Optical constants

Refractive index of LLF1 (SCHOTT)

LLF1: n,k 0.31–2.5 µm

Data
formula 2 + tabulated k
Range
0.31–2.5 µm
Temperature
293 K
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
1.54814
Extinction coefficient k
5.99587e-09
Permittivity ε1
2.39673
Permittivity ε2
1.85649e-08
Absorption coefficient α
0.00128227 cm⁻¹
Penetration depth δ = λ/(2πk)
1.55973e+10 nm
Abbe number Vd
45.75
Chromatic dispersion dn/dλ
-0.0612487 µm⁻¹
Group index ng
1.58413
Group velocity dispersion
113.811 fs²/mm
Dispersion parameter D
-620.897 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

# LLF1 (SCHOTT): LLF1
schott_llf1 = ls.fetch_refractiveindex("specs", "SCHOTT-optical", "LLF1", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(schott_llf1.range_nm)  # (310, 2500) nm
eps = schott_llf1.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=1.21640125λ2λ2−0.00857807248+0.13366454λ2λ2−0.0420143003+0.883399468λ2λ2−107.59306

Valid from 0.31 to 2.5 µm.

Coefficients as stored
CiValue
C10.0
C21.21640125
C30.00857807248
C40.13366454
C50.0420143003
C60.883399468
C7107.59306

Comments and conditions

lead containing glass type

Conditions

temperature
293 K

Properties

thermal dispersion
type: formula A, coefficients: 3.25e-07 1.74e-08 -6.12e-11 6.53e-07 2.58e-10 0.233
nd
1.54814
Vd
45.75
glass code
548458.294
glass status
standard
density
value: 2940
thermal expansion
value: 8.1e-06, temperature range: 243 343; value: 9.2e-06, temperature range: 293 573
dPgF
-0.0009
resistance
acid: 1.0; stain: 0.0; alkali: 2.0; climatic: 1.0; phosphate: 1.0

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = 9.93e-07 K⁻¹ at 633 nm, dn/dT = 3.15e-07 K⁻¹ at 1310 nm, dn/dT = 2.64e-07 K⁻¹ at 1550 nm

