Optical constants

Refractive index of BPM51 (OHARA)

BPM51: n,k 0.3–2.4 µm

Data
formula 2 + tabulated k
Range
0.3–2.4 µm
Temperature
298 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength. Note: k data cover 310-2400 nm only; k = 0 elsewhere in the n range 300-2400 nm.

At one wavelength

Range 0.3–2.4 µm
Refractive index n
1.61339
Extinction coefficient k
8.27428e-09
Permittivity ε1
2.60304
Permittivity ε2
2.66994e-08
Absorption coefficient α
0.00176953 cm⁻¹
Penetration depth δ = λ/(2πk)
1.13024e+10 nm
Abbe number Vd
44.267
Chromatic dispersion dn/dλ
-0.0710062 µm⁻¹
Group index ng
1.65512
Group velocity dispersion
129.346 fs²/mm
Dispersion parameter D
-705.648 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

# BPM51 (OHARA): BPM51
ohara_bpm51 = ls.fetch_refractiveindex("specs", "OHARA-optical", "BPM51", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(ohara_bpm51.range_nm)  # (300, 2400) nm
eps = ohara_bpm51.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

Sellmeier (C in µm²) (formula 2), λ in µm
n2−1=1.37436455λ2λ2−0.00877165624+0.174025602λ2λ2−0.0405249716+0.905485504λ2λ2−72.7685343

Valid from 0.3 to 2.4 µm.

Coefficients as stored
CiValue
C10.0
C21.37436455
C30.00877165624
C40.174025602
C50.0405249716
C60.905485504
C772.7685343

Comments and conditions

Conditions

temperature
298 K

Properties

thermal dispersion
type: formula A, coefficients: 7.297e-06 0.0 0.0 0.0 0.0 0.0
nd
1.613397
Vd
44.266767
glass code
613443
glass status
preferred
density
value: 3240
thermal expansion
value: 5.2e-06, temperature range: 243 343; value: 6.2e-06, temperature range: 293 573
dPgF
-0.0084
resistance
acid: 53.2; phosphate: 4.2

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 298.0 K): dn/dT = 3.61e-06 K⁻¹ at 633 nm, dn/dT = 3.52e-06 K⁻¹ at 1310 nm, dn/dT = 3.50e-06 K⁻¹ at 1550 nm
Notes on the source data (kept exactly as published):
  • k data cover 310-2400 nm only; k = 0 elsewhere in the n range 300-2400 nm

