Optical constants

Refractive index of BAC4 (HOYA)

BAC4: n,k 0.365–1.014 µm

Data: formula 3 + tabulated k
Range: 0.365–1.014 µm
Temperature: 293 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.56883
Extinction coefficient k: 1.40486e-08

Permittivity ε₁: 2.46122
Permittivity ε₂: 4.40798e-08

Absorption coefficient α: 0.00300443 cm⁻¹
Penetration depth δ = λ/(2πk): 6.65683e+09 nm

Abbe number V_d: 56.044
Chromatic dispersion dn/dλ: -0.0523131 µm⁻¹

Group index n_g: 1.59957
Group velocity dispersion: 92.4203 fs²/mm

Dispersion parameter D: -504.202 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

# BAC4 (HOYA): BAC4
hoya_bac4 = ls.fetch_refractiveindex("specs", "HOYA-optical", "BAC4", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hoya_bac4.range_nm)  # (365.01, 1013.98) nm
eps = hoya_bac4.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_fca5e9904cff/lightsmith"
hoya_bac4 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hoya_bac4.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (hoya-bac4/hoya).

# ... load hoya_bac4 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hoya_bac4)],
    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} = 2.4196645 - 0.0083329314 λ^{2.0} + 0.01539739 λ^{- 2.0} - 0.00017391654 λ^{- 4.0} + 6.218322 \times 10^{-5} λ^{- 6.0} - 3.062131 \times 10^{-6} λ^{- 8.0}

Valid from 0.36501 to 1.01398 µm.

Coefficients as stored

C_i	Value
C1	2.4196645
C2	-0.0083329314
C3	2.0
C4	0.01539739
C5	-2.0
C6	-0.00017391654
C7	-4.0
C8	6.218322e-05
C9	-6.0
C10	-3.062131e-06
C11	-8.0

Comments and conditions

General glass Type

Conditions

temperature: 293 K

Properties

thermal dispersion: type: formula A, coefficients: 9.31e-06 1.09e-08 -5.68e-11 4.67e-07 7.99e-10 0.248
nd: 1.56883
Vd: 56.04
glass code: 569560
density: value: 2850
thermal expansion: value: 5.3e-06, temperature range: 243 343; value: 6.9e-06, temperature range: 293 573
dPgF: 0.001
resistance: acid: 1.0; stain: 1.0; climatic: 1.0

Thermo-optic coefficient

Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = 4.96e-06 K⁻¹ at 633 nm

References

HOYA Zemax catalog 2017-04-01 (obtained from http://www.hoya-opticalworld.com)

Cite

HOYA Zemax catalog 2017-04-01 (obtained from http://www.hoya-opticalworld.com); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 421 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