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
LLF1 (SCHOTT), LLF1: n and k versus wavelength
λ (µm)nk
0.311.6038484.544200e-06
0.3116261.6028274.004694e-06
0.3132611.6018263.462357e-06
0.3149041.6008442.917176e-06
0.3165561.5998822.369135e-06
0.3182161.5989371.818220e-06
0.3198851.5980111.264414e-06
0.321.5979481.226400e-06
0.3215631.5971021.114466e-06
0.323251.5962099.936980e-07
0.3249461.5953348.722966e-07
0.326651.5944747.502585e-07
0.3283641.5936296.275802e-07
0.3300861.59285.042585e-07
0.3318181.5919853.802898e-07
0.3335581.5911842.556709e-07
0.3341.5909842.240300e-07
0.3353081.5903982.099118e-07
0.3370671.5896251.909236e-07
0.3388351.5888651.718358e-07
0.3406121.5881181.526479e-07
0.3423991.5873841.333594e-07
0.3441951.5866621.139696e-07
0.3461.5859529.447816e-08
0.3478151.5852537.488446e-08
0.349641.5845665.518799e-08
0.351.5844325.129700e-08
0.3514741.583894.844704e-08
0.3533171.5832254.488143e-08
0.3551711.5825714.129712e-08
0.3570341.5819273.769400e-08
0.3589061.5812933.407199e-08
0.3607891.5806693.043097e-08
0.3626821.5800552.677086e-08
0.3645841.5794512.309155e-08
0.3651.579322.228700e-08
0.3664961.5788552.130206e-08
0.3684191.5782692.003671e-08
0.371.5777961.899600e-08
0.3703511.5776921.884163e-08
0.3722941.5771231.798822e-08
0.3742471.5765631.713033e-08
0.376211.5760111.626794e-08
0.3781831.5754681.540102e-08
0.381.5749771.460300e-08
0.3801671.5749321.452557e-08
0.3821611.5744051.360192e-08
0.3841661.5738851.267342e-08
0.3861811.5733721.174005e-08
0.3882071.5728671.080178e-08
0.391.5724289.971200e-09
0.3902431.5723699.937814e-09
0.392291.5718799.656698e-09
0.3943481.5713959.374108e-09
0.3964161.5709189.090035e-09
0.3984961.5704488.804472e-09
0.41.5701148.597900e-09
0.4005861.5699858.491875e-09
0.4026871.5695288.111756e-09
0.40481.5690777.729644e-09
0.4051.5690357.693400e-09
0.4069231.5686327.566212e-09
0.4090581.5681947.425036e-09
0.4112031.5677627.283119e-09
0.413361.5673357.140458e-09
0.4155281.5669146.997049e-09
0.4177081.5664996.852887e-09
0.4198991.566096.707969e-09
0.421.5660716.701300e-09
0.4221021.5656866.551709e-09
0.4243161.5652876.394119e-09
0.4265421.5648946.235702e-09
0.4287791.5645066.076454e-09
0.4310281.5641235.916371e-09
0.4332891.5637455.755448e-09
0.4355621.5633725.593681e-09
0.4361.5633015.562500e-09
0.4378471.5630045.586052e-09
0.4401431.5626415.615345e-09
0.4424521.5622825.644791e-09
0.4447731.5619285.674392e-09
0.4471061.5615785.704148e-09
0.4494511.5612335.734060e-09
0.4518091.5608925.764129e-09
0.4541791.5605565.794356e-09
0.4565611.5602245.824741e-09
0.4589561.5598965.855286e-09
0.461.5597555.868600e-09
0.4613641.5595725.885999e-09
0.4637841.5592525.916879e-09
0.4662161.5589375.947921e-09
0.4686621.5586255.979126e-09
0.471121.5583176.010495e-09
0.4735921.5580126.042028e-09
0.4760761.5577126.073726e-09
0.4785731.5574156.105591e-09
0.4810831.5571226.137623e-09
0.4836071.5568326.169823e-09
0.4861441.5565466.202192e-09
0.4886941.5562636.234731e-09
0.4912571.5559846.267440e-09
0.4938341.5557076.300321e-09
0.4964241.5554356.333374e-09
0.4990281.5551656.366601e-09
0.51.5550666.379000e-09
0.5016461.5548996.337594e-09
0.5042771.5546366.271398e-09
0.5069221.5543766.204855e-09
0.5095821.5541196.137962e-09
0.5122551.5538656.070719e-09
0.5149421.5536146.003123e-09
0.5176431.5533665.935172e-09
0.5203581.553125.866865e-09
0.5230871.5528785.798200e-09
0.5258311.5526385.729174e-09
0.528591.5524015.659787e-09
0.5313621.5521675.590035e-09
0.5341491.5519355.519918e-09
0.5369511.5517075.449433e-09
0.5397681.551485.378578e-09
0.5425991.5512565.307351e-09
0.5454451.5510355.235751e-09
0.5461.5509925.221800e-09
0.5483071.5508165.243855e-09
0.5511831.55065.271356e-09
0.5540741.5503865.299001e-09
0.556981.5501745.326791e-09
0.5599021.5499655.354727e-09
0.5628391.5497585.382809e-09
0.5657911.5495535.411039e-09
0.5687591.5493515.439417e-09
0.5717421.5491515.467943e-09
0.5747421.5489525.496620e-09
0.5777561.5487565.525446e-09
0.581.5486135.546900e-09
0.5807871.5485635.593387e-09
0.5838331.5483715.773359e-09
0.5868961.5481815.954276e-09
