Optical constants

Refractive index of E-FD4 (HOYA)

E-FD4: n,k 0.365–1.014 µm

Data
formula 3 + tabulated k
Range
0.365–1.014 µm
Temperature
293 K
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength. Note: k data cover 370-1550 nm only; k = 0 elsewhere in the n range 365.01-1013.98 nm.

At one wavelength

Range 0.365–1.014 µm
Refractive index n
1.75519
Extinction coefficient k
2.23480e-08
Permittivity ε1
3.08071
Permittivity ε2
7.84503e-08
Absorption coefficient α
0.00477933 cm⁻¹
Penetration depth δ = λ/(2πk)
4.18468e+09 nm
Abbe number Vd
27.53
Chromatic dispersion dn/dλ
-0.137649 µm⁻¹
Group index ng
1.83608
Group velocity dispersion
281.122 fs²/mm
Dispersion parameter D
-1533.67 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

# E-FD4 (HOYA): E-FD4
hoya_e_fd4 = ls.fetch_refractiveindex("specs", "HOYA-optical", "E-FD4", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hoya_e_fd4.range_nm)  # (365.01, 1013.98) nm
eps = hoya_e_fd4.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

Polynomial (formula 3), λ in µm
n2=2.9673173−0.013989565⁢λ2.0+0.03345668⁢λ−2.0+0.0030717804⁢λ−4.0−0.00026682435⁢λ−6.0+2.8950241×10-5⁢λ−8.0

Valid from 0.36501 to 1.01398 µm.

Coefficients as stored
CiValue
C12.9673173
C2-0.013989565
C32.0
C40.03345668
C5-2.0
C60.0030717804
C7-4.0
C8-0.00026682435
C9-6.0
C102.8950241e-05
C11-8.0

Comments and conditions

General glass Type

Conditions

temperature
293 K

Properties

thermal dispersion
type: formula A, coefficients: 1.675e-07 0.0 0.0 0.0 0.0 0.0
nd
1.75520
Vd
27.53
glass code
755275
density
value: 3230
thermal expansion
value: 8.7e-06, temperature range: 243 343; value: 1e-05, temperature range: 293 573
dPgF
0.0103
resistance
acid: 1.0; stain: 1.0; climatic: 1.0

Thermo-optic coefficient

  • Schott thermal-dispersion model (reference temperature 293.0 K): dn/dT = 9.87e-08 K⁻¹ at 633 nm
Notes on the source data (kept exactly as published):
  • k data cover 370-1550 nm only; k = 0 elsewhere in the n range 365.01-1013.98 nm

