Optical constants

Refractive index of K4A (CDGM)

K4A: n,k 0.365–2.325 µm

Data
formula 2 + tabulated k
Range
0.365–2.325 µm
Temperature
293 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.365–2.325 µm
Refractive index n
1.50802
Extinction coefficient k
2.34385e-08
Permittivity ε1
2.27412
Permittivity ε2
7.06913e-08
Absorption coefficient α
0.00501254 cm⁻¹
Penetration depth δ = λ/(2πk)
3.98999e+09 nm
Abbe number Vd
61.053
Chromatic dispersion dn/dλ
-0.0430982 µm⁻¹
Group index ng
1.53334
Group velocity dispersion
73.2855 fs²/mm
Dispersion parameter D
-399.811 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

# K4A (CDGM): K4A
cdgm_k4a = ls.fetch_refractiveindex("specs", "CDGM-optical", "K4A", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(cdgm_k4a.range_nm)  # (365, 2325) nm
eps = cdgm_k4a.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=0.749532263λ2λ2−0.0148033503+0.494866234λ2λ2+0.000264092219+0.96016866λ2λ2−95.7190154

Valid from 0.365 to 2.325 µm.

Coefficients as stored
CiValue
C10.0
C20.749532263
C30.0148033503
C40.494866234
C5-0.000264092219
C60.96016866
C795.7190154

Comments and conditions

Conditions

temperature
293 K

Properties

thermal dispersion
type: formula A, coefficients: 7.37e-06 2.2e-08 -6.81e-12 4.56e-07 4.32e-10 0.199
nd
1.508020
Vd
61.052897
glass code
508611
density
value: 2430
thermal expansion
value: 4.7e-06, temperature range: 243 343; value: 5.2e-06, temperature range: 293 573
dPgF
-0.0028
resistance
climatic: 1.0

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = 3.64e-06 K⁻¹ at 633 nm, dn/dT = 3.15e-06 K⁻¹ at 1310 nm, dn/dT = 3.10e-06 K⁻¹ at 1550 nm