BAC4 (HOYA), BAC4: n and k versus wavelength
λ (µm)	n	k
0.36501	1.59402	1.455796e-07
0.365946	1.5938	1.385222e-07
0.366884	1.593582	1.314466e-07
0.367825	1.593365	1.243530e-07
0.368768	1.593149	1.172411e-07
0.369713	1.592934	1.101111e-07
0.37	1.59287	1.079500e-07
0.370661	1.592721	1.056690e-07
0.371612	1.592509	1.023912e-07
0.372565	1.592298	9.910496e-08
0.37352	1.592088	9.581033e-08
0.374477	1.59188	9.250725e-08
0.375438	1.591672	8.919570e-08
0.3764	1.591466	8.587565e-08
0.377365	1.591261	8.254710e-08
0.378333	1.591058	7.921001e-08
0.379303	1.590855	7.586437e-08
0.38	1.590711	7.346000e-08
0.380275	1.590654	7.272868e-08
0.38125	1.590453	7.013953e-08
0.382228	1.590254	6.754374e-08
0.383208	1.590057	6.494130e-08
0.38419	1.58986	6.233218e-08
0.385176	1.589664	5.971638e-08
0.386163	1.58947	5.709386e-08
0.387153	1.589277	5.446463e-08
0.388146	1.589084	5.182865e-08
0.389141	1.588893	4.918591e-08
0.39	1.58873	4.690500e-08
0.390139	1.588703	4.678733e-08
0.391139	1.588515	4.593938e-08
0.392142	1.588327	4.508925e-08
0.393147	1.58814	4.423694e-08
0.394155	1.587955	4.338244e-08
0.395166	1.58777	4.252575e-08
0.396179	1.587587	4.166687e-08
0.397195	1.587405	4.080578e-08
0.398213	1.587223	3.994249e-08
0.399234	1.587043	3.907698e-08
0.4	1.586909	3.842800e-08
0.400258	1.586864	3.836559e-08
0.401284	1.586686	3.811739e-08
0.402313	1.586509	3.786856e-08
0.403345	1.586333	3.761909e-08
0.404379	1.586158	3.736897e-08
0.405416	1.585984	3.711822e-08
0.406455	1.585811	3.686682e-08
0.407497	1.585639	3.661478e-08
0.408542	1.585468	3.636210e-08
0.40959	1.585299	3.610876e-08
0.41064	1.58513	3.585478e-08
0.411693	1.584962	3.560014e-08
0.412748	1.584795	3.534485e-08
0.413806	1.584629	3.508891e-08
0.414867	1.584464	3.483231e-08
0.415931	1.5843	3.457505e-08
0.416998	1.584137	3.431713e-08
0.418067	1.583975	3.405856e-08
0.419139	1.583814	3.379932e-08
0.42	1.583685	3.359100e-08
0.420213	1.583653	3.357035e-08
0.421291	1.583494	3.346606e-08
0.422371	1.583336	3.336150e-08
0.423454	1.583178	3.325667e-08
0.42454	1.583022	3.315157e-08
0.425628	1.582866	3.304620e-08
0.426719	1.582711	3.294056e-08
0.427813	1.582558	3.283466e-08
0.42891	1.582405	3.272848e-08
0.43001	1.582253	3.262202e-08
0.431113	1.582102	3.251530e-08
0.432218	1.581951	3.240830e-08
0.433326	1.581802	3.230103e-08
0.434437	1.581653	3.219348e-08
0.435551	1.581506	3.208566e-08
0.436668	1.581359	3.197755e-08
0.437787	1.581213	3.186918e-08
0.43891	1.581068	3.176052e-08
0.44	1.580928	3.165500e-08
0.440035	1.580923	3.165103e-08
0.441163	1.58078	3.152393e-08
0.442295	1.580637	3.139651e-08
0.443429	1.580495	3.126876e-08
0.444566	1.580354	3.114069e-08
0.445705	1.580214	3.101228e-08
0.446848	1.580075	3.088355e-08
0.447994	1.579936	3.075449e-08
0.449143	1.579798	3.062509e-08
0.450294	1.579661	3.049537e-08
0.451449	1.579525	3.036531e-08
0.452606	1.579389	3.023491e-08
0.453767	1.579255	3.010419e-08
0.45493	1.579121	2.997313e-08
0.456097	1.578988	2.984173e-08
0.457266	1.578855	2.970999e-08
0.458438	1.578724	2.957792e-08
0.459614	1.578593	2.944551e-08
0.46	1.57855	2.940200e-08
0.460792	1.578462	2.914790e-08
0.461974	1.578333	2.876895e-08
0.463158	1.578204	2.838903e-08
0.464346	1.578076	2.800813e-08
0.465536	1.577949	2.762625e-08
0.46673	1.577822	2.724340e-08
0.467927	1.577696	2.685957e-08
0.469126	1.577571	2.647475e-08
0.470329	1.577447	2.608894e-08
0.471535	1.577323	2.570215e-08
0.472744	1.5772	2.531436e-08
0.473956	1.577078	2.492558e-08
0.475171	1.576956	2.453580e-08
0.47639	1.576835	2.414502e-08
0.477611	1.576714	2.375324e-08
0.478836	1.576595	2.336046e-08
0.48	1.576482	2.298700e-08
0.480063	1.576476	2.297736e-08
