Optical constants

Refractive index of 4786 (HIKARI)

4786: n,k 0.3261–2.325 µm

Data
formula 2 + tabulated k
Range
0.3261–2.325 µm
Temperature
295.65 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.3261–2.325 µm
Refractive index n
1.4741
Extinction coefficient k
4.67830e-09
Permittivity ε1
2.17296
Permittivity ε2
1.37925e-08
Absorption coefficient α
0.0010005 cm⁻¹
Penetration depth δ = λ/(2πk)
1.99901e+10 nm
Abbe number Vd
86.78
Chromatic dispersion dn/dλ
-0.0283306 µm⁻¹
Group index ng
1.49074
Group velocity dispersion
48.4875 fs²/mm
Dispersion parameter D
-264.525 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

# 4786 (HIKARI): 4786
hikari_4786 = ls.fetch_refractiveindex("specs", "HIKARI-misc", "4786", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hikari_4786.range_nm)  # (326.11, 2325.42) nm
eps = hikari_4786.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=0.795944286λ2λ2−0.00371401467+0.356650937λ2λ2−0.0125884185+0.98008113λ2λ2−190.314843

Valid from 0.32611 to 2.32542 µm.

Coefficients as stored
CiValue
C10.0
C20.795944286
C30.00371401467
C40.356650937
C50.0125884185
C60.98008113
C7190.314843

Comments and conditions

Conditions

temperature
295.65 K

Properties

thermal dispersion
type: formula A, coefficients: -1.68e-05 -6.33e-09 2.67e-13 4.08e-07 4.89e-10 0.0942
nd
1.474099
Vd
86.779772
density
value: 3550
thermal expansion
value: 1.25e-05, temperature range: 243 343
dPgF
0.0363
resistance
acid: 4.0; alkali: 4.0; climatic: 1.0

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 295.65 K): dn/dT = -6.26e-06 K⁻¹ at 633 nm, dn/dT = -6.49e-06 K⁻¹ at 1310 nm, dn/dT = -6.49e-06 K⁻¹ at 1550 nm

