Optical constants

Refractive index of PbTiO₃ (Lead titanate)

Singh et al. 1972: n(e) 0.45–1.15 µm

Data: formula 2
Range: 0.45–1.15 µm
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: 2.686
Extinction coefficient k: 0

Permittivity ε₁: 7.21462
Permittivity ε₂: 0

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

Abbe number V_d: 13.499
Chromatic dispersion dn/dλ: -0.622716 µm⁻¹

Group index n_g: 3.05191
Group velocity dispersion: 1331.22 fs²/mm

Dispersion parameter D: -7262.5 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

# PbTiO3 (Lead titanate): Singh et al. 1972: n(e) 0.45–1.15 µm
pbtio3 = ls.fetch_refractiveindex("main", "PbTiO3", "Singh-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(pbtio3.range_nm)  # (450, 1150) nm
eps = pbtio3.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_c7d4ad6b8be1/lightsmith"
pbtio3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(pbtio3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (pbtio3/singh-1972-e).

# ... load pbtio3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=pbtio3)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=450, 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_c7d4ad6b8be1/lightsmith?model=drude_lorentz"
pbtio3_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{5.366 λ^{2}}{λ^{2} - 0.047148}

Valid from 0.45 to 1.15 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	5.366
C3	0.047148

Comments and conditions

Extraordinary ray (e)

Conditions

direction: e

References

S. Singh, J. P. Remeika, J. R. Potopowicz. Nonlinear optical properties of ferroelectric lead titanate. Appl. Phys. Lett. 20, 135, 1972

doi:10.1063/1.1654078 Nonlinear Optical Properties of Ferroelectric Lead Titanate, Applied Physics Letters (1972)

Cite

S. Singh, J. P. Remeika and J. R. Potopowicz. Nonlinear Optical Properties of Ferroelectric Lead Titanate. Applied Physics Letters, 20, 135-137 (1972), doi:10.1063/1.1654078; 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