0.481294	1.576357	2.279008e-08
0.482528	1.57624	2.260232e-08
0.483765	1.576123	2.241408e-08
0.485006	1.576006	2.222536e-08
0.486249	1.57589	2.203616e-08
0.487496	1.575775	2.184647e-08
0.488746	1.575661	2.165629e-08
0.489999	1.575547	2.146563e-08
0.491255	1.575433	2.127448e-08
0.492515	1.575321	2.108284e-08
0.493778	1.575209	2.089070e-08
0.495044	1.575097	2.069808e-08
0.496313	1.574986	2.050495e-08
0.497586	1.574876	2.031134e-08
0.498861	1.574767	2.011723e-08
0.5	1.574669	1.994400e-08
0.500141	1.574658	1.992490e-08
0.501423	1.574549	1.975066e-08
0.502709	1.574441	1.957597e-08
0.503997	1.574334	1.940083e-08
0.50529	1.574227	1.922524e-08
0.506585	1.574121	1.904920e-08
0.507884	1.574016	1.887271e-08
0.509186	1.573911	1.869577e-08
0.510492	1.573806	1.851837e-08
0.511801	1.573702	1.834052e-08
0.513113	1.573599	1.816221e-08
0.514429	1.573496	1.798345e-08
0.515748	1.573394	1.780423e-08
0.51707	1.573292	1.762454e-08
0.518396	1.573191	1.744440e-08
0.519725	1.57309	1.726380e-08
0.521057	1.57299	1.708273e-08
0.522393	1.572891	1.690120e-08
0.523733	1.572792	1.671920e-08
0.525076	1.572693	1.653673e-08
0.526422	1.572595	1.635380e-08
0.527772	1.572498	1.617040e-08
0.529125	1.572401	1.598653e-08
0.530481	1.572304	1.580219e-08
0.531842	1.572208	1.561737e-08
0.533205	1.572113	1.543208e-08
0.534572	1.572018	1.524632e-08
0.535943	1.571923	1.506008e-08
0.537317	1.571829	1.487336e-08
0.538695	1.571736	1.468616e-08
0.540076	1.571643	1.449849e-08
0.541461	1.57155	1.431033e-08
0.542849	1.571458	1.412169e-08
0.544241	1.571366	1.393256e-08
0.545636	1.571275	1.374295e-08
0.547035	1.571185	1.355286e-08
0.548438	1.571094	1.336228e-08
0.549844	1.571005	1.317120e-08
0.55	1.570995	1.315000e-08
0.551254	1.570915	1.317996e-08
0.552667	1.570826	1.321374e-08
0.554084	1.570738	1.324761e-08
0.555505	1.57065	1.328156e-08
0.556929	1.570563	1.331561e-08
0.558357	1.570476	1.334973e-08
0.559789	1.570389	1.338395e-08
0.561224	1.570303	1.341825e-08
0.562663	1.570217	1.345264e-08
0.564106	1.570132	1.348712e-08
0.565552	1.570047	1.352169e-08
0.567002	1.569962	1.355635e-08
0.568456	1.569878	1.359109e-08
0.569913	1.569794	1.362593e-08
0.571374	1.569711	1.366085e-08
0.572839	1.569628	1.369586e-08
0.574308	1.569546	1.373097e-08
0.575781	1.569464	1.376616e-08
0.577257	1.569382	1.380144e-08
0.578737	1.569301	1.383682e-08
0.580221	1.56922	1.387228e-08
0.581709	1.56914	1.390784e-08
0.5832	1.56906	1.394348e-08
0.584695	1.56898	1.397922e-08
0.586195	1.568901	1.401505e-08
0.587697	1.568822	1.405097e-08
0.589204	1.568744	1.408698e-08
0.590715	1.568665	1.412309e-08
0.59223	1.568588	1.415929e-08
0.593748	1.56851	1.419558e-08
0.59527	1.568433	1.423196e-08
0.596797	1.568357	1.426844e-08
0.598327	1.56828	1.430501e-08
0.599861	1.568204	1.434168e-08
0.6	1.568198	1.434500e-08
0.601399	1.568129	1.466908e-08
0.602941	1.568054	1.502629e-08
0.604487	1.567979	1.538442e-08
0.606037	1.567904	1.574347e-08
0.607591	1.56783	1.610343e-08
0.609148	1.567756	1.646432e-08
0.61071	1.567683	1.682614e-08
0.612276	1.56761	1.718888e-08
0.613846	1.567537	1.755255e-08
0.61542	1.567465	1.791716e-08
0.616998	1.567393	1.828270e-08
0.61858	1.567321	1.864918e-08
0.620166	1.56725	1.901659e-08
0.621756	1.567178	1.938495e-08
0.62335	1.567108	1.975426e-08
0.624948	1.567037	2.012451e-08
0.626551	1.566967	2.049571e-08
0.628157	1.566897	2.086786e-08
0.629768	1.566828	2.124096e-08
0.631382	1.566759	2.161502e-08
0.633001	1.56669	2.199005e-08
0.634624	1.566621	2.236603e-08
0.636251	1.566553	2.274298e-08
0.637883	1.566485	2.312089e-08
0.639518	1.566418	2.349977e-08
0.641158	1.56635	2.387963e-08
0.642802	1.566283	2.426045e-08
