Optical constants

Refractive index of BaB₂O₄ (Barium borate, BBO)

Eimerl et al. 1987: n(e) 0.22–1.06 µm

Data: formula 4
Range: 0.22–1.06 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: 1.55252
Extinction coefficient k: 0

Permittivity ε₁: 2.41031
Permittivity ε₂: 0

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

Abbe number V_d: 61.321
Chromatic dispersion dn/dλ: -0.0462399 µm⁻¹

Group index n_g: 1.57969
Group velocity dispersion: 85.4073 fs²/mm

Dispersion parameter D: -465.942 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

# BaB2O4 (Barium borate, BBO): Eimerl et al. 1987: n(e) 0.22–1.06 µm
bab2o4 = ls.fetch_refractiveindex("main", "BaB2O4", "Eimerl-e", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bab2o4.range_nm)  # (220, 1060) nm
eps = bab2o4.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_f1d1991451c6/lightsmith"
bab2o4 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bab2o4.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (bab2o4/eimerl-1987-e).

# ... load bab2o4 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=bab2o4)],
    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} = 2.373 + \frac{0.0128 λ^{0.0}}{λ^{2} - {0.0156}^{1.0}} - 0.0044 λ^{2.0}

Valid from 0.22 to 1.06 µm.

Coefficients as stored

C_i	Value
C1	2.373
C2	0.0128
C3	0.0
C4	0.0156
C5	1.0
C6	0.0
C7	0.0
C8	0.0
C9	1.0
C10	-0.0044
C11	2.0

Comments and conditions

Beta barium borate (ß-BaB₂O₄, BBO). Extraordinary ray (e).

Conditions

direction: e

References

D. Eimerl, L. Davis, S. Velsko, E. K. Graham, A. Zalkin. Optical, mechanical, and thermal properties of barium borate. J. Appl. Phys., 62, 1968-1983 (1987)

doi:10.1063/1.339536 Optical, mechanical, and thermal properties of barium borate, Journal of Applied Physics (1987)

Cite

D. Eimerl, L. Davis, S. Velsko, E. K. Graham and A. Zalkin. Optical, mechanical, and thermal properties of barium borate. Journal of Applied Physics, 62, 1968-1983 (1987), doi:10.1063/1.339536; 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

