Optical constants

Refractive index of BAL12 (OHARA)

BAL12: n,k 0.365–0.9 µm

Data: formula 3 + tabulated k
Range: 0.365–0.9 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 340-700 nm only; k = 0 elsewhere in the n range 365-900 nm.

At one wavelength

Refractive index n: 1.53995
Extinction coefficient k: 9.36134e-09

Permittivity ε₁: 2.37146
Permittivity ε₂: 2.88321e-08

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

Abbe number V_d: 59.454
Chromatic dispersion dn/dλ: -0.0468563 µm⁻¹

Group index n_g: 1.56749
Group velocity dispersion: 83.153 fs²/mm

Dispersion parameter D: -453.644 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

# BAL12 (OHARA): BAL12
ohara_bal12 = ls.fetch_refractiveindex("specs", "OHARA-optical", "BAL12", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ohara_bal12.range_nm)  # (365, 900) nm
eps = ohara_bal12.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_5de42d2b3617/lightsmith"
ohara_bal12 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(ohara_bal12.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (ohara-bal12/ohara).

# ... load ohara_bal12 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=ohara_bal12)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=900, 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} = 2.339135 - 0.009645053 λ^{2.0} + 0.01072238 λ^{- 2.0} + 0.0007185158 λ^{- 4.0} - 6.911301 \times 10^{-5} λ^{- 6.0} + 3.543402 \times 10^{-6} λ^{- 8.0}

Valid from 0.365 to 0.9 µm.

Coefficients as stored

C_i	Value
C1	2.339135
C2	-0.009645053
C3	2.0
C4	0.01072238
C5	-2.0
C6	0.0007185158
C7	-4.0
C8	-6.911301e-05
C9	-6.0
C10	3.543402e-06
C11	-8.0

Comments and conditions

Conditions

temperature: 298 K

Properties

thermal dispersion: type: formula A, coefficients: 3.2683e-06 0.0 0.0 0.0 0.0 0.0
nd: 1.539955
Vd: 59.454008
glass code: 540595
glass status: preferred
density: value: 2750
thermal expansion: value: 8.3e-06, temperature range: 243 343; value: 1.01e-05, temperature range: 293 573
dPgF: -0.001

Thermo-optic coefficient

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

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

k data cover 340-700 nm only; k = 0 elsewhere in the n range 365-900 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 413 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