0.64445	1.566217	2.464226e-08
0.646102	1.56615	2.502504e-08
0.647759	1.566084	2.540880e-08
0.64942	1.566018	2.579355e-08
0.65	1.565995	2.592800e-08
0.651085	1.565953	2.584986e-08
0.652754	1.565887	2.572960e-08
0.654428	1.565823	2.560903e-08
0.656106	1.565758	2.548815e-08
0.657788	1.565693	2.536696e-08
0.659474	1.565629	2.524546e-08
0.661165	1.565565	2.512365e-08
0.662861	1.565502	2.500153e-08
0.66456	1.565439	2.487909e-08
0.666264	1.565376	2.475634e-08
0.667972	1.565313	2.463328e-08
0.669685	1.56525	2.450990e-08
0.671402	1.565188	2.438620e-08
0.673123	1.565126	2.426219e-08
0.674849	1.565065	2.413786e-08
0.67658	1.565003	2.401321e-08
0.678314	1.564942	2.388824e-08
0.680053	1.564881	2.376295e-08
0.681797	1.56482	2.363734e-08
0.683545	1.56476	2.351140e-08
0.685298	1.5647	2.338515e-08
0.687055	1.56464	2.325857e-08
0.688816	1.56458	2.313166e-08
0.690583	1.564521	2.300443e-08
0.692353	1.564462	2.287687e-08
0.694128	1.564403	2.274899e-08
0.695908	1.564344	2.262078e-08
0.697692	1.564286	2.249224e-08
0.699481	1.564228	2.236337e-08
0.7	1.564211	2.232600e-08
0.701275	1.56417	2.221398e-08
0.703073	1.564112	2.205597e-08
0.704875	1.564055	2.189755e-08
0.706683	1.563997	2.173873e-08
0.708495	1.56394	2.157950e-08
0.710311	1.563883	2.141986e-08
0.712132	1.563827	2.125981e-08
0.713958	1.563771	2.109935e-08
0.715789	1.563714	2.093848e-08
0.717624	1.563659	2.077720e-08
0.719464	1.563603	2.061550e-08
0.721309	1.563547	2.045339e-08
0.723158	1.563492	2.029086e-08
0.725012	1.563437	2.012792e-08
0.726871	1.563382	1.996456e-08
0.728735	1.563328	1.980078e-08
0.730603	1.563273	1.963658e-08
0.732477	1.563219	1.947196e-08
0.734355	1.563165	1.930692e-08
0.736237	1.563111	1.914145e-08
0.738125	1.563058	1.897556e-08
0.740018	1.563004	1.880925e-08
0.741915	1.562951	1.864250e-08
0.743817	1.562898	1.847533e-08
0.745724	1.562845	1.830774e-08
0.747636	1.562793	1.813971e-08
0.749553	1.56274	1.797125e-08
0.75	1.562728	1.793200e-08
0.751475	1.562688	1.766130e-08
0.753402	1.562636	1.730774e-08
0.755334	1.562584	1.695328e-08
0.75727	1.562533	1.659790e-08
0.759212	1.562481	1.624161e-08
0.761159	1.56243	1.588441e-08
0.76311	1.562379	1.552630e-08
0.765067	1.562328	1.516726e-08
0.767028	1.562277	1.480731e-08
0.768995	1.562227	1.444643e-08
0.770967	1.562176	1.408463e-08
0.772943	1.562126	1.372190e-08
0.774925	1.562076	1.335824e-08
0.776912	1.562026	1.299364e-08
0.778904	1.561977	1.262812e-08
0.78	1.56195	1.242700e-08
0.780901	1.561927	1.244133e-08
0.782903	1.561878	1.247316e-08
0.784911	1.561829	1.250508e-08
0.786923	1.56178	1.253708e-08
0.788941	1.561731	1.256916e-08
0.790964	1.561682	1.260132e-08
0.792992	1.561634	1.263357e-08
0.795025	1.561586	1.266589e-08
0.797063	1.561537	1.269830e-08
0.799107	1.561489	1.273080e-08
0.8	1.561469	1.274500e-08
0.801156	1.561442	1.276341e-08
0.80321	1.561394	1.279614e-08
0.805269	1.561346	1.282896e-08
0.807334	1.561299	1.286185e-08
0.809404	1.561252	1.289484e-08
0.811479	1.561205	1.292790e-08
0.81356	1.561158	1.296105e-08
0.815646	1.561111	1.299429e-08
0.817737	1.561064	1.302761e-08
0.819834	1.561018	1.306102e-08
0.821936	1.560972	1.309451e-08
0.824043	1.560925	1.312809e-08
0.826156	1.560879	1.316175e-08
0.828274	1.560833	1.319550e-08
0.83	1.560796	1.322300e-08
0.830398	1.560788	1.322935e-08
0.832527	1.560742	1.326331e-08
0.834662	1.560697	1.329735e-08
0.836802	1.560651	1.333149e-08
0.838947	1.560606	1.336571e-08
0.841098	1.560561	1.340002e-08
0.843255	1.560516	1.343441e-08
0.845417	1.560471	1.346890e-08
0.847584	1.560426	1.350347e-08
0.849758	1.560382	1.353813e-08
0.85	1.560377	1.354200e-08
0.851936	1.560337	1.357283e-08
0.854121	1.560293	1.360760e-08
