Optical constants
Refractive index of GaAs (Gallium arsenide)
Franta et al. 2026: n,k 0.922–400 µm; 370 K
- Data
- tabulated nk
- Range
- 0.9223–399.6 µm
- Points
- 6315
- Temperature
- 370 K
- Licence
- CC0-1.0
Plot
Click the plot to set the calculator wavelength.
At one wavelength
- Refractive index n
- 3.19858
- Extinction coefficient k
- 0.00866788
- Permittivity ε1
- 10.2308
- Permittivity ε2
- 0.0554498
- Absorption coefficient α
- 56.7311 cm⁻¹
- Penetration depth δ = λ/(2πk)
- 352540 nm
- Abbe number Vd
- —
- Chromatic dispersion dn/dλ
- 0.0139645 µm⁻¹
- Group index ng
- 2.93046
- Group velocity dispersion
- — fs²/mm
- Dispersion parameter D
- — ps/(nm·km)
- Photon energy
- 0.0645751 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
# GaAs (Gallium arsenide): Franta et al. 2026: n,k 0.922–400 µm; 370 K
gaas = ls.fetch_refractiveindex("main", "GaAs", "Franta-370K", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(gaas.range_nm) # (922.322, 399638) nm
eps = gaas.eps([19200]) # complex permittivity
Downloads the original record once (pinned to the imported snapshot) and caches it.
import json, urllib.request
import lightsmith as ls
url = "https://materials.lightsmith.dev/v1/datasets/ds_53a20f09e38c/lightsmith"
gaas = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(gaas.source) # citation and provenance travel with the data
Any dataset here, as the library's Tabulated material (gaas/franta-2026-370k).
# ... load gaas as above, then:
sim = ls.Simulation(
particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=gaas)],
medium_index=1.0,
wavelengths=ls.WavelengthRange(start_nm=923, stop_nm=1000, num=81),
)
res = ls.solve(sim) # exact Mie for a sphere
print(res.q_ext) # extinction efficiency at each wavelength
Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).
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.
Comments and conditions
Conditions
- temperature
- 370 K
References
- doi:10.1063/5.0314388 Dispersion models describing coupled systems in doped crystals. II. Infrared phonon excitations in GaAs single crystals and phonon–plasmon coupling in Zn-doped GaAs, Journal of Applied Physics (2026)
Cite
Daniel Franta, Beáta Hroncová, Mihai-George Mureșan and Stefan Zollner. Dispersion models describing coupled systems in doped crystals. II. Infrared phonon excitations in GaAs single crystals and phonon–plasmon coupling in Zn-doped GaAs. Journal of Applied Physics, 139, 175704 (2026), doi:10.1063/5.0314388; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)
Data
