Optical constants

Refractive index of BAL15 (OHARA)

BAL15: n,k 0.3–2.4 µm

Data: formula 3 + tabulated k
Range: 0.3–2.4 µm
Temperature: 298 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength. Note: k data cover 300-900 nm only; k = 0 elsewhere in the n range 300-2400 nm.

At one wavelength

Refractive index n: 1.55671
Extinction coefficient k: 9.36134e-09

Permittivity ε₁: 2.42334
Permittivity ε₂: 2.91458e-08

Absorption coefficient α: 0.00200201 cm⁻¹
Penetration depth δ = λ/(2πk): 9.98996e+09 nm

Abbe number V_d: 58.689
Chromatic dispersion dn/dλ: -0.0489775 µm⁻¹

Group index n_g: 1.58549
Group velocity dispersion: 85.9155 fs²/mm

Dispersion parameter D: -468.715 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

# BAL15 (OHARA): BAL15
ohara_bal15 = ls.fetch_refractiveindex("specs", "OHARA-optical", "BAL15", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ohara_bal15.range_nm)  # (300, 2400) nm
eps = ohara_bal15.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_5c12626ebad7/lightsmith"
ohara_bal15 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ohara_bal15.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ohara-bal15/ohara).

# ... load ohara_bal15 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ohara_bal15)],
    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

Polynomial (formula 3), λ in µm

n^{2} = 2.3876453 - 0.0097564209 λ^{2.0} + 0.01254688 λ^{- 2.0} + 0.00038108489 λ^{- 4.0} - 2.3656347 \times 10^{-5} λ^{- 6.0} + 1.5068491 \times 10^{-6} λ^{- 8.0}

Valid from 0.3 to 2.4 µm.

Coefficients as stored

C_i	Value
C1	2.3876453
C2	-0.0097564209
C3	2.0
C4	0.01254688
C5	-2.0
C6	0.00038108489
C7	-4.0
C8	-2.3656347e-05
C9	-6.0
C10	1.5068491e-06
C11	-8.0

Comments and conditions

Conditions

temperature: 298 K

Properties

thermal dispersion: type: formula A, coefficients: 3.255e-06 0.0 0.0 0.0 0.0 0.0
nd: 1.556711
Vd: 58.689461
glass code: 557587
glass status: preferred
density: value: 2920
thermal expansion: value: 7.4e-06, temperature range: 243 343; value: 8.5e-06, temperature range: 293 573
dPgF: -0.0023
resistance: acid: 2.2; phosphate: 2.0

Thermo-optic coefficient

Schott thermal-dispersion model (reference temperature 298.0 K): dn/dT = 1.48e-06 K⁻¹ at 633 nm, dn/dT = 1.45e-06 K⁻¹ at 1310 nm, dn/dT = 1.45e-06 K⁻¹ at 1550 nm

Notes on the source data (kept exactly as published):

k data cover 300-900 nm only; k = 0 elsewhere in the n range 300-2400 nm

References

OHARA Zemax catalog 2017-11-30 (obtained from http://www.ohara-inc.co.jp)
See also OHARA glass data sheets

Cite

OHARA Zemax catalog 2017-11-30 (obtained from http://www.ohara-inc.co.jp); See also OHARA glass data sheets; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 420 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

