Optical constants

Refractive index of Bi (Bismuth)

Hagemann et al. 1974: n,k 0.00155–6.20 µm

Data: tabulated nk
Range: 2.48e-06–6.199 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: 2.14528
Extinction coefficient k: 2.98799

Permittivity ε₁: -4.32588
Permittivity ε₂: 12.8201

Absorption coefficient α: 639010 cm⁻¹
Penetration depth δ = λ/(2πk): 31.2984 nm

Abbe number V_d: —
Chromatic dispersion dn/dλ: 3.05645 µm⁻¹

Group index n_g: 0.349306
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

# Bi (Bismuth): Hagemann et al. 1974: n,k 0.00155–6.20 µm
bi = ls.fetch_refractiveindex("main", "Bi", "Hagemann", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(bi.range_nm)  # (0.00248, 6199) nm
eps = bi.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_1ef39096d230/lightsmith"
bi = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(bi.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (bi/hagemann-1974).

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

References

1) H.-J. Hagemann, W. Gudat, C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al₂O₃. J. Opt. Soc. Am. 65, 742-744 (1975)
2) H.-J. Hagemann, W. Gudat, and C. Kunz. DESY report SR-74/7 (1974)

doi:10.1364/josa.65.000742 Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3, Journal of the Optical Society of America (1975)

Cite

H.-J. Hagemann, W. Gudat and C. Kunz. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al_2O_3. Journal of the Optical Society of America, 65, 742 (1975), doi:10.1364/josa.65.000742; H.-J. Hagemann, W. Gudat, and C. Kunz. DESY report SR-74/7 (1974); 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

