Optical constants

Refractive index of BaGa₄S₇ (Barium gallium sulfide, BGS)

Badikov et al 2010: n(β) 0.420–9.50 µm

Data: formula 4
Range: 0.42–9.5 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: 2.38484
Extinction coefficient k: 0

Permittivity ε₁: 5.68746
Permittivity ε₂: 0

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

Abbe number V_d: 17.124
Chromatic dispersion dn/dλ: -0.415029 µm⁻¹

Group index n_g: 2.62871
Group velocity dispersion: 782.64 fs²/mm

Dispersion parameter D: -4269.72 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

# BaGa4S7 (Barium gallium sulfide, BGS): Badikov et al 2010: n(β) 0.420–9.50 µm
baga4s7 = ls.fetch_refractiveindex("main", "BaGa4S7", "Badikov-β", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(baga4s7.range_nm)  # (420, 9500) nm
eps = baga4s7.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_8bb2580a6a2e/lightsmith"
baga4s7 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(baga4s7.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (baga4s7/badikov-2010-2).

# ... load baga4s7 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=baga4s7)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=420, 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} = 7.812188 + \frac{0.182439 λ^{0.0}}{λ^{2} - {0.015907}^{1.0}} + \frac{2653.548 λ^{0.0}}{λ^{2} - {990.979}^{1.0}}

Valid from 0.42 to 9.5 µm.

Coefficients as stored

C_i	Value
C1	7.812188
C2	0.182439
C3	0.0
C4	0.015907
C5	1.0
C6	2653.548
C7	0.0
C8	990.979
C9	1.0

Comments and conditions

n_β; room temperature.

Conditions

direction: beta

References

V. Badikov, D. Badikov, G. Shevyrdyaeva, A. Tyazhev, G. Marchev, V. Panyutin, V. Petrov, A. Kwasniewski. Phase-matching properties of BaGa₄S₇ and BaGa₄Se₇: Wide-bandgap nonlinear crystals for the mid-infrared. Phys. Status Solidi RRL, 5, 31–33 (2010)

doi:10.1002/pssr.201004425 Phase‐matching properties of BaGa4S7 and BaGa4Se7: Wide‐bandgap nonlinear crystals for the mid‐infrared, physica status solidi (RRL) – Rapid Research Letters (2010)

Cite

Valeriy Badikov et al.. Phase‐matching properties of BaGa4S7 and BaGa4Se7: Wide‐bandgap nonlinear crystals for the mid‐infrared. physica status solidi (RRL) – Rapid Research Letters, 5, 31-33 (2010), doi:10.1002/pssr.201004425; 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