BaB2O4 (Barium borate, BBO), Eimerl et al. 1987: n(e) 0.22–1.06 µm: n and k versus wavelength
λ (µm)	n
0.22	1.662237
0.220869	1.660881
0.221741	1.659544
0.222616	1.658227
0.223495	1.656929
0.224378	1.655649
0.225264	1.654386
0.226153	1.653142
0.227046	1.651915
0.227943	1.650705
0.228843	1.649511
0.229747	1.648334
0.230654	1.647174
0.231565	1.646029
0.232479	1.644899
0.233397	1.643785
0.234318	1.642685
0.235244	1.641601
0.236173	1.640531
0.237105	1.639475
0.238041	1.638433
0.238981	1.637404
0.239925	1.636389
0.240872	1.635388
0.241823	1.634399
0.242778	1.633423
0.243737	1.63246
0.244699	1.631509
0.245666	1.63057
0.246636	1.629643
0.247609	1.628728
0.248587	1.627824
0.249569	1.626932
0.250554	1.62605
0.251544	1.62518
0.252537	1.624321
0.253534	1.623472
0.254535	1.622634
0.25554	1.621806
0.256549	1.620988
0.257562	1.62018
0.258579	1.619382
0.2596	1.618593
0.260625	1.617814
0.261654	1.617045
0.262688	1.616284
0.263725	1.615533
0.264766	1.614791
0.265812	1.614057
0.266861	1.613332
0.267915	1.612616
0.268973	1.611908
0.270035	1.611208
0.271101	1.610516
0.272172	1.609833
0.273246	1.609157
0.274325	1.608489
0.275409	1.607829
0.276496	1.607177
0.277588	1.606532
0.278684	1.605894
0.279784	1.605263
0.280889	1.60464
0.281998	1.604023
0.283112	1.603414
0.28423	1.602811
0.285352	1.602216
0.286479	1.601626
0.28761	1.601044
0.288746	1.600467
0.289886	1.599898
0.29103	1.599334
0.292179	1.598777
0.293333	1.598226
0.294491	1.59768
0.295654	1.597141
0.296822	1.596608
0.297994	1.59608
0.29917	1.595558
0.300352	1.595042
0.301538	1.594531
0.302728	1.594026
0.303924	1.593526
0.305124	1.593032
0.306329	1.592543
0.307538	1.592059
0.308753	1.59158
0.309972	1.591106
0.311196	1.590637
0.312424	1.590173
0.313658	1.589714
0.314897	1.58926
0.31614	1.58881
0.317388	1.588366
0.318642	1.587926
0.3199	1.58749
0.321163	1.587059
0.322431	1.586632
0.323704	1.58621
0.324982	1.585792
0.326266	1.585378
0.327554	1.584969
0.328847	1.584564
0.330146	1.584163
0.331449	1.583765
0.332758	1.583372
0.334072	1.582983
0.335391	1.582598
0.336716	1.582217
0.338045	1.58184
0.33938	1.581466
0.34072	1.581096
0.342065	1.58073
0.343416	1.580367
0.344772	1.580008
0.346134	1.579653
0.3475	1.579301
0.348872	1.578953
0.35025	1.578608
0.351633	1.578266
0.353021	1.577928
0.354415	1.577593
0.355815	1.577262
0.35722	1.576933
0.35863	1.576608
0.360046	1.576286
0.361468	1.575967
0.362895	1.575651
0.364328	1.575339
0.365767	1.575029
0.367211	1.574722
0.368661	1.574418
0.370117	1.574117
0.371578	1.573819
0.373046	1.573524
0.374519	1.573232
0.375997	1.572942
0.377482	1.572656
0.378973	1.572372
0.380469	1.57209
0.381971	1.571811
0.38348	1.571535
0.384994	1.571262
0.386514	1.570991
0.38804	1.570723
0.389572	1.570457
0.391111	1.570193
0.392655	1.569933
0.394206	1.569674
0.395762	1.569418
0.397325	1.569164
0.398894	1.568913
0.400469	1.568664
0.40205	1.568417
0.403638	1.568173
0.405231	1.567931
0.406832	1.567691
0.408438	1.567453
0.410051	1.567218
0.41167	1.566984
0.413295	1.566753
0.414927	1.566524
0.416566	1.566297
0.418211	1.566072
0.419862	1.565849
0.42152	1.565628
0.423184	1.565409
0.424855	1.565193
0.426533	1.564978
0.428217	1.564765
0.429908	1.564553
0.431605	1.564344
0.43331	1.564137
0.435021	1.563932
0.436738	1.563728
0.438463	1.563526
0.440194	1.563326
0.441932	1.563128
0.443677	1.562931
0.445429	1.562737
0.447188	1.562544
0.448954	1.562352
0.450727	1.562163
0.452506	1.561975
0.454293	1.561789
0.456087	1.561604
0.457888	1.561421
0.459696	1.56124
0.461511	1.56106
0.463333	1.560882
0.465163	1.560705
0.467	1.56053
0.468844	1.560356
0.470695	1.560184
0.472554	1.560014
0.47442	1.559845
0.476293	1.559677
0.478174	1.559511
0.480062	1.559346
0.481957	1.559183
0.48386	1.559021
0.485771	1.55886
0.487689	1.558701
0.489615	1.558543
0.491548	1.558387
0.493489	1.558232
0.495438	1.558078
0.497394	1.557925
0.499358	1.557774
0.50133	1.557624
0.503309	1.557476
0.505297	1.557328
0.507292	1.557182
0.509295	1.557037
0.511306	1.556894
0.513325	1.556751
0.515352	1.55661
0.517387	1.55647
0.51943	1.556331
0.521481	1.556193
0.52354	1.556056
0.525607	1.555921
0.527683	1.555787
0.529766	1.555653
0.531858	1.555521
0.533958	1.55539
0.536067	1.55526
0.538183	1.555131
0.540308	1.555004
0.542442	1.554877
0.544584	1.554751
0.546734	1.554627
0.548893	1.554503
0.55106	1.55438
0.553236	1.554259
0.555421	1.554138
0.557614	1.554018
0.559816	1.5539
0.562026	1.553782
0.564245	1.553665
0.566473	1.553549
0.56871	1.553434
0.570956	1.55332
0.57321	1.553207
0.575474	1.553095
0.577746	1.552984
0.580027	1.552873
0.582318	1.552764
0.584617	1.552655
0.586925	1.552548
0.589243	1.552441
0.59157	1.552335
0.593905	1.552229
0.596251	1.552125
0.598605	1.552022
0.600969	1.551919
0.603342	1.551817
0.605724	1.551716
0.608116	1.551615
0.610517	1.551516
0.612928	1.551417
0.615348	1.551319
0.617778	1.551222
0.620217	1.551125
0.622666	1.551029
0.625125	1.550934
0.627593	1.55084
0.630071	1.550747
0.632559	1.550654
0.635057	1.550561
0.637564	1.55047
0.640082	1.550379
0.642609	1.550289
0.645147	1.5502
0.647694	1.550111
0.650252	1.550023
0.652819	1.549936
0.655397	1.549849
0.657985	1.549763
0.660583	1.549678
0.663191	1.549593
0.66581	1.549509
0.668439	1.549425
0.671079	1.549342
0.673728	1.54926
0.676389	1.549178
0.67906	1.549097
0.681741	1.549016
0.684433	1.548937
0.687135	1.548857
0.689849	1.548778
0.692573	1.5487
0.695307	1.548623
0.698053	1.548545
0.700809	1.548469
0.703576	1.548393
0.706355	1.548318
0.709144	1.548243
0.711944	1.548168
0.714755	1.548094
0.717577	1.548021
0.720411	1.547948
0.723255	1.547876
0.726111	1.547804
0.728978	1.547733
0.731857	1.547662
0.734747	1.547592
0.737648	1.547522
0.740561	1.547453
0.743485	1.547384
0.74642	1.547315
0.749368	1.547247
0.752327	1.54718
0.755297	1.547113
0.75828	1.547046
0.761274	1.54698
0.76428	1.546914
0.767298	1.546849
0.770328	1.546784
0.773369	1.54672
0.776423	1.546656
0.779489	1.546592
0.782567	1.546529
0.785657	1.546467
0.788759	1.546404
0.791874	1.546342
0.795	1.546281
0.79814	1.54622
0.801291	1.546159
0.804455	1.546098
0.807632	1.546038
0.810821	1.545979
0.814022	1.545919
0.817236	1.545861
0.820463	1.545802
0.823703	1.545744
0.826956	1.545686
0.830221	1.545629
0.833499	1.545571
0.83679	1.545515
0.840095	1.545458
0.843412	1.545402
0.846742	1.545346
0.850086	1.545291
0.853442	1.545236
0.856812	1.545181
0.860195	1.545126
0.863592	1.545072
0.867002	1.545018
0.870425	1.544965
0.873862	1.544911
0.877313	1.544859
0.880777	1.544806
0.884255	1.544753
0.887746	1.544701
0.891252	1.544649
0.894771	1.544598
0.898304	1.544547
0.901851	1.544496
0.905412	1.544445
0.908987	1.544394
0.912577	1.544344
0.91618	1.544294
0.919798	1.544245
0.92343	1.544195
0.927076	1.544146
0.930737	1.544097
0.934412	1.544048
0.938101	1.544
0.941806	1.543952
0.945524	1.543903
0.949258	1.543856
0.953006	1.543808
0.956769	1.543761
0.960547	1.543714
0.96434	1.543667
0.968148	1.54362
0.971971	1.543574
0.975809	1.543527
0.979662	1.543481
0.98353	1.543435
0.987414	1.54339
0.991313	1.543344
0.995227	1.543299
0.999157	1.543254
1.0031	1.543209
1.00706	1.543164
1.01104	1.54312
1.01503	1.543075
1.01904	1.543031
1.02306	1.542987
1.0271	1.542943
1.03116	1.5429
1.03523	1.542856
1.03932	1.542813
1.04342	1.542769
1.04754	1.542726
1.05168	1.542683
1.05583	1.542641
1.06	1.542598