BAL15 (OHARA), BAL15: n and k versus wavelength
λ (µm)	n	k
0.3	1.601169	7.684500e-06
0.301568	1.60043	6.972164e-06
0.303143	1.599705	6.256107e-06
0.304727	1.598992	5.536307e-06
0.30632	1.598291	4.812747e-06
0.30792	1.597602	4.085405e-06
0.309529	1.596925	3.354264e-06
0.31	1.59673	3.140300e-06
0.311147	1.596259	2.944372e-06
0.312772	1.595604	2.666537e-06
0.314407	1.59496	2.387250e-06
0.316049	1.594326	2.106503e-06
0.317701	1.593703	1.824290e-06
0.319361	1.593089	1.540602e-06
0.32	1.592856	1.431400e-06
0.32103	1.592485	1.354682e-06
0.322707	1.59189	1.229705e-06
0.324393	1.591305	1.104074e-06
0.326088	1.590729	9.777876e-07
0.327792	1.590161	8.508411e-07
0.329505	1.589602	7.232312e-07
0.33	1.589443	6.863600e-07
0.331227	1.589052	6.445868e-07
0.332958	1.588509	5.856569e-07
0.334697	1.587975	5.264191e-07
0.336446	1.587448	4.668717e-07
0.338204	1.586929	4.070132e-07
0.339971	1.586418	3.468418e-07
0.34	1.58641	3.458700e-07
0.341748	1.585914	3.181345e-07
0.343534	1.585417	2.897988e-07
0.345329	1.584927	2.613150e-07
0.347133	1.584444	2.326824e-07
0.348947	1.583968	2.039002e-07
0.35	1.583695	1.871900e-07
0.35077	1.583498	1.808616e-07
0.352603	1.583035	1.658028e-07
0.354446	1.582578	1.506654e-07
0.356298	1.582127	1.354488e-07
0.358159	1.581683	1.201528e-07
0.36	1.581251	1.050300e-07
0.360031	1.581244	1.049175e-07
0.361912	1.580811	9.804734e-08
0.363803	1.580384	9.114132e-08
0.365704	1.579963	8.419921e-08
0.367615	1.579547	7.722083e-08
0.369536	1.579137	7.020598e-08
0.37	1.579039	6.851100e-08
0.371467	1.578732	6.651853e-08
0.373408	1.578332	6.388188e-08
0.375359	1.577937	6.123144e-08
0.37732	1.577547	5.856716e-08
0.379292	1.577163	5.588895e-08
0.38	1.577026	5.492700e-08
0.381274	1.576783	5.190366e-08
0.383266	1.576408	4.717486e-08
0.385269	1.576037	4.242136e-08
0.387282	1.575672	3.764302e-08
0.389305	1.575311	3.283971e-08
0.39	1.575188	3.119100e-08
0.39134	1.574954	2.957878e-08
0.393384	1.574602	2.711781e-08
0.39544	1.574254	2.464398e-08
0.397506	1.57391	2.215723e-08
0.399583	1.573571	1.965748e-08
0.4	1.573503	1.915600e-08
0.401671	1.573235	1.895520e-08
0.40377	1.572904	1.870303e-08
0.40588	1.572577	1.844954e-08
0.408001	1.572253	1.819472e-08
0.410133	1.571934	1.793857e-08
0.412276	1.571618	1.768109e-08
0.41443	1.571306	1.742225e-08
0.416595	1.570998	1.716207e-08
0.418772	1.570693	1.690053e-08
0.42	1.570524	1.675300e-08
0.42096	1.570392	1.696038e-08
0.42316	1.570095	1.743539e-08
0.425371	1.569801	1.791288e-08
0.427594	1.56951	1.839287e-08
0.429828	1.569223	1.887536e-08
0.432074	1.568939	1.936037e-08
0.434332	1.568659	1.984792e-08
0.436601	1.568381	2.033802e-08
0.438882	1.568107	2.083067e-08
0.44	1.567975	2.107200e-08
0.441176	1.567836	2.091192e-08
0.443481	1.567568	2.059806e-08
0.445798	1.567304	2.028256e-08
0.448128	1.567042	1.996542e-08
0.450469	1.566783	1.964661e-08
0.452823	1.566527	1.932614e-08
0.455189	1.566274	1.900399e-08
0.457568	1.566024	1.868016e-08
0.459959	1.565776	1.835464e-08
0.46	1.565772	1.834900e-08
0.462362	1.565532	1.799010e-08
0.464778	1.56529	1.762300e-08
0.467206	1.565051	1.725398e-08
0.469648	1.564814	1.688303e-08
0.472102	1.56458	1.651014e-08
0.474569	1.564349	1.613530e-08
0.477048	1.56412	1.575851e-08
0.479541	1.563893	1.537974e-08
0.48	1.563852	1.531000e-08
0.482047	1.56367	1.537519e-08
0.484566	1.563448	1.545541e-08
0.487098	1.563229	1.553606e-08
0.489643	1.563013	1.561712e-08
0.492201	1.562798	1.569861e-08
0.494773	1.562587	1.578052e-08
0.497358	1.562377	1.586286e-08
0.499957	1.562169	1.594564e-08
0.5	1.562166	1.594700e-08
0.50257	1.561964	1.557776e-08