BaGa4S7 (Barium gallium sulfide, BGS), Badikov et al 2010: n(β) 0.420–9.50 µm: n and k versus wavelength
λ (µm)	n
0.42	2.504146
0.423296	2.500278
0.426617	2.496476
0.429965	2.492738
0.433339	2.489063
0.43674	2.48545
0.440167	2.481899
0.443621	2.478407
0.447102	2.474974
0.450611	2.471599
0.454147	2.46828
0.45771	2.465017
0.461302	2.461808
0.464922	2.458654
0.46857	2.455551
0.472247	2.452501
0.475953	2.449501
0.479688	2.446551
0.483452	2.44365
0.487246	2.440797
0.491069	2.437991
0.494923	2.435232
0.498806	2.432518
0.502721	2.429849
0.506666	2.427224
0.510641	2.424643
0.514649	2.422103
0.518687	2.419606
0.522757	2.417149
0.526859	2.414733
0.530994	2.412356
0.535161	2.410018
0.53936	2.407718
0.543593	2.405456
0.547858	2.403231
0.552157	2.401042
0.55649	2.398888
0.560857	2.39677
0.565258	2.394686
0.569694	2.392636
0.574164	2.390619
0.57867	2.388635
0.583211	2.386682
0.587787	2.384762
0.5924	2.382872
0.597048	2.381013
0.601734	2.379184
0.606455	2.377385
0.611214	2.375614
0.616011	2.373872
0.620845	2.372158
0.625716	2.370471
0.630627	2.368812
0.635575	2.367179
0.640563	2.365572
0.645589	2.363992
0.650655	2.362436
0.655761	2.360905
0.660907	2.359399
0.666093	2.357917
0.67132	2.356458
0.676588	2.355023
0.681897	2.35361
0.687248	2.35222
0.692641	2.350852
0.698076	2.349506
0.703554	2.348181
0.709075	2.346878
0.71464	2.345595
0.720247	2.344332
0.725899	2.343089
0.731596	2.341866
0.737336	2.340663
0.743122	2.339478
0.748954	2.338312
0.754831	2.337164
0.760754	2.336035
0.766724	2.334923
0.772741	2.333829
0.778804	2.332752
0.784916	2.331692
0.791075	2.330649
0.797283	2.329622
0.803539	2.328611
0.809845	2.327616
0.8162	2.326637
0.822605	2.325673
0.82906	2.324724
0.835565	2.32379
0.842122	2.32287
0.848731	2.321965
0.855391	2.321074
0.862103	2.320197
0.868868	2.319333
0.875686	2.318483
0.882558	2.317646
0.889483	2.316823
0.896463	2.316012
0.903498	2.315213
0.910588	2.314427
0.917733	2.313653
0.924935	2.312891
0.932193	2.312141
0.939508	2.311402
0.946881	2.310675
0.954311	2.309959
0.9618	2.309254
0.969347	2.308559
0.976954	2.307876
0.98462	2.307203
0.992346	2.30654
1.00013	2.305887
1.00798	2.305245
1.01589	2.304612
1.02386	2.303989
1.0319	2.303375
1.04	2.302771
1.04816	2.302176
1.05638	2.301589
1.06467	2.301012
1.07303	2.300444
1.08145	2.299884
1.08993	2.299332
1.09848	2.298789
1.1071	2.298254
1.11579	2.297727
1.12455	2.297208
1.13337	2.296697
1.14227	2.296193
1.15123	2.295697
1.16026	2.295209
1.16937	2.294727
1.17854	2.294253
1.18779	2.293786
1.19711	2.293325
1.20651	2.292872
1.21598	2.292425
1.22552	2.291985
1.23513	2.291551
1.24483	2.291123
1.25459	2.290702
1.26444	2.290287
1.27436	2.289878
1.28436	2.289474
1.29444	2.289077
1.3046	2.288686
1.31484	2.2883
1.32515	2.287919
1.33555	2.287544
1.34603	2.287174
1.35659	2.28681
1.36724	2.286451
1.37797	2.286096
1.38878	2.285747
1.39968	2.285403
1.41066	2.285063
1.42173	2.284729
1.43289	2.284398
1.44413	2.284073
1.45547	2.283752
1.46689	2.283435
1.4784	2.283122
1.49	2.282814
1.50169	2.28251
1.51348	2.28221
1.52535	2.281914
1.53732	2.281622
1.54939	2.281334
1.56154	2.28105
1.5738	2.280769
1.58615	2.280492
1.59859	2.280219
1.61114	2.279949
1.62378	2.279683
1.63652	2.27942
1.64937	2.27916
1.66231	2.278904
1.67535	2.27865
1.6885	2.2784
1.70175	2.278153
1.7151	2.277909
1.72856	2.277668
1.74213	2.27743
1.7558	2.277194
1.76958	2.276962
1.78346	2.276732
1.79746	2.276505
1.81156	2.27628
1.82578	2.276058
1.8401	2.275838
1.85454	2.275621
1.8691	2.275406
1.88376	2.275193
1.89855	2.274983
1.91344	2.274775
1.92846	2.274569
1.94359	2.274365
1.95884	2.274164
1.97421	2.273964
1.98971	2.273766
2.00532	2.27357
2.02106	2.273376
2.03692	2.273184
2.0529	2.272994
2.06901	2.272805
2.08525	2.272618
2.10161	2.272433
2.1181	2.272249
2.13472	2.272067
2.15147	2.271886
2.16836	2.271707
2.18537	2.271529
2.20252	2.271353
2.2198	2.271178
2.23722	2.271004
2.25478	2.270831
2.27247	2.27066
2.2903	2.270489
2.30828	2.27032
2.32639	2.270152
2.34465	2.269985
2.36304	2.269818
2.38159	2.269653
2.40028	2.269489
2.41911	2.269325
2.43809	2.269163
2.45723	2.269001
2.47651	2.26884
2.49594	2.268679
2.51553	2.268519
2.53527	2.26836
2.55516	2.268201
2.57521	2.268043
2.59542	2.267886
2.61579	2.267729
2.63632	2.267572
2.657	2.267415
