Optical constants

Refractive index of KNbO₃ (Potassium niobate)

Umemura et al. 1999: n(β) 0.40–5.3 µm

Data: formula 4
Range: 0.4–5.3 µm
Temperature: 295 K
Optical axis: beta
Licence: CC0-1.0

Biaxial crystal, axes: beta

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 2.29575
Extinction coefficient k: 0

Permittivity ε₁: 5.27047
Permittivity ε₂: 0

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

Abbe number V_d: 15.963
Chromatic dispersion dn/dλ: -0.400242 µm⁻¹

Group index n_g: 2.53093
Group velocity dispersion: 882.642 fs²/mm

Dispersion parameter D: -4815.28 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

# KNbO3 (Potassium niobate): Umemura et al. 1999: n(β) 0.40–5.3 µm
knbo3 = ls.fetch_refractiveindex("main", "KNbO3", "Umemura-β", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(knbo3.range_nm)  # (400, 5300) nm
eps = knbo3.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_683d75734437/lightsmith"
knbo3 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(knbo3.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (knbo3/umemura-1999-2).

# ... load knbo3 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=knbo3)],
    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"]).

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} = 4.8353 + \frac{0.12808 λ^{0.0}}{λ^{2} - {0.05674}^{1.0}} - 0.02528 λ^{2.0} + 1.859 \times 10^{-6} λ^{4.0} - 1.0689 \times 10^{-6} λ^{6.0}

Valid from 0.4 to 5.3 µm.

Coefficients as stored

C_i	Value
C1	4.8353
C2	0.12808
C3	0.0
C4	0.05674
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	1.0
C10	-0.02528
C11	2.0
C12	1.859e-06
C13	4.0
C14	-1.0689e-06
C15	6.0

Comments and conditions

n_β; 22 °C.

Conditions

temperature: 295 K
direction: beta

References

N. Umemura, K. Yoshida, and K. Kato. Phase-matching properties of KNbO₃ in the mid-infrared, Appl Opt. 38, 991-994 (1999)

doi:10.1364/ao.38.000991 Phase-matching properties of KNbO_3 in the mid-infrared, Applied Optics (1999)

Cite

Nobuhiro Umemura, Kunio Yoshida and Kiyoshi Kato. Phase-matching properties of KNbO_3 in the mid-infrared. Applied Optics, 38, 991 (1999), doi:10.1364/ao.38.000991; 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

