Optical constants

Refractive index of Hf (Hafnium)

Windt et al. 1988: n,k 0.00240–0.122 µm

Data: tabulated nk
Range: 0.00236–0.1216 µm
Points: 36
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 0.926191
Extinction coefficient k: 0.0464242

Permittivity ε₁: 0.855675
Permittivity ε₂: 0.0859954

Absorption coefficient α: 345198 cm⁻¹
Penetration depth δ = λ/(2πk): 57.9378 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -7.04735 µm⁻¹

Group index n_g: 1.04529
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — ps/(nm·km)
Photon energy: 73.3634 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

# Hf (Hafnium): Windt et al. 1988: n,k 0.00240–0.122 µm
hf = ls.fetch_refractiveindex("main", "Hf", "Windt", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(hf.range_nm)  # (2.36, 121.57) nm
eps = hf.eps([16.9])  # 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_d6d2f6002796/lightsmith"
hf = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(hf.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (hf/windt-1988).

# ... load hf as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=hf)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=3, stop_nm=121, 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.

References

D. L. Windt, W. C. Cash, M. Scott, P. Arendt, B. Newnam, R. F. Fisher, A. B. Swartzlander. Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å. Appl. Opt. 27, 246-278 (1988)

doi:10.1364/ao.27.000246 Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å, Applied Optics (1988)

Cite

David L. Windt et al.. Optical constants for thin films of Ti, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Ir, Os, Pt, and Au from 24 Å to 1216 Å. Applied Optics, 27, 246 (1988), doi:10.1364/ao.27.000246; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

36 rows as published

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

Hf (Hafnium), Windt et al. 1988: n,k 0.00240–0.122 µm: n and k versus wavelength
λ (µm)	n	k
0.00236	0.99705	0.00163
0.00316	0.99598	0.00279
0.00447	0.99169	0.0066
0.00676	0.9848	0.0119
0.0114	0.9638	0.0238
0.01355	0.9498	0.0342
0.01714	0.9245	0.0473
0.0243	0.802	0.179
0.02563	0.79	0.216
0.03038	0.928	0.278
0.0327	0.918	0.337
0.03568	0.929	0.337
0.03793	1.04	0.454
0.04059	0.894	0.278
0.04478	0.847	0.315
0.04607	0.842	0.294
0.04895	0.883	0.387
0.05391	0.828	0.313
0.05843	0.801	0.386
0.06163	0.814	0.403
0.06714	0.804	0.483
0.07185	0.853	0.55
0.07359	0.843	0.588
0.07437	0.856	0.602
0.08345	0.813	0.785
0.0878	0.808	0.873
0.09198	0.885	0.965
0.09321	0.96	1.01
0.09888	0.912	1.03
0.10258	1.07	1.13
0.10482	1.11	1.14
0.10667	1.19	1.18
0.10857	1.15	1.17
0.1135	1.27	1.2
0.12007	1.25	1.18
0.12157	1.39	1.19

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: —

Hf (Hafnium): all datasets

Windt et al. 1988: n,k 0.00240–0.122 µm n,k 0.00236–0.1216 µm default

About Hf (Hafnium)

Hafnium (Hf) is a transition metal that possesses intriguing optical properties, notably its high refractive index. Although not typically used in its pure form for optical applications, hafnium is often used as an additive in various optical materials, such as in the fabrication of optical coatings. One of its most well-known applications is in hafnium oxide (HfO₂), which is used as a high-index layer in anti-reflective and mirror coatings. Additionally, hafnium is employed in other specialized optical environments where its high melting point and resistance to corrosion offer advantages. Beyond optics, hafnium is widely used in the aerospace industry for its high-temperature stability, and in the nuclear industry for its high thermal neutron-absorption cross-section.

More about Hf (Hafnium) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Hf/nk/Windt.yml
ID: ds_d6d2f6002796
API: /v1/datasets/ds_d6d2f6002796

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