References

Cite

NIKON Zemax catalog 2017-11 (obtained from http://www.nikon.com); See also NIKON i-line glass data sheet; 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
4786 (HIKARI), 4786: n and k versus wavelength
λ (µm)nk
0.326111.4928952.596436e-09
0.327721.4926172.609247e-09
0.3293371.4923432.622122e-09
0.331.4922312.627400e-09
0.3309621.4920712.635061e-09
0.3325961.4918032.648063e-09
0.3342371.4915372.661130e-09
0.3358871.4912752.674261e-09
0.3375451.4910162.687457e-09
0.3392111.4907592.700718e-09
0.341.4906392.707000e-09
0.3408851.4905062.960889e-09
0.3425671.4902553.443581e-09
0.3442581.4900073.928654e-09
0.3459571.4897624.416122e-09
0.3476651.4895194.905996e-09
0.3493811.4892795.398288e-09
0.351.4891945.576000e-09
0.3511051.4890425.593602e-09
0.3528381.4888085.621207e-09
0.3545791.4885765.648948e-09
0.3563291.4883475.676825e-09
0.3580881.488125.704841e-09
0.3598551.4878965.732995e-09
0.361.4878785.735300e-09
0.3616311.4876745.761304e-09
0.3634161.4874555.789754e-09
0.3651.4872635.815000e-09
0.365211.4872385.694592e-09
0.3670121.4870234.660249e-09
0.3688241.4868113.620801e-09
0.371.4866752.945800e-09
0.3706441.4866012.950933e-09
0.3724731.4863932.965513e-09
0.3743121.4861882.980164e-09
0.3761591.4859852.994888e-09
0.3780161.4857843.009685e-09
0.3798811.4855853.024554e-09
0.381.4855723.025500e-09
0.3817561.4853883.039480e-09
0.383641.4851933.054478e-09
0.3855341.4850013.069550e-09
0.3874371.4848113.084696e-09
0.3893491.4846223.099917e-09
0.391.4845593.105100e-09
0.391271.4844363.115213e-09
0.3932021.4842513.130585e-09
0.3951421.4840693.146032e-09
0.3970921.4838893.161556e-09
0.3990521.483713.177157e-09
0.41.4836253.184700e-09
0.4010221.4835333.192834e-09
0.4030011.4833593.208589e-09
0.404991.4831863.224421e-09
0.4069891.4830153.240332e-09
0.4089981.4828453.256321e-09
0.4110161.4826783.272389e-09
0.4130451.4825123.288537e-09
0.4150831.4823483.304764e-09
0.4171321.4821853.321071e-09
0.4191911.4820253.337459e-09
0.421.4819623.343900e-09
0.421261.4818663.353934e-09
0.4233391.4817083.370494e-09
0.4254281.4815533.387136e-09
0.4275281.4813993.403860e-09
0.4296381.4812463.420667e-09
0.4317581.4810953.437556e-09
0.4338891.4809463.454529e-09
0.4360311.4807983.471586e-09
0.4381831.4806523.488727e-09
0.441.480533.503200e-09
0.4403461.4805073.505951e-09
0.4425191.4803633.523250e-09
0.4447031.4802223.540635e-09
0.4468981.4800813.558106e-09
0.4491031.4799423.575663e-09
0.451321.4798043.593307e-09
0.4535471.4796683.611038e-09
0.4557861.4795333.628856e-09
0.4580351.47943.646763e-09
0.461.4792853.662400e-09
0.4602961.4792683.664757e-09
0.4625681.4791373.682841e-09
0.4648511.4790083.701013e-09
0.4671451.4788793.719276e-09
0.4694511.4787523.737628e-09
0.4717681.4786273.756071e-09
0.4740961.4785023.774606e-09
0.4764361.4783793.793231e-09
0.4787881.4782573.811949e-09
0.481.4781953.821600e-09
0.4811511.4781363.830764e-09
0.4835251.4780173.849679e-09
0.4859121.4778993.868687e-09
0.488311.4777813.887789e-09
0.490721.4776653.906985e-09
0.4931421.477553.926276e-09
0.4955761.4774373.945662e-09
0.4980221.4773243.965144e-09
0.51.4772343.980900e-09
0.500481.4772123.984720e-09
0.502951.4771024.004387e-09
0.5054321.4769924.024151e-09
0.5079271.4768844.044013e-09
0.5104341.4767764.063973e-09
0.5129531.476674.084031e-09
0.5154851.4765654.104188e-09
0.5180291.4764614.124445e-09
0.5205851.4763574.144802e-09
0.5231551.4762554.165259e-09
0.5257371.4761544.185817e-09
0.5283321.4760534.206476e-09
0.5309391.4759544.227238e-09
0.533561.4758554.248102e-09
0.5361931.4757584.269069e-09
0.5388391.4756614.290139e-09
0.5414991.4755654.311314e-09
0.5441711.475474.332593e-09
0.5468571.4753764.353977e-09
0.5495561.4752834.375467e-09
0.551.4752684.379000e-09
0.5522691.4751914.397058e-09
0.5549941.4750994.418754e-09
0.5577331.4750094.440558e-09
0.5604861.4749194.462470e-09
0.5632521.474834.484489e-09
0.5660321.4747424.506617e-09
0.5688261.4746544.528855e-09
0.5716331.4745684.551202e-09
0.5744551.4744824.573660e-09
0.577291.4743974.596228e-09
0.5801391.4743134.618908e-09
0.5830021.4742294.641700e-09
0.585881.4741474.664604e-09
0.5887711.4740654.687621e-09