References

Cite

HOYA Zemax catalog 2017-04-01 (obtained from http://www.hoya-opticalworld.com); Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 421 wavelengths, the same grid as the API and the library
E-FD4 (HOYA), E-FD4: n and k versus wavelength
λ (µm)nk
0.365011.8353950
0.3659461.8345230
0.3668841.8336610
0.3678251.8328080
0.3687681.8319640
0.3697131.831130
0.371.8308794.874300e-06
0.3706611.8303044.671131e-06
0.3716121.8294864.379179e-06
0.3725651.8286784.086479e-06
0.373521.8278773.793028e-06
0.3744771.8270853.498825e-06
0.3754381.8263023.203867e-06
0.37641.8255262.908154e-06
0.3773651.8247582.611682e-06
0.3783331.8239982.314450e-06
0.3793031.8232462.016455e-06
0.381.8227121.802300e-06
0.3802751.8225021.774120e-06
0.381251.8217651.674354e-06
0.3822281.8210351.574332e-06
0.3832081.8203121.474053e-06
0.384191.8195971.373518e-06
0.3851761.8188891.272724e-06
0.3861631.8181871.171672e-06
0.3871531.8174931.070361e-06
0.3881461.8168059.687905e-07
0.3891411.8161248.669593e-07
0.391.8155437.790700e-07
0.3901391.815457.741055e-07
0.3911391.8147827.383287e-07
0.3921421.814127.024601e-07
0.3931471.8134656.664995e-07
0.3941551.8128166.304468e-07
0.3951661.8121735.943016e-07
0.3961791.8115365.580638e-07
0.3971951.8109055.217330e-07
0.3982131.810284.853091e-07
0.3992341.809664.487918e-07
0.41.8092014.214100e-07
0.4002581.8090474.184580e-07
0.4012841.8084384.067177e-07
0.4023131.8078363.949473e-07
0.4033451.8072393.831468e-07
0.4043791.8066473.713159e-07
0.4054161.8060613.594548e-07
0.4064551.805483.475632e-07
0.4074971.8049043.356412e-07
0.4085421.8043333.236885e-07
0.409591.8037683.117053e-07
0.410641.8032072.996913e-07
0.4116931.8026512.876465e-07
0.4127481.80212.755708e-07
0.4138061.8015542.634642e-07
0.4148671.8010132.513265e-07
0.4159311.8004762.391577e-07
0.4169981.7999442.269577e-07
0.4180671.7994162.147264e-07
0.4191391.7988932.024637e-07
0.421.7984771.926100e-07
0.4202131.7983741.918475e-07
0.4212911.797861.879963e-07
0.4223711.797351.841352e-07
0.4234541.7968451.802642e-07
0.424541.7963431.763833e-07
0.4256281.7958461.724924e-07
0.4267191.7953531.685916e-07
0.4278131.7948641.646808e-07
0.428911.7943791.607599e-07
0.430011.7938971.568290e-07
0.4311131.793421.528880e-07
0.4322181.7929471.489369e-07
0.4333261.7924781.449756e-07
0.4344371.7920121.410042e-07
0.4355511.791551.370227e-07
0.4366681.7910921.330309e-07
0.4377871.7906371.290289e-07
0.438911.7901861.250166e-07
0.441.7897531.211200e-07
0.4400351.7897391.210765e-07
0.4411631.7892951.196839e-07
0.4422951.7888541.182878e-07
0.4434291.7884171.168880e-07
0.4445661.7879841.154847e-07
0.4457051.7875541.140778e-07
0.4468481.7871271.126673e-07
0.4479941.7867031.112531e-07
0.4491431.7862831.098354e-07
0.4502941.7858661.084139e-07
0.4514491.7854521.069889e-07
0.4526061.7850411.055602e-07
0.4537671.7846341.041278e-07
0.454931.7842291.026918e-07
0.4560971.7838281.012521e-07
0.4572661.7834299.980867e-08
0.4584381.7830349.836156e-08
0.4596141.7826419.691073e-08
0.461.7825139.643400e-08
0.4607921.7822529.536243e-08
0.4619741.7818659.376434e-08
0.4631581.7814819.216214e-08
