Optical constants

Refractive index of J-BALF4 (HIKARI)

J-BALF4: n,k 0.365–2.058 µm

Data
formula 3 + tabulated k
Range
0.365–2.058 µm
Temperature
296 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.365–2.058 µm
Refractive index n
1.57957
Extinction coefficient k
1.51379e-08
Permittivity ε1
2.49503
Permittivity ε2
4.78225e-08
Absorption coefficient α
0.00323737 cm⁻¹
Penetration depth δ = λ/(2πk)
6.17785e+09 nm
Abbe number Vd
53.743
Chromatic dispersion dn/dλ
-0.05548 µm⁻¹
Group index ng
1.61217
Group velocity dispersion
99.7593 fs²/mm
Dispersion parameter D
-544.24 ps/(nm·km)
Photon energy
2.11001 eV

ε = (n + ik)², α = 4πk/λ, ng = 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

# J-BALF4 (HIKARI): J-BALF4
hikari_j_balf4 = ls.fetch_refractiveindex("specs", "HIKARI-optical", "J-BALF4", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hikari_j_balf4.range_nm)  # (365.015, 2058.09) nm
eps = hikari_j_balf4.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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
n2=2.45156936−0.00835914203⁢λ2.0−8.88499407×10-5⁢λ4.0+0.0153016408⁢λ−2.0+0.00022451288⁢λ−4.0+5.89498036×10-6⁢λ−6.0+2.59209632×10-7⁢λ−8.0

Valid from 0.365015 to 2.05809 µm.

Coefficients as stored
CiValue
C12.45156936
C2-0.00835914203
C32.0
C4-8.88499407e-05
C54.0
C60.0153016408
C7-2.0
C80.00022451288
C9-4.0
C105.89498036e-06
C11-6.0
C122.59209632e-07
C13-8.0

Comments and conditions

Conditions

temperature
296 K

Properties

thermal dispersion
type: formula A, coefficients: 3.191e-07 1.2703e-08 -2.0786e-13 6.7769e-07 7.3747e-10 0.17881
nd
1.579570
Vd
53.742830
density
value: 3130
thermal expansion
value: 8e-06, temperature range: 243 343
dPgF
-0.0023
resistance
phosphate: 3.0

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 296.0 K): dn/dT = 1.02e-06 K⁻¹ at 633 nm, dn/dT = 3.34e-07 K⁻¹ at 1310 nm, dn/dT = 2.78e-07 K⁻¹ at 1550 nm