0.5916771.4739834.710752e-09
0.5945981.4739034.733997e-09
0.5975321.4738234.757356e-09
0.61.4737564.777000e-09
0.6004811.4737444.780832e-09
0.6034451.4736654.804429e-09
0.6064231.4735874.828142e-09
0.6094161.473514.851973e-09
0.6124241.4734344.875921e-09
0.6154471.4733584.899987e-09
0.6184841.4732834.924172e-09
0.6215371.4732084.948476e-09
0.6246041.4731344.972900e-09
0.6276871.4730614.997445e-09
0.6307851.4729885.022111e-09
0.6338981.4729165.046898e-09
0.6370271.4728445.071808e-09
0.6401711.4727745.096841e-09
0.6433311.4727035.121998e-09
0.6465061.4726335.147278e-09
0.6496971.4725645.172684e-09
0.651.4725585.175100e-09
0.6529031.4724965.198214e-09
0.6561251.4724285.223871e-09
0.6593641.472365.249655e-09
0.6626181.4722935.275565e-09
0.6658881.4722275.301604e-09
0.6691751.4721615.327771e-09
0.6724781.4720955.354067e-09
0.6757971.472035.380493e-09
0.6791321.4719665.407049e-09
0.6824841.4719025.433737e-09
0.6858521.4718385.460556e-09
0.6892371.4717755.487508e-09
0.6926391.4717135.514592e-09
0.6960581.4716515.541811e-09
0.6994931.4715895.569163e-09
0.71.471585.573200e-09
0.7029451.4715285.596651e-09
0.7064151.4714685.624274e-09
0.7099011.4714075.652034e-09
0.7134051.4713485.679930e-09
0.7169261.4712885.707964e-09
0.7204641.4712295.736137e-09
0.724021.4711715.764449e-09
0.7275941.4711135.792900e-09
0.7311851.4710555.821492e-09
0.7347931.4709985.850225e-09
0.738421.4709415.879100e-09
0.7420641.4708845.908117e-09
0.7457271.4708285.937278e-09
0.7494071.4707725.966582e-09
0.7531061.4707175.996031e-09
0.7568231.4706626.025626e-09
0.7605581.4706076.055366e-09
0.7643121.4705536.085253e-09
0.7680841.4704996.115288e-09
0.7718751.4704456.145471e-09
0.7756851.4703926.175803e-09
0.7795131.4703396.206285e-09
0.7833611.4702866.236917e-09
0.7872271.4702346.267700e-09
0.7911121.4701826.298635e-09
0.7950171.470136.329723e-09
0.7989411.4700786.360965e-09
0.81.4700656.369400e-09
0.8028841.4700276.599191e-09
0.8068461.4699766.914958e-09
0.8108291.4699267.232283e-09
0.814831.4698767.551174e-09
0.8188521.4698267.871639e-09
0.8228931.4697768.193685e-09
0.8269551.4697268.517321e-09
0.8310361.4696778.842554e-09
0.8351381.4696289.169393e-09
0.839261.4695799.497845e-09
0.8434021.4695319.827917e-09
0.8475641.4694831.015962e-08
0.8517481.4694351.049296e-08
0.8559511.4693871.082794e-08
0.8601761.4693391.116458e-08
0.8644211.4692921.150288e-08
0.8686881.4692451.184285e-08
0.8729751.4691981.218449e-08
0.8772841.4691511.252783e-08
0.8816131.4691051.287285e-08
0.8859651.4690591.321958e-08
0.8903371.4690131.356802e-08
0.8947321.4689671.391819e-08
0.8991481.4689211.427008e-08
0.91.4689121.433800e-08
0.9035851.4688751.439511e-08
0.9080451.468831.446616e-08
0.9125271.4687851.453755e-08
0.917031.468741.460929e-08
0.9215561.4686951.468139e-08
0.9261051.468651.475385e-08
0.9306761.4686051.482666e-08
0.9352691.4685611.489983e-08
0.9398851.4685171.497337e-08
0.9445241.4684721.504726e-08
0.9491851.4684281.512152e-08
0.953871.4683841.519615e-08
0.9585781.4683411.527115e-08
0.9633091.4682971.534651e-08
0.9680631.4682531.542225e-08
0.9728411.468211.549836e-08
0.9776431.4681671.557485e-08
0.9824681.4681231.565171e-08
0.9873171.468081.572896e-08
0.992191.4680371.580658e-08
0.9970871.4679941.588459e-08
11.4679691.593100e-08
1.002011.4679511.586698e-08
1.006951.4679081.570930e-08
1.011921.4678661.555084e-08
1.016921.4678231.539160e-08
1.021941.467781.523157e-08
1.026981.4677381.507075e-08
1.032051.4676951.490914e-08
1.037141.4676531.474673e-08
1.042261.4676111.458352e-08
1.047411.4675681.441950e-08
1.052571.4675261.425467e-08
1.057771.4674841.408903e-08
1.062991.4674411.392258e-08
1.068241.4673991.375530e-08
1.073511.4673571.358720e-08
1.078811.4673151.341826e-08
1.084131.4672731.324849e-08
1.089481.4672311.307789e-08
1.094861.4671881.290644e-08
1.100261.4671461.273415e-08
1.105691.4671041.256100e-08
1.111151.4670621.238700e-08
1.116641.467021.221215e-08
1.122151.4669781.203643e-08
1.127681.4669351.185984e-08
1.133251.4668931.168238e-08
1.138841.4668511.150404e-08
1.144461.4668091.132483e-08
1.150111.4667661.114473e-08
1.155791.4667241.096374e-08
1.161491.4666821.078186e-08
1.167231.4666391.059908e-08
