Optical constants

Refractive index of HfO₂ (Hafnium dioxide, Hafnia)

Al-Kuhaili 2004: n 0.2–2.0 µm

Data: formula 5
Range: 0.2–2 µm
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.89805
Extinction coefficient k: 0

Permittivity ε₁: 3.60261
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: 46.65
Chromatic dispersion dn/dλ: -0.0950268 µm⁻¹

Group index n_g: 1.95389
Group velocity dispersion: 214.805 fs²/mm

Dispersion parameter D: -1171.87 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = 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

# HfO2 (Hafnium dioxide, Hafnia): Al-Kuhaili 2004: n 0.2–2.0 µm
hfo2 = ls.fetch_refractiveindex("main", "HfO2", "Al-Kuhaili", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hfo2.range_nm)  # (200, 2000) nm
eps = hfo2.eps([633])  # 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_f562c901da87/lightsmith"
hfo2 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hfo2.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (hfo2/al-kuhaili-2004).

# ... load hfo2 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hfo2)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, 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"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

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

Cauchy (formula 5), λ in µm

n = 1.875 + 0.00628 λ^{- 2.0} + 0.00058 λ^{- 4.0}

Valid from 0.2 to 2.0 µm.

Coefficients as stored

C_i	Value
C1	1.875
C2	0.00628
C3	-2.0
C4	0.00058
C5	-4.0

Comments and conditions

Thin films of hafnium oxide deposited by electron beam evaporation.

References

M. F. Al-Kuhaili. Optical properties of hafnium oxide thin films and their application in energy-efficient windows. Opt. Mat. 27, 383-387 (2004)

doi:10.1016/j.optmat.2004.04.014 Optical properties of hafnium oxide thin films and their application in energy-efficient windows, Optical Materials (2004)

Cite

M.F. Al-Kuhaili. Optical properties of hafnium oxide thin films and their application in energy-efficient windows. Optical Materials, 27, 383-387 (2004), doi:10.1016/j.optmat.2004.04.014; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

