Optical constants

Refractive index of P-BK7 (SCHOTT)

P-BK7: n,k 0.31–2.5 µm

Data
formula 2 + tabulated k
Range
0.31–2.5 µm
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.31–2.5 µm
Refractive index n
1.5164
Extinction coefficient k
5.61959e-09
Permittivity ε1
2.29946
Permittivity ε2
1.70431e-08
Absorption coefficient α
0.0012018 cm⁻¹
Penetration depth δ = λ/(2πk)
1.66417e+10 nm
Abbe number Vd
64.06
Chromatic dispersion dn/dλ
-0.0418625 µm⁻¹
Group index ng
1.541
Group velocity dispersion
70.017 fs²/mm
Dispersion parameter D
-381.98 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

# P-BK7 (SCHOTT): P-BK7
schott_p_bk7 = ls.fetch_refractiveindex("specs", "SCHOTT-optical", "P-BK7", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(schott_p_bk7.range_nm)  # (310, 2500) nm
eps = schott_p_bk7.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=1.18318503λ2λ2−0.00722141956+0.0871756426λ2λ2−0.0268216805+1.03133701λ2λ2−101.702362

Valid from 0.31 to 2.5 µm.

Coefficients as stored
CiValue
C10.0
C21.18318503
C30.00722141956
C40.0871756426
C50.0268216805
C61.03133701
C7101.702362

Comments and conditions

suitable for precision molding

Properties

nd
1.5164
Vd
64.06
glass code
516641.243
glass status
standard
density
value: 2433
thermal expansion
value: 5.99e-06, temperature range: 243 343; value: 7.32e-06, temperature range: 293 573
dPgF
-0.0025
resistance
acid: 1.0; stain: 0.0; alkali: 2.3; climatic: 1.0; phosphate: 2.3