0.4643461.78119.055584e-08
0.4655361.7807228.894542e-08
0.466731.7803468.733087e-08
0.4679271.7799748.571218e-08
0.4691261.7796048.408934e-08
0.4703291.7792368.246234e-08
0.4715351.7788728.083117e-08
0.4727441.778517.919582e-08
0.4739561.778157.755627e-08
0.4751711.7777937.591252e-08
0.476391.7774397.426455e-08
0.4776111.7770877.261236e-08
0.4788361.7767387.095593e-08
0.481.7764096.938100e-08
0.4800631.7763916.932612e-08
0.4812941.7760476.826044e-08
0.4825281.7757056.719202e-08
0.4837651.7753656.612086e-08
0.4850061.7750286.504696e-08
0.4862491.7746946.397030e-08
0.4874961.7743616.289089e-08
0.4887461.7740316.180870e-08
0.4899991.7737036.072374e-08
0.4912551.7733785.963600e-08
0.4925151.7730545.854547e-08
0.4937781.7727335.745215e-08
0.4950441.7724145.635602e-08
0.4963131.7720985.525708e-08
0.4975861.7717835.415532e-08
0.4988611.7714715.305074e-08
0.51.7711945.206500e-08
0.5001411.771165.196797e-08
0.5014231.7708525.108256e-08
0.5027091.7705465.019488e-08
0.5039971.7702424.930493e-08
0.505291.769944.841269e-08
0.5065851.769644.751817e-08
0.5078841.7693424.662135e-08
0.5091861.7690464.572224e-08
0.5104921.7687534.482082e-08
0.5118011.7684614.391709e-08
0.5131131.768174.301104e-08
0.5144291.7678824.210266e-08
0.5157481.7675964.119196e-08
0.517071.7673124.027893e-08
0.5183961.7670293.936355e-08
0.5197251.7667493.844582e-08
0.5210571.766473.752575e-08
0.5223931.7661933.660331e-08
0.5237331.7659183.567851e-08
0.5250761.7656443.475133e-08
0.5264221.7653733.382178e-08
0.5277721.7651033.288985e-08
0.5291251.7648353.195553e-08
0.5304811.7645693.101881e-08
0.5318421.7643043.007969e-08
0.5332051.7640412.913816e-08
0.5345721.763782.819422e-08
0.5359431.763522.724786e-08
0.5373171.7632622.629907e-08
0.5386951.7630062.534785e-08
0.5400761.7627512.439419e-08
0.5414611.7624982.343808e-08
0.5428491.7622472.247952e-08
0.5442411.7619972.151851e-08
0.5456361.7617492.055503e-08
0.5470351.7615021.958908e-08
0.5484381.7612571.862066e-08
0.5498441.7610131.764975e-08
0.551.7609861.754200e-08
0.5512541.7607711.770225e-08
0.5526671.7605311.788291e-08
0.5540841.7602921.806404e-08
0.5555051.7600541.824562e-08
0.5569291.7598181.842768e-08
0.5583571.7595831.861020e-08
0.5597891.759351.879319e-08
0.5612241.7591181.897664e-08
0.5626631.7588881.916057e-08
0.5641061.7586591.934497e-08
0.5655521.7584321.952984e-08
0.5670021.7582061.971519e-08
0.5684561.7579811.990101e-08
0.5699131.7577582.008731e-08
0.5713741.7575362.027408e-08
0.5728391.7573152.046134e-08
0.5743081.7570962.064907e-08
0.5757811.7568782.083729e-08
0.5772571.7566612.102599e-08
0.5787371.7564462.121517e-08
0.5802211.7562322.140484e-08
0.5817091.7560192.159499e-08
0.58321.7558082.178563e-08
0.5846951.7555982.197676e-08
0.5861951.7553892.216838e-08
0.5876971.7551812.236049e-08
0.5892041.7549752.255310e-08
0.5907151.7547692.274619e-08
0.592231.7545662.293979e-08
0.5937481.7543632.313388e-08
0.595271.7541612.332846e-08
0.5967971.7539612.352355e-08
0.5983271.7537622.371914e-08
0.5998611.7535642.391522e-08
0.61.7535462.393300e-08
0.6013991.7533672.384344e-08
0.6029411.7531712.374472e-08