HfO2 (Hafnium dioxide, Hafnia), Al-Kuhaili 2004: n 0.2–2.0 µm: n and k versus wavelength
λ (µm)	n
0.2	2.3945
0.201158	2.384426
0.202322	2.374562
0.203493	2.364903
0.20467	2.355444
0.205855	2.346181
0.207046	2.337111
0.208245	2.328227
0.20945	2.319528
0.210662	2.311008
0.211881	2.302664
0.213108	2.294492
0.214341	2.286488
0.215581	2.278649
0.216829	2.270971
0.218084	2.26345
0.219346	2.256084
0.220616	2.248869
0.221893	2.241801
0.223177	2.234878
0.224468	2.228096
0.225768	2.221452
0.227074	2.214944
0.228388	2.208569
0.22971	2.202323
0.23104	2.196203
0.232377	2.190208
0.233722	2.184335
0.235074	2.17858
0.236435	2.172942
0.237803	2.167417
0.23918	2.162004
0.240564	2.156701
0.241956	2.151503
0.243357	2.146411
0.244765	2.14142
0.246182	2.13653
0.247606	2.131737
0.249039	2.127041
0.250481	2.122438
0.25193	2.117927
0.253388	2.113506
0.254855	2.109173
0.25633	2.104926
0.257814	2.100764
0.259306	2.096684
0.260806	2.092685
0.262316	2.088765
0.263834	2.084922
0.265361	2.081155
0.266897	2.077463
0.268441	2.073843
0.269995	2.070294
0.271558	2.066815
0.273129	2.063404
0.27471	2.060059
0.2763	2.05678
0.277899	2.053565
0.279507	2.050413
0.281125	2.047322
0.282752	2.044291
0.284389	2.041319
0.286035	2.038405
0.28769	2.035547
0.289355	2.032744
0.29103	2.029995
0.292714	2.0273
0.294408	2.024656
0.296112	2.022063
0.297826	2.019519
0.299549	2.017024
0.301283	2.014578
0.303027	2.012177
0.304781	2.009823
0.306545	2.007513
0.308319	2.005247
0.310103	2.003025
0.311898	2.000844
0.313703	1.998705
0.315519	1.996606
0.317345	1.994546
0.319181	1.992526
0.321029	1.990543
0.322887	1.988598
0.324755	1.986689
0.326635	1.984816
0.328525	1.982978
0.330427	1.981174
0.332339	1.979403
0.334262	1.977666
0.336197	1.975961
0.338143	1.974287
0.3401	1.972645
0.342068	1.971032
0.344048	1.96945
0.346039	1.967896
0.348042	1.966372
0.350056	1.964875
0.352082	1.963405
0.35412	1.961962
0.356169	1.960546
0.358231	1.959156
0.360304	1.95779
0.362389	1.95645
0.364487	1.955134
0.366596	1.953841
0.368718	1.952572
0.370852	1.951326
0.372998	1.950103
0.375157	1.948901
0.377328	1.947721
0.379512	1.946562
0.381708	1.945423
0.383918	1.944305
0.38614	1.943207
0.388374	1.942128
0.390622	1.941069
0.392883	1.940028
0.395157	1.939006
0.397444	1.938001
0.399744	1.937015
0.402057	1.936045
0.404384	1.935093
0.406725	1.934157
0.409079	1.933238
0.411446	1.932335
0.413828	1.931447
0.416223	1.930575
0.418632	1.929718
0.421054	1.928876
0.423491	1.928049
0.425942	1.927235
0.428407	1.926436
0.430887	1.92565
0.433381	1.924878
0.435889	1.924119
0.438412	1.923373
0.440949	1.92264
0.443501	1.92192
0.446068	1.921211
0.44865	1.920515
0.451246	1.91983
0.453858	1.919157
0.456484	1.918495
0.459126	1.917844
0.461784	1.917205
0.464456	1.916576
0.467144	1.915957
0.469848	1.915349
0.472567	1.914751
0.475302	1.914163
0.478053	1.913585
0.48082	1.913016
0.483603	1.912456
0.486402	1.911906
0.489217	1.911365
0.492048	1.910833
0.494896	1.91031
0.49776	1.909795
0.500641	1.909288
0.503538	1.90879
0.506453	1.9083
0.509384	1.907818
0.512332	1.907344
0.515297	1.906877
0.518279	1.906418
0.521279	1.905966
0.524296	1.905522
0.52733	1.905084
0.530382	1.904654
0.533452	1.904231
0.536539	1.903814
0.539644	1.903404
0.542768	1.903
0.545909	1.902603
0.549068	1.902212
0.552246	1.901828
0.555442	1.901449
0.558657	1.901076
0.56189	1.90071
0.565142	1.900349
0.568413	1.899993
0.571703	1.899643
0.575012	1.899299
0.57834	1.89896
0.581687	1.898626
0.585053	1.898298
0.588439	1.897974
0.591845	1.897656
0.59527	1.897342
0.598715	1.897033
0.602181	1.896729
0.605666	1.89643
0.609171	1.896135
0.612697	1.895845
0.616243	1.895559
0.619809	1.895277
0.623396	1.895
0.627004	1.894727
0.630633	1.894458
0.634283	1.894193
0.637954	1.893932
0.641646	1.893675
0.64536	1.893422
0.649095	1.893173
0.652852	1.892927
0.65663	1.892685
0.66043	1.892447
0.664253	1.892212
0.668097	1.891981
0.671964	1.891753
0.675853	1.891528
0.679764	1.891307
0.683698	1.891089
0.687655	1.890874
0.691635	1.890663
0.695638	1.890454
0.699664	1.890249
0.703714	1.890046
0.707786	1.889847
0.711883	1.88965
0.716003	1.889457
0.720147	1.889266