6315 rows as published| λ (µm) | n | k |
|---|---|---|
| 0.922322 | 3.59923385956 | 0.0 |
| 0.923209 | 3.59799017055 | 0.0 |
| 0.924097 | 3.59676605382 | 0.0 |
| 0.924986 | 3.59556077526 | 0.0 |
| 0.925876 | 3.59437363987 | 0.0 |
| 0.926767 | 3.59320398922 | 0.0 |
| 0.927659 | 3.59205119902 | 0.0 |
| 0.928551 | 3.59091467694 | 0.0 |
| 0.929444 | 3.58979386055 | 0.0 |
| 0.930338 | 3.58868821548 | 0.0 |
| 0.931233 | 3.58759723361 | 0.0 |
| 0.932129 | 3.58652043155 | 0.0 |
| 0.933026 | 3.58545734904 | 0.0 |
| 0.933924 | 3.58440754765 | 0.0 |
| 0.934822 | 3.58337060944 | 0.0 |
| 0.935722 | 3.58234613577 | 0.0 |
| 0.936622 | 3.5813337462 | 0.0 |
| 0.937523 | 3.58033307744 | 0.0 |
| 0.938425 | 3.57934378238 | 0.0 |
| 0.939328 | 3.57836552918 | 0.0 |
| 0.940231 | 3.57739800045 | 0.0 |
| 0.941136 | 3.57644089243 | 0.0 |
| 0.942041 | 3.57549391428 | 0.0 |
| 0.942947 | 3.57455678739 | 0.0 |
| 0.943855 | 3.57362924469 | 0.0 |
| 0.944763 | 3.57271103013 | 0.0 |
| 0.945672 | 3.57180189801 | 0.0 |
| 0.946581 | 3.57090161253 | 0.0 |
| 0.947492 | 3.57000994724 | 0.0 |
| 0.948404 | 3.56912668461 | 0.0 |
| 0.949316 | 3.56825161556 | 0.0 |
| 0.950229 | 3.56738453903 | 0.0 |
| 0.951143 | 3.56652526163 | 0.0 |
| 0.952058 | 3.56567359724 | 0.0 |
| 0.952974 | 3.5648293667 | 0.0 |
| 0.953891 | 3.56399239741 | 0.0 |
| 0.954809 | 3.5631625231 | 0.0 |
| 0.955727 | 3.56233958351 | 0.0 |
| 0.956647 | 3.56152342407 | 0.0 |
| 0.957567 | 3.56071389571 | 0.0 |
| 0.958488 | 3.55991085457 | 0.0 |
| 0.95941 | 3.55911416179 | 0.0 |
| 0.960333 | 3.55832368326 | 0.0 |
| 0.961257 | 3.55753928944 | 0.0 |
| 0.962182 | 3.55676085513 | 0.0 |
| 0.963108 | 3.55598825934 | 0.0 |
| 0.964034 | 3.55522138503 | 0.0 |
| 0.964962 | 3.55446011901 | 0.0 |
| 0.96589 | 3.55370435175 | 0.0 |
| 0.966819 | 3.55295397724 | 0.0 |
| 0.967749 | 3.55220889281 | 0.0 |
| 0.968681 | 3.55146899904 | 0.0 |
| 0.969612 | 3.55073419961 | 0.0 |
| 0.970545 | 3.55000440115 | 0.0 |
| 0.971479 | 3.54927951318 | 0.0 |
| 0.972414 | 3.54855944794 | 0.0 |
| 0.973349 | 3.54784412029 | 0.0 |
| 0.974285 | 3.54713344765 | 0.0 |
| 0.975223 | 3.54642734985 | 0.0 |
| 0.976161 | 3.54572574909 | 0.0 |
| 0.9771 | 3.54502856979 | 0.0 |
| 0.97804 | 3.54433573855 | 0.0 |
| 0.978981 | 3.54364718406 | 0.0 |
| 0.979923 | 3.54296283701 | 0.0 |
| 0.980866 | 3.54228263002 | 0.0 |
| 0.981809 | 3.5416064976 | 0.0 |
| 0.982754 | 3.54093437602 | 0.0 |
| 0.983699 | 3.5402662033 | 0.0 |
| 0.984646 | 3.53960191913 | 0.0 |
| 0.985593 | 3.53894146482 | 0.0 |
| 0.986541 | 3.5382847832 | 0.0 |