References

Cite

NIKON Zemax catalog 2017-11 (obtained from http://www.nikon.com); See also HIKARI 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 421 wavelengths, the same grid as the API and the library
J-BALF4 (HIKARI), J-BALF4: n and k versus wavelength
λ (µm)nk
0.3650151.6066312.896828e-07
0.3666011.6062232.624878e-07
0.3681931.6058192.351747e-07
0.3697931.6054212.077430e-07
0.371.6053692.041900e-07
0.3713991.6050261.911318e-07
0.3730131.6046361.760751e-07
0.3746331.604251.609530e-07
0.3762611.6038681.457653e-07
0.3778951.603491.305115e-07
0.3795371.6031171.151915e-07
0.381.6030121.108700e-07
0.3811861.6027471.059102e-07
0.3828421.6023829.898327e-08
0.3845051.602029.202630e-08
0.3861751.6016628.503910e-08
0.3878531.6013087.802155e-08
0.3895381.6009587.097352e-08
0.391.6008636.904000e-08
0.391231.6006126.567125e-08
0.392931.6002696.101640e-08
0.3946371.599935.634133e-08
0.3963511.5995945.164594e-08
0.3980731.5992624.693016e-08
0.3998021.5989344.219390e-08
0.41.5988964.165200e-08
0.4015391.5986094.051270e-08
0.4032831.5982873.922133e-08
0.4050351.5979683.792436e-08
0.4067951.5976533.662175e-08
0.4085621.5973413.531348e-08
0.4103371.5970333.399953e-08
0.412121.5967273.267987e-08
0.413911.5964253.135448e-08
0.4157081.5961263.002333e-08
0.4175141.5958292.868640e-08
0.4193281.5955362.734366e-08
0.421.5954292.684600e-08
0.4211491.5952462.671669e-08
0.4229791.5949592.651086e-08
0.4248171.5946752.630414e-08
0.4266621.5943932.609652e-08
0.4285161.5941142.588800e-08
0.4303771.5938392.567858e-08
0.4322471.5935652.546824e-08
0.4341251.5932952.525699e-08
0.436011.5930272.504482e-08
0.4379051.5927622.483173e-08
0.4398071.59252.461772e-08
0.441.5924742.459600e-08
0.4417181.592242.469201e-08
0.4436371.5919832.479928e-08
0.4455641.5917282.490702e-08
0.4474991.5914762.501522e-08
0.4494431.5912262.512389e-08
0.4513961.5909792.523303e-08
0.4533571.5907342.534265e-08
0.4553261.5904922.545275e-08
0.4573041.5902522.556332e-08
0.4592911.5900142.567437e-08
0.461.589932.571400e-08
0.4612861.5897782.529156e-08
0.463291.5895452.463347e-08
0.4653031.5893142.397252e-08
0.4673241.5890852.330870e-08
0.4693541.5888592.264199e-08
0.4713931.5886342.197239e-08
0.4734411.5884122.129987e-08
0.4754981.5881922.062444e-08
0.4775641.5879741.994607e-08
0.4796381.5877581.926476e-08
0.481.587721.914600e-08
0.4817221.5875441.887056e-08
0.4838151.5873321.853583e-08
0.4859171.5871221.819965e-08
0.4880271.5869141.786200e-08
0.4901481.5867081.752289e-08
0.4922771.5865031.718231e-08
0.4944151.5863011.684025e-08
0.4965631.5861011.649670e-08
0.4987211.5859021.615165e-08
0.51.5857861.594700e-08
0.5008871.5857061.597530e-08
0.5030631.5855111.604471e-08
0.5052481.5853181.611443e-08
0.5074431.5851261.618444e-08
0.5096481.5849371.625477e-08
0.5118621.5847491.632539e-08
0.5140861.5845631.639633e-08
0.5163191.5843781.646757e-08
0.5185621.5841961.653912e-08
0.5208151.5840151.661099e-08
0.5230771.5838351.668316e-08
0.5253491.5836571.675565e-08
0.5276321.5834811.682845e-08
0.5299241.5833061.690157e-08
0.5322261.5831331.697501e-08
0.5345381.5829621.704877e-08
0.536861.5827921.712284e-08
0.5391931.5826231.719724e-08
0.5415351.5824561.727196e-08
0.5438871.5822911.734701e-08
0.546251.5821261.742238e-08
0.5486231.5819641.749808e-08
0.551.581871.754200e-08
0.5510071.5818031.747764e-08
0.55341.5816431.732458e-08
0.5558041.5814841.717087e-08
0.5582191.5813271.701648e-08
0.5606441.5811721.686142e-08
0.563081.5810171.670569e-08
0.5655261.5808641.654929e-08
0.5679821.5807121.639220e-08
0.570451.5805621.623443e-08
0.5729281.5804131.607598e-08
0.5754171.5802651.591683e-08
0.5779171.5801181.575700e-08
0.5804271.5799731.559647e-08
0.5829491.5798291.543525e-08
0.5854811.5796861.527332e-08
0.5880251.5795441.511069e-08
0.5905791.5794041.494736e-08
0.5931451.5792641.478331e-08
0.5957221.5791261.461855e-08
0.598311.5789891.445308e-08
0.61.5789011.434500e-08
0.6009091.5788531.455555e-08
0.6035191.5787191.516030e-08
0.6061411.5785851.576767e-08
0.6087741.5784521.637768e-08
0.6114191.5783211.699035e-08
0.6140751.578191.760567e-08
0.6167431.5780611.822367e-08