0.6044871.7529772.364575e-08
0.6060371.7527832.354653e-08
0.6075911.7525912.344705e-08
0.6091481.75242.334732e-08
0.610711.752212.324733e-08
0.6122761.7520212.314708e-08
0.6138461.7518332.304658e-08
0.615421.7516462.294582e-08
0.6169981.7514612.284480e-08
0.618581.7512762.274353e-08
0.6201661.7510932.264199e-08
0.6217561.750912.254019e-08
0.623351.7507292.243813e-08
0.6249481.7505492.233581e-08
0.6265511.7503692.223323e-08
0.6281571.7501912.213039e-08
0.6297681.7500142.202728e-08
0.6313821.7498372.192390e-08
0.6330011.7496622.182027e-08
0.6346241.7494882.171636e-08
0.6362511.7493152.161219e-08
0.6378831.7491422.150775e-08
0.6395181.7489712.140305e-08
0.6411581.7488012.129808e-08
0.6428021.7486312.119283e-08
0.644451.7484632.108732e-08
0.6461021.7482952.098154e-08
0.6477591.7481292.087548e-08
0.649421.7479632.076915e-08
0.651.7479052.073200e-08
0.6510851.7477982.113114e-08
0.6527541.7476342.174539e-08
0.6544281.7474712.236123e-08
0.6561061.7473092.297864e-08
0.6577881.7471482.359763e-08
0.6594741.7469882.421821e-08
0.6611651.7468292.484039e-08
0.6628611.746672.546416e-08
0.664561.7465132.608952e-08
0.6662641.7463562.671649e-08
0.6679721.74622.734507e-08
0.6696851.7460452.797526e-08
0.6714021.7458912.860707e-08
0.6731231.7457382.924049e-08
0.6748491.7455852.987554e-08
0.676581.7454343.051222e-08
0.6783141.7452833.115053e-08
0.6800531.7451333.179048e-08
0.6817971.7449833.243207e-08
0.6835451.7448353.307530e-08
0.6852981.7446873.372018e-08
0.6870551.7445413.436672e-08
0.6888161.7443943.501491e-08
0.6905831.7442493.566477e-08
0.6923531.7441053.631629e-08
0.6941281.7439613.696948e-08
0.6959081.7438183.762435e-08
0.6976921.7436763.828089e-08
0.6994811.7435343.893912e-08
0.71.7434933.913000e-08
0.7012751.7433943.858958e-08
0.7030731.7432543.782728e-08
0.7048751.7431143.706303e-08
0.7066831.7429763.629681e-08
0.7084951.7428383.552863e-08
0.7103111.7427013.475849e-08
0.7121321.7425643.398636e-08
0.7139581.7424293.321226e-08
0.7157891.7422943.243618e-08
0.7176241.742163.165810e-08
0.7194641.7420263.087803e-08
0.7213091.7418933.009596e-08
0.7231581.7417612.931188e-08
0.7250121.7416292.852579e-08
0.7268711.7414982.773769e-08
0.7287351.7413682.694757e-08
0.7306031.7412392.615542e-08
0.7324771.741112.536124e-08
0.7343551.7409812.456502e-08
0.7362371.7408542.376676e-08
0.7381251.7407272.296646e-08
0.7400181.7406012.216410e-08
0.7419151.7404752.135969e-08
0.7438171.740352.055321e-08
0.7457241.7402251.974467e-08
0.7476361.7401021.893405e-08
0.7495531.7399781.812136e-08
0.751.739951.793200e-08
0.7514751.7398561.766130e-08
0.7534021.7397341.730774e-08
0.7553341.7396121.695328e-08
0.757271.7394911.659790e-08
0.7592121.7393711.624161e-08
0.7611591.7392521.588441e-08
0.763111.7391331.552630e-08
0.7650671.7390141.516726e-08
0.7670281.7388961.480731e-08
0.7689951.7387791.444643e-08
0.7709671.7386621.408463e-08
0.7729431.7385461.372190e-08
0.7749251.738431.335824e-08
0.7769121.7383151.299364e-08
0.7789041.73821.262812e-08
0.781.7381381.242700e-08
0.7809011.7380861.244133e-08
0.7829031.7379731.247316e-08
0.7849111.737861.250508e-08