0.505196	1.561761	1.520042e-08
0.507835	1.56156	1.482110e-08
0.510489	1.561362	1.443980e-08
0.513156	1.561165	1.405650e-08
0.515838	1.560971	1.367121e-08
0.518533	1.560778	1.328390e-08
0.521243	1.560588	1.289457e-08
0.523966	1.560399	1.250320e-08
0.526704	1.560213	1.210979e-08
0.529456	1.560028	1.171432e-08
0.532223	1.559846	1.131678e-08
0.535004	1.559665	1.091717e-08
0.537799	1.559486	1.051547e-08
0.540609	1.559309	1.011167e-08
0.543434	1.559134	9.705766e-09
0.546274	1.558961	9.297737e-09
0.549128	1.558789	8.887575e-09
0.55	1.558737	8.762300e-09
0.551998	1.558619	8.794124e-09
0.554882	1.558451	8.840077e-09
0.557781	1.558284	8.886270e-09
0.560696	1.55812	8.932705e-09
0.563626	1.557956	8.979382e-09
0.566571	1.557795	9.026303e-09
0.569531	1.557635	9.073469e-09
0.572507	1.557477	9.120881e-09
0.575498	1.55732	9.168542e-09
0.578506	1.557165	9.216451e-09
0.581528	1.557011	9.264611e-09
0.584567	1.556859	9.313022e-09
0.587622	1.556708	9.361687e-09
0.590692	1.556559	9.410605e-09
0.593779	1.556411	9.459779e-09
0.596881	1.556265	9.509211e-09
0.6	1.55612	9.558900e-09
0.603135	1.555976	9.933995e-09
0.606287	1.555834	1.031105e-08
0.609455	1.555693	1.069007e-08
0.612639	1.555553	1.107108e-08
0.61584	1.555415	1.145408e-08
0.619058	1.555278	1.183907e-08
0.622293	1.555142	1.222608e-08
0.625545	1.555008	1.261511e-08
0.628813	1.554875	1.300618e-08
0.632099	1.554743	1.339929e-08
0.635402	1.554612	1.379445e-08
0.638722	1.554482	1.419167e-08
0.642059	1.554354	1.459098e-08
0.645414	1.554227	1.499236e-08
0.648787	1.5541	1.539585e-08
0.65	1.554055	1.554100e-08
0.652177	1.553975	1.534992e-08
0.655585	1.553851	1.505078e-08
0.65901	1.553729	1.475008e-08
0.662454	1.553607	1.444781e-08
0.665915	1.553486	1.414396e-08
0.669395	1.553366	1.383853e-08
0.672892	1.553248	1.353150e-08
0.676409	1.55313	1.322286e-08
0.679943	1.553013	1.291261e-08
0.683496	1.552897	1.260074e-08
0.687067	1.552783	1.228724e-08
0.690657	1.552669	1.197210e-08
0.694266	1.552556	1.165532e-08
0.697894	1.552444	1.133688e-08
0.7	1.55238	1.115200e-08
0.701541	1.552333	1.117654e-08
0.705206	1.552223	1.123494e-08
0.708891	1.552113	1.129364e-08
0.712595	1.552005	1.135264e-08
0.716319	1.551897	1.141196e-08
0.720062	1.551791	1.147158e-08
0.723824	1.551685	1.153152e-08
0.727606	1.55158	1.159177e-08
0.731408	1.551475	1.165233e-08
0.73523	1.551372	1.171321e-08
0.739072	1.551269	1.177441e-08
0.742934	1.551167	1.183593e-08
0.746816	1.551066	1.189777e-08
0.750718	1.550965	1.195994e-08
0.754641	1.550865	1.202242e-08
0.758584	1.550766	1.208524e-08
0.762547	1.550667	1.214838e-08
0.766532	1.55057	1.221185e-08
0.770537	1.550473	1.227566e-08
0.774564	1.550376	1.233980e-08
0.778611	1.55028	1.240427e-08
0.782679	1.550185	1.246908e-08
0.786769	1.55009	1.253423e-08
0.79088	1.549997	1.259972e-08
0.795012	1.549903	1.266555e-08
0.799167	1.54981	1.273172e-08
0.8	1.549792	1.274500e-08
0.803342	1.549718	1.303823e-08
0.80754	1.549626	1.340649e-08
0.81176	1.549535	1.377668e-08
0.816001	1.549445	1.414880e-08
0.820265	1.549355	1.452286e-08
0.824551	1.549265	1.489888e-08
0.82886	1.549176	1.527686e-08
0.833191	1.549088	1.565682e-08
0.837544	1.549	1.603876e-08
0.841921	1.548912	1.642270e-08
0.84632	1.548825	1.680865e-08
0.850742	1.548738	1.719661e-08
0.855187	1.548652	1.758660e-08
0.859656	1.548566	1.797862e-08
0.864148	1.548481	1.837270e-08
0.868663	1.548396	1.876883e-08
0.873202	1.548311	1.916704e-08
0.877765	1.548227	1.956732e-08
0.882351	1.548143	1.996970e-08
0.886962	1.54806	2.037418e-08
0.891597	1.547977	2.078077e-08
0.896255	1.547894	2.118948e-08
0.9	1.547828	2.151800e-08
0.900939	1.547812	0