0.6194221.5779331.884435e-08
0.6221131.5778051.946772e-08
0.6248161.5776792.009381e-08
0.627531.5775542.072261e-08
0.6302561.5774292.135415e-08
0.6329941.5773062.198843e-08
0.6357441.5771842.262547e-08
0.6385061.5770632.326527e-08
0.641281.5769422.390785e-08
0.6440661.5768232.455323e-08
0.6468641.5767042.520141e-08
0.6496741.5765872.585240e-08
0.651.5765732.592800e-08
0.6524961.576472.602754e-08
0.6553311.5763542.614058e-08
0.6581781.5762392.625412e-08
0.6610371.5761252.636815e-08
0.6639081.5760122.648267e-08
0.6667931.57592.659769e-08
0.6696891.5757882.671321e-08
0.6725991.5756782.682923e-08
0.6755211.5755682.694576e-08
0.6784551.5754592.706279e-08
0.6814031.5753512.718033e-08
0.6843631.5752442.729839e-08
0.6873361.5751372.741695e-08
0.6903221.5750312.753603e-08
0.6933211.5749262.765563e-08
0.6963331.5748222.777574e-08
0.6993581.5747182.789638e-08
0.71.5746972.792200e-08
0.7023961.5746162.832444e-08
0.7054471.5745142.883701e-08
0.7085121.5744122.935181e-08
0.711591.5743122.986884e-08
0.7146811.5742123.038812e-08
0.7177861.5741133.090965e-08
0.7209041.5740143.143345e-08
0.7240361.5739163.195953e-08
0.7271811.5738193.248789e-08
0.730341.5737233.301855e-08
0.7335131.5736273.355151e-08
0.73671.5735323.408679e-08
0.73991.5734373.462439e-08
0.7431141.5733433.516433e-08
0.7463421.573253.570661e-08
0.7495851.5731583.625125e-08
0.7528411.5730653.679825e-08
0.7561121.5729743.734764e-08
0.7593961.5728833.789940e-08
0.7626951.5727933.845357e-08
0.7660091.5727033.901014e-08
0.7693361.5726143.956913e-08
0.7726791.5725254.013055e-08
0.7760351.5724374.069441e-08
0.7794071.572354.126072e-08
0.7827931.5722634.182948e-08
0.7861931.5721774.240072e-08
0.7896091.5720914.297444e-08
0.7930391.5720054.355066e-08
0.7964841.571924.412937e-08
0.7999441.5718364.471060e-08
0.81.5718354.472000e-08
0.8034191.5717524.368118e-08
0.8069091.5716694.262078e-08
0.8104151.5715864.155576e-08
0.8139351.5715034.048613e-08
0.8174711.5714213.941184e-08
0.8210231.571343.833289e-08
0.8245891.5712593.724925e-08
0.8281721.5711783.616090e-08
0.8317691.5710983.506783e-08
0.8353831.5710183.397000e-08
0.8390121.5709393.286741e-08
0.8426571.570863.176003e-08
0.8463171.5707823.064784e-08
0.8499941.5707032.953081e-08
0.8536871.5706262.840893e-08
0.8573951.5705482.728218e-08
0.861121.5704722.615054e-08
0.8648611.5703952.501397e-08
0.8686181.5703192.387247e-08
0.8723911.5702432.272602e-08
0.8761811.5701682.157458e-08
0.8799881.5700932.041814e-08
0.8838111.5700181.925667e-08
0.887651.5699431.809016e-08
0.8915061.5698691.691858e-08
0.8953791.5697961.574191e-08
0.8992691.5697221.456013e-08
0.91.5697091.433800e-08
0.9031751.5696491.489552e-08
0.9070991.5695761.558439e-08
0.911041.5695041.627625e-08
0.9149981.5694321.697112e-08
0.9189721.569361.766900e-08
0.9229651.5692881.836992e-08
0.9269741.5692171.907388e-08
0.9310011.5691461.978090e-08
0.9350461.5690752.049099e-08
0.9391081.5690052.120416e-08
0.9431881.5689352.192044e-08
0.9472851.5688652.263982e-08
0.95141.5687952.336233e-08
0.9555331.5687252.408798e-08
0.9596841.5686562.481678e-08
0.9638531.5685872.554875e-08
0.9680411.5685182.628390e-08
0.9722461.568452.702224e-08
0.976471.5683812.776379e-08
0.9807121.5683132.850856e-08
0.9849721.5682452.925656e-08
0.9892511.5681783.000782e-08
0.9935491.568113.076234e-08
0.9978651.5680433.152013e-08
11.5680093.189500e-08
1.00221.5679753.175446e-08
1.006551.5679083.147632e-08
1.010931.5678423.119697e-08
1.015321.5677753.091641e-08
1.019731.5677083.063463e-08
1.024161.5676423.035162e-08
1.028611.5675763.006738e-08
1.033081.567512.978191e-08
1.037561.5674442.949520e-08
1.042071.5673782.920724e-08
1.04661.5673122.891804e-08
1.051151.5672472.862757e-08
1.055711.5671812.833585e-08
1.06031.5671162.804285e-08
1.06491.5670512.774859e-08
1.069531.5669862.745304e-08
1.074181.566922.715621e-08
1.078841.5668562.685810e-08
1.083531.5667912.655868e-08
1.088241.5667262.625797e-08
1.092961.5666612.595595e-08
1.097711.5665972.565262e-08
1.102481.5665322.534797e-08
1.107271.5664672.504200e-08
1.112081.5664032.473469e-08
1.116911.5663392.442606e-08
1.121761.5662742.411608e-08
