Optical constants

Refractive index of LiB₃O₅ (Lithium triborate, LBO)

Chen et al. 1989: n(β) 0.289–1.06 µm

Data: formula 4
Range: 0.2894–1.064 µm
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: 1.60334
Extinction coefficient k: 0

Permittivity ε₁: 2.57071
Permittivity ε₂: 0

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

Abbe number V_d: 58.438
Chromatic dispersion dn/dλ: -0.0540604 µm⁻¹

Group index n_g: 1.63511
Group velocity dispersion: 88.4917 fs²/mm

Dispersion parameter D: -482.769 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

# LiB3O5 (Lithium triborate, LBO): Chen et al. 1989: n(β) 0.289–1.06 µm
lib3o5 = ls.fetch_refractiveindex("main", "LiB3O5", "Chen-β", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(lib3o5.range_nm)  # (289.4, 1064) nm
eps = lib3o5.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_bdaaf192f3cd/lightsmith"
lib3o5 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(lib3o5.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (lib3o5/chen-1989-2).

# ... load lib3o5 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=lib3o5)],
    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} = 2.525 + \frac{0.017123 λ^{0.0}}{λ^{2} - {- 0.0060517}^{1.0}} - 0.0087838 λ^{2.0}

Valid from 0.2894 to 1.064 µm.

Coefficients as stored

C_i	Value
C1	2.525
C2	0.017123
C3	0.0
C4	-0.0060517
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	1.0
C10	-0.0087838
C11	2.0

Comments and conditions

n_β; Room temperature.

Conditions

direction: beta

References

1) C Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, S. Lin. New nonlinear-optical crystal: LiB₃O₅. J Opt. Soc. Am. 6, 616-621 (1989)
2) F. Hanson and D. Dick. Blue parametric generation from temperature-tuned LiB₃O₅. Opt. Lett. 16, 205-207 (1991).
* Ref. 2 provides a dispersion formulas based on the experimental data from Ref. 1

doi:10.1364/josab.6.000616 New nonlinear-optical crystal: LiB_3O_5, Journal of the Optical Society of America B (1989)
doi:10.1364/ol.16.000205 Blue parametric generation from temperature-tuned LiB_3O_5, Optics Letters (1991)

Cite

Chuangtian Chen et al.. New nonlinear-optical crystal: LiB_3O_5. Journal of the Optical Society of America B, 6, 616 (1989), doi:10.1364/josab.6.000616; Frank Hanson and David Dick. Blue parametric generation from temperature-tuned LiB_3O_5. Optics Letters, 16, 205 (1991), doi:10.1364/ol.16.000205; 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