0.5899741.5479936.136141e-09
0.5930691.5478076.318960e-09
0.596181.5476246.502738e-09
0.5993071.5474426.687480e-09
0.6024511.5472626.873191e-09
0.6056111.5470847.059876e-09
0.6087881.5469077.247541e-09
0.6119811.5467337.436190e-09
0.6151911.546567.625828e-09
0.6184181.546397.816462e-09
0.621.5463077.909900e-09
0.6216621.546227.931106e-09
0.6249231.5460537.972707e-09
0.6282011.5458878.014526e-09
0.6314961.5457238.056565e-09
0.6348091.5455618.098824e-09
0.6381391.54548.141305e-09
0.6414861.5452418.184008e-09
0.6448511.5450838.226936e-09
0.6482341.5449278.270089e-09
0.6516341.5447738.313468e-09
0.6550521.544628.357075e-09
0.6584881.5444688.400910e-09
0.661.5444028.420200e-09
0.6619421.5443188.336419e-09
0.6654141.544178.186629e-09
0.6689051.5440228.036052e-09
0.6724131.5438777.884686e-09
0.6759411.5437327.732526e-09
0.6794861.5435897.579567e-09
0.683051.5434477.425807e-09
0.6866331.5433077.271239e-09
0.6902351.5431687.115861e-09
0.6938561.543036.959668e-09
0.6974951.5428946.802656e-09
0.71.5428016.694600e-09
0.7011541.5427586.716487e-09
0.7048321.5426246.786249e-09
0.7085291.5424916.856376e-09
0.7122461.542366.926871e-09
0.7159821.5422296.997736e-09
0.7197371.54217.068972e-09
0.7235131.5419727.140583e-09
0.7273081.5418447.212568e-09
0.7311231.5417187.284932e-09
0.7349581.5415947.357675e-09
0.7388131.541477.430800e-09
0.7426891.5413477.504308e-09
0.7465841.5412257.578202e-09
0.7505011.5411047.652483e-09
0.7544371.5409857.727154e-09
0.7583951.5408667.802217e-09
0.7623731.5407487.877673e-09
0.7663721.5406317.953525e-09
0.7703921.5405158.029775e-09
0.7744331.54048.106426e-09
0.7784951.5402868.183478e-09
0.7825791.5401738.260934e-09
0.7866841.5400618.338797e-09
0.790811.539958.417068e-09
0.7949581.5398398.495749e-09
0.7991281.5397298.574844e-09
0.803321.539628.654353e-09
0.8075341.5395128.734279e-09
0.811771.5394058.814625e-09
0.8160281.5392988.895392e-09
0.8203081.5391938.976583e-09
0.8246111.5390889.058199e-09
0.8289371.5389839.140244e-09
0.8332851.538889.222719e-09
0.8376561.5387779.305627e-09
0.842051.5386759.388969e-09
0.8464671.5385749.472749e-09
0.8509071.5384739.556968e-09
0.855371.5383739.641629e-09
0.8598571.5382739.726734e-09
0.8643671.5381759.812285e-09
0.8689011.5380769.898286e-09
0.8734591.5379799.984737e-09
0.8780411.5378821.007164e-08
0.8826471.5377861.015900e-08
0.8872771.537691.024682e-08
0.8919311.5375951.033510e-08
0.8966091.53751.042384e-08
0.9013131.5374061.051305e-08
0.906041.5373121.060273e-08
0.9107931.5372191.069287e-08
0.9155711.5371271.078349e-08
0.9203731.5370351.087459e-08
0.9252011.5369431.096616e-08
0.9300541.5368521.105821e-08
0.9349331.5367611.115075e-08
0.9398371.5366711.124377e-08
0.9447671.5365811.133728e-08
0.9497221.5364921.143128e-08
0.9547041.5364031.152577e-08
0.9597121.5363141.162076e-08
0.9647461.5362261.171625e-08
0.9698071.5361391.181223e-08
0.9748941.5360511.190872e-08
0.9800081.5359641.200572e-08
0.9851481.5358781.210323e-08
0.9903161.5357911.220124e-08
0.995511.5357051.229978e-08
1.000731.535621.239882e-08
1.005981.5355351.249839e-08
1.011261.5354491.259848e-08
1.016561.5353651.269910e-08
1.02191.535281.280024e-08
1.027261.5351961.290191e-08
1.032641.5351121.300412e-08
1.038061.5350291.310686e-08
1.043511.5349451.321015e-08
1.048981.5348621.331397e-08
1.054481.5347791.341834e-08
1.061.5346961.352300e-08
1.060011.5346961.352400e-08
1.065571.5346141.394308e-08
1.071161.5345311.436436e-08
1.076781.5344491.478785e-08
1.082431.5343671.521356e-08
1.088111.5342851.564150e-08
1.093821.5342041.607168e-08
1.099551.5341221.650413e-08
1.105321.5340411.693884e-08
1.111121.5339591.737583e-08
1.116951.5338781.781511e-08
1.122811.5337971.825670e-08
1.12871.5337161.870060e-08
1.134621.5336351.914684e-08
1.140571.5335541.959541e-08
1.146551.5334742.004634e-08
1.152561.5333932.049963e-08
1.158611.5333122.095530e-08
1.164691.5332322.141336e-08
1.17081.5331512.187382e-08
1.176941.533072.233670e-08
1.183111.532992.280200e-08
1.189321.5329092.326975e-08
1.195561.5328292.373995e-08
1.201831.5327482.421261e-08