0.724315	1.889078
0.728507	1.888892
0.732723	1.888709
0.736964	1.888529
0.741229	1.888352
0.745519	1.888177
0.749833	1.888004
0.754173	1.887834
0.758538	1.887666
0.762928	1.887501
0.767344	1.887338
0.771785	1.887178
0.776251	1.88702
0.780744	1.886863
0.785263	1.88671
0.789807	1.886558
0.794379	1.886408
0.798976	1.886261
0.8036	1.886116
0.808251	1.885972
0.812929	1.885831
0.817634	1.885692
0.822366	1.885554
0.827125	1.885419
0.831912	1.885285
0.836727	1.885153
0.84157	1.885023
0.84644	1.884895
0.851339	1.884769
0.856266	1.884644
0.861222	1.884521
0.866207	1.8844
0.87122	1.884281
0.876262	1.884163
0.881333	1.884046
0.886434	1.883932
0.891565	1.883818
0.896725	1.883707
0.901914	1.883597
0.907134	1.883488
0.912384	1.883381
0.917665	1.883275
0.922976	1.883171
0.928318	1.883068
0.93369	1.882967
0.939094	1.882867
0.944529	1.882768
0.949996	1.882671
0.955494	1.882575
0.961024	1.88248
0.966586	1.882386
0.97218	1.882294
0.977807	1.882203
0.983466	1.882113
0.989158	1.882024
0.994883	1.881937
1.00064	1.88185
1.00643	1.881765
1.01226	1.881681
1.01812	1.881598
1.02401	1.881516
1.02993	1.881436
1.03589	1.881356
1.04189	1.881277
1.04792	1.8812
1.05399	1.881123
1.06009	1.881048
1.06622	1.880973
1.07239	1.880899
1.0786	1.880827
1.08484	1.880755
1.09112	1.880684
1.09743	1.880614
1.10379	1.880545
1.11017	1.880477
1.1166	1.88041
1.12306	1.880344
1.12956	1.880278
1.1361	1.880214
1.14267	1.88015
1.14929	1.880087
1.15594	1.880025
1.16263	1.879963
1.16936	1.879903
1.17613	1.879843
1.18293	1.879784
1.18978	1.879726
1.19666	1.879668
1.20359	1.879612
1.21056	1.879555
1.21756	1.8795
1.22461	1.879445
1.2317	1.879392
1.23882	1.879338
1.24599	1.879286
1.25321	1.879234
1.26046	1.879183
1.26775	1.879132
1.27509	1.879082
1.28247	1.879033
1.28989	1.878984
1.29736	1.878936
1.30487	1.878888
1.31242	1.878841
1.32002	1.878795
1.32765	1.878749
1.33534	1.878704
1.34307	1.87866
1.35084	1.878616
1.35866	1.878572
1.36652	1.878529
1.37443	1.878487
1.38238	1.878445
1.39039	1.878404
1.39843	1.878363
1.40653	1.878323
1.41467	1.878283
1.42285	1.878243
1.43109	1.878205
1.43937	1.878166
1.4477	1.878128
1.45608	1.878091
1.46451	1.878054
1.47298	1.878018
1.48151	1.877982
1.49008	1.877946
1.49871	1.877911
1.50738	1.877876
1.5161	1.877842
1.52488	1.877808
1.5337	1.877775
1.54258	1.877742
1.55151	1.877709
1.56049	1.877677
1.56952	1.877645
1.5786	1.877613
1.58774	1.877582
1.59693	1.877552
1.60617	1.877521
1.61547	1.877492
1.62482	1.877462
1.63422	1.877433
1.64368	1.877404
1.65319	1.877375
1.66276	1.877347
1.67238	1.87732
1.68206	1.877292
1.6918	1.877265
1.70159	1.877238
1.71144	1.877212
1.72134	1.877186
1.7313	1.87716
1.74132	1.877134
1.7514	1.877109
1.76154	1.877084
1.77173	1.877059
1.78199	1.877035
1.7923	1.877011
1.80267	1.876987
1.81311	1.876964
1.8236	1.876941
1.83415	1.876918
1.84477	1.876895
1.85545	1.876873
1.86619	1.876851
1.87699	1.876829
1.88785	1.876808
1.89878	1.876786
1.90976	1.876765
1.92082	1.876745
1.93193	1.876724
1.94312	1.876704
1.95436	1.876684
1.96567	1.876664
1.97705	1.876645
1.98849	1.876625
2	1.876606

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

HfO₂ (Hafnium dioxide, Hafnia): all datasets

Thin film

About HfO2 (Hafnium dioxide, Hafnia)

Hafnium dioxide (HfO₂) is a high-index, low-absorption material used extensively in optical applications. It is especially valuable for making thin-film dielectric coatings for mirrors, anti-reflective coatings, and beam splitters. Due to its excellent thermal stability and resistance to chemical corrosion, it is well-suited for harsh environments. Additionally, its high refractive index makes it an attractive material for planar waveguides and other integrated optics components. Beyond its optical uses, hafnium dioxide is also a key material in the fabrication of advanced gate dielectrics in field-effect transistors, contributing to the miniaturization and performance improvement of electronic devices.

More about HfO2 (Hafnium dioxide, Hafnia) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/HfO2/nk/Al-Kuhaili.yml
ID: ds_f562c901da87
API: /v1/datasets/ds_f562c901da87

Plot