2.651414
0.62593	2.651067
0.626623	2.650721
0.627317	2.650376
0.628012	2.650032
0.628708	2.649688
0.629405	2.649346
0.630102	2.649005
0.6308	2.648664
0.631499	2.648325
0.632199	2.647986
0.632899	2.647648
0.633601	2.647311
0.634303	2.646975
0.635005	2.64664
0.635709	2.646306
0.636413	2.645973
0.637118	2.645641
0.637824	2.645309
0.638531	2.644979
0.639238	2.644649
0.639947	2.64432
0.640656	2.643992
0.641366	2.643665
0.642076	2.643339
0.642788	2.643014
0.6435	2.642689
0.644213	2.642365
0.644927	2.642043
0.645641	2.641721
0.646356	2.6414
0.647073	2.64108
0.64779	2.64076
0.648507	2.640442
0.649226	2.640124
0.649945	2.639807
0.650665	2.639491
0.651386	2.639176
0.652108	2.638862
0.65283	2.638549
0.653554	2.638236
0.654278	2.637924
0.655003	2.637613
0.655728	2.637303
0.656455	2.636994
0.657182	2.636685
0.65791	2.636378
0.658639	2.636071
0.659369	2.635765
0.6601	2.635459
0.660831	2.635155
0.661563	2.634851
0.662296	2.634548
0.66303	2.634246
0.663765	2.633945
0.6645	2.633645
0.665236	2.633345
0.665973	2.633046
0.666711	2.632748
0.66745	2.632451
0.668189	2.632154
0.66893	2.631858
0.669671	2.631563
0.670413	2.631269
0.671156	2.630976
0.671899	2.630683
0.672644	2.630391
0.673389	2.6301
0.674135	2.62981
0.674882	2.62952
0.67563	2.629231
0.676378	2.628943
0.677128	2.628656
0.677878	2.628369
0.678629	2.628083
0.679381	2.627798
0.680134	2.627514
0.680887	2.62723
0.681642	2.626947
0.682397	2.626665
0.683153	2.626384
0.68391	2.626103
0.684668	2.625823
0.685426	2.625544
0.686186	2.625265
0.686946	2.624987
0.687707	2.62471
0.688469	2.624434
0.689232	2.624159
0.689995	2.623884
0.69076	2.623609
0.691525	2.623336
0.692291	2.623063
0.693058	2.622791
0.693826	2.62252
0.694595	2.622249
0.695365	2.621979
0.696135	2.62171
0.696906	2.621441
0.697678	2.621174
0.698451	2.620906
0.699225	2.62064
0.7	2.620374

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: —

Bi₄Ti₃O₁₂ (Bismuth titanate, BTO): all datasets

About Bi4Ti3O12 (Bismuth titanate, BTO)

Bi₄Ti₃O₁₂, commonly referred to as bismuth titanate (BTO), is a ferroelectric material that has attracted considerable attention for its diverse range of applications, from non-volatile memories to piezoelectric devices. In optics, BTO has been investigated as a nonlinear optical material and as a candidate for photonic applications where electric field-controlled refractive index changes are advantageous. One of its most notable properties is its high Curie temperature, which makes it stable over a wide temperature range. Additionally, the material has a high spontaneous polarization and a large electro-optic coefficient, making it suitable for modulators and switches. BTO can be synthesized using various methods such as sol-gel, chemical vapor deposition (CVD), and pulsed laser deposition (PLD). Its compatibility with silicon technology also makes it appealing for integrated optics applications. However, like many bismuth compounds, it requires careful handling and processing due to the toxicity of bismuth. Overall, BTO's unique ferroelectric and electro-optic properties make it a material of keen interest for researchers exploring new avenues in photonic and optoelectronic devices.

More about Bi4Ti3O12 (Bismuth titanate, BTO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Bi4Ti3O12/nk/Simon-a.yml
ID: ds_ebd362c012d9
API: /v1/datasets/ds_ebd362c012d9

Plot