1.208131.5326682.468776e-08
1.214471.5325872.516540e-08
1.220841.5325062.564554e-08
1.227241.5324252.612820e-08
1.233681.5323442.661340e-08
1.240151.5322642.710114e-08
1.246661.5321832.759143e-08
1.25321.5321012.808430e-08
1.259771.532022.857976e-08
1.266381.5319392.907781e-08
1.273021.5318572.957848e-08
1.27971.5317763.008177e-08
1.286411.5316943.058770e-08
1.293161.5316123.109629e-08
1.299941.531533.160754e-08
1.306761.5314483.212148e-08
1.313621.5313653.263811e-08
1.320511.5312833.315745e-08
1.327431.53123.367951e-08
1.33441.5311173.420432e-08
1.34141.5310333.473188e-08
1.348431.530953.526220e-08
1.355511.5308663.579531e-08
1.362621.5307823.633121e-08
1.369761.5306983.686992e-08
1.376951.5306133.741146e-08
1.384171.5305283.795584e-08
1.391431.5304433.850308e-08
1.398731.5303583.905318e-08
1.406071.5302723.960617e-08
1.413441.5301864.016207e-08
1.420861.5300994.072087e-08
1.428311.5300134.128261e-08
1.43581.5299264.184730e-08
1.443331.5298384.241495e-08
1.45091.529754.298557e-08
1.458521.5296624.355919e-08
1.466171.5295734.413582e-08
1.473861.5294844.471547e-08
1.481591.5293954.529816e-08
1.489361.5293054.588391e-08
1.497171.5292144.647273e-08
1.505031.5291234.706465e-08
1.512921.5290324.765966e-08
1.520861.528944.825780e-08
1.528831.5288484.885907e-08
1.531.5288344.894700e-08
1.536851.5287556.521239e-08
1.544911.5286628.434665e-08
1.553021.5285681.035813e-07
1.561161.5284741.229168e-07
1.569351.5283791.423537e-07
1.577591.5282831.618926e-07
1.585861.5281871.815340e-07
1.594181.5280912.012784e-07
1.602541.5279932.211264e-07
1.610951.5278962.410785e-07
1.61941.5277972.611353e-07
1.627891.5276982.812973e-07
1.636431.5275983.015650e-07
1.645021.5274983.219390e-07
1.653641.5273973.424199e-07
1.662321.5272953.630083e-07
1.671041.5271933.837046e-07
1.67981.527094.045095e-07
1.688611.5269864.254235e-07
1.697471.5268814.464473e-07
1.706381.5267764.675813e-07
1.715331.526674.888262e-07
1.724321.5265635.101825e-07
1.733371.5264555.316508e-07
1.742461.5263475.532318e-07
1.75161.5262385.749259e-07
1.760791.5261285.967339e-07
1.770031.5260176.186562e-07
1.779311.5259056.406935e-07
1.788641.5257926.628465e-07
1.798031.5256796.851156e-07
1.807461.5255647.075015e-07
1.816941.5254497.300049e-07
1.826471.5253337.526263e-07
1.836051.5252157.753664e-07
1.845681.5250977.982257e-07
1.855361.5249788.212050e-07
1.865091.5248588.443048e-07
1.874881.5247378.675257e-07
1.884711.5246158.908685e-07
1.89461.5244919.143337e-07
1.904541.5243679.379220e-07
1.914531.5242429.616341e-07
1.924571.5241159.854705e-07
1.934671.5239881.009432e-06
1.944811.5238591.033519e-06
1.955011.5237291.057733e-06
1.965271.5235981.082073e-06
1.971.5235381.093300e-06
1.975581.5234661.133605e-06
1.985941.5233331.208474e-06
1.996361.5231981.283736e-06
2.006831.5230621.359393e-06
2.017361.5229251.435447e-06
2.027941.5227871.511900e-06
2.038581.5226471.588753e-06
2.049271.5225061.666010e-06
2.060021.5223641.743672e-06
2.070831.5222211.821742e-06
2.081691.5220761.900221e-06
2.092611.5219291.979111e-06
2.103581.5217822.058416e-06
2.114621.5216322.138136e-06
2.125711.5214822.218275e-06
2.136861.521332.298834e-06
2.148071.5211762.379815e-06
2.159341.5210212.461222e-06
2.170661.5208642.543055e-06
2.182051.5207062.625318e-06
2.19351.5205472.708012e-06
2.2051.5203852.791140e-06
2.216571.5202222.874704e-06
2.22821.5200582.958706e-06
2.239881.5198913.043149e-06
2.251631.5197243.128034e-06
2.263441.5195543.213366e-06
2.275321.5193823.299144e-06
2.287251.5192093.385373e-06
2.299251.5190343.472054e-06
2.311311.5188573.559190e-06
2.323431.5186793.646782e-06
2.3251.5186563.658100e-06
2.335621.5184983.770852e-06
2.347871.5183163.900914e-06
2.360191.5181324.031657e-06
2.372571.5179454.163086e-06
2.385011.5177574.295205e-06
2.397521.5175674.428017e-06
2.41011.5173744.561525e-06
2.422741.517184.695734e-06
2.435451.5169844.830647e-06
2.448231.5167854.966267e-06
2.461071.5165845.102599e-06
2.473981.5163815.239646e-06
2.486951.5161765.377412e-06
2.51.5159695.515900e-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
—