References

Cite

CDGM Zemax catalog 2022-06 (obtained from http://www.cdgmgd.com); See also CDGM optical 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 425 wavelengths, the same grid as the API and the library
K4A (CDGM), K4A: n and k versus wavelength
λ (µm)nk
0.3651.5283252.580100e-07
0.3666981.5280052.322621e-07
0.3684031.527692.063945e-07
0.371.5273981.821800e-07
0.3701171.5273771.814564e-07
0.3718381.5270681.708035e-07
0.3735681.5267631.601011e-07
0.3753061.5264611.493489e-07
0.3770511.5261621.385467e-07
0.3788051.5258661.276943e-07
0.381.5256671.203000e-07
0.3805671.5255741.175735e-07
0.3823371.5252841.090618e-07
0.3841161.5249981.005105e-07
0.3859021.5247159.191938e-08
0.3876971.5244358.328833e-08
0.38951.5241587.461712e-08
0.391.5240827.221500e-08
0.3913121.5238846.947604e-08
0.3931321.5236136.567672e-08
0.3949611.5233456.185973e-08
0.3967981.523085.802498e-08
0.3986441.5228175.417239e-08
0.41.5226275.134100e-08
0.4004981.5225585.115166e-08
0.4023611.5223015.044313e-08
0.4042321.5220464.973130e-08
0.4061121.5217954.901616e-08
0.4080011.5215464.829769e-08
0.4098991.52134.757588e-08
0.4118061.5210564.685071e-08
0.4137211.5208154.612218e-08
0.4156451.5205764.539025e-08
0.4175791.520344.465492e-08
0.4195211.5201064.391616e-08
0.421.5200494.373400e-08
0.4214721.5198744.336553e-08
0.4234331.5196454.287494e-08
0.4254021.5194194.238207e-08
0.4273811.5191954.188690e-08
0.4293691.5189734.138943e-08
0.4313661.5187534.088965e-08
0.4333721.5185354.038754e-08
0.4353881.518323.988310e-08
0.4374131.5181073.937631e-08
0.4394481.5178963.886716e-08
0.441.5178393.872900e-08
0.4414921.5176873.830865e-08
0.4435451.517483.773007e-08
0.4456091.5172753.714880e-08
0.4476811.5170733.656482e-08
0.4497641.5168723.597813e-08
0.4518561.5166743.538871e-08
0.4539571.5164773.479655e-08
0.4560691.5162823.420163e-08
0.458191.5160893.360394e-08
0.461.5159273.309400e-08
0.4603211.5158993.305524e-08
0.4624621.515713.279691e-08
0.4646131.5155223.253739e-08
0.4667751.5153373.227665e-08
0.4689461.5151543.201471e-08
0.4711271.5149723.175154e-08
0.4733181.5147923.148716e-08
0.475521.5146143.122154e-08
0.4777321.5144373.095468e-08
0.4799541.5142623.068659e-08
0.481.5142593.068100e-08
0.4821861.5140893.038249e-08
0.4844291.5139183.007623e-08
0.4866821.5137482.976855e-08
0.4889461.513582.945944e-08
0.491221.5134132.914889e-08
0.4935051.5132482.883690e-08
0.49581.5130852.852346e-08
0.4981071.5129232.820855e-08
0.51.5127912.795000e-08
0.5004231.5127622.789910e-08
0.5027511.5126032.761927e-08
0.5050891.5124462.733814e-08
0.5074391.512292.705571e-08
0.5097991.5121352.677195e-08
0.512171.5119822.648688e-08
0.5145531.511832.620049e-08
0.5169461.511682.591276e-08
0.519351.5115312.562369e-08
0.5217661.5113842.533328e-08
0.5241931.5112372.504152e-08
0.5266311.5110922.474840e-08
0.5290811.5109492.445391e-08
0.5315421.5108072.415806e-08
0.5340141.5106662.386083e-08
0.5364981.5105262.356222e-08
0.5389931.5103872.326222e-08
0.54151.510252.296082e-08
0.5440191.5101142.265803e-08
0.5465491.5099792.235382e-08
0.5490921.5098452.204820e-08
0.551.5097982.193900e-08
0.5516461.5097132.200463e-08
0.5542121.5095812.210696e-08
0.5567891.5094512.220976e-08
0.5593791.5093222.231304e-08
0.5619811.5091942.241680e-08
0.5645951.5090672.252105e-08
0.5672211.5089412.262578e-08
0.5698591.5088172.273100e-08
0.572511.5086932.283670e-08
0.5751731.508572.294290e-08
0.5778481.5084492.304959e-08
0.5805361.5083282.315678e-08
0.5832361.5082082.326447e-08
0.5859491.508092.337265e-08
0.5886751.5079722.348134e-08
0.5914131.5078562.359054e-08
0.5941641.507742.370024e-08
0.5969271.5076252.381046e-08
0.5997041.5075112.392119e-08
0.61.5074992.393300e-08
0.6024931.5073982.377339e-08
0.6052961.5072862.359398e-08
0.6081111.5071752.341373e-08
0.610941.5070652.323265e-08
0.6137811.5069562.305073e-08
0.6166361.5068472.286796e-08
0.6195041.5067392.268434e-08
0.6223861.5066332.249986e-08
0.6252811.5065272.231453e-08
0.6281891.5064212.212833e-08
0.6311111.5063172.194127e-08
0.6340471.5062132.175334e-08
0.6369961.5061112.156454e-08
0.6399591.5060092.137485e-08
0.6429351.5059072.118429e-08