References

Cite

SCHOTT Zemax catalog 2017-01-20b (obtained from http://www.schott.com); See also SCHOTT 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 422 wavelengths, the same grid as the API and the library
P-BK7 (SCHOTT), P-BK7: n and k versus wavelength
λ (µm)nk
0.311.5489583.860200e-06
0.3116261.5484493.468864e-06
0.3132611.5479473.075474e-06
0.3149041.5474512.680022e-06
0.3165561.5469622.282495e-06
0.3182161.546481.882882e-06
0.3198851.5460041.481174e-06
0.321.5459721.453600e-06
0.3215631.5455351.328641e-06
0.323251.5450721.193820e-06
0.3249461.5446141.058292e-06
0.326651.5441639.220527e-07
0.3283641.5437187.850990e-07
0.3300861.5432786.474270e-07
0.3318181.5428445.090328e-07
0.3335581.5424163.699127e-07
0.3341.5423093.345900e-07
0.3353081.5419933.138508e-07
0.3370671.5415762.859577e-07
0.3388351.5411642.579182e-07
0.3406121.5407572.297317e-07
0.3423991.5403562.013973e-07
0.3441951.5399591.729143e-07
0.3461.5395681.442819e-07
0.3478151.5391811.154993e-07
0.349641.5387998.656576e-08
0.351.5387258.085000e-08
0.3514741.5384227.603140e-08
0.3533171.538057.000280e-08
0.3551711.5376826.394258e-08
0.3570341.5373195.785057e-08
0.3589061.5369615.172661e-08
0.3607891.5366064.557052e-08
0.3626821.5362563.938214e-08
0.3645841.5359113.316130e-08
0.3651.5358363.180100e-08
0.3664961.5355692.976438e-08
0.3684191.5352322.714793e-08
0.371.5349592.499600e-08
0.3703511.5348992.471692e-08
0.3722941.534572.317406e-08
0.3742471.5342452.162310e-08
0.376211.5339242.006400e-08
0.3781831.5336061.849673e-08
0.381.5333191.705400e-08
0.3801671.5332931.697749e-08
0.3821611.5329831.606476e-08
0.3841661.5326761.514725e-08
0.3861811.5323741.422492e-08
0.3882071.5320751.329776e-08
0.391.5318141.247700e-08
0.3902431.5317791.242230e-08
0.392291.5314871.196172e-08
0.3943481.5311991.149873e-08
0.3964161.5309141.103331e-08
0.3984961.5306321.056545e-08
0.41.5304311.022700e-08
0.4005861.5303531.008971e-08
0.4026871.5300789.597513e-09
0.40481.5298069.102731e-09
0.4051.529789.055800e-09
0.4069231.5295378.926292e-09
0.4090581.5292718.782540e-09
0.4112031.5290088.638034e-09
0.413361.5287488.492770e-09
0.4155281.5284918.346745e-09
0.4177081.5282378.199953e-09
0.4198991.5279868.052391e-09
0.421.5279748.045600e-09
0.4221021.5277378.085861e-09
0.4243161.5274928.128276e-09
0.4265421.5272498.170912e-09
0.4287791.5270098.213773e-09
0.4310281.5267728.256858e-09
0.4332891.5265378.300169e-09
0.4355621.5263058.343708e-09
0.4361.5262618.352100e-09
0.4378471.5260768.274187e-09
0.4401431.5258498.177285e-09
0.4424521.5256248.079875e-09
0.4447731.5254027.981953e-09
0.4471061.5251837.883518e-09
0.4494511.5249667.784567e-09
0.4518091.5247517.685097e-09
0.4541791.5245397.585104e-09
0.4565611.5243287.484588e-09
0.4589561.5241217.383544e-09
0.461.5240317.339500e-09
0.4613641.5239157.306758e-09
0.4637841.5237127.248646e-09
0.4662161.523517.190229e-09
0.4686621.5233117.131506e-09
0.471121.5231157.072475e-09
0.4735921.522927.013134e-09
0.4760761.5227276.953482e-09
0.4785731.5225366.893517e-09
0.4810831.5223486.833237e-09
0.4836071.5221616.772641e-09
0.4861441.5219766.711728e-09
0.4886941.5217936.650495e-09
0.4912571.5216126.588940e-09
0.4938341.5214336.527063e-09
0.4964241.5212566.464861e-09
0.4990281.5210816.402333e-09
0.51.5210166.379000e-09
0.5016461.5209076.337594e-09
0.5042771.5207356.271398e-09
0.5069221.5205656.204855e-09
0.5095821.5203976.137962e-09
0.5122551.5202316.070719e-09
0.5149421.5200666.003123e-09
0.5176431.5199025.935172e-09
0.5203581.5197415.866865e-09
0.5230871.5195815.798200e-09
0.5258311.5194225.729174e-09
0.528591.5192665.659787e-09
0.5313621.519115.590035e-09
0.5341491.5189575.519918e-09
0.5369511.5188045.449433e-09
0.5397681.5186545.378578e-09
0.5425991.5185045.307351e-09
0.5454451.5183565.235751e-09
0.5461.5183285.221800e-09
0.5483071.518215.243855e-09
0.5511831.5180655.271356e-09
0.5540741.5179215.299001e-09
0.556981.5177795.326791e-09
0.5599021.5176385.354727e-09
0.5628391.5174995.382809e-09
0.5657911.5173615.411039e-09
0.5687591.5172245.439417e-09
0.5717421.5170885.467943e-09
0.5747421.5169545.496620e-09
0.5777561.516825.525446e-09