| 0.98749 | 3.53763181864 | 0.0 |
| 0.98844 | 3.53698251692 | 0.0 |
| 0.989391 | 3.53633682525 | 0.0 |
| 0.990343 | 3.53569469217 | 0.0 |
| 0.991296 | 3.53505606753 | 0.0 |
| 0.992249 | 3.53442090243 | 0.0 |
| 0.993204 | 3.53378914922 | 0.0 |
| 0.994159 | 3.53316076139 | 0.0 |
| 0.995116 | 3.53253569358 | 0.0 |
| 0.996073 | 3.53191390155 | 0.0 |
| 0.997031 | 3.53129534211 | 0.0 |
| 0.997991 | 3.53067997309 | 0.0 |
| 0.998951 | 3.53006775334 | 0.0 |
| 0.999912 | 3.52945864266 | 0.0 |
| 1.00087 | 3.52885260181 | 0.0 |
| 1.00184 | 3.52824959243 | 0.0 |
| 1.0028 | 3.52764957704 | 0.0 |
| 1.00377 | 3.52705251904 | 0.0 |
| 1.00473 | 3.52645838262 | 0.0 |
| 1.0057 | 3.5258671328 | 0.0 |
| 1.00666 | 3.52527873534 | 0.0 |
| 1.00763 | 3.52469315679 | 0.0 |
| 1.0086 | 3.52411036441 | 0.0 |
| 1.00957 | 3.52353032617 | 0.0 |
| 1.01054 | 3.52295301072 | 0.0 |
| 1.01152 | 3.52237838739 | 0.0 |
| 1.01249 | 3.52180642616 | 0.0 |
| 1.01346 | 3.52123709762 | 0.0 |
| 1.01444 | 3.52067037299 | 0.0 |
| 1.01541 | 3.52010622407 | 0.0 |
| 1.01639 | 3.51954462325 | 0.0 |
| 1.01737 | 3.51898554346 | 0.0 |
| 1.01835 | 3.51842895819 | 0.0 |
| 1.01933 | 3.51787484146 | 0.0 |
| 1.02031 | 3.5173231678 | 0.0 |
| 1.02129 | 3.51677391223 | 0.0 |
| 1.02227 | 3.51622705028 | 0.0 |
| 1.02326 | 3.51568255793 | 0.0 |
| 1.02424 | 3.51514041164 | 0.0 |
| 1.02523 | 3.51460058831 | 0.0 |
| 1.02621 | 3.51406306527 | 0.0 |
| 1.0272 | 3.51352782028 | 0.0 |
| 1.02819 | 3.51299483152 | 0.0 |
| 1.02918 | 3.51246407757 | 0.0 |
| 1.03017 | 3.51193553739 | 0.0 |
| 1.03116 | 3.51140919035 | 0.0 |
| 1.03215 | 3.51088501616 | 0.0 |
| 1.03314 | 3.5103629949 | 0.0 |
| 1.03414 | 3.50984310703 | 0.0 |
| 1.03513 | 3.50932533333 | 0.0 |
| 1.03613 | 3.50880965492 | 0.0 |
| 1.03712 | 3.50829605325 | 0.0 |
| 1.03812 | 3.50778451009 | 0.0 |
| 1.03912 | 3.50727500752 | 0.0 |
| 1.04012 | 3.50676752793 | 0.0 |
| 1.04112 | 3.50626205399 | 0.0 |
| 1.04212 | 3.50575856869 | 0.0 |
| 1.04313 | 3.50525705527 | 0.0 |
| 1.04413 | 3.50475749726 | 0.0 |
| 1.04513 | 3.50425987847 | 0.0 |
| 1.04614 | 3.50376418295 | 0.0 |
| 1.04715 | 3.50327039502 | 0.0 |
| 1.04815 | 3.50277849926 | 0.0 |
| 1.04916 | 3.50228848047 | 0.0 |
| 1.05017 | 3.50180032372 | 0.0 |
| 1.05118 | 3.50131401428 | 0.0 |
| 1.05219 | 3.50082953767 | 0.0 |
| 1.0532 | 3.50034687963 | 0.0 |
| 1.05422 | 3.49986602612 | 0.0 |
| 1.05523 | 3.49938696331 | 0.0 |
| 1.05625 | 3.49890967758 | 0.0 |
| 1.05726 | 3.49843415551 | 0.0 |
| 1.05828 | 3.49796038387 | 0.0 |
| 1.0593 | 3.49748834966 | 0.0 |
| 1.06032 | 3.49701804003 | 0.0 |