PbTiO3 (Lead titanate), Singh et al. 1972: n(e) 0.45–1.15 µm: n and k versus wavelength
λ (µm)	n
0.45	2.827461
0.451059	2.825701
0.452121	2.823954
0.453186	2.822219
0.454253	2.820496
0.455322	2.818784
0.456394	2.817084
0.457469	2.815396
0.458546	2.81372
0.459625	2.812054
0.460707	2.8104
0.461792	2.808758
0.462879	2.807126
0.463969	2.805506
0.465061	2.803896
0.466156	2.802297
0.467254	2.800709
0.468354	2.799132
0.469456	2.797565
0.470562	2.796008
0.47167	2.794462
0.47278	2.792927
0.473893	2.791401
0.475009	2.789886
0.476127	2.78838
0.477248	2.786885
0.478372	2.785399
0.479498	2.783924
0.480627	2.782458
0.481758	2.781001
0.482893	2.779554
0.484029	2.778117
0.485169	2.776689
0.486311	2.77527
0.487456	2.773861
0.488604	2.772461
0.489754	2.771069
0.490907	2.769687
0.492063	2.768314
0.493221	2.76695
0.494383	2.765594
0.495547	2.764248
0.496713	2.762909
0.497883	2.76158
0.499055	2.760259
0.50023	2.758946
0.501407	2.757642
0.502588	2.756346
0.503771	2.755059
0.504957	2.753779
0.506146	2.752508
0.507338	2.751245
0.508532	2.74999
0.509729	2.748742
0.510929	2.747503
0.512132	2.746271
0.513338	2.745048
0.514547	2.743832
0.515758	2.742623
0.516972	2.741422
0.518189	2.740229
0.519409	2.739043
0.520632	2.737864
0.521858	2.736693
0.523087	2.735529
0.524318	2.734373
0.525552	2.733223
0.52679	2.732081
0.52803	2.730946
0.529273	2.729818
0.530519	2.728696
0.531768	2.727582
0.53302	2.726474
0.534275	2.725374
0.535533	2.72428
0.536794	2.723193
0.538058	2.722112
0.539324	2.721038
0.540594	2.719971
0.541867	2.71891
0.543143	2.717856
0.544421	2.716808
0.545703	2.715766
0.546988	2.714731
0.548276	2.713702
0.549566	2.712679
0.55086	2.711662
0.552157	2.710652
0.553457	2.709648
0.55476	2.708649
0.556066	2.707657
0.557375	2.706671
0.558688	2.70569
0.560003	2.704716
0.561321	2.703747
0.562643	2.702784
0.563968	2.701827
0.565295	2.700876
0.566626	2.69993
0.56796	2.69899
0.569297	2.698056
0.570638	2.697127
0.571981	2.696203
0.573328	2.695285
0.574678	2.694373
0.576031	2.693465
0.577387	2.692564
0.578746	2.691667
0.580109	2.690776
0.581474	2.68989
0.582843	2.689009
0.584216	2.688134
0.585591	2.687263
0.58697	2.686398
0.588352	2.685538
0.589737	2.684683
0.591125	2.683833
0.592517	2.682987
0.593912	2.682147
0.59531	2.681312
0.596712	2.680481
0.598116	2.679655
0.599525	2.678834
0.600936	2.678018
0.602351	2.677207
0.603769	2.6764
0.60519	2.675598
0.606615	2.6748
0.608043	2.674008
0.609475	2.673219
0.61091	2.672436
0.612348	2.671656
0.61379	2.670882
0.615235	2.670111
0.616683	2.669345
0.618135	2.668584
0.619591	2.667827
0.621049	2.667074
0.622511	2.666326
0.623977	2.665581
0.625446	2.664841
0.626919	2.664106
0.628394	2.663374
0.629874	2.662647
0.631357	2.661923
0.632843	2.661204
0.634333	2.660489
0.635827	2.659778
0.637324	2.659071
0.638824	2.658368
0.640328	2.657669
0.641836	2.656974
0.643347	2.656283
0.644861	2.655596
0.646379	2.654912
0.647901	2.654233
0.649427	2.653557
0.650956	2.652885
0.652488	2.652217
0.654024	2.651552
0.655564	2.650892
0.657107	2.650235
0.658655	2.649581
0.660205	2.648932
0.66176	2.648286
0.663318	2.647643
0.664879	2.647004
0.666445	2.646369
0.668014	2.645737
0.669586	2.645109
0.671163	2.644484
0.672743	2.643863
0.674327	2.643245
0.675914	2.642631
0.677506	2.64202
0.679101	2.641412
0.680699	2.640808
0.682302	2.640207
0.683908	2.639609
0.685519	2.639015
0.687132	2.638424
0.68875	2.637836
0.690372	2.637252
0.691997	2.63667
0.693626	2.636092
0.695259	2.635517
0.696896	2.634945
0.698537	2.634377
0.700181	2.633811
0.70183	2.633249
0.703482	2.632689
0.705138	2.632133
0.706799	2.63158
0.708463	2.631029
0.710131	2.630482
0.711802	2.629938
0.713478	2.629396
0.715158	2.628858
0.716842	2.628323
0.718529	2.62779
0.720221	2.62726
0.721917	2.626734
0.723616	2.62621
0.72532	2.625689
0.727028	2.62517
0.728739	2.624655
0.730455	2.624142
0.732175	2.623632
0.733898	2.623125
0.735626	2.622621
0.737358	2.622119
0.739094	2.62162
0.740834	2.621124
0.742578	2.62063
0.744327	2.620139
0.746079	2.619651
0.747835	2.619165
0.749596	2.618682
0.751361	2.618202
0.75313	2.617724
0.754903	2.617248
0.75668	2.616776
0.758462	2.616305
0.760247	2.615838
0.762037	2.615372