0.581.5167235.546900e-09
0.5807871.5166885.554427e-09
0.5838331.5165585.583567e-09
0.5868961.5164285.612859e-09
0.5899741.51635.642306e-09
0.5930691.5161735.671906e-09
0.596181.5160465.701662e-09
0.5993071.5159225.731575e-09
0.6024511.5157985.761644e-09
0.6056111.5156755.791870e-09
0.6087881.5155535.822256e-09
0.6119811.5154335.852800e-09
0.6151911.5153135.883505e-09
0.6184181.5151945.914371e-09
0.621.5151375.929500e-09
0.6216621.5150775.945395e-09
0.6249231.514965.976577e-09
0.6282011.5148456.007923e-09
0.6314961.514736.039434e-09
0.6348091.5146176.071110e-09
0.6381391.5145046.102951e-09
0.6414861.5143926.134960e-09
0.6448511.5142816.167137e-09
0.6482341.5141716.199483e-09
0.6516341.5140626.231998e-09
0.6550521.5139546.264684e-09
0.6584881.5138476.297541e-09
0.661.51386.312000e-09
0.6619421.513746.330576e-09
0.6654141.5136346.363787e-09
0.6689051.513536.397173e-09
0.6724131.5134266.430734e-09
0.6759411.5133226.464471e-09
0.6794861.513226.498385e-09
0.683051.5131186.532477e-09
0.6866331.5130176.566748e-09
0.6902351.5129176.601198e-09
0.6938561.5128176.635829e-09
0.6974951.5127196.670642e-09
0.71.5126516.694600e-09
0.7011541.512626.683962e-09
0.7048321.5125236.650056e-09
0.7085291.5124266.615972e-09
0.7122461.512336.581710e-09
0.7159821.5122356.547267e-09
0.7197371.512146.512644e-09
0.7235131.5120466.477840e-09
0.7273081.5119536.442852e-09
0.7311231.511866.407682e-09
0.7349581.5117676.372326e-09
0.7388131.5116766.336786e-09
0.7426891.5115856.301059e-09
0.7465841.5114946.265144e-09
0.7505011.5114046.229041e-09
0.7544371.5113156.192749e-09
0.7583951.5112266.156266e-09
0.7623731.5111376.119592e-09
0.7663721.511056.082726e-09
0.7703921.5109626.045666e-09
0.7744331.5108756.008412e-09
0.7784951.5107895.970962e-09
0.7825791.5107035.933316e-09
0.7866841.5106175.895473e-09
0.790811.5105325.857431e-09
0.7949581.5104485.819189e-09
0.7991281.5103645.780747e-09
0.803321.510285.742103e-09
0.8075341.5101975.703257e-09
0.811771.5101145.664207e-09
0.8160281.5100315.624951e-09
0.8203081.5099495.585490e-09
0.8246111.5098675.545822e-09
0.8289371.5097865.505946e-09
0.8332851.5097055.465861e-09
0.8376561.5096245.425566e-09
0.842051.5095435.385059e-09
0.8464671.5094635.344339e-09
0.8509071.5093845.303406e-09
0.855371.5093045.262259e-09
0.8598571.5092255.220895e-09
0.8643671.5091465.179315e-09
0.8689011.5090675.137516e-09
0.8734591.5089895.095498e-09
0.8780411.5089115.053260e-09
0.8826471.5088335.010800e-09
0.8872771.5087564.968118e-09
0.8919311.5086784.925211e-09
0.8966091.5086014.882080e-09
0.9013131.5085244.838722e-09
0.906041.5084474.795137e-09
0.9107931.5083714.751323e-09
0.9155711.5082944.707279e-09
0.9203731.5082184.663005e-09
0.9252011.5081424.618498e-09
0.9300541.5080664.573758e-09
0.9349331.5079914.528783e-09
0.9398371.5079154.483572e-09
0.9447671.507844.438123e-09
0.9497221.5077644.392437e-09
0.9547041.5076894.346511e-09
0.9597121.5076144.300344e-09
0.9647461.5075394.253935e-09
0.9698071.5074644.207282e-09
0.9748941.5073894.160385e-09
0.9800081.5073144.113241e-09
0.9851481.507244.065851e-09
0.9903161.5071654.018211e-09
0.995511.507093.970322e-09
1.000731.5070163.922182e-09
1.005981.5069413.873789e-09
1.011261.5068673.825142e-09
1.016561.5067923.776240e-09
1.02191.5067183.727082e-09
1.027261.5066433.677666e-09
1.032641.5065693.627990e-09
1.038061.5064943.578054e-09
1.043511.5064193.527856e-09
1.048981.5063453.477395e-09
1.054481.506273.426669e-09
1.061.5061953.375800e-09
1.060011.5061953.378636e-09
1.065571.506124.561486e-09
1.071161.5060455.750540e-09
1.076781.505976.945831e-09
1.082431.5058958.147393e-09
1.088111.505829.355257e-09
1.093821.5057451.056946e-08
1.099551.5056691.179003e-08
1.105321.5055941.301700e-08
1.111121.5055181.425040e-08
1.116951.5054421.549028e-08
1.122811.5053661.673666e-08
1.12871.505291.798958e-08
1.134621.5052141.924907e-08
1.140571.5051372.051517e-08
1.146551.505062.178791e-08
1.152561.5049832.306732e-08
1.158611.5049062.435345e-08
1.164691.5048292.564632e-08
1.17081.5047512.694598e-08
1.176941.5046732.825245e-08
1.183111.5045952.956577e-08
1.189321.5045173.088599e-08