BAL12 (OHARA), BAL12: n and k versus wavelength
λ (µm)	n	k
0.365	1.562317	4.674150e-08
0.365827	1.562144	4.538376e-08
0.366655	1.561972	4.402295e-08
0.367485	1.5618	4.265906e-08
0.368317	1.56163	4.129208e-08
0.369151	1.561461	3.992200e-08
0.369987	1.561292	3.854882e-08
0.37	1.56129	3.852800e-08
0.370825	1.561125	3.836124e-08
0.371665	1.560959	3.819153e-08
0.372506	1.560793	3.802144e-08
0.37335	1.560629	3.785096e-08
0.374195	1.560465	3.768010e-08
0.375043	1.560302	3.750885e-08
0.375892	1.56014	3.733721e-08
0.376743	1.55998	3.716519e-08
0.377596	1.55982	3.699277e-08
0.378451	1.55966	3.681997e-08
0.379308	1.559502	3.664677e-08
0.38	1.559375	3.650700e-08
0.380167	1.559345	3.631324e-08
0.381028	1.559188	3.531643e-08
0.381891	1.559033	3.431737e-08
0.382756	1.558878	3.331605e-08
0.383623	1.558724	3.231245e-08
0.384491	1.558571	3.130659e-08
0.385362	1.558419	3.029845e-08
0.386235	1.558267	2.928802e-08
0.387109	1.558117	2.827531e-08
0.387986	1.557967	2.726030e-08
0.388864	1.557818	2.624300e-08
0.389745	1.55767	2.522339e-08
0.39	1.557627	2.492800e-08
0.390627	1.557522	2.456583e-08
0.391512	1.557375	2.405527e-08
0.392399	1.55723	2.354354e-08
0.393287	1.557085	2.303066e-08
0.394178	1.55694	2.251662e-08
0.39507	1.556797	2.200141e-08
0.395965	1.556654	2.148503e-08
0.396862	1.556512	2.096749e-08
0.39776	1.55637	2.044877e-08
0.398661	1.55623	1.992888e-08
0.399564	1.55609	1.940781e-08
0.4	1.556023	1.915600e-08
0.400469	1.555951	1.909971e-08
0.401375	1.555813	1.899075e-08
0.402284	1.555675	1.888154e-08
0.403195	1.555538	1.877209e-08
0.404108	1.555402	1.866239e-08
0.405023	1.555266	1.855245e-08
0.40594	1.555131	1.844225e-08
0.40686	1.554997	1.833180e-08
0.407781	1.554864	1.822111e-08
0.408704	1.554731	1.811016e-08
0.40963	1.554599	1.799896e-08
0.410558	1.554468	1.788751e-08
0.411487	1.554337	1.777581e-08
0.412419	1.554207	1.766386e-08
0.413353	1.554077	1.755165e-08
0.414289	1.553949	1.743918e-08
0.415227	1.55382	1.732647e-08
0.416167	1.553693	1.721349e-08
0.41711	1.553566	1.710026e-08
0.418054	1.55344	1.698678e-08
0.419001	1.553314	1.687304e-08
0.41995	1.55319	1.675904e-08
0.42	1.553183	1.675300e-08
0.420901	1.553065	1.694751e-08
0.421854	1.552942	1.715333e-08
0.422809	1.552819	1.735962e-08
0.423767	1.552696	1.756638e-08
0.424726	1.552574	1.777361e-08
0.425688	1.552453	1.798130e-08
0.426652	1.552333	1.818947e-08
0.427618	1.552213	1.839810e-08
0.428586	1.552093	1.860721e-08
0.429557	1.551974	1.881680e-08
0.43053	1.551856	1.902685e-08
0.431504	1.551738	1.923739e-08
0.432482	1.551621	1.944840e-08
0.433461	1.551505	1.965988e-08
0.434442	1.551389	1.987185e-08
0.435426	1.551274	2.008430e-08
0.436412	1.551159	2.029722e-08
0.4374	1.551045	2.051063e-08
0.438391	1.550931	2.072453e-08
0.439384	1.550818	2.093891e-08
0.44	1.550748	2.107200e-08
0.440379	1.550705	2.102045e-08
0.441376	1.550593	2.088468e-08
0.442375	1.550482	2.074860e-08
0.443377	1.550371	2.061221e-08
0.444381	1.550261	2.047551e-08
0.445387	1.550151	2.033851e-08