0.763831	2.61491
0.76563	2.614449
0.767432	2.613991
0.769239	2.613536
0.77105	2.613083
0.772865	2.612633
0.774685	2.612184
0.776509	2.611739
0.778337	2.611295
0.780169	2.610854
0.782006	2.610415
0.783847	2.609979
0.785693	2.609545
0.787542	2.609113
0.789397	2.608684
0.791255	2.608256
0.793118	2.607831
0.794985	2.607409
0.796857	2.606988
0.798733	2.60657
0.800613	2.606154
0.802498	2.60574
0.804388	2.605329
0.806281	2.604919
0.80818	2.604512
0.810082	2.604107
0.811989	2.603703
0.813901	2.603303
0.815817	2.602904
0.817738	2.602507
0.819663	2.602112
0.821593	2.60172
0.823527	2.601329
0.825466	2.600941
0.82741	2.600554
0.829358	2.60017
0.83131	2.599787
0.833267	2.599407
0.835229	2.599029
0.837195	2.598652
0.839166	2.598278
0.841142	2.597905
0.843122	2.597535
0.845107	2.597166
0.847097	2.596799
0.849091	2.596434
0.85109	2.596072
0.853094	2.595711
0.855103	2.595351
0.857116	2.594994
0.859134	2.594639
0.861156	2.594285
0.863184	2.593933
0.865216	2.593584
0.867253	2.593235
0.869295	2.592889
0.871341	2.592545
0.873393	2.592202
0.875449	2.591861
0.87751	2.591522
0.879576	2.591184
0.881647	2.590849
0.883723	2.590515
0.885803	2.590183
0.887889	2.589852
0.889979	2.589523
0.892074	2.589196
0.894175	2.588871
0.89628	2.588547
0.89839	2.588225
0.900505	2.587905
0.902625	2.587586
0.90475	2.587269
0.90688	2.586953
0.909015	2.586639
0.911155	2.586327
0.913301	2.586017
0.915451	2.585707
0.917606	2.5854
0.919766	2.585094
0.921932	2.58479
0.924102	2.584487
0.926278	2.584186
0.928459	2.583886
0.930645	2.583588
0.932836	2.583291
0.935032	2.582996
0.937233	2.582703
0.93944	2.582411
0.941651	2.58212
0.943868	2.581831
0.946091	2.581543
0.948318	2.581257
0.950551	2.580972
0.952789	2.580689
0.955032	2.580407
0.95728	2.580127
0.959534	2.579848
0.961793	2.579571
0.964057	2.579294
0.966327	2.57902
0.968602	2.578746
0.970882	2.578474
0.973168	2.578204
0.975459	2.577935
0.977756	2.577667
0.980058	2.577401
0.982365	2.577135
0.984678	2.576872
0.986996	2.576609
0.98932	2.576348
0.991649	2.576088
0.993984	2.57583
0.996324	2.575573
0.99867	2.575317
1.00102	2.575062
1.00338	2.574809
1.00574	2.574557
1.00811	2.574307
1.01048	2.574057
1.01286	2.573809
1.01524	2.573562
1.01763	2.573316
1.02003	2.573072
1.02243	2.572829
1.02484	2.572587
1.02725	2.572346
1.02967	2.572106
1.03209	2.571868
1.03452	2.571631
1.03696	2.571395
1.0394	2.57116
1.04185	2.570927
1.0443	2.570694
1.04676	2.570463
1.04922	2.570233
1.05169	2.570004
1.05417	2.569776
1.05665	2.56955
1.05914	2.569324
1.06163	2.5691
1.06413	2.568876
1.06664	2.568654
1.06915	2.568433
1.07167	2.568213
1.07419	2.567995
1.07672	2.567777
1.07925	2.56756
1.08179	2.567345
1.08434	2.56713
1.08689	2.566917
1.08945	2.566705
1.09202	2.566493
1.09459	2.566283
1.09717	2.566074
1.09975	2.565866
1.10234	2.565659
1.10493	2.565453
1.10754	2.565248
1.11014	2.565044
1.11276	2.564841
1.11538	2.564639
1.118	2.564438
1.12063	2.564238
1.12327	2.564039
1.12592	2.563841
1.12857	2.563644
1.13122	2.563448
1.13389	2.563253
1.13656	2.563059
1.13923	2.562866
1.14192	2.562674
1.1446	2.562483
1.1473	2.562293
1.15	2.562103

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: —

PbTiO₃ (Lead titanate): all datasets

About PbTiO3 (Lead titanate)

Lead titanate (PbTiO₃) is a ferroelectric material known for its exceptional piezoelectric and dielectric properties. Due to these unique characteristics, it is widely used in the fabrication of capacitors, sensors, actuators, and various other electronic components. PbTiO₃ forms the base material for lead zirconate titanate (PZT), one of the most well-researched piezoelectric materials. PZT is a solid solution of PbTiO₃ and PbZrO₃, exhibiting enhanced piezoelectric properties. In the realm of optics, PbTiO₃ thin films have been explored for non-linear optical applications and as an electro-optic modulator material. However, environmental concerns associated with lead have prompted research into lead-free alternatives for many of its applications.

More about PbTiO3 (Lead titanate) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/PbTiO3/nk/Singh-e.yml
ID: ds_c7d4ad6b8be1
API: /v1/datasets/ds_c7d4ad6b8be1

Plot