KNbO3 (Potassium niobate), Umemura et al. 1999: n(β) 0.40–5.3 µm: n and k versus wavelength
λ (µm)	n
0.4	2.464066
0.402599	2.459066
0.405215	2.45419
0.407847	2.449431
0.410497	2.444787
0.413164	2.440254
0.415849	2.435828
0.418551	2.431506
0.42127	2.427284
0.424007	2.423159
0.426762	2.419129
0.429535	2.415189
0.432325	2.411339
0.435134	2.407574
0.437962	2.403892
0.440807	2.400291
0.443671	2.396769
0.446554	2.393323
0.449455	2.38995
0.452375	2.38665
0.455314	2.383419
0.458273	2.380256
0.46125	2.377159
0.464247	2.374126
0.467263	2.371156
0.470299	2.368246
0.473355	2.365395
0.47643	2.362601
0.479526	2.359864
0.482641	2.357181
0.485777	2.354551
0.488933	2.351972
0.49211	2.349444
0.495307	2.346965
0.498526	2.344534
0.501765	2.342149
0.505025	2.33981
0.508306	2.337515
0.511608	2.335263
0.514932	2.333054
0.518278	2.330885
0.521645	2.328757
0.525035	2.326667
0.528446	2.324617
0.531879	2.322603
0.535335	2.320626
0.538813	2.318684
0.542314	2.316777
0.545838	2.314905
0.549384	2.313065
0.552953	2.311258
0.556546	2.309482
0.560162	2.307738
0.563802	2.306023
0.567465	2.304339
0.571152	2.302683
0.574862	2.301056
0.578597	2.299456
0.582357	2.297884
0.58614	2.296337
0.589949	2.294817
0.593782	2.293323
0.59764	2.291853
0.601523	2.290407
0.605431	2.288985
0.609364	2.287587
0.613324	2.286211
0.617308	2.284857
0.621319	2.283526
0.625356	2.282216
0.629419	2.280926
0.633509	2.279658
0.637625	2.278409
0.641767	2.27718
0.645937	2.275971
0.650134	2.27478
0.654358	2.273608
0.658609	2.272454
0.662889	2.271317
0.667196	2.270199
0.67153	2.269097
0.675893	2.268012
0.680285	2.266943
0.684705	2.265891
0.689153	2.264854
0.693631	2.263833
0.698138	2.262827
0.702674	2.261836
0.707239	2.260859
0.711834	2.259897
0.716459	2.258948
0.721114	2.258014
0.725799	2.257093
0.730515	2.256185
0.735261	2.25529
0.740038	2.254408
0.744847	2.253538
0.749686	2.252681
0.754557	2.251835
0.759459	2.251002
0.764394	2.25018
0.76936	2.249369
0.774359	2.248569
0.77939	2.24778
0.784454	2.247002
0.789551	2.246235
0.79468	2.245478
0.799844	2.244731
0.80504	2.243993
0.810271	2.243266
0.815535	2.242548
0.820834	2.241839
0.826167	2.24114
0.831535	2.240449
0.836938	2.239768
0.842375	2.239095
0.847848	2.238431
0.853357	2.237774
0.858902	2.237127
0.864482	2.236487
0.870099	2.235855
0.875752	2.235231
0.881442	2.234614
0.887169	2.234005
0.892933	2.233403
0.898734	2.232808
0.904574	2.23222
0.910451	2.231639
0.916366	2.231065
0.92232	2.230497
0.928313	2.229936
0.934344	2.229382
0.940415	2.228833
0.946525	2.228291
0.952674	2.227754
0.958864	2.227224
0.965094	2.226699
0.971365	2.22618
0.977676	2.225666
0.984028	2.225158
0.990421	2.224655
0.996856	2.224157
1.00333	2.223664
1.00985	2.223176
1.01641	2.222693
1.02302	2.222215
1.02966	2.221742
1.03635	2.221273
1.04309	2.220808
1.04986	2.220348
1.05669	2.219892
1.06355	2.219441
1.07046	2.218993
1.07742	2.218549
1.08442	2.218109
1.09146	2.217673
1.09855	2.217241
1.10569	2.216813
1.11287	2.216387
1.12011	2.215966
1.12738	2.215548
1.13471	2.215132
1.14208	2.214721
1.1495	2.214312
1.15697	2.213906
1.16449	2.213503
1.17205	2.213104
1.17967	2.212706
1.18733	2.212312
1.19505	2.21192
1.20281	2.211531
1.21063	2.211144
1.21849	2.21076
1.22641	2.210378
1.23438	2.209998
1.2424	2.209621
1.25047	2.209245
1.25859	2.208872
1.26677	2.2085
1.275	2.208131
1.28328	2.207763
1.29162	2.207397
1.30001	2.207033
1.30846	2.20667
1.31696	2.206309
1.32552	2.205949
1.33413	2.205591
1.3428	2.205234
1.35152	2.204879
1.3603	2.204524
1.36914	2.204171
1.37804	2.203819
1.38699	2.203467
1.396	2.203117
1.40507	2.202768
1.4142	2.202419
1.42339	2.202071
1.43264	2.201724
1.44195	2.201378
1.45131	2.201032
1.46074	2.200687
1.47024	2.200342
1.47979	2.199997
1.4894	2.199653
1.49908	2.199308
1.50882	2.198965
1.51862	2.198621
1.52849	2.198277
1.53842	2.197933
1.54841	2.19759
1.55848	2.197246
1.5686	2.196902
1.57879	2.196557
1.58905	2.196213
1.59937	2.195868
1.60977	2.195522
1.62023	2.195176
1.63075	2.19483
1.64135	2.194482
1.65201	2.194135
1.66274	2.193786
1.67355	2.193437
1.68442	2.193086
1.69537	2.192735