2.67785	2.267259
2.69887	2.267104
2.72004	2.266948
2.74139	2.266793
2.7629	2.266638
2.78458	2.266483
2.80643	2.266328
2.82846	2.266173
2.85065	2.266019
2.87302	2.265864
2.89557	2.265709
2.91829	2.265554
2.94119	2.265399
2.96427	2.265244
2.98753	2.265088
3.01097	2.264933
3.0346	2.264777
3.05841	2.26462
3.08241	2.264464
3.1066	2.264307
3.13098	2.264149
3.15555	2.263991
3.18031	2.263833
3.20527	2.263674
3.23042	2.263514
3.25577	2.263354
3.28132	2.263193
3.30707	2.263031
3.33302	2.262868
3.35917	2.262705
3.38553	2.262541
3.4121	2.262376
3.43887	2.26221
3.46586	2.262043
3.49306	2.261874
3.52047	2.261705
3.54809	2.261535
3.57593	2.261364
3.604	2.261191
3.63228	2.261017
3.66078	2.260842
3.68951	2.260665
3.71846	2.260488
3.74764	2.260308
3.77705	2.260127
3.80668	2.259945
3.83656	2.259761
3.86666	2.259576
3.897	2.259388
3.92759	2.259199
3.95841	2.259009
3.98947	2.258816
4.02077	2.258622
4.05233	2.258425
4.08412	2.258227
4.11617	2.258027
4.14847	2.257824
4.18103	2.25762
4.21384	2.257413
4.2469	2.257204
4.28023	2.256993
4.31382	2.256779
4.34767	2.256563
4.38178	2.256344
4.41617	2.256123
4.45082	2.255899
4.48575	2.255673
4.52095	2.255444
4.55643	2.255212
4.59218	2.254977
4.62822	2.254739
4.66454	2.254499
4.70114	2.254255
4.73803	2.254008
4.77521	2.253758
4.81268	2.253505
4.85045	2.253248
4.88851	2.252988
4.92687	2.252725
4.96553	2.252457
5.0045	2.252187
5.04377	2.251912
5.08335	2.251634
5.12324	2.251352
5.16344	2.251066
5.20396	2.250776
5.24479	2.250482
5.28595	2.250184
5.32743	2.249881
5.36924	2.249574
5.41137	2.249263
5.45383	2.248947
5.49663	2.248626
5.53976	2.248301
5.58323	2.247971
5.62705	2.247636
5.6712	2.247296
5.71571	2.246951
5.76056	2.2466
5.80576	2.246244
5.85132	2.245883
5.89724	2.245516
5.94351	2.245144
5.99015	2.244766
6.03716	2.244381
6.08453	2.243991
6.13228	2.243595
6.1804	2.243192
6.2289	2.242784
6.27778	2.242368
6.32704	2.241946
6.37669	2.241517
6.42673	2.241081
6.47716	2.240639
6.52799	2.240189
6.57921	2.239731
6.63084	2.239266
6.68288	2.238794
6.73532	2.238314
6.78817	2.237826
6.84144	2.237329
6.89512	2.236825
6.94923	2.236312
7.00376	2.23579
7.05872	2.23526
7.11411	2.234721
7.16994	2.234172
7.2262	2.233614
7.28291	2.233047
7.34006	2.23247
7.39766	2.231883
7.45571	2.231286
7.51421	2.230679
7.57318	2.230061
7.6326	2.229433
7.6925	2.228793
7.75286	2.228143
7.8137	2.227481
7.87502	2.226807
7.93681	2.226121
7.99909	2.225423
8.06186	2.224713
8.12513	2.22399
8.18889	2.223254
8.25315	2.222505
8.31791	2.221742
8.38318	2.220966
8.44897	2.220176
8.51527	2.219371
8.58209	2.218551
8.64943	2.217717
8.7173	2.216867
8.78571	2.216001
8.85465	2.215119
8.92414	2.214221
8.99417	2.213307
9.06474	2.212375
9.13588	2.211425
9.20757	2.210458
9.27982	2.209473
9.35264	2.208468
9.42603	2.207445
9.5	2.206402

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: —

BaGa₄S₇ (Barium gallium sulfide, BGS): all datasets

About BaGa4S7 (Barium gallium sulfide, BGS)

BaGa₄S₇, often abbreviated as BGS in scientific literature and industry documents, is a nonlinear optical crystal known for its high phase-matching capabilities, especially in the visible and near-infrared regions. This material is particularly valuable for frequency conversion applications, such as second-harmonic generation (SHG) and sum-frequency generation (SFG), owing to its high nonlinear optical coefficients. BaGa₄S₇ is also known for its high laser damage threshold, making it a robust choice for high-power optical applications. Typically grown through methods like the Bridgman technique, the crystal can be precisely cut and polished to create high-quality optical elements. One consideration for users is the material's sensitivity to moisture and chemicals, which necessitates careful handling and storage to preserve its optical properties. Despite this, BaGa₄S₇ remains a highly attractive material for various nonlinear optical applications, especially those requiring wide tunability, high power-handling, and efficient phase-matching capabilities.

BaGa4S7 - The Materials project

More about BaGa4S7 (Barium gallium sulfide, BGS) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/BaGa4S7/nk/Badikov-beta.yml
ID: ds_8bb2580a6a2e
API: /v1/datasets/ds_8bb2580a6a2e

Plot