LiB3O5 (Lithium triborate, LBO), Chen et al. 1989: n(β) 0.289–1.06 µm: n and k versus wavelength
λ (µm)	n
0.2894	1.647706
0.290346	1.647353
0.291295	1.647003
0.292247	1.646654
0.293202	1.646307
0.29416	1.645962
0.295122	1.645618
0.296086	1.645277
0.297054	1.644937
0.298025	1.6446
0.298999	1.644264
0.299976	1.64393
0.300957	1.643597
0.301941	1.643267
0.302927	1.642938
0.303918	1.642611
0.304911	1.642286
0.305907	1.641963
0.306907	1.641641
0.30791	1.641322
0.308917	1.641003
0.309926	1.640687
0.310939	1.640373
0.311956	1.64006
0.312975	1.639749
0.313998	1.639439
0.315025	1.639131
0.316054	1.638825
0.317087	1.638521
0.318124	1.638218
0.319163	1.637917
0.320207	1.637618
0.321253	1.63732
0.322303	1.637024
0.323357	1.63673
0.324413	1.636437
0.325474	1.636146
0.326538	1.635857
0.327605	1.635569
0.328676	1.635282
0.32975	1.634998
0.330828	1.634715
0.331909	1.634433
0.332994	1.634153
0.334082	1.633875
0.335174	1.633598
0.336269	1.633322
0.337369	1.633049
0.338471	1.632776
0.339578	1.632506
0.340687	1.632236
0.341801	1.631969
0.342918	1.631702
0.344039	1.631438
0.345163	1.631174
0.346291	1.630913
0.347423	1.630652
0.348559	1.630394
0.349698	1.630136
0.350841	1.62988
0.351988	1.629626
0.353138	1.629373
0.354292	1.629121
0.35545	1.628871
0.356612	1.628622
0.357778	1.628375
0.358947	1.628129
0.36012	1.627885
0.361297	1.627641
0.362478	1.6274
0.363663	1.627159
0.364852	1.62692
0.366044	1.626682
0.36724	1.626446
0.368441	1.626211
0.369645	1.625977
0.370853	1.625745
0.372065	1.625514
0.373281	1.625284
0.374501	1.625056
0.375725	1.624829
0.376953	1.624603
0.378186	1.624378
0.379422	1.624155
0.380662	1.623933
0.381906	1.623712
0.383154	1.623493
0.384406	1.623275
0.385663	1.623058
0.386923	1.622842
0.388188	1.622627
0.389457	1.622414
0.39073	1.622202
0.392007	1.621991
0.393288	1.621782
0.394573	1.621573
0.395863	1.621366
0.397157	1.62116
0.398455	1.620955
0.399757	1.620752
0.401064	1.620549
0.402375	1.620348
0.40369	1.620147
0.405009	1.619948
0.406333	1.61975
0.407661	1.619554
0.408994	1.619358
0.41033	1.619164
0.411671	1.61897
0.413017	1.618778
0.414367	1.618587
0.415721	1.618397
0.41708	1.618208
0.418443	1.61802
0.419811	1.617833
0.421183	1.617647
0.42256	1.617462
0.423941	1.617279
0.425326	1.617096
0.426717	1.616915
0.428111	1.616734
0.42951	1.616555
0.430914	1.616376
0.432323	1.616199
0.433736	1.616023
0.435153	1.615847
0.436576	1.615673
0.438003	1.6155
0.439434	1.615327
0.44087	1.615156
0.442311	1.614986
0.443757	1.614816
0.445207	1.614648
0.446663	1.61448
0.448122	1.614314
0.449587	1.614148
0.451057	1.613984
0.452531	1.61382
0.45401	1.613658
0.455494	1.613496
0.456983	1.613335
0.458476	1.613175
0.459975	1.613016
0.461478	1.612858
0.462986	1.612701
0.4645	1.612545
0.466018	1.61239
0.467541	1.612235
0.469069	1.612082
0.470602	1.611929
0.47214	1.611777
0.473684	1.611626
0.475232	1.611476
0.476785	1.611327
0.478343	1.611179
0.479907	1.611031
0.481475	1.610884
0.483049	1.610739
0.484628	1.610594
0.486212	1.610449
0.487801	1.610306
0.489395	1.610164
0.490995	1.610022
0.4926	1.609881
0.49421	1.609741
0.495825	1.609602
0.497446	1.609463
0.499071	1.609326
0.500703	1.609189
0.502339	1.609052
0.503981	1.608917
0.505628	1.608783
0.507281	1.608649
0.508939	1.608516
0.510602	1.608383
0.512271	1.608252
0.513945	1.608121
0.515625	1.607991
0.517311	1.607862
0.519001	1.607733
0.520698	1.607605
0.5224	1.607478
0.524107	1.607352
0.52582	1.607226
0.527539	1.607101
0.529263	1.606977
0.530993	1.606853
0.532728	1.60673
0.534469	1.606608
0.536216	1.606487
0.537969	1.606366
0.539727	1.606246
0.541491	1.606126
0.543261	1.606007
0.545037	1.605889
0.546818	1.605772
0.548605	1.605655
0.550398	1.605539
0.552197	1.605423
0.554002	1.605308
0.555813	1.605194
0.55763	1.605081
0.559452	1.604968
0.561281	1.604855
0.563115	1.604744
0.564956	1.604633
0.566802	1.604522
0.568655	1.604412
0.570513	1.604303
0.572378	1.604194
0.574249	1.604086
0.576126	1.603979
0.578009	1.603872
0.579898	1.603766
0.581793	1.60366
0.583695	1.603555
0.585603	1.60345
0.587517	1.603346
0.589437	1.603243
0.591363	1.60314
0.593296	1.603038
0.595235	1.602936
0.597181	1.602835