1.126641.566212.380475e-08
1.131531.5661462.349208e-08
1.136451.5660812.317804e-08
1.141381.5660172.286264e-08
1.146341.5659532.254587e-08
1.151321.5658892.222772e-08
1.156321.5658242.190819e-08
1.161351.565762.158728e-08
1.166391.5656962.126497e-08
1.171461.5656322.094126e-08
1.176551.5655672.061614e-08
1.181661.5655032.028961e-08
1.186791.5654391.996166e-08
1.191951.5653741.963229e-08
1.197131.565311.930149e-08
1.21.5652751.911800e-08
1.202331.5652461.980655e-08
1.207551.5651812.135110e-08
1.21281.5651172.290236e-08
1.218071.5650522.446036e-08
1.223361.5649882.602513e-08
1.228671.5649232.759670e-08
1.234011.5648582.917509e-08
1.239371.5647933.076034e-08
1.244751.5647283.235248e-08
1.250161.5646633.395153e-08
1.255591.5645983.555753e-08
1.261051.5645333.717051e-08
1.266531.5644683.879049e-08
1.272031.5644024.041752e-08
1.277551.5643374.205161e-08
1.28311.5642714.369280e-08
1.288681.5642064.534111e-08
1.294281.564144.699659e-08
1.29991.5640744.865927e-08
1.305551.5640075.032916e-08
1.311221.5639415.200631e-08
1.316911.5638755.369074e-08
1.322641.5638085.538249e-08
1.328381.5637415.708160e-08
1.334151.5636745.878808e-08
1.339951.5636076.050198e-08
1.345771.563546.222332e-08
1.351621.5634726.395214e-08
1.357491.5634056.568847e-08
1.363381.5633376.743234e-08
1.369311.5632696.918379e-08
1.375261.56327.094285e-08
1.381231.5631327.270955e-08
1.387231.5630637.448392e-08
1.393261.5629947.626600e-08
1.399311.5629257.805583e-08
1.41.5629177.826000e-08
1.405391.5628567.959904e-08
1.411491.5627868.111621e-08
1.417631.5627168.263998e-08
1.423781.5626468.417037e-08
1.429971.5625768.570740e-08
1.436181.5625058.725111e-08
1.442421.5624348.880153e-08
1.448691.5623639.035869e-08
1.454981.5622919.192261e-08
1.46131.5622199.349332e-08
1.467651.5621479.507085e-08
1.474031.5620759.665524e-08
1.480431.5620029.824652e-08
1.486861.5619299.984470e-08
1.493321.5618561.014498e-07
1.499811.5617821.030619e-07
1.506321.5617081.046810e-07
1.512871.5616341.063072e-07
1.519441.5615591.079404e-07
1.526041.5614841.095807e-07
1.532671.5614091.112281e-07
1.539331.5613331.128827e-07
1.546011.5612571.145444e-07
1.552731.5611811.162134e-07
1.559481.5611041.178897e-07
1.566251.5610271.195732e-07
1.573051.5609491.212640e-07
1.579891.5608711.229622e-07
1.586751.5607921.246678e-07
1.593641.5607141.263807e-07
1.61.5606411.279600e-07
1.600571.5606341.285431e-07
1.607521.5605551.356820e-07
1.61451.5604741.428519e-07
1.621521.5603941.500529e-07
1.628561.5603131.572853e-07
1.635641.5602311.645490e-07
1.642741.5601491.718443e-07
1.649881.5600671.791713e-07
1.657051.5599841.865302e-07
1.664251.55991.939210e-07
1.671481.5598172.013439e-07
1.678741.5597322.087990e-07
1.686031.5596472.162866e-07
1.693351.5595622.238067e-07
1.700711.5594762.313594e-07
1.70811.5593892.389450e-07
1.715521.5593022.465635e-07
1.722971.5592152.542151e-07
1.730461.5591272.618999e-07
1.737971.5590382.696181e-07
1.745521.5589492.773699e-07
1.753111.5588592.851553e-07
1.760721.5587692.929746e-07
1.768371.5586783.008278e-07
1.776051.5585863.087151e-07
1.783771.5584943.166367e-07
1.791521.5584013.245927e-07
1.79931.5583083.325833e-07
1.81.5582993.333000e-07
1.807121.5582143.433827e-07
1.814971.5581193.545022e-07
1.822851.5580243.656700e-07
1.830771.5579283.768864e-07
1.838731.5578313.881514e-07
1.846711.5577343.994654e-07
1.854741.5576364.108286e-07
1.862791.5575374.222411e-07
1.870891.5574384.337032e-07
1.879011.5573384.452151e-07
1.887181.5572374.567770e-07
1.895371.5571354.683891e-07
1.903611.5570334.800517e-07
1.911881.556934.917649e-07
1.920181.5568265.035290e-07
1.928531.5567215.153443e-07
1.93691.5566165.272108e-07
1.945321.556515.391289e-07
1.953771.5564035.510988e-07
1.962261.5562955.631207e-07
1.970781.5561875.751948e-07
1.979341.5560775.873213e-07
1.987941.5559675.995006e-07
1.996581.5558566.117327e-07
21.5558126.165800e-07
2.005251.5557446.452608e-07
2.013961.5556316.928383e-07
2.022711.5555187.406226e-07
2.03151.5554037.886144e-07
2.040321.5552888.368147e-07
2.049191.5551718.852244e-07
2.058091.5550549.338443e-07

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—