References

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 427 wavelengths, the same grid as the API and the library
BPM51 (OHARA), BPM51: n and k versus wavelength
λ (µm)nk
0.31.6847040
0.3015681.6834030
0.3031431.6821290
0.3047271.6808810
0.306321.6796570
0.307921.6784580
0.3095291.6772820
0.311.6769438.650300e-06
0.3111471.6761298.143392e-06
0.3127721.6749987.424571e-06
0.3144071.6738886.701993e-06
0.3160491.6727995.975641e-06
0.3177011.6717315.245492e-06
0.3193611.6706824.511529e-06
0.321.6702854.229000e-06
0.321031.6696524.041303e-06
0.3227071.6686413.735536e-06
0.3243931.6676483.428172e-06
0.3260881.6666723.119201e-06
0.3277921.6657142.808616e-06
0.3295051.6647732.496408e-06
0.331.6645052.406200e-06
0.3312271.6638482.291808e-06
0.3329581.6629382.130434e-06
0.3346971.6620441.968217e-06
0.3364461.6611661.805152e-06
0.3382041.6603021.641235e-06
0.3399711.6594521.476461e-06
0.341.6594381.473800e-06
0.3417481.6586161.376119e-06
0.3435341.6577951.276325e-06
0.3453291.6569861.176009e-06
0.3471331.6561911.075168e-06
0.3489471.6554089.738012e-07
0.351.6549619.149500e-07
0.350771.6546388.882661e-07
0.3526031.653888.247704e-07
0.3544461.6531347.609429e-07
0.3562981.6523996.967819e-07
0.3581591.6516766.322857e-07
0.361.6509765.685200e-07
0.3600311.6509645.678254e-07
0.3619121.6502635.254221e-07
0.3638031.6495734.827973e-07
0.3657041.6488934.399497e-07
0.3676151.6482243.968782e-07
0.3695361.6475643.535817e-07
0.371.6474073.431200e-07
0.3714671.6469143.211814e-07
0.3734081.6462742.921499e-07
0.3753591.6456432.629666e-07
0.377321.6450222.336309e-07
0.3792921.6444092.041418e-07
0.381.6441921.935500e-07
0.3812741.6438061.846224e-07
0.3832661.6432111.706587e-07
0.3852691.6426251.566221e-07
0.3872821.6420471.425121e-07
0.3893051.6414771.283285e-07
0.391.6412841.234600e-07
0.391341.6409151.172798e-07
0.3933841.6403611.078462e-07
0.395441.6398159.836319e-08
0.3975061.6392768.883067e-08
0.3995831.6387457.924834e-08
0.41.638647.732600e-08
0.4016711.6382217.395362e-08
0.403771.6377046.971840e-08
0.405881.6371956.546105e-08
0.4080011.6366926.118145e-08
0.4101331.6361965.687949e-08
0.4122761.6357075.255505e-08
0.414431.6352244.820801e-08
0.4165951.6347484.383826e-08
0.4187721.6342783.944567e-08
0.421.6340173.696800e-08
0.420961.6338143.620472e-08
0.423161.6333573.445647e-08
0.4253711.6329053.269908e-08
0.4275941.6324593.093250e-08
0.4298281.6320192.915670e-08
0.4320741.6315852.737162e-08
0.4343321.6311572.557720e-08
0.4366011.6307332.377342e-08
0.4388821.6303162.196020e-08
0.441.6301142.107200e-08
0.4411761.6299032.069576e-08
0.4434811.6294961.995808e-08
0.4457981.6290941.921655e-08
0.4481281.6286971.847114e-08
0.4504691.6283051.772184e-08
0.4528231.6279181.696862e-08
0.4551891.6275361.621146e-08
0.4575681.6271581.545035e-08
0.4599591.6267851.468526e-08
0.461.6267791.467200e-08
0.4623621.6264171.429456e-08
0.4647781.6260531.390849e-08
0.4672061.6256941.352041e-08
0.4696481.6253391.313029e-08
0.4721021.6249881.273814e-08
0.4745691.6246421.234394e-08
0.4770481.62431.194768e-08
0.4795411.6239621.154934e-08
0.481.62391.147600e-08
0.4820471.6236281.111677e-08
0.4845661.6232971.067468e-08
0.4870981.6229711.023028e-08
0.4896431.6226499.783559e-09
0.4922011.622339.334504e-09
0.4947731.6220158.883103e-09
0.4973581.6217048.429342e-09
0.4999571.6213977.973211e-09
0.51.6213927.965700e-09
0.502571.6210937.781372e-09
0.5051961.6207927.592996e-09
0.5078351.6204957.403635e-09
0.5104891.6202027.213284e-09
0.5131561.6199117.021939e-09
0.5158381.6196246.829594e-09
0.5185331.6193416.636244e-09
0.5212431.619066.441884e-09
0.5239661.6187836.246508e-09
0.5267041.6185096.050111e-09
0.5294561.6182385.852688e-09
0.5322231.6179695.654234e-09
0.5350041.6177045.454742e-09
0.5377991.6174425.254208e-09
0.5406091.6171835.052626e-09
0.5434341.6169264.849991e-09
0.5462741.6166724.646297e-09
0.5491281.6164214.441539e-09
0.551.6163464.379000e-09
0.5519981.6161734.585938e-09
0.5548821.6159284.884747e-09
0.5577811.6156855.185118e-09
0.5606961.6154455.487059e-09
0.5636261.6152075.790577e-09
0.5665711.6149726.095681e-09