0.905646	1.54773	0
0.910378	1.547648	0
0.915135	1.547567	0
0.919917	1.547486	0
0.924724	1.547405	0
0.929556	1.547324	0
0.934413	1.547244	0
0.939295	1.547164	0
0.944204	1.547084	0
0.949137	1.547005	0
0.954097	1.546925	0
0.959082	1.546846	0
0.964093	1.546767	0
0.969131	1.546689	0
0.974195	1.54661	0
0.979285	1.546532	0
0.984402	1.546454	0
0.989546	1.546376	0
0.994717	1.546298	0
0.999914	1.546221	0
1.00514	1.546143	0
1.01039	1.546066	0
1.01567	1.545989	0
1.02098	1.545912	0
1.02631	1.545835	0
1.03168	1.545758	0
1.03707	1.545681	0
1.04249	1.545604	0
1.04793	1.545528	0
1.05341	1.545451	0
1.05891	1.545375	0
1.06445	1.545298	0
1.07001	1.545222	0
1.0756	1.545145	0
1.08122	1.545069	0
1.08687	1.544992	0
1.09255	1.544916	0
1.09826	1.544839	0
1.104	1.544763	0
1.10976	1.544687	0
1.11556	1.54461	0
1.12139	1.544533	0
1.12725	1.544457	0
1.13314	1.54438	0
1.13906	1.544303	0
1.14501	1.544227	0
1.151	1.54415	0
1.15701	1.544073	0
1.16306	1.543996	0
1.16913	1.543918	0
1.17524	1.543841	0
1.18138	1.543764	0
1.18756	1.543686	0
1.19376	1.543608	0
1.2	1.54353	0
1.20627	1.543452	0
1.21257	1.543374	0
1.21891	1.543295	0
1.22528	1.543217	0
1.23168	1.543138	0
1.23812	1.543059	0
1.24459	1.542979	0
1.25109	1.5429	0
1.25763	1.54282	0
1.2642	1.54274	0
1.2708	1.54266	0
1.27744	1.542579	0
1.28412	1.542498	0
1.29083	1.542417	0
1.29757	1.542336	0
1.30435	1.542254	0
1.31117	1.542172	0
1.31802	1.54209	0
1.32491	1.542007	0
1.33183	1.541924	0
1.33879	1.541841	0
1.34578	1.541757	0
1.35282	1.541673	0
1.35989	1.541589	0
1.36699	1.541504	0
1.37413	1.541419	0
1.38131	1.541333	0
1.38853	1.541247	0
1.39579	1.54116	0
1.40308	1.541073	0
1.41041	1.540986	0
1.41778	1.540898	0
1.42519	1.54081	0
1.43264	1.540721	0
1.44012	1.540632	0
1.44765	1.540542	0
1.45521	1.540452	0
1.46282	1.540361	0
1.47046	1.54027	0
1.47814	1.540178	0
1.48587	1.540086	0
1.49363	1.539993	0
1.50144	1.539899	0
1.50928	1.539805	0
1.51717	1.539711	0
1.52509	1.539615	0
1.53306	1.53952	0
1.54107	1.539423	0
1.54913	1.539326	0
1.55722	1.539228	0
1.56536	1.53913	0
1.57354	1.539031	0
1.58176	1.538931	0
1.59002	1.538831	0
1.59833	1.53873	0
1.60668	1.538628	0
1.61508	1.538525	0
1.62352	1.538422	0
1.632	1.538318	0
1.64053	1.538214	0
1.6491	1.538108	0
1.65772	1.538002	0
1.66638	1.537895	0
1.67509	1.537787	0
1.68384	1.537678	0
1.69264	1.537569	0
1.70148	1.537458	0
1.71037	1.537347	0
1.71931	1.537235	0
1.7283	1.537122	0
1.73733	1.537009	0
1.7464	1.536894	0
1.75553	1.536778	0
1.7647	1.536662	0
1.77392	1.536544	0
1.78319	1.536426	0
1.79251	1.536307	0
1.80188	1.536186	0
1.81129	1.536065	0
1.82076	1.535943	0
1.83027	1.535819	0
1.83983	1.535695	0
1.84945	1.53557	0
1.85911	1.535443	0
1.86883	1.535316	0
1.87859	1.535187	0
1.88841	1.535057	0
1.89827	1.534926	0
1.90819	1.534795	0
1.91816	1.534661	0
1.92819	1.534527	0
1.93826	1.534392	0
1.94839	1.534255	0
1.95857	1.534117	0
1.9688	1.533978	0
1.97909	1.533838	0
1.98943	1.533697	0
1.99983	1.533554	0
2.01028	1.53341	0
2.02078	1.533264	0
2.03134	1.533118	0
2.04196	1.53297	0
2.05263	1.53282	0
2.06335	1.53267	0
2.07413	1.532517	0
2.08497	1.532364	0
2.09586	1.532209	0
2.10682	1.532053	0
2.11782	1.531895	0
2.12889	1.531736	0
2.14001	1.531575	0
2.1512	1.531413	0
2.16244	1.531249	0
2.17374	1.531084	0
2.1851	1.530917	0
2.19651	1.530748	0
2.20799	1.530578	0
2.21953	1.530407	0
2.23112	1.530233	0
2.24278	1.530059	0
2.2545	1.529882	0
2.26628	1.529704	0
2.27812	1.529524	0
2.29003	1.529342	0
2.30199	1.529158	0
2.31402	1.528973	0
2.32611	1.528786	0
2.33827	1.528597	0
2.35049	1.528407	0
2.36277	1.528214	0
2.37511	1.52802	0
2.38752	1.527823	0
2.4	1.527625	0