1.70638	2.192383
1.71747	2.19203
1.72863	2.191675
1.73986	2.19132
1.75116	2.190963
1.76254	2.190605
1.77399	2.190245
1.78552	2.189884
1.79712	2.189522
1.80879	2.189158
1.82055	2.188792
1.83237	2.188425
1.84428	2.188056
1.85626	2.187685
1.86832	2.187312
1.88046	2.186937
1.89268	2.18656
1.90498	2.186181
1.91735	2.1858
1.92981	2.185417
1.94235	2.185031
1.95497	2.184643
1.96767	2.184253
1.98046	2.18386
1.99332	2.183465
2.00627	2.183067
2.01931	2.182666
2.03243	2.182262
2.04563	2.181856
2.05892	2.181447
2.0723	2.181034
2.08577	2.180619
2.09932	2.1802
2.11296	2.179779
2.12669	2.179353
2.1405	2.178925
2.15441	2.178493
2.16841	2.178058
2.1825	2.177619
2.19668	2.177176
2.21095	2.17673
2.22531	2.17628
2.23977	2.175825
2.25432	2.175367
2.26897	2.174905
2.28371	2.174439
2.29855	2.173968
2.31349	2.173493
2.32852	2.173014
2.34365	2.17253
2.35887	2.172041
2.3742	2.171548
2.38962	2.17105
2.40515	2.170548
2.42078	2.17004
2.43651	2.169527
2.45234	2.169009
2.46827	2.168486
2.48431	2.167958
2.50045	2.167424
2.51669	2.166885
2.53304	2.16634
2.5495	2.16579
2.56607	2.165233
2.58274	2.164671
2.59952	2.164103
2.61641	2.163528
2.63341	2.162947
2.65052	2.16236
2.66774	2.161767
2.68507	2.161167
2.70252	2.16056
2.72008	2.159947
2.73775	2.159327
2.75554	2.1587
2.77344	2.158065
2.79146	2.157424
2.8096	2.156775
2.82785	2.156118
2.84622	2.155454
2.86472	2.154782
2.88333	2.154103
2.90206	2.153415
2.92092	2.152719
2.9399	2.152016
2.959	2.151303
2.97822	2.150582
2.99757	2.149853
3.01705	2.149115
3.03665	2.148367
3.05638	2.147611
3.07624	2.146846
3.09622	2.146071
3.11634	2.145286
3.13659	2.144492
3.15697	2.143688
3.17748	2.142874
3.19812	2.14205
3.2189	2.141216
3.23982	2.140371
3.26087	2.139515
3.28205	2.138649
3.30338	2.137772
3.32484	2.136883
3.34644	2.135983
3.36818	2.135072
3.39007	2.134149
3.41209	2.133214
3.43426	2.132267
3.45658	2.131307
3.47903	2.130335
3.50164	2.12935
3.52439	2.128353
3.54729	2.127342
3.57034	2.126318
3.59353	2.125281
3.61688	2.124229
3.64038	2.123164
3.66403	2.122084
3.68784	2.12099
3.7118	2.119882
3.73592	2.118758
3.76019	2.117619
3.78462	2.116465
3.80921	2.115295
3.83396	2.114109
3.85887	2.112907
3.88394	2.111688
3.90917	2.110453
3.93457	2.109201
3.96014	2.107931
3.98587	2.106644
4.01176	2.105338
4.03783	2.104015
4.06406	2.102673
4.09047	2.101312
4.11704	2.099932
4.14379	2.098532
4.17072	2.097113
4.19782	2.095673
4.22509	2.094213
4.25254	2.092731
4.28017	2.091229
4.30798	2.089705
4.33597	2.088159
4.36414	2.08659
4.3925	2.084999
4.42103	2.083384
4.44976	2.081746
4.47867	2.080083
4.50777	2.078396
4.53706	2.076684
4.56653	2.074947
4.5962	2.073183
4.62607	2.071394
4.65612	2.069577
4.68637	2.067733
4.71682	2.065861
4.74747	2.06396
4.77831	2.06203
4.80936	2.060071
4.84061	2.058082
4.87206	2.056062
4.90371	2.05401
4.93557	2.051927
4.96764	2.049811
4.99992	2.047662
5.0324	2.045478
5.0651	2.043261
5.09801	2.041007
5.13113	2.038718
5.16447	2.036392
5.19802	2.034028
5.2318	2.031626
5.26579	2.029185
5.3	2.026704

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: —

KNbO₃ (Potassium niobate): all datasets

About KNbO3 (Potassium niobate)

Potassium niobate (KNbO₃) is a ferroelectric crystal with notable nonlinear optical properties. It is widely used in a range of optical applications, including frequency doubling, optical parametric oscillation, and electro-optic modulation. Due to its high damage threshold and broad phase-matching capabilities, it has become a material of choice for nonlinear optical applications in the visible and near-infrared spectral ranges. KNbO₃ is also known for its photorefractive properties, which are exploited in data storage and holography. However, the material is sensitive to moisture and can degrade over time if not properly stored, requiring a controlled environment for long-term use.

More about KNbO3 (Potassium niobate) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/KNbO3/nk/Umemura-beta.yml
ID: ds_683d75734437
API: /v1/datasets/ds_683d75734437

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