Optical constants

Refractive index of Mo (Molybdenum)

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

Data: tabulated nk
Range: 0.01759–2.48 µm
Points: 150
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 4.26494
Extinction coefficient k: 3.88409

Permittivity ε₁: 3.10352
Permittivity ε₂: 33.1308

Absorption coefficient α: 830648 cm⁻¹
Penetration depth δ = λ/(2πk): 24.0776 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 0.630081 µm⁻¹

Group index n_g: 3.8947
Group velocity dispersion: — fs²/mm

Dispersion parameter D: — 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

# Mo (Molybdenum): Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm
mo = ls.fetch_refractiveindex("main", "Mo", "Werner-DFT", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(mo.range_nm)  # (17.586, 2479.68) nm
eps = mo.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_25055df9feb0/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/werner-2009-dft).

# ... 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=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.

Comments and conditions

Theoretical density function theory (DFT) calculations.

References

W. S. M. Werner, K. Glantschnig, C. Ambrosch-Draxl. Optical constants and inelastic electron-scattering data for 17 elemental metals. J. Phys Chem Ref. Data 38, 1013-1092 (2009)

doi:10.1063/1.3243762 Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals, Journal of Physical and Chemical Reference Data (2009)

Cite

Wolfgang S. M. Werner, Kathrin Glantschnig and Claudia Ambrosch-Draxl. Optical Constants and Inelastic Electron-Scattering Data for 17 Elemental Metals. Journal of Physical and Chemical Reference Data, 38, 1013-1092 (2009), doi:10.1063/1.3243762; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

150 rows as published

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

Mo (Molybdenum), Werner et al. 2009: DFT calculations; n,k 0.0176–2.48 µm: n and k versus wavelength
λ (µm)	n	k
0.017586	0.8674	0.0184
0.017712	0.8639	0.0168
0.017839	0.8598	0.0157
0.017969	0.8551	0.0158
0.0181	0.8504	0.0159
0.018233	0.8452	0.0177
0.018368	0.8411	0.0208
0.018505	0.8382	0.0239
0.018644	0.8359	0.0257
0.018785	0.8335	0.0276
0.018929	0.8306	0.0307
0.019074	0.8325	0.0318
0.019222	0.8288	0.029
0.019373	0.8233	0.0285
0.019525	0.8161	0.0306
0.01968	0.8125	0.0351
0.019837	0.8084	0.0396
0.019997	0.8158	0.0392
0.02016	0.8069	0.0341
0.020325	0.8002	0.0356
0.020493	0.7934	0.0391
0.020664	0.7904	0.0424
0.020838	0.786	0.042
0.021014	0.779	0.0436
0.021194	0.776	0.047
0.021377	0.7706	0.0435
0.021562	0.7595	0.0428
0.021752	0.747	0.0448
0.021944	0.7353	0.0517
0.02214	0.7229	0.0595
0.022339	0.7155	0.0769
0.022543	0.7152	0.0867
0.022749	0.7198	0.0952
0.02296	0.7195	0.0876
0.023175	0.7012	0.082
0.023393	0.6808	0.0918
0.023616	0.6612	0.1059
0.023843	0.6578	0.1292
0.024075	0.6566	0.1553
0.024311	0.6585	0.1602
0.024551	0.6512	0.1643
0.024797	0.6421	0.1853
0.025047	0.6453	0.2061
0.025303	0.6434	0.2168
0.025564	0.6437	0.2353
0.02583	0.6503	0.2606
0.026102	0.6869	0.2912
0.02638	0.7156	0.2627
0.026663	0.7204	0.2408
0.026953	0.7237	0.2162
0.027249	0.6963	0.1637
0.027552	0.6254	0.1615
0.027862	0.5674	0.1895
0.028178	0.5362	0.2247
0.028502	0.502	0.257
0.028834	0.4713	0.3034
0.029173	0.4528	0.3522
0.02952	0.4258	0.4004
0.029876	0.4034	0.4698
0.03024	0.391	0.5485
0.030613	0.3823	0.6318
0.030996	0.3966	0.769
0.031388	0.5026	0.9113
0.031791	0.5831	0.9365
0.032204	0.654	1.0581
0.032627	0.915	1.0776
0.033062	0.874	1.1567
0.033509	1.2781	1.1302
0.033968	1.3758	1.0158
0.03444	1.5385	0.8775
0.034925	1.683	0.675
0.035424	1.7136	0.3458
0.035937	1.4811	0.1367
0.036466	1.3129	0.1207
0.03701	1.2226	0.1211
0.037571	1.1523	0.1332
0.038149	1.1034	0.1282
0.038745	1.0502	0.1376
0.03936	1.0264	0.1598
0.039995	0.9974	0.1544
0.040651	0.9946	0.1709
0.041328	0.9647	0.1254
0.042029	0.9107	0.1109
0.042753	0.8522	0.1109
0.043503	0.7959	0.1395
0.04428	0.7599	0.1658
0.045085	0.7213	0.1955
0.04592	0.6961	0.2335
0.046786	0.6787	0.2483
0.047686	0.6609	0.2807
0.048621	0.6443	0.2778
0.049594	0.5855	0.2844
0.050606	0.526	0.3204
0.05166	0.4575	0.3705
0.052759	0.3898	0.4593
0.053906	0.3602	0.6122
0.055104	0.4751	0.7209
0.056356	0.5187	0.7036
0.057667	0.5023	0.7545
0.05904	0.5098	0.77
0.06048	0.4545	0.8041
0.061992	0.4169	0.8971
0.063582	0.4028	1.0155
0.065255	0.3799	1.1833
0.067018	0.5292	1.4853
0.06888	0.8273	1.433
0.070848	0.9772	1.447
0.072932	1.0799	1.4033
0.075142	1.2995	1.3582
0.07749	1.3794	1.0852
0.07999	1.2642	0.9322
0.082656	1.0842	0.92
0.085506	1.0211	0.9867
0.08856	1.0002	1.0753
0.09184	1.042	1.1574
0.095372	1.122	1.1819
0.099187	1.165	1.1867
0.10332	1.2983	1.1565
0.107812	1.3869	0.871
0.112713	1.0234	0.5462
0.11808	0.5353	0.7921
0.123984	0.3936	1.1318
0.13051	0.3503	1.4201
0.13776	0.3514	1.6963
0.145864	0.3927	1.9797
0.15498	0.4917	2.279
0.165312	0.7461	2.5866
0.17712	0.7072	2.4393
0.190745	0.7526	2.9412
0.20664	0.9627	3.3904
0.225426	1.3668	3.7328
0.247968	1.7944	4.0968
0.261019	2.1087	4.3512
0.27552	2.6584	4.4493
0.291728	3.237	4.4317
0.30996	3.5886	3.835
0.330625	3.5107	3.5863
0.354241	3.5029	3.5206
0.38149	3.4643	3.4566
0.413281	3.418	3.578
0.450852	3.5133	3.7943
0.495937	3.7199	3.9914
0.551041	4.2419	4.0292
0.619921	4.2853	3.7558
0.708481	4.1798	3.6071
0.826561	3.5493	3.5691
0.991874	2.5588	4.5351
1.239842	1.9617	6.5098
1.653123	1.6462	9.6342
2.479684	2.0985	15.8077

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/Werner-DFT.yml
ID: ds_25055df9feb0
API: /v1/datasets/ds_25055df9feb0

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