Bi (Bismuth), Hagemann et al. 1974: n,k 0.00155–6.20 µm: n and k versus wavelength
λ (µm)	n	k
2.48e-06	1.0	2.02e-11
4.133e-06	1.0	1.19e-10
1.24e-05	1.0	5.71e-09
1.378e-05	1.0	7.13e-09
1.459e-05	1.0	2.56e-09
2.48e-05	1.0	1.6e-08
4.133e-05	1.0	9.48e-08
6.199e-05	1.0	4.13e-07
8.266e-05	1.0	7.04e-07
8.856e-05	1.0	9.36e-07
9.537e-05	1.0	4.95e-07
0.0001033	1.0	6.63e-07
0.000124	1.0	1.21e-06
0.000155	1.0	2.64e-06
0.0002066	1.0	7.69e-06
0.00031	1.0	2.93e-05
0.0003542	1.0	4.5e-05
0.0003757	1.0	5.23e-05
0.0003875	1.0	5.42e-05
0.0003999	1.0	5.18e-05
0.0004133	1.0	5.57e-05
0.0004428	1.0	6.92e-05
0.0004769	1.0	6.67e-05
0.0004959	1.0	7.39e-05
0.0005061	1.0	6.45e-05
0.0005166	1.0	3.34e-05
0.0005636	1.0	4.54e-05
0.0006199	1.0	6.27e-05
0.0006888	1.0	8.82e-05
0.0007749	1.0	0.000129
0.0008856	0.999	0.000198
0.0009537	0.999	0.000256
0.001033	0.999	0.000329
0.001127	0.999	0.000434
0.00124	0.999	0.000579
0.001305	0.999	0.000701
0.001378	0.999	0.000839
0.001459	0.999	0.000973
0.00155	0.999	0.00112
0.001653	0.998	0.00126
0.001771	0.998	0.00145
0.001907	0.998	0.00164
0.002066	0.998	0.00188
0.002254	0.998	0.00214
0.00248	0.998	0.00245
0.002583	0.998	0.00259
0.002695	0.997	0.00276
0.002818	0.997	0.00294
0.002952	0.997	0.00314
0.0031	0.997	0.00335
0.003179	0.997	0.00345
0.003263	0.997	0.00355
0.003351	0.997	0.00365
0.003444	0.997	0.00376
0.003542	0.997	0.00387
0.003647	0.997	0.00398
0.003757	0.997	0.00405
0.003875	0.997	0.00411
0.003999	0.997	0.00416
0.004133	0.997	0.00418
0.004275	0.997	0.00417
0.004428	0.996	0.00412
0.004592	0.996	0.00403
0.004769	0.996	0.00364
0.004959	0.996	0.00315
0.005166	0.995	0.00293
0.005391	0.994	0.00285
0.005636	0.993	0.00279
0.005904	0.991	0.00279
0.006199	0.99	0.00283
0.006525	0.988	0.00299
0.006888	0.986	0.00331
0.007293	0.984	0.00381
0.007749	0.98	0.00448
0.008266	0.976	0.00603
0.008551	0.974	0.00726
0.008856	0.972	0.00867
0.009184	0.969	0.0104
0.009537	0.966	0.0122
0.009919	0.964	0.0143
0.01033	0.96	0.017
0.01078	0.956	0.0205
0.01127	0.953	0.0251
0.01181	0.949	0.03
0.0124	0.945	0.0359
0.01305	0.94	0.0437
0.01378	0.935	0.0536
0.01459	0.933	0.0671
0.0155	0.932	0.0807
0.01653	0.933	0.0985
0.01771	0.942	0.12
0.01907	0.955	0.132
0.02066	0.966	0.151
0.02101	0.97	0.155
0.02138	0.975	0.159
0.02175	0.981	0.162
0.02214	0.987	0.165
0.02254	0.993	0.167
0.02296	1.0	0.167
0.02339	1.007	0.168
0.02384	1.014	0.167
0.02431	1.022	0.167
0.0248	1.027	0.16
0.02583	1.033	0.152
0.02695	1.036	0.149
0.02818	1.041	0.144
0.02952	1.048	0.142
0.031	1.051	0.131
0.03263	1.046	0.12
0.03444	1.038	0.114
0.03647	1.027	0.109
0.03757	1.02	0.108
0.03875	1.009	0.108
0.03999	0.997	0.115
0.04133	0.987	0.127
0.04203	0.988	0.138
0.04275	0.991	0.143
0.0435	0.987	0.149
0.04428	0.998	0.172
0.04509	1.035	0.15
0.04592	1.011	0.128
0.04679	0.998	0.138
0.04769	0.999	0.146
0.04862	1.001	0.152
0.04959	1.004	0.168
0.05061	1.07	0.183
0.05166	1.065	0.0739
0.05276	1.013	0.0609
0.05391	0.981	0.0622
0.05636	0.936	0.0717
0.06199	0.856	0.103
0.06888	0.763	0.168
0.07749	0.692	0.293
0.08856	0.64	0.456
0.1033	0.627	0.681
0.124	0.71	0.968
0.155	0.904	1.3
0.2066	1.364	1.54
0.248	1.482	1.52
0.31	1.517	1.7
0.3542	1.541	1.85
0.4133	1.556	2.27
0.4959	1.865	2.67
0.6199	2.244	3.1
0.8266	2.861	3.89
1.24	5.036	4.84
1.55	6.247	4.52
2.066	7.466	3.87
3.1	8.572	2.21
6.199	6.908	1.47

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: —

Bi (Bismuth): 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 Bi (Bismuth)

Bismuth (Bi) is a heavy, brittle metal with a number of unique properties, including a low thermal conductivity and a high electrical resistivity. While it is not traditionally used in mainstream optical applications, bismuth compounds like bismuth germanate (BGO) and bismuth silicate (BSO) have garnered attention in scintillation detectors and nonlinear optics, respectively. Pure bismuth has a high refractive index and is transparent to various infrared wavelengths, making it potentially useful for specialized optical components in the IR range. However, it is mostly used in alloyed or compound form due to its brittleness and difficulty in fabrication. One key limitation in using bismuth or its compounds in optical applications is its relatively low melting point, which restricts its utility in high-temperature environments. Nonetheless, the metal's unique electrical and thermal properties, as well as its capacity to form compounds with interesting optical characteristics, make it a subject of ongoing research in the field of material science and optics.

More about Bi (Bismuth) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/main/Bi/nk/Hagemann.yml
ID: ds_1ef39096d230
API: /v1/datasets/ds_1ef39096d230

Plot