| 1.06134 | 3.49654944233 | 0.0 |
| 1.06236 | 3.49608254412 | 0.0 |
| 1.06338 | 3.49561733309 | 0.0 |
| 1.0644 | 3.49515379715 | 0.0 |
| 1.06543 | 3.49469192435 | 0.0 |
| 1.06645 | 3.49423170292 | 0.0 |
| 1.06748 | 3.49377312126 | 0.0 |
| 1.06851 | 3.49331616791 | 0.0 |
| 1.06953 | 3.4928608316 | 0.0 |
| 1.07056 | 3.49240710118 | 0.0 |
| 1.07159 | 3.49195496566 | 0.0 |
| 1.07262 | 3.49150441422 | 0.0 |
| 1.07365 | 3.49105543616 | 0.0 |
| 1.07469 | 3.49060802093 | 0.0 |
| 1.07572 | 3.49016215812 | 0.0 |
| 1.07676 | 3.48971783746 | 0.0 |
| 1.07779 | 3.48927504881 | 0.0 |
| 1.07883 | 3.48883378214 | 0.0 |
| 1.07987 | 3.48839402759 | 0.0 |
| 1.08091 | 3.4879557754 | 0.0 |
| 1.08195 | 3.48751901593 | 0.0 |
| 1.08299 | 3.48708373967 | 0.0 |
| 1.08403 | 3.48664993723 | 0.0 |
| 1.08507 | 3.48621759933 | 0.0 |
| 1.08612 | 3.48578671681 | 0.0 |
| 1.08716 | 3.48535728062 | 0.0 |
| 1.08821 | 3.48492928183 | 0.0 |
| 1.08925 | 3.48450271158 | 0.0 |
| 1.0903 | 3.48407756117 | 0.0 |
| 1.09135 | 3.48365382196 | 0.0 |
| 1.0924 | 3.48323148544 | 0.0 |
| 1.09345 | 3.48281054319 | 0.0 |
| 1.0945 | 3.48239098687 | 0.0 |
| 1.09556 | 3.48197280828 | 0.0 |
| 1.09661 | 3.48155599927 | 0.0 |
| 1.09766 | 3.4811405518 | 0.0 |
| 1.09872 | 3.48072645794 | 0.0 |
| 1.09978 | 3.48031370983 | 0.0 |
| 1.10084 | 3.47990229968 | 0.0 |
| 1.10189 | 3.47949221983 | 0.0 |
| 1.10295 | 3.47908346268 | 0.0 |
| 1.10402 | 3.47867602071 | 0.0 |
| 1.10508 | 3.47826988649 | 0.0 |
| 1.10614 | 3.47786505267 | 0.0 |
| 1.10721 | 3.47746151199 | 0.0 |
| 1.10827 | 3.47705925724 | 0.0 |
| 1.10934 | 3.47665828132 | 0.0 |
| 1.1104 | 3.47625857718 | 0.0 |
| 1.11147 | 3.47586013786 | 0.0 |
| 1.11254 | 3.47546295645 | 0.0 |
| 1.11361 | 3.47506702615 | 0.0 |
| 1.11468 | 3.4746723402 | 0.0 |
| 1.11576 | 3.47427889192 | 0.0 |
| 1.11683 | 3.4738866747 | 0.0 |
| 1.1179 | 3.47349568198 | 0.0 |
| 1.11898 | 3.4731059073 | 0.0 |
| 1.12006 | 3.47271734423 | 0.0 |
| 1.12113 | 3.47232998642 | 0.0 |
| 1.12221 | 3.47194382759 | 0.0 |
| 1.12329 | 3.47155886151 | 0.0 |
| 1.12437 | 3.47117508202 | 0.0 |
| 1.12545 | 3.470792483 | 0.0 |
| 1.12654 | 3.47041105842 | 0.0 |
| 1.12762 | 3.47003080229 | 0.0 |
| 1.1287 | 3.46965170867 | 0.0 |
| 1.12979 | 3.46927377169 | 0.0 |
| 1.13088 | 3.46889698554 | 0.0 |
| 1.13197 | 3.46852134444 | 0.0 |
| 1.13305 | 3.4681468427 | 0.0 |
| 1.13414 | 3.46777347465 | 0.0 |
| 1.13524 | 3.46740123469 | 0.0 |
| 1.13633 | 3.46703011726 | 0.0 |
| 1.13742 | 3.46666011687 | 0.0 |
| 1.13852 | 3.46629122806 | 0.0 |
| 1.13961 | 3.46592344543 | 0.0 |