1.195561.5044383.221312e-08
1.201831.5043593.354722e-08
1.208131.504283.488832e-08
1.214471.5042013.623645e-08
1.220841.5041213.759166e-08
1.227241.5040413.895397e-08
1.233681.503964.032343e-08
1.240151.503884.170007e-08
1.246661.5037994.308394e-08
1.25321.5037174.447506e-08
1.259771.5036354.587348e-08
1.266381.5035534.727924e-08
1.273021.5034714.869236e-08
1.27971.5033885.011291e-08
1.286411.5033045.154090e-08
1.293161.503225.297638e-08
1.299941.5031365.441940e-08
1.306761.5030525.586998e-08
1.313621.5029675.732817e-08
1.320511.5028815.879401e-08
1.327431.5027956.026754e-08
1.33441.5027096.174880e-08
1.34141.5026226.323783e-08
1.348431.5025346.473467e-08
1.355511.5024466.623936e-08
1.362621.5023586.775194e-08
1.369761.5022696.927246e-08
1.376951.502187.080095e-08
1.384171.502097.233746e-08
1.391431.5019997.388204e-08
1.398731.5019087.543471e-08
1.406071.5018167.699553e-08
1.413441.5017247.856453e-08
1.420861.5016318.014177e-08
1.428311.5015378.172728e-08
1.43581.5014438.332110e-08
1.443331.5013488.492329e-08
1.45091.5012538.653388e-08
1.458521.5011578.815291e-08
1.466171.501068.978045e-08
1.473861.5009629.141651e-08
1.481591.5008649.306116e-08
1.489361.5007659.471444e-08
1.497171.5006669.637639e-08
1.505031.5005659.804706e-08
1.512921.5004649.972649e-08
1.520861.5003621.014147e-07
1.528831.500261.031118e-07
1.531.5002451.033600e-07
1.536851.5001571.098936e-07
1.544911.5000521.175795e-07
1.553021.4999471.253057e-07
1.561161.4998421.330725e-07
1.569351.4997351.408800e-07
1.577591.4996271.487285e-07
1.585861.4995191.566181e-07
1.594181.499411.645491e-07
1.602541.49931.725217e-07
1.610951.4991891.805362e-07
1.61941.4990771.885927e-07
1.627891.4989641.966914e-07
1.636431.498852.048326e-07
1.645021.4987352.130166e-07
1.653641.498622.212434e-07
1.662321.4985032.295134e-07
1.671041.4983852.378268e-07
1.67981.4982662.461838e-07
1.688611.4981472.545846e-07
1.697471.4980262.630295e-07
1.706381.4979042.715187e-07
1.715331.4977812.800525e-07
1.724321.4976572.886310e-07
1.733371.4975312.972544e-07
1.742461.4974053.059232e-07
1.75161.4972783.146374e-07
1.760791.4971493.233973e-07
1.770031.4970193.322031e-07
1.779311.4968883.410552e-07
1.788641.4967563.499537e-07
1.798031.4966223.588988e-07
1.807461.4964883.678909e-07
1.816941.4963523.769301e-07
1.826471.4962143.860168e-07
1.836051.4960763.951511e-07
1.845681.4959364.043334e-07
1.855361.4957954.135638e-07
1.865091.4956524.228426e-07
1.874881.4955084.321701e-07
1.884711.4953634.415465e-07
1.89461.4952164.509721e-07
1.904541.4950684.604471e-07
1.914531.4949184.699719e-07
1.924571.4947674.795466e-07
1.934671.4946144.891715e-07
1.944811.494464.988469e-07
1.955011.4943045.085731e-07
1.965271.4941475.183503e-07
1.971.4940745.228600e-07
1.975581.4939885.561238e-07
1.985941.4938276.179138e-07
1.996361.4936656.800279e-07
2.006831.4935017.424678e-07
2.017361.4933368.052353e-07
2.027941.4931698.683320e-07
2.038581.4939.317597e-07
2.049271.4928299.955201e-07
2.060021.4926571.059615e-06
2.070831.4924831.124046e-06
2.081691.4923071.188815e-06
2.092611.4921291.253924e-06
2.103581.4919491.319374e-06
2.114621.4917671.385168e-06
2.125711.4915841.451306e-06
2.136861.4913981.517792e-06
2.148071.4912111.584626e-06
2.159341.4910211.651811e-06
2.170661.490831.719349e-06
2.182051.4906361.787240e-06
2.19351.4904411.855488e-06
2.2051.4902431.924094e-06
2.216571.4900431.993060e-06
2.22821.4898412.062387e-06
2.239881.4896372.132078e-06
2.251631.489432.202135e-06
2.263441.4892222.272559e-06
2.275321.4890112.343352e-06
2.287251.4887972.414517e-06
2.299251.4885812.486055e-06
2.311311.4883632.557969e-06
2.323431.4881432.630259e-06
2.3251.4881142.639600e-06
2.335621.487922.854435e-06
2.347871.4876943.102250e-06
2.360191.4874663.351365e-06
2.372571.4872363.601787e-06
2.385011.4870033.853522e-06
2.397521.4867674.106578e-06
2.41011.4865284.360961e-06
2.422741.4862874.616679e-06
2.435451.4860434.873738e-06
2.448231.4857975.132145e-06
2.461071.4855475.391908e-06
2.473981.4852955.653033e-06
2.486951.4850395.915528e-06
2.51.4847816.179400e-06

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
—