Optical constants

Refractive index of Mo (Molybdenum)

Windt et al. 1988: n,k 0.0024–0.1216 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: 0.880365
Extinction coefficient k: 0.0267186

Permittivity ε₁: 0.774329
Permittivity ε₂: 0.0470442

Absorption coefficient α: 198672 cm⁻¹
Penetration depth δ = λ/(2πk): 100.669 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: -18.1894 µm⁻¹

Group index n_g: 1.18777
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

# Mo (Molybdenum): Windt et al. 1988: n,k 0.0024–0.1216 µm
mo = ls.fetch_refractiveindex("main", "Mo", "Windt", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mo.range_nm)  # (2.36, 121.57) nm
eps = mo.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_0b5b6fc02d51/lightsmith"
mo = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(mo.source)  # citation and provenance travel with the data

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

# ... load mo as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=mo)],
    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

Mo (Molybdenum), Windt et al. 1988: n,k 0.0024–0.1216 µm: n and k versus wavelength
λ (µm)	n	k
0.00236	0.99744	0.00164
0.00316	0.9974	0.00194
0.00447	0.99724	0.00439
0.00676	0.9889	0.00197
0.0114	0.9581	0.00501
0.01355	0.9413	0.00604
0.01714	0.876	0.0282
0.0243	0.813	0.169
0.02563	0.832	0.168
0.03038	0.876	0.25
0.0327	0.912	0.255
0.03568	0.891	0.179
0.03793	0.832	0.157
0.04059	0.797	0.17
0.04478	0.749	0.203
0.04607	0.705	0.234
0.04895	0.695	0.325
0.05391	0.673	0.464
0.05843	0.672	0.57
0.06163	0.712	0.608
0.06714	0.798	0.779
0.07185	0.845	0.734
0.07359	0.902	0.807
0.07437	0.909	0.78
0.08345	0.968	0.778
0.0878	1.04	0.807
0.09198	1.08	0.838
0.09321	1.03	0.791
0.09888	1.08	0.786
0.10258	1.15	0.759
0.10482	1.11	0.745
0.10667	1.17	0.725
0.10857	1.11	0.722
0.1135	1.08	0.677
0.12007	1.1	0.757
0.12157	1.09	0.773

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: —

Mo (Molybdenum): all datasets

Experimental data

Models and simulations

Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm n,k 0.01759–2.48 µm

About Mo (Molybdenum)

Molybdenum (Mo) is a silver-white, hard, transition metal. Known for its high melting points, strength, and resistance to corrosion, especially at high temperatures, it is invaluable in applications that demand materials capable of withstanding intense heat, such as in the production of furnace equipment and as filaments for light bulbs. In optics, molybdenum mirrors are favored for their robustness and durability, especially in high-power laser applications. The metal's reflective properties make it suitable for use as a coating for certain wavelengths, particularly in the deep ultraviolet spectral region.

More about Mo (Molybdenum) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Mo/nk/Windt.yml
ID: ds_0b5b6fc02d51
API: /v1/datasets/ds_0b5b6fc02d51

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