| 1.14071 | 3.46555676362 | 0.0 |
| 1.1418 | 3.46519117732 | 0.0 |
| 1.1429 | 3.46482668129 | 0.0 |
| 1.144 | 3.4644632703 | 0.0 |
| 1.1451 | 3.46410093918 | 0.0 |
| 1.1462 | 3.46373968283 | 0.0 |
| 1.14731 | 3.46337949614 | 0.0 |
| 1.14841 | 3.46302037411 | 0.0 |
| 1.14952 | 3.46266231172 | 0.0 |
| 1.15062 | 3.46230530404 | 0.0 |
| 1.15173 | 3.46194934615 | 0.0 |
| 1.15284 | 3.46159443321 | 0.0 |
| 1.15395 | 3.46124056037 | 0.0 |
| 1.15506 | 3.46088772286 | 0.0 |
| 1.15617 | 3.46053591594 | 0.0 |
| 1.15728 | 3.4601851349 | 0.0 |
| 1.15839 | 3.45983537507 | 0.0 |
| 1.15951 | 3.45948663183 | 0.0 |
| 1.16062 | 3.45913890059 | 0.0 |
| 1.16174 | 3.4587921768 | 0.0 |
| 1.16286 | 3.45844645593 | 0.0 |
| 1.16398 | 3.45810173353 | 0.0 |
| 1.1651 | 3.45775800512 | 0.0 |
| 1.16622 | 3.45741526632 | 0.0 |
| 1.16734 | 3.45707351275 | 0.0 |
| 1.16846 | 3.45673274006 | 0.0 |
| 1.16959 | 3.45639294395 | 0.0 |
| 1.17071 | 3.45605412016 | 0.0 |
| 1.17184 | 3.45571626443 | 0.0 |
| 1.17296 | 3.45537937258 | 0.0 |
| 1.17409 | 3.45504344041 | 0.0 |
| 1.17522 | 3.4547084638 | 0.0 |
| 1.17635 | 3.45437443862 | 0.0 |
| 1.17748 | 3.45404136081 | 0.0 |
| 1.17862 | 3.45370922631 | 0.0 |
| 1.17975 | 3.4533780311 | 0.0 |
| 1.18089 | 3.4530477712 | 0.0 |
| 1.18202 | 3.45271844264 | 0.0 |
| 1.18316 | 3.4523900415 | 0.0 |
| 1.1843 | 3.45206256387 | 0.0 |
| 1.18544 | 3.45173600589 | 0.0 |
| 1.18658 | 3.45141036371 | 0.0 |
| 1.18772 | 3.4510856335 | 0.0 |
| 1.18886 | 3.45076181149 | 0.0 |
| 1.19001 | 3.45043889391 | 0.0 |
| 1.19115 | 3.45011687702 | 0.0 |
| 1.1923 | 3.44979575712 | 0.0 |
| 1.19344 | 3.44947553053 | 0.0 |
| 1.19459 | 3.44915619358 | 0.0 |
| 1.19574 | 3.44883774265 | 0.0 |
| 1.19689 | 3.44852017414 | 0.0 |
| 1.19804 | 3.44820348445 | 0.0 |
| 1.19919 | 3.44788767004 | 0.0 |
| 1.20035 | 3.44757272737 | 0.0 |
| 1.2015 | 3.44725865294 | 0.0 |
| 1.20266 | 3.44694544326 | 0.0 |
| 1.20382 | 3.44663309488 | 0.0 |
| 1.20497 | 3.44632160435 | 0.0 |
| 1.20613 | 3.44601096827 | 0.0 |
| 1.20729 | 3.44570118324 | 0.0 |
| 1.20846 | 3.4453922459 | 0.0 |
| 1.20962 | 3.4450841529 | 0.0 |
| 1.21078 | 3.44477690092 | 0.0 |
| 1.21195 | 3.44447048666 | 0.0 |
| 1.21311 | 3.44416490683 | 0.0 |
| 1.21428 | 3.44386015818 | 0.0 |
| 1.21545 | 3.44355623748 | 0.0 |
| 1.21662 | 3.4432531415 | 0.0 |
| 1.21779 | 3.44295086705 | 0.0 |
| 1.21896 | 3.44264941095 | 0.0 |
| 1.22013 | 3.44234877006 | 0.0 |
| 1.22131 | 3.44204894124 | 0.0 |
| 1.22248 | 3.44174992136 | 0.0 |
| 1.22366 | 3.44145170735 | 0.0 |
| 1.22483 | 3.44115429612 | 0.0 |