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: —

BAL15 (OHARA): all datasets

BAL (Barium, low-index)

BAL15 n,k 0.3–2.4 µm default

About BAL15 (OHARA)

Ohara Group is an international group of companies with headquarters in Japan and subsidiaries in Japan (Ohara, Inc.), United States (Ohara Corporation), and Germany (Ohara, GmbH). Ohara is known for its specialization in high-quality optical glass, ceramics, and other advanced materials. With a history spanning over a century, Ohara has been at the forefront of optical innovations, producing a wide range of specialized glass types including low-dispersion and high-refractive-index materials. These are used in various demanding applications like telescopes, microscopes, and high-performance camera lenses. The company's commitment to research and development has led to groundbreaking products such as low thermal expansion glass-ceramics and other specialty materials used in semiconductor manufacturing and space telescopes. With stringent quality control procedures, Ohara ensures that its optical glass meets the highest standards of clarity, consistency, and performance. Their materials are widely regarded for their exceptional quality and are often used in scientific research, aerospace, and other fields where precision and reliability are paramount. Ohara's reputation for technical excellence and innovation makes it a key player in the global optics and materials science industries, providing cutting-edge solutions for a range of complex applications.

More about BAL15 (OHARA) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/ohara/optical/BAL15.yml
ID: ds_5c12626ebad7
API: /v1/datasets/ds_5c12626ebad7

Plot