0.7869231.7377471.253708e-08
0.7889411.7376351.256916e-08
0.7909641.7375241.260132e-08
0.7929921.7374131.263357e-08
0.7950251.7373031.266589e-08
0.7970631.7371931.269830e-08
0.7991071.7370841.273080e-08
0.81.7370361.274500e-08
0.8011561.7369751.276341e-08
0.803211.7368661.279614e-08
0.8052691.7367591.282896e-08
0.8073341.7366511.286185e-08
0.8094041.7365441.289484e-08
0.8114791.7364381.292790e-08
0.813561.7363321.296105e-08
0.8156461.7362261.299429e-08
0.8177371.7361211.302761e-08
0.8198341.7360171.306102e-08
0.8219361.7359131.309451e-08
0.8240431.7358091.312809e-08
0.8261561.7357061.316175e-08
0.8282741.7356031.319550e-08
0.831.735521.322300e-08
0.8303981.7355011.322935e-08
0.8325271.7353991.326331e-08
0.8346621.7352981.329735e-08
0.8368021.7351971.333149e-08
0.8389471.7350961.336571e-08
0.8410981.7349961.340002e-08
0.8432551.7348971.343441e-08
0.8454171.7347971.346890e-08
0.8475841.7346991.350347e-08
0.8497581.73461.353813e-08
0.851.7345891.354200e-08
0.8519361.7345021.357283e-08
0.8541211.7344051.360760e-08
0.8563111.7343071.364247e-08
0.8585061.7342111.367742e-08
0.8607071.7341141.371246e-08
0.8629141.7340181.374759e-08
0.8651271.7339231.378282e-08
0.8673451.7338281.381813e-08
0.8695691.7337331.385353e-08
0.8717981.7336381.388903e-08
0.8740331.7335441.392461e-08
0.8762741.733451.396029e-08
0.8785211.7333571.399606e-08
0.8807741.7332641.403192e-08
0.8830321.7331721.406787e-08
0.8852961.7330791.410391e-08
0.8875661.7329881.414005e-08
0.8898421.7328961.417628e-08
0.8921231.7328051.421260e-08
0.8944111.7327141.424902e-08
0.8967041.7326241.428552e-08
0.8990031.7325331.432213e-08
0.91.7324951.433800e-08
0.9013081.7324441.435885e-08
0.9036191.7323541.439568e-08
0.9059361.7322651.443261e-08
0.9082581.7321761.446964e-08
0.9105871.7320881.450676e-08
0.9129221.7321.454398e-08
0.9152631.7319121.458129e-08
0.9176091.7318241.461869e-08
0.9199621.7317371.465619e-08
0.9223211.731651.469379e-08
0.9246861.7315641.473149e-08
0.9270561.7314781.476928e-08
0.9294331.7313921.480717e-08
0.9318161.7313061.484515e-08
0.9342061.7312211.488324e-08
0.9366011.7311361.492142e-08
0.9390021.7310511.495970e-08
0.941411.7309661.499807e-08
0.9438241.7308821.503655e-08
0.9462441.7307981.507512e-08
0.948671.7307151.511379e-08
0.951.7306691.513500e-08
0.9511021.7306311.515254e-08
0.9535411.7305481.519137e-08
0.9559851.7304651.523029e-08
0.9584371.7303831.526931e-08
0.9608941.7303011.530843e-08
0.9633581.7302191.534765e-08
0.9658281.7301371.538698e-08
0.9683041.7300551.542640e-08
0.9707871.7299741.546592e-08
0.9732761.7298931.550555e-08
0.9757711.7298121.554528e-08
0.9782731.7297321.558511e-08
0.9807811.7296521.562504e-08
0.9832961.7295721.566507e-08
0.9858171.7294921.570521e-08
0.9883451.7294121.574545e-08
0.9908791.7293331.578579e-08
0.9934191.7292541.582624e-08
0.9959671.7291751.586679e-08
0.998521.7290971.590744e-08
11.7290511.593100e-08
1.001081.7290181.594822e-08
1.003651.728941.598913e-08
1.006221.7288621.603015e-08
1.00881.7287841.607128e-08
1.011391.7287071.611251e-08
1.013981.728631.615384e-08

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
—