0.5695311.6147396.402379e-09
0.5725071.6145096.710680e-09
0.5754981.6142817.020592e-09
0.5785061.6140557.332123e-09
0.5815281.6138327.645282e-09
0.5845671.6136117.960077e-09
0.5876221.6133938.276518e-09
0.5906921.6131768.594611e-09
0.5937791.6129628.914367e-09
0.5968811.612759.235794e-09
0.61.6125419.558900e-09
0.6031351.6123339.608818e-09
0.6062871.6121279.658996e-09
0.6094551.6119249.709437e-09
0.6126391.6117229.760141e-09
0.615841.6115239.811111e-09
0.6190581.6113259.862346e-09
0.6222931.611139.913850e-09
0.6255451.6109369.965622e-09
0.6288131.6107441.001766e-08
0.6320991.6105541.006998e-08
0.6354021.6103661.012257e-08
0.6387221.6101791.017543e-08
0.6420591.6099951.022857e-08
0.6454141.6098121.028199e-08
0.6487871.6096311.033568e-08
0.651.6095661.035500e-08
0.6521771.6094511.014681e-08
0.6555851.6092749.820908e-09
0.659011.6090979.493298e-09
0.6624541.6089239.163977e-09
0.6659151.608758.832935e-09
0.6693951.6085798.500164e-09
0.6728921.6084098.165653e-09
0.6764091.608247.829395e-09
0.6799431.6080747.491379e-09
0.6834961.6079087.151598e-09
0.6870671.6077446.810041e-09
0.6906571.6075826.466699e-09
0.6942661.6074216.121563e-09
0.6978941.6072615.774624e-09
0.71.6071695.573200e-09
0.7015411.6071035.683682e-09
0.7052061.6069465.946580e-09
0.7088911.606796.210851e-09
0.7125951.6066366.476504e-09
0.7163191.6064836.743544e-09
0.7200621.6063317.011980e-09
0.7238241.606187.281819e-09
0.7276061.6060317.553067e-09
0.7314081.6058837.825733e-09
0.735231.6057368.099823e-09
0.7390721.605598.375346e-09
0.7429341.6054458.652308e-09
0.7468161.6053018.930718e-09
0.7507181.6051599.210582e-09
0.7546411.6050179.491909e-09
0.7585841.6048779.774706e-09
0.7625471.6047381.005898e-08
0.7665321.6045991.034474e-08
0.7705371.6044621.063199e-08
0.7745641.6043261.092075e-08
0.7786111.6041911.121101e-08
0.7826791.6040561.150279e-08
0.7867691.6039231.179609e-08
0.790881.603791.209093e-08
0.7950121.6036591.238731e-08
0.7991671.6035281.268523e-08
0.81.6035021.274500e-08
0.8033421.6033981.279825e-08
0.807541.6032691.286511e-08
0.811761.6031411.293233e-08
0.8160011.6030141.299990e-08
0.8202651.6028871.306782e-08
0.8245511.6027611.313610e-08
0.828861.6026361.320473e-08
0.8331911.6025121.327373e-08
0.8375441.6023891.334308e-08
0.8419211.6022661.341280e-08
0.846321.6021441.348288e-08
0.8507421.6020231.355332e-08
0.8551871.6019021.362414e-08
0.8596561.6017821.369532e-08
0.8641481.6016631.376688e-08
0.8686631.6015441.383881e-08
0.8732021.6014261.391111e-08
0.8777651.6013081.398380e-08
0.8823511.6011921.405686e-08
0.8869621.6010751.413030e-08
0.8915971.600961.420413e-08
0.8962551.6008441.427835e-08
0.91.6007531.433800e-08
0.9009391.600731.442783e-08
0.9056461.6006161.487839e-08
0.9103781.6005021.533131e-08
0.9151351.6003891.578660e-08
0.9199171.6002761.624427e-08
0.9247241.6001641.670432e-08
0.9295561.6000521.716678e-08
0.9344131.5999411.763166e-08
0.9392951.599831.809897e-08
0.9442041.599721.856872e-08
0.9491371.599611.904092e-08
0.9540971.59951.951559e-08
0.9590821.5993911.999274e-08
0.9640931.5992822.047239e-08
0.9691311.5991732.095454e-08
0.9741951.5990652.143921e-08
0.9792851.5989572.192641e-08
0.9844021.5988492.241616e-08
0.9895461.5987422.290846e-08
0.9947171.5986352.340334e-08
0.9999141.5985282.390081e-08
11.5985262.390900e-08
1.005141.5984212.378589e-08
1.010391.5983152.366008e-08
1.015671.5982092.353361e-08
1.020981.5981032.340647e-08
1.026311.5979972.327868e-08
1.031681.5978922.315021e-08
1.037071.5977872.302108e-08
1.042491.5976812.289127e-08
1.047931.5975762.276078e-08
1.053411.5974712.262961e-08
1.058911.5973672.249775e-08
1.064451.5972622.236521e-08
1.070011.5971582.223197e-08
1.07561.5970532.209804e-08
1.081221.5969492.196340e-08
1.086871.5968452.182807e-08
1.092551.596742.169202e-08
1.098261.5966362.155527e-08
1.1041.5965322.141780e-08
1.109761.5964282.127961e-08
1.115561.5963242.114070e-08
1.121391.5962192.100107e-08
1.127251.5961152.086070e-08
1.133141.5960112.071960e-08
1.139061.5959072.057777e-08
1.145011.5958022.043519e-08
1.1511.5956982.029187e-08
1.157011.5955932.014780e-08
1.163061.5954892.000297e-08