0.6459261.5058072.099283e-08
0.648931.5057072.080049e-08
0.651.5056722.073200e-08
0.6519491.5056082.079412e-08
0.6549811.505512.089079e-08
0.6580281.5054122.098792e-08
0.6610881.5053152.108549e-08
0.6641631.5052192.118352e-08
0.6672521.5051232.128201e-08
0.6703561.5050292.138095e-08
0.6734741.5049342.148035e-08
0.6766071.5048412.158022e-08
0.6797541.5047482.168055e-08
0.6829151.5046562.178135e-08
0.6860921.5045642.188261e-08
0.6892831.5044732.198435e-08
0.6924891.5043822.208656e-08
0.695711.5042932.218924e-08
0.6989461.5042032.229241e-08
0.71.5041742.232600e-08
0.7021971.5041152.239609e-08
0.7054631.5040272.250028e-08
0.7087451.5039392.260496e-08
0.7120411.5038522.271012e-08
0.7153531.5037662.281577e-08
0.7186811.503682.292191e-08
0.7220231.5035942.302855e-08
0.7253821.5035092.313568e-08
0.7287561.5034252.324331e-08
0.7321461.5033412.335144e-08
0.7355511.5032582.346008e-08
0.7389721.5031752.356922e-08
0.7424091.5030932.367886e-08
0.7458631.5030112.378902e-08
0.7493321.5029292.389969e-08
0.7528171.5028482.401087e-08
0.7563191.5027682.412257e-08
0.7598371.5026872.423479e-08
0.7633711.5026082.434754e-08
0.7669221.5025282.446080e-08
0.7704891.502452.457460e-08
0.7740731.5023712.468892e-08
0.7776731.5022932.480378e-08
0.781291.5022152.491916e-08
0.7849241.5021382.503509e-08
0.7885751.5020612.515156e-08
0.7922431.5019852.526856e-08
0.7959281.5019082.538611e-08
0.799631.5018332.550421e-08
0.81.5018252.551600e-08
0.803351.5017572.516809e-08
0.8070861.5016822.478000e-08
0.810841.5016072.439011e-08
0.8146121.5015332.399840e-08
0.8184011.5014592.360487e-08
0.8222081.5013852.320952e-08
0.8260321.5013112.281232e-08
0.8298741.5012382.241327e-08
0.8337341.5011652.201237e-08
0.8376121.5010922.160960e-08
0.8415081.501022.120496e-08
0.8454221.5009482.079844e-08
0.8493551.5008762.039003e-08
0.851.5008642.032300e-08
0.8533051.5008042.040200e-08
0.8572741.5007332.049685e-08
0.8612621.5006622.059215e-08
0.8652681.5005912.068790e-08
0.8692921.500522.078409e-08
0.8733361.500452.088072e-08
0.8773981.500382.097781e-08
0.8814791.500312.107535e-08
0.8855791.500242.117334e-08
0.8896981.500172.127179e-08
0.8938361.5001012.137069e-08
0.8979941.5000322.147006e-08
0.91.4999992.151800e-08
0.9021711.4999632.156993e-08
0.9063671.4998942.167030e-08
0.9105831.4998252.177114e-08
0.9148181.4997572.187245e-08
0.9190731.4996882.197424e-08
0.9233481.499622.207649e-08
0.9276431.4995522.217922e-08
0.9319581.4994842.228243e-08
0.9362931.4994162.238612e-08
0.9406481.4993482.249030e-08
0.9450231.4992812.259495e-08
0.9494191.4992132.270009e-08
0.951.4992042.271400e-08
0.9538351.4991462.280565e-08
0.9582711.4990792.291169e-08
0.9627291.4990112.301821e-08
0.9672071.4989442.312524e-08
0.9717051.4988772.323276e-08
0.9762251.498812.334078e-08
0.9807661.4987432.344930e-08
0.9853281.4986762.355833e-08
0.9899111.4986092.366787e-08
0.9945151.4985432.377791e-08
0.9991411.4984762.388847e-08
11.4984642.390900e-08
1.003791.4984092.399960e-08
1.008461.4983432.411127e-08
1.013151.4982762.422345e-08
1.017861.4982092.433616e-08
1.022591.4981432.444939e-08
1.027351.4980762.456315e-08
1.032131.4980092.467744e-08
1.036931.4979432.479226e-08
1.041751.4978762.490761e-08
1.04661.4978092.502350e-08
1.051471.4977432.513993e-08
1.056361.4976762.525690e-08
1.061.4976262.534400e-08
1.061271.4976092.528745e-08
1.066211.4975422.506793e-08
1.071171.4974752.484738e-08
1.076151.4974082.462581e-08
1.081151.4973412.440321e-08
1.086181.4972742.417957e-08
1.091241.4972072.395489e-08
1.096311.497142.372917e-08
1.101411.4970722.350239e-08
1.106531.4970052.327457e-08
1.111681.4969372.304568e-08
1.116851.4968692.281572e-08
1.122051.4968022.258470e-08
1.127271.4967342.235261e-08
1.132511.4966662.211943e-08
1.137781.4965982.188517e-08
1.143071.4965292.164982e-08
1.148391.4964612.141337e-08
1.153731.4963922.117583e-08
1.159091.4963232.093718e-08
1.164481.4962542.069742e-08
1.16991.4961852.045654e-08
1.175341.4961162.021455e-08
1.180811.4960461.997143e-08
1.18631.4959771.972717e-08
1.191821.4959071.948179e-08
1.197361.4958371.923526e-08
1.21.4958031.911800e-08
1.202931.4957662.247169e-08
1.208531.4956962.887017e-08