1.172991.4665971.041540e-08
1.178781.4665541.023081e-08
1.184591.4665111.004531e-08
1.190441.4664699.858896e-09
1.196321.4664269.671561e-09
1.21.4663999.554100e-09
1.202221.4663839.695654e-09
1.208151.466341.007392e-08
1.214121.4662971.045404e-08
1.220111.4662541.083605e-08
1.226131.4662111.121994e-08
1.232181.4661681.160572e-08
1.238261.4661241.199341e-08
1.244381.4660811.238301e-08
1.250521.4660371.277454e-08
1.256691.4659931.316800e-08
1.262891.4659491.356340e-08
1.269121.4659051.396075e-08
1.275391.4658611.436006e-08
1.281681.4658171.476134e-08
1.288011.4657731.516460e-08
1.294371.4657281.556986e-08
1.300751.4656841.597711e-08
1.307171.4656391.638637e-08
1.313631.4655941.679766e-08
1.320111.4655491.721097e-08
1.326621.4655031.762633e-08
1.333171.4654581.804373e-08
1.339751.4654121.846319e-08
1.346361.4653661.888473e-08
1.353011.465321.930834e-08
1.359691.4652741.973404e-08
1.36641.4652282.016185e-08
1.373141.4651812.059177e-08
1.379921.4651342.102381e-08
1.386731.4650872.145798e-08
1.393571.465042.189429e-08
1.41.4649962.230400e-08
1.400451.4649932.245545e-08
1.407361.4649452.477564e-08
1.414311.4648972.710729e-08
1.421291.4648492.945044e-08
1.42831.4648013.180516e-08
1.435351.4647523.417151e-08
1.442441.4647033.654953e-08
1.449561.4646543.893928e-08
1.456711.4646054.134084e-08
1.46391.4645554.375424e-08
1.471131.4645064.617956e-08
1.478391.4644554.861684e-08
1.485681.4644055.106616e-08
1.493021.4643545.352756e-08
1.500381.4643035.600112e-08
1.507791.4642525.848688e-08
1.515231.4642016.098491e-08
1.522711.4641496.349526e-08
1.530231.4640966.601801e-08
1.537781.4640446.855321e-08
1.545371.4639917.110092e-08
1.552991.4639387.366121e-08
1.560661.4638857.623413e-08
1.568361.4638317.881975e-08
1.57611.4637778.141813e-08
1.583881.4637228.402934e-08
1.59171.4636678.665344e-08
1.599551.4636128.929048e-08
1.61.4636098.944000e-08
1.607451.4635569.254966e-08
1.615381.46359.586153e-08
1.623361.4634449.918974e-08
1.631371.4633871.025344e-07
1.639421.463331.058955e-07
1.647511.4632731.092733e-07
1.655641.4632151.126677e-07
1.663811.4631571.160788e-07
1.672021.4630981.195068e-07
1.680281.4630391.229517e-07
1.688571.4629791.264137e-07
1.69691.4629191.298927e-07
1.705281.4628591.333888e-07
1.71371.4627981.369023e-07
1.722151.4627371.404330e-07
1.730651.4626751.439812e-07
1.739191.4626131.475469e-07
1.747781.462551.511302e-07
1.75641.4624871.547312e-07
1.765071.4624231.583500e-07
1.773791.4623591.619866e-07
1.782541.4622941.656412e-07
1.791341.4622291.693138e-07
1.81.4621651.729300e-07
1.800181.4621631.730772e-07
1.809061.4620971.804005e-07
1.817991.462031.877599e-07
1.826961.4619631.951557e-07
1.835981.4618952.025879e-07
1.845041.4618272.100568e-07
1.854151.4617582.175626e-07
1.86331.4616892.251055e-07
1.87251.4616192.326855e-07
1.881741.4615482.403030e-07
1.891031.4614772.479581e-07
1.900361.4614052.556510e-07
1.909741.4613332.633818e-07
1.919161.461262.711508e-07
1.928641.4611862.789581e-07
1.938151.4611122.868039e-07
1.947721.4610372.946885e-07
1.957331.4609613.026120e-07
1.966991.4608853.105746e-07
1.97671.4608083.185765e-07
1.986461.4607313.266179e-07
1.996261.4606533.346990e-07
21.4606233.377800e-07
2.006111.4605743.520977e-07
2.016021.4604953.752818e-07
2.025971.4604143.985803e-07
2.035971.4603334.219939e-07
2.046011.4602524.455229e-07
2.056111.4601694.691681e-07
2.066261.4600864.929301e-07
2.076461.4600025.168092e-07
2.086711.4599185.408063e-07
2.0971.4598325.649218e-07
2.107351.4597465.891563e-07
2.117761.4596596.135104e-07
2.128211.4595726.379847e-07
2.138711.4594836.625798e-07
2.149271.4593946.872963e-07
2.159871.4593037.121348e-07
2.170531.4592127.370959e-07
2.181251.4591217.621801e-07
2.192011.4590287.873882e-07
2.21.4589598.060900e-07
2.202831.4589348.054340e-07
2.21371.458848.029155e-07
2.224631.4587458.003846e-07
2.235611.4586487.978411e-07
2.246641.4585517.952851e-07
2.257731.4584537.927165e-07
2.268871.4583547.901352e-07
2.280071.4582547.875412e-07
2.291331.4581537.849344e-07
2.302631.4580527.823147e-07
2.3141.4579497.796821e-07
2.325421.4578457.770365e-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
—