0.446396	1.550042	2.020119e-08
0.447407	1.549933	2.006357e-08
0.44842	1.549825	1.992563e-08
0.449435	1.549717	1.978738e-08
0.450453	1.54961	1.964881e-08
0.451473	1.549503	1.950994e-08
0.452495	1.549397	1.937075e-08
0.45352	1.549291	1.923124e-08
0.454547	1.549186	1.909142e-08
0.455576	1.549082	1.895128e-08
0.456608	1.548978	1.881082e-08
0.457642	1.548874	1.867004e-08
0.458678	1.548771	1.852895e-08
0.459717	1.548668	1.838754e-08
0.46	1.54864	1.834900e-08
0.460758	1.548566	1.823383e-08
0.461801	1.548464	1.807529e-08
0.462847	1.548363	1.791639e-08
0.463895	1.548263	1.775713e-08
0.464946	1.548163	1.759751e-08
0.465998	1.548063	1.743753e-08
0.467054	1.547964	1.727719e-08
0.468111	1.547865	1.711648e-08
0.469171	1.547767	1.695541e-08
0.470234	1.547669	1.679398e-08
0.471299	1.547571	1.663218e-08
0.472366	1.547475	1.647001e-08
0.473435	1.547378	1.630748e-08
0.474508	1.547282	1.614458e-08
0.475582	1.547187	1.598131e-08
0.476659	1.547092	1.581767e-08
0.477738	1.546997	1.565365e-08
0.47882	1.546903	1.548927e-08
0.479904	1.546809	1.532452e-08
0.48	1.546801	1.531000e-08
0.480991	1.546716	1.494602e-08
0.48208	1.546623	1.454606e-08
0.483172	1.546531	1.414519e-08
0.484266	1.546439	1.374341e-08
0.485363	1.546347	1.334072e-08
0.486462	1.546256	1.293712e-08
0.487563	1.546165	1.253261e-08
0.488667	1.546075	1.212718e-08
0.489774	1.545985	1.172083e-08
0.490883	1.545896	1.131356e-08
0.491995	1.545807	1.090537e-08
0.493109	1.545718	1.049625e-08
0.494225	1.54563	1.008621e-08
0.495345	1.545542	9.675244e-09
0.496466	1.545455	9.263344e-09
0.49759	1.545368	8.850511e-09
0.498717	1.545282	8.436743e-09
0.499847	1.545196	8.022038e-09
0.5	1.545184	7.965700e-09
0.500978	1.54511	7.981289e-09
0.502113	1.545025	7.999363e-09
0.50325	1.54494	8.017478e-09
0.50439	1.544855	8.035634e-09
0.505532	1.544771	8.053831e-09
0.506676	1.544687	8.072069e-09
0.507824	1.544604	8.090348e-09
0.508974	1.544521	8.108669e-09
0.510126	1.544438	8.127032e-09
0.511281	1.544356	8.145436e-09
0.512439	1.544274	8.163882e-09
0.5136	1.544193	8.182369e-09
0.514763	1.544112	8.200898e-09
0.515928	1.544031	8.219470e-09
0.517097	1.543951	8.238083e-09
0.518268	1.543871	8.256738e-09
0.519441	1.543791	8.275436e-09
0.520617	1.543712	8.294176e-09
0.521796	1.543633	8.312959e-09
0.522978	1.543555	8.331784e-09
0.524162	1.543476	8.350651e-09
0.525349	1.543399	8.369562e-09
0.526539	1.543321	8.388515e-09
0.527731	1.543244	8.407511e-09
0.528926	1.543167	8.426550e-09
0.530124	1.543091	8.445632e-09
0.531324	1.543015	8.464758e-09
0.532527	1.542939	8.483927e-09
0.533733	1.542864	8.503139e-09
0.534942	1.542789	8.522395e-09
0.536153	1.542714	8.541694e-09
0.537367	1.54264	8.561037e-09
0.538584	1.542566	8.580424e-09
0.539804	1.542492	8.599854e-09
0.541026	1.542419	8.619329e-09
0.542251	1.542346	8.638848e-09
0.543479	1.542273	8.658411e-09
0.54471	1.542201	8.678018e-09
0.545943	1.542129	8.697670e-09
0.54718	1.542057	8.717366e-09
0.548419	1.541986	8.737107e-09
0.549661	1.541915	8.756892e-09
0.55	1.541895	8.762300e-09