1.214151.4956253.529843e-08
1.21981.4955544.175658e-08
1.225471.4954834.824477e-08
1.231171.4954115.476313e-08
1.23691.495346.131182e-08
1.242651.4952686.789097e-08
1.248431.4951957.450072e-08
1.254241.4951238.114121e-08
1.260071.495058.781259e-08
1.265931.4949779.451501e-08
1.271821.4949031.012486e-07
1.277741.494831.080135e-07
1.283681.4947561.148099e-07
1.289651.4946811.216379e-07
1.295651.4946071.284976e-07
1.301671.4945321.353893e-07
1.307731.4944561.423130e-07
1.313811.4943811.492689e-07
1.319921.4943051.562571e-07
1.326061.4942281.632779e-07
1.332231.4941521.703313e-07
1.338431.4940751.774176e-07
1.344651.4939971.845368e-07
1.350911.4939191.916891e-07
1.357191.4938411.988746e-07
1.36351.4937622.060936e-07
1.369851.4936832.133462e-07
1.376221.4936042.206325e-07
1.382621.4935242.279527e-07
1.389051.4934432.353070e-07
1.395511.4933632.426954e-07
1.41.4933062.478300e-07
1.4021.4932812.459890e-07
1.408521.49322.399893e-07
1.415071.4931172.339616e-07
1.421661.4930352.279059e-07
1.428271.4929522.218221e-07
1.434911.4928682.157100e-07
1.441591.4927842.095694e-07
1.448291.4926992.034002e-07
1.455031.4926141.972024e-07
1.46181.4925291.909758e-07
1.468591.4924421.847201e-07
1.475431.4923561.784354e-07
1.482291.4922681.721215e-07
1.489181.4921811.657781e-07
1.496111.4920921.594053e-07
1.503071.4920031.530029e-07
1.510061.4919141.465706e-07
1.517081.4918241.401084e-07
1.524141.4917331.336162e-07
1.531231.4916421.270938e-07
1.538351.491551.205410e-07
1.545511.4914571.139578e-07
1.55271.4913641.073439e-07
1.559921.491271.006993e-07
1.567171.4911769.402380e-08
1.574461.491088.731722e-08
1.581791.4909858.057945e-08
1.589141.4908887.381034e-08
1.596541.4907916.700974e-08
1.61.4907456.382200e-08
1.603961.4906936.426528e-08
1.611421.4905946.510015e-08
1.618921.4904956.593891e-08
1.626451.4903956.678157e-08
1.634011.4902946.762815e-08
1.641611.4901936.847866e-08
1.649251.490096.933313e-08
1.656921.4899877.019158e-08
1.664631.4898837.105402e-08
1.672371.4897797.192047e-08
1.680151.4896737.279095e-08
1.687961.4895677.366547e-08
1.695811.489467.454407e-08
1.70371.4893527.542675e-08
1.711631.4892437.631354e-08
1.719591.4891337.720446e-08
1.727591.4890237.809951e-08
1.735621.4889117.899874e-08
1.743691.4887997.990214e-08
1.751811.4886868.080974e-08
1.759951.4885728.172157e-08
1.768141.4884578.263764e-08
1.776361.4883418.355797e-08
1.784631.4882248.448258e-08
1.792931.4881068.541149e-08
1.81.4880058.620300e-08
1.801271.4879878.872680e-08
1.809641.4878671.054233e-07
1.818061.4877461.221975e-07
1.826521.4876241.390498e-07
1.835011.4875011.559804e-07
1.843551.4873771.729897e-07
1.852121.4872521.900782e-07
1.860741.4871262.072462e-07
1.869391.4869992.244940e-07
1.878091.4868712.418220e-07
1.886821.4867412.592307e-07
1.89561.4866112.767203e-07
1.904421.4864792.942912e-07
1.913281.4863463.119439e-07
1.922181.4862133.296787e-07
1.931121.4860773.474960e-07
1.94011.4859413.653962e-07
1.949121.4858043.833796e-07
1.958191.4856654.014466e-07
1.96731.4855254.195977e-07
1.976451.4853834.378333e-07
1.985641.4852414.561536e-07
1.994881.4850974.745592e-07
21.4850174.847700e-07
2.004161.4849525.245159e-07
2.013481.4848066.136868e-07
2.022841.4846587.032724e-07
2.032251.4845097.932747e-07
2.04171.4843588.836957e-07
2.05121.4842069.745372e-07
2.060741.4840531.065801e-06
2.070331.4838981.157490e-06
2.079961.4837421.249605e-06
2.089631.4835851.342148e-06
2.099351.4834251.435122e-06
2.109121.4832651.528529e-06
2.118931.4831031.622370e-06
2.128781.4829391.716647e-06
2.138681.4827741.811363e-06
2.148631.4826071.906519e-06
2.158621.4824392.002118e-06
2.168671.4822692.098162e-06
2.178751.4820982.194652e-06
2.188891.4819252.291592e-06
2.199071.481752.388982e-06
2.21.4817342.397900e-06
2.20931.4815732.530070e-06
2.219571.4813952.676171e-06
2.22991.4812152.822952e-06
2.240271.4810332.970416e-06
2.250691.480853.118565e-06
2.261161.4806653.267404e-06
2.271671.4804783.416935e-06
2.282241.4802893.567161e-06
2.292861.4800983.718087e-06
2.303521.4799053.869714e-06
2.314241.4797114.022046e-06
2.3251.4795144.175088e-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
—