| 1.22601 | 3.44085768461 | 0.0 |
| 1.22719 | 3.44056186979 | 0.0 |
| 1.22837 | 3.44026684864 | 0.0 |
| 1.22955 | 3.43997261816 | 0.0 |
| 1.23074 | 3.43967917538 | 0.0 |
| 1.23192 | 3.43938651732 | 0.0 |
| 1.23311 | 3.43909464104 | 0.0 |
| 1.23429 | 3.43880354362 | 0.0 |
| 1.23548 | 3.43851322215 | 0.0 |
| 1.23667 | 3.43822367373 | 0.0 |
| 1.23786 | 3.4379348955 | 0.0 |
| 1.23905 | 3.43764688459 | 0.0 |
| 1.24024 | 3.43735963816 | 0.0 |
| 1.24143 | 3.4370731534 | 0.0 |
| 1.24263 | 3.4367874275 | 0.0 |
| 1.24382 | 3.43650245767 | 0.0 |
| 1.24502 | 3.43621824113 | 0.0 |
| 1.24622 | 3.43593477513 | 0.0 |
| 1.24742 | 3.43565205693 | 0.0 |
| 1.24862 | 3.4353700838 | 0.0 |
| 1.24982 | 3.43508885304 | 0.0 |
| 1.25102 | 3.43480836195 | 0.0 |
| 1.25222 | 3.43452860785 | 0.0 |
| 1.25343 | 3.43424958809 | 0.0 |
| 1.25464 | 3.43397130001 | 0.0 |
| 1.25584 | 3.43369374099 | 0.0 |
| 1.25705 | 3.4334169084 | 0.0 |
| 1.25826 | 3.43314079965 | 0.0 |
| 1.25947 | 3.43286541215 | 0.0 |
| 1.26068 | 3.43259074332 | 0.0 |
| 1.26189 | 3.4323167906 | 0.0 |
| 1.26311 | 3.43204355146 | 0.0 |
| 1.26432 | 3.43177102336 | 0.0 |
| 1.26554 | 3.43149920379 | 0.0 |
| 1.26676 | 3.43122809024 | 0.0 |
| 1.26798 | 3.43095768023 | 0.0 |
| 1.2692 | 3.43068797127 | 0.0 |
| 1.27042 | 3.43041896092 | 0.0 |
| 1.27164 | 3.43015064672 | 0.0 |
| 1.27286 | 3.42988302623 | 0.0 |
| 1.27409 | 3.42961609704 | 0.0 |
| 1.27531 | 3.42934985674 | 0.0 |
| 1.27654 | 3.42908430294 | 0.0 |
| 1.27777 | 3.42881943324 | 0.0 |
| 1.279 | 3.42855524528 | 0.0 |
| 1.28023 | 3.42829173671 | 0.0 |
| 1.28146 | 3.42802890517 | 0.0 |
| 1.28269 | 3.42776674835 | 0.0 |
| 1.28393 | 3.42750526391 | 0.0 |
| 1.28516 | 3.42724444955 | 0.0 |
| 1.2864 | 3.42698430297 | 0.0 |
| 1.28764 | 3.4267248219 | 0.0 |
| 1.28887 | 3.42646600405 | 0.0 |
| 1.29011 | 3.42620784717 | 0.0 |
| 1.29136 | 3.42595034901 | 0.0 |
| 1.2926 | 3.42569350734 | 0.0 |
| 1.29384 | 3.42543731992 | 0.0 |
| 1.29509 | 3.42518178455 | 0.0 |
| 1.29633 | 3.42492689903 | 0.0 |
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Showing 2,000 of 6315 rows. Download the CSV for all of them.
Optical transmission calculator
Free-standing sample in vacuum, normal incidence- Transmittance T
- —
- Reflectance R
- —
Fresnel reflection calculator
- Rp
- —
- Rs
- —
- R = (Rp+Rs)/2
- —
- Phase φp
- —
- Phase φs
- —
- Brewster angle θB
- —
- Critical angle θC
- —
Undoped GaAs. Heterogenous data processing combining ellipsometric and spectrophotometric measurements with previously published refractive index. Temperature 370 K.