1.169131.5953841.985739e-08
1.175241.5952791.971105e-08
1.181381.5951741.956395e-08
1.187561.5950691.941607e-08
1.193761.5949641.926742e-08
1.21.5948581.911800e-08
1.21.5948581.911800e-08
1.206271.5947522.915742e-08
1.212571.5946473.924929e-08
1.218911.594544.939389e-08
1.225281.5944345.959151e-08
1.231681.5943286.984241e-08
1.238121.5942218.014687e-08
1.244591.5941149.050518e-08
1.251091.5940061.009176e-07
1.257631.5938991.113844e-07
1.26421.5937911.219060e-07
1.27081.5936821.324825e-07
1.277441.5935741.431143e-07
1.284121.5934651.538016e-07
1.290831.5933561.645447e-07
1.297571.5932461.753440e-07
1.304351.5931361.861998e-07
1.311171.5930251.971122e-07
1.318021.5929152.080817e-07
1.324911.5928032.191085e-07
1.331831.5926912.301929e-07
1.338791.5925792.413353e-07
1.345781.5924672.525358e-07
1.352821.5923532.637949e-07
1.359891.592242.751128e-07
1.366991.5921262.864898e-07
1.374131.5920112.979263e-07
1.381311.5918963.094226e-07
1.388531.591783.209789e-07
1.395791.5916643.325956e-07
1.41.5915963.393400e-07
1.403081.5915473.372762e-07
1.410411.5914293.323652e-07
1.417781.5913113.274286e-07
1.425191.5911933.224662e-07
1.432641.5910733.174778e-07
1.440121.5909533.124634e-07
1.447651.5908323.074228e-07
1.455211.5907113.023559e-07
1.462821.5905892.972624e-07
1.470461.5904662.921424e-07
1.478141.5903432.869956e-07
1.485871.5902182.818219e-07
1.493631.5900932.766212e-07
1.501441.5899672.713933e-07
1.509281.5898412.661381e-07
1.517171.5897132.608554e-07
1.525091.5895852.555451e-07
1.533061.5894562.502071e-07
1.541071.5893262.448412e-07
1.549131.5891952.394473e-07
1.557221.5890632.340251e-07
1.565361.5889312.285746e-07
1.573541.5887972.230957e-07
1.581761.5886632.175881e-07
1.590021.5885272.120518e-07
1.598331.5883912.064865e-07
1.61.5883632.053700e-07
1.606681.5882532.125954e-07
1.615081.5881152.216695e-07
1.623521.5879752.307910e-07
1.6321.5878352.399601e-07
1.640531.5876932.491772e-07
1.64911.587552.584424e-07
1.657721.5874062.677560e-07
1.666381.5872612.771183e-07
1.675091.5871152.865295e-07
1.683841.5869682.959899e-07
1.692641.5868193.054997e-07
1.701481.586673.150593e-07
1.710371.5865193.246687e-07
1.719311.5863673.343284e-07
1.72831.5862133.440386e-07
1.737331.5860583.537995e-07
1.74641.5859023.636114e-07
1.755531.5857453.734745e-07
1.76471.5855863.833892e-07
1.773921.5854263.933557e-07
1.783191.5852644.033743e-07
1.792511.5851014.134452e-07
1.81.584974.215400e-07
1.801881.5849374.293904e-07
1.811291.5847714.687677e-07
1.820761.5846045.083508e-07
1.830271.5844355.481407e-07
1.839831.5842645.881386e-07
1.849451.5840926.283454e-07
1.859111.5839196.687623e-07
1.868831.5837447.093904e-07
1.878591.5835677.502308e-07
1.888411.5833887.912846e-07
1.898271.5832088.325530e-07
1.908191.5830268.740369e-07
1.918161.5828439.157376e-07
1.928191.5826579.576563e-07
1.938261.582479.997939e-07
1.948391.5822811.042152e-06
1.958571.582091.084731e-06
1.96881.5818971.127533e-06
1.979091.5817031.170558e-06
1.989431.5815061.213808e-06
1.999831.5813081.257284e-06
21.5813041.258000e-06
2.010281.5811071.464262e-06
2.020781.5809041.675054e-06
2.031341.58071.886948e-06
2.041961.5804932.099950e-06
2.052631.5802842.314064e-06
2.063351.5800732.529297e-06
2.074131.579862.745655e-06
2.084971.5796452.963143e-06
2.095861.5794273.181768e-06
2.106821.5792073.401535e-06
2.117821.5789853.622450e-06
2.128891.578763.844520e-06
2.140011.5785334.067750e-06
2.15121.5783044.292146e-06
2.162441.5780724.517715e-06
2.173741.5778384.744463e-06
2.18511.5776014.972396e-06
2.196511.5773625.201519e-06
2.21.5772885.271500e-06
2.207991.5771195.653403e-06
2.219531.5768756.204856e-06
2.231121.5766276.759190e-06
2.242781.5763777.316421e-06
2.25451.5761247.876563e-06
2.266281.5758698.439633e-06
2.278121.575619.005644e-06
2.290031.5753499.574613e-06
2.301991.5750851.014655e-05
2.314021.5748171.072149e-05
2.326111.5745471.129942e-05
2.338271.5742731.188037e-05
2.350491.5739971.246436e-05
2.362771.5737171.305141e-05
2.375111.5734341.364152e-05
2.387521.5731481.423471e-05
2.41.5728591.483100e-05

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
—