0.550905	1.541844	8.776722e-09
0.552153	1.541774	8.796598e-09
0.553403	1.541704	8.816518e-09
0.554656	1.541634	8.836483e-09
0.555912	1.541564	8.856494e-09
0.557171	1.541495	8.876550e-09
0.558433	1.541426	8.896651e-09
0.559697	1.541358	8.916798e-09
0.560965	1.541289	8.936990e-09
0.562235	1.541221	8.957228e-09
0.563508	1.541154	8.977512e-09
0.564784	1.541086	8.997842e-09
0.566063	1.541019	9.018218e-09
0.567345	1.540953	9.038640e-09
0.56863	1.540886	9.059108e-09
0.569917	1.54082	9.079623e-09
0.571208	1.540754	9.100184e-09
0.572501	1.540688	9.120792e-09
0.573798	1.540623	9.141446e-09
0.575097	1.540558	9.162147e-09
0.576399	1.540493	9.182895e-09
0.577705	1.540429	9.203690e-09
0.579013	1.540365	9.224532e-09
0.580324	1.540301	9.245421e-09
0.581638	1.540237	9.266358e-09
0.582955	1.540174	9.287342e-09
0.584275	1.540111	9.308373e-09
0.585598	1.540048	9.329452e-09
0.586924	1.539985	9.350579e-09
0.588253	1.539923	9.371754e-09
0.589586	1.539861	9.392977e-09
0.590921	1.539799	9.414247e-09
0.592259	1.539738	9.435566e-09
0.5936	1.539677	9.456933e-09
0.594944	1.539616	9.478349e-09
0.596291	1.539555	9.499813e-09
0.597642	1.539494	9.521325e-09
0.598995	1.539434	9.542887e-09
0.6	1.53939	9.558900e-09
0.600351	1.539374	9.600929e-09
0.601711	1.539315	9.763579e-09
0.603073	1.539255	9.926597e-09
0.604439	1.539196	1.008998e-08
0.605808	1.539137	1.025374e-08
0.60718	1.539078	1.041787e-08
0.608554	1.53902	1.058237e-08
0.609932	1.538962	1.074724e-08
0.611314	1.538904	1.091249e-08
0.612698	1.538846	1.107811e-08
0.614085	1.538789	1.124410e-08
0.615476	1.538731	1.141047e-08
0.61687	1.538674	1.157722e-08
0.618267	1.538618	1.174434e-08
0.619667	1.538561	1.191185e-08
0.62107	1.538505	1.207973e-08
0.622476	1.538449	1.224799e-08
0.623886	1.538393	1.241664e-08
0.625299	1.538337	1.258566e-08
0.626714	1.538282	1.275507e-08
0.628134	1.538227	1.292486e-08
0.629556	1.538172	1.309504e-08
0.630982	1.538117	1.326560e-08
0.63241	1.538063	1.343655e-08
0.633843	1.538009	1.360789e-08
0.635278	1.537955	1.377961e-08
0.636716	1.537901	1.395172e-08
0.638158	1.537847	1.412422e-08
0.639603	1.537794	1.429712e-08
0.641052	1.537741	1.447040e-08
0.642503	1.537688	1.464408e-08
0.643958	1.537635	1.481815e-08
0.645416	1.537582	1.499261e-08
0.646878	1.53753	1.516747e-08
0.648343	1.537478	1.534273e-08
0.649811	1.537426	1.551838e-08
0.65	1.537419	1.554100e-08
0.651282	1.537374	1.542843e-08
0.652757	1.537323	1.529897e-08
0.654235	1.537272	1.516922e-08
0.655717	1.53722	1.503918e-08
0.657202	1.53717	1.490884e-08
0.65869	1.537119	1.477820e-08
0.660181	1.537068	1.464727e-08
0.661676	1.537018	1.451605e-08
0.663175	1.536968	1.438452e-08
0.664676	1.536918	1.425270e-08
0.666182	1.536868	1.412058e-08
0.66769	1.536819	1.398816e-08
0.669202	1.536769	1.385544e-08
0.670717	1.53672	1.372242e-08
0.672236	1.536671	1.358910e-08
0.673759	1.536622	1.345548e-08
0.675284	1.536574	1.332155e-08
0.676813	1.536525	1.318732e-08
0.678346	1.536477	1.305279e-08
0.679882	1.536429	1.291795e-08