0.856311	1.560249	1.364247e-08
0.858506	1.560205	1.367742e-08
0.860707	1.560161	1.371246e-08
0.862914	1.560117	1.374759e-08
0.865127	1.560073	1.378282e-08
0.867345	1.56003	1.381813e-08
0.869569	1.559986	1.385353e-08
0.871798	1.559943	1.388903e-08
0.874033	1.5599	1.392461e-08
0.876274	1.559856	1.396029e-08
0.878521	1.559813	1.399606e-08
0.880774	1.55977	1.403192e-08
0.883032	1.559728	1.406787e-08
0.885296	1.559685	1.410391e-08
0.887566	1.559642	1.414005e-08
0.889842	1.5596	1.417628e-08
0.892123	1.559558	1.421260e-08
0.894411	1.559515	1.424902e-08
0.896704	1.559473	1.428552e-08
0.899003	1.559431	1.432213e-08
0.9	1.559413	1.433800e-08
0.901308	1.559389	1.435885e-08
0.903619	1.559347	1.439568e-08
0.905936	1.559306	1.443261e-08
0.908258	1.559264	1.446964e-08
0.910587	1.559222	1.450676e-08
0.912922	1.559181	1.454398e-08
0.915263	1.55914	1.458129e-08
0.917609	1.559098	1.461869e-08
0.919962	1.559057	1.465619e-08
0.922321	1.559016	1.469379e-08
0.924686	1.558975	1.473149e-08
0.927056	1.558934	1.476928e-08
0.929433	1.558893	1.480717e-08
0.931816	1.558853	1.484515e-08
0.934206	1.558812	1.488324e-08
0.936601	1.558771	1.492142e-08
0.939002	1.558731	1.495970e-08
0.94141	1.55869	1.499807e-08
0.943824	1.55865	1.503655e-08
0.946244	1.55861	1.507512e-08
0.94867	1.55857	1.511379e-08
0.95	1.558548	1.513500e-08
0.951102	1.55853	1.515254e-08
0.953541	1.55849	1.519137e-08
0.955985	1.55845	1.523029e-08
0.958437	1.55841	1.526931e-08
0.960894	1.55837	1.530843e-08
0.963358	1.55833	1.534765e-08
0.965828	1.558291	1.538698e-08
0.968304	1.558251	1.542640e-08
0.970787	1.558212	1.546592e-08
0.973276	1.558172	1.550555e-08
0.975771	1.558133	1.554528e-08
0.978273	1.558094	1.558511e-08
0.980781	1.558055	1.562504e-08
0.983296	1.558015	1.566507e-08
0.985817	1.557976	1.570521e-08
0.988345	1.557937	1.574545e-08
0.990879	1.557898	1.578579e-08
0.993419	1.557859	1.582624e-08
0.995967	1.557821	1.586679e-08
0.99852	1.557782	1.590744e-08
1	1.557759	1.593100e-08
1.00108	1.557743	1.594822e-08
1.00365	1.557704	1.598913e-08
1.00622	1.557666	1.603015e-08
1.0088	1.557627	1.607128e-08
1.01139	1.557589	1.611251e-08
1.01398	1.55755	1.615384e-08

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: —

BAC4 (HOYA): all datasets

BaC (Barium crown)

BAC4 n,k 0.365–1.014 µm default

About BAC4 (HOYA)

HOYA Corporation is a global technology company based in Japan, known for its diverse range of products in the fields of healthcare and optics. In the optical industry, HOYA is particularly recognized for its high-quality optical glass and lens technologies. The company produces a wide array of optical products, from eyeglass lenses with advanced coatings to specialized glass materials used in cameras, telescopes, and other precision optical instruments. HOYA's expertise extends to various types of optical glass, including low-dispersion and high-refractive-index materials, which find applications in situations requiring exceptional optical clarity and performance. Beyond its contributions to optics, HOYA has also ventured into medical technologies, making it a multi-faceted company with a broad impact. With a commitment to innovation and quality, HOYA has earned a reputation as a leader in its field, consistently delivering products that set industry standards for performance and reliability. Their expansive portfolio and technological prowess make them a go-to provider for both consumer and industrial optical solutions.

More about BAC4 (HOYA) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/specs/hoya/optical/BAC4.yml
ID: ds_fca5e9904cff
API: /v1/datasets/ds_fca5e9904cff

Plot