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: —

BaB₂O₄ (Barium borate, BBO): all datasets

About BaB2O4 (Barium borate, BBO)

BaB₂O₄, commonly known as beta-barium borate (BBO), is a nonlinear optical crystal with a wide transparency range, extending from the ultraviolet to the near-infrared. Known for its high damage threshold and phase-matching capabilities, BBO is frequently employed in frequency doubling, tripling, and other nonlinear processes in laser systems. Its crystal structure allows for phase-matching over a wide range of wavelengths, making it highly versatile for different optical applications. BBO crystals also offer the advantages of a high refractive index and strong birefringence, which contribute to their effectiveness in nonlinear processes. However, the material is hygroscopic and requires careful handling to prevent surface degradation over time. Despite this, its broad phase-matching capabilities and high damage threshold make BaB₂O₄ one of the most popular choices for nonlinear optics, particularly in applications requiring high peak intensities or broad tunability across various wavelengths. Overall, BBO continues to be a material of significant interest in the field of nonlinear optics, both for its well-established applications and for its potential in emerging technologies. Most common allotrope: Beta barium borate (β-BaB₂O₄).

More about BaB2O4 (Barium borate, BBO) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/BaB2O4/nk/Eimerl-e.yml
ID: ds_f1d1991451c6
API: /v1/datasets/ds_f1d1991451c6

Plot