0.681422	1.536381	1.278281e-08
0.682965	1.536333	1.264736e-08
0.684511	1.536286	1.251160e-08
0.686061	1.536238	1.237554e-08
0.687615	1.536191	1.223917e-08
0.689172	1.536144	1.210249e-08
0.690733	1.536097	1.196550e-08
0.692297	1.536051	1.182820e-08
0.693864	1.536004	1.169059e-08
0.695436	1.535958	1.155267e-08
0.69701	1.535912	1.141443e-08
0.698589	1.535866	1.127588e-08
0.7	1.535825	1.115200e-08
0.700171	1.53582	0
0.701756	1.535774	0
0.703345	1.535729	0
0.704938	1.535683	0
0.706534	1.535638	0
0.708134	1.535593	0
0.709738	1.535548	0
0.711345	1.535504	0
0.712956	1.535459	0
0.71457	1.535415	0
0.716188	1.53537	0
0.71781	1.535326	0
0.719435	1.535282	0
0.721065	1.535239	0
0.722697	1.535195	0
0.724334	1.535151	0
0.725974	1.535108	0
0.727618	1.535065	0
0.729266	1.535022	0
0.730917	1.534979	0
0.732572	1.534936	0
0.734231	1.534894	0
0.735894	1.534851	0
0.73756	1.534809	0
0.73923	1.534766	0
0.740904	1.534724	0
0.742582	1.534682	0
0.744264	1.534641	0
0.745949	1.534599	0
0.747638	1.534557	0
0.749331	1.534516	0
0.751028	1.534475	0
0.752729	1.534434	0
0.754433	1.534393	0
0.756142	1.534352	0
0.757854	1.534311	0
0.75957	1.53427	0
0.76129	1.53423	0
0.763014	1.53419	0
0.764742	1.534149	0
0.766473	1.534109	0
0.768209	1.534069	0
0.769949	1.534029	0
0.771692	1.533989	0
0.77344	1.53395	0
0.775191	1.53391	0
0.776946	1.533871	0
0.778706	1.533832	0
0.780469	1.533792	0
0.782236	1.533753	0
0.784008	1.533714	0
0.785783	1.533675	0
0.787563	1.533637	0
0.789346	1.533598	0
0.791133	1.53356	0
0.792925	1.533521	0
0.79472	1.533483	0
0.79652	1.533445	0
0.798324	1.533407	0
0.800131	1.533369	0
0.801943	1.533331	0
0.803759	1.533293	0
0.805579	1.533255	0
0.807404	1.533218	0
0.809232	1.53318	0
0.811064	1.533143	0
0.812901	1.533105	0
0.814742	1.533068	0
0.816587	1.533031	0
0.818436	1.532994	0
0.820289	1.532957	0
0.822147	1.53292	0
0.824008	1.532884	0
0.825874	1.532847	0
0.827744	1.53281	0
0.829619	1.532774	0
0.831498	1.532738	0
0.83338	1.532701	0
0.835268	1.532665	0
0.837159	1.532629	0
0.839055	1.532593	0
0.840955	1.532557	0
0.842859	1.532521	0
0.844768	1.532485	0
0.846681	1.53245	0
0.848598	1.532414	0
0.850519	1.532379	0
0.852445	1.532343	0
0.854376	1.532308	0
0.85631	1.532272	0
0.85825	1.532237	0
0.860193	1.532202	0
0.862141	1.532167	0
0.864093	1.532132	0
0.86605	1.532097	0
0.868011	1.532062	0
0.869977	1.532027	0
0.871947	1.531993	0
0.873921	1.531958	0
0.8759	1.531923	0
0.877883	1.531889	0
0.879871	1.531854	0
0.881864	1.53182	0
0.883861	1.531786	0
0.885862	1.531751	0
0.887868	1.531717	0
0.889879	1.531683	0
0.891894	1.531649	0
0.893914	1.531615	0
0.895938	1.531581	0
0.897967	1.531547	0
0.9	1.531513	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: —

BAL12 (OHARA): all datasets

BAL (Barium, low-index)

BAL12 n,k 0.365–0.9 µm default

About BAL12 (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 BAL12 (OHARA) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/ohara/optical/BAL12.yml
ID: ds_5de42d2b3617
API: /v1/datasets/ds_5de42d2b3617

Plot