0.599133	1.602734
0.601091	1.602634
0.603056	1.602535
0.605027	1.602436
0.607004	1.602337
0.608988	1.602239
0.610979	1.602142
0.612976	1.602045
0.614979	1.601949
0.616989	1.601853
0.619006	1.601758
0.621029	1.601663
0.623059	1.601568
0.625095	1.601475
0.627138	1.601381
0.629188	1.601288
0.631244	1.601196
0.633308	1.601104
0.635377	1.601013
0.637454	1.600922
0.639538	1.600832
0.641628	1.600742
0.643725	1.600652
0.645829	1.600563
0.64794	1.600475
0.650058	1.600386
0.652182	1.600299
0.654314	1.600212
0.656453	1.600125
0.658598	1.600039
0.660751	1.599953
0.66291	1.599867
0.665077	1.599782
0.667251	1.599698
0.669432	1.599614
0.67162	1.59953
0.673815	1.599447
0.676017	1.599364
0.678227	1.599281
0.680443	1.599199
0.682667	1.599118
0.684899	1.599036
0.687137	1.598956
0.689383	1.598875
0.691636	1.598795
0.693897	1.598716
0.696165	1.598636
0.69844	1.598558
0.700723	1.598479
0.703013	1.598401
0.705311	1.598323
0.707616	1.598246
0.709929	1.598169
0.712249	1.598092
0.714577	1.598016
0.716913	1.59794
0.719256	1.597865
0.721607	1.59779
0.723965	1.597715
0.726332	1.59764
0.728706	1.597566
0.731087	1.597493
0.733477	1.597419
0.735874	1.597346
0.738279	1.597273
0.740692	1.597201
0.743113	1.597129
0.745542	1.597057
0.747979	1.596986
0.750424	1.596915
0.752876	1.596844
0.755337	1.596774
0.757806	1.596703
0.760283	1.596634
0.762768	1.596564
0.765261	1.596495
0.767762	1.596426
0.770271	1.596357
0.772789	1.596289
0.775315	1.596221
0.777849	1.596153
0.780391	1.596086
0.782942	1.596019
0.785501	1.595952
0.788068	1.595885
0.790644	1.595819
0.793228	1.595753
0.795821	1.595687
0.798422	1.595622
0.801031	1.595556
0.803649	1.595491
0.806276	1.595427
0.808911	1.595362
0.811555	1.595298
0.814208	1.595234
0.816869	1.595171
0.819539	1.595107
0.822218	1.595044
0.824905	1.594981
0.827601	1.594918
0.830306	1.594856
0.83302	1.594794
0.835742	1.594732
0.838474	1.59467
0.841215	1.594609
0.843964	1.594547
0.846722	1.594486
0.84949	1.594425
0.852266	1.594365
0.855052	1.594304
0.857847	1.594244
0.860651	1.594184
0.863464	1.594124
0.866286	1.594065
0.869117	1.594005
0.871958	1.593946
0.874808	1.593887
0.877667	1.593829
0.880536	1.59377
0.883414	1.593712
0.886301	1.593653
0.889198	1.593596
0.892104	1.593538
0.89502	1.59348
0.897945	1.593423
0.90088	1.593365
0.903824	1.593308
0.906779	1.593251
0.909742	1.593195
0.912716	1.593138
0.915699	1.593082
0.918692	1.593025
0.921695	1.592969
0.924707	1.592913
0.927729	1.592858
0.930762	1.592802
0.933804	1.592747
0.936856	1.592691
0.939918	1.592636
0.94299	1.592581
0.946072	1.592526
0.949164	1.592472
0.952267	1.592417
0.955379	1.592363
0.958502	1.592308
0.961634	1.592254
0.964777	1.5922
0.967931	1.592146
0.971094	1.592092
0.974268	1.592039
0.977453	1.591985
0.980647	1.591932
0.983853	1.591879
0.987068	1.591825
0.990294	1.591772
0.993531	1.591719
0.996778	1.591666
1.00004	1.591614
1.0033	1.591561
1.00658	1.591509
1.00987	1.591456
1.01317	1.591404
1.01649	1.591352
1.01981	1.591299
1.02314	1.591247
1.02649	1.591195
1.02984	1.591143
1.03321	1.591092
1.03658	1.59104
1.03997	1.590988
1.04337	1.590937
1.04678	1.590885
1.0502	1.590834
1.05363	1.590783
1.05708	1.590731
1.06053	1.59068
1.064	1.590629

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: —

LiB₃O₅ (Lithium triborate, LBO): all datasets

About LiB3O5 (Lithium triborate, LBO)

Lithium triborate (LiB₃O₅, commonly abbreviated as LBO) is a nonlinear optical crystal that is highly useful for frequency conversion processes, including second and third harmonic generation, sum and difference frequency generation, and optical parametric oscillation. LBO crystals offer wide transparency ranges, broad phase-matching capabilities, and high damage thresholds, making them ideal for high-power laser applications. It is also appreciated for its good mechanical and thermal stability. Overall, LBO is a versatile and widely-used material in various optical and laser-based technologies.

More about LiB3O5 (Lithium triborate, LBO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/LiB3O5/nk/Chen-beta.yml
ID: ds_bdaaf192f3cd
API: /v1/datasets/ds_bdaaf192f3cd

Plot