Optical constants

Refractive index of C₆H₆ (Benzene)

Moutzouris et al. 2013: n 0.450–1.55 µm

Data: formula 3
Range: 0.45–1.551 µm
Temperature: 300 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.49575
Extinction coefficient k: 0

Permittivity ε₁: 2.23726
Permittivity ε₂: 0

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

Abbe number V_d: 30.381
Chromatic dispersion dn/dλ: -0.0809656 µm⁻¹

Group index n_g: 1.54332
Group velocity dispersion: 172.112 fs²/mm

Dispersion parameter D: -938.962 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

# C6H6 (Benzene): Moutzouris et al. 2013: n 0.450–1.55 µm
c6h6 = ls.fetch_refractiveindex("organic", "benzene", "Moutzouris", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(c6h6.range_nm)  # (450, 1551) nm
eps = c6h6.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_44c7e8d3c065/lightsmith"
c6h6 = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(c6h6.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (benzene/moutzouris-2013).

# ... load c6h6 as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=c6h6)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=450, 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

Polynomial (formula 3), λ in µm

n^{2} = 2.170184597 + 0.00059399 λ^{2.0} + 0.02303464 λ^{- 2.0} - 0.000499485 λ^{- 4.0} + 0.000178796 λ^{- 6.0}

Valid from 0.45 to 1.551 µm.

Coefficients as stored

C_i	Value
C1	2.170184597
C2	0.00059399
C3	2.0
C4	0.02303464
C5	-2.0
C6	-0.000499485
C7	-4.0
C8	0.000178796
C9	-6.0

Comments and conditions

300 K (27 °C).

Conditions

temperature: 300 K

References

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, D. Triantis. Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared. Appl. Phys. B 116, 617-622 (2013)

doi:10.1007/s00340-013-5744-3 Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared, Applied Physics B (2013)

Cite

Konstantinos Moutzouris et al.. Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared. Applied Physics B, 116, 617-622 (2013), doi:10.1007/s00340-013-5744-3; 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

C6H6 (Benzene), Moutzouris et al. 2013: n 0.450–1.55 µm: n and k versus wavelength
λ (µm)	n
0.45	1.5144
0.451398	1.514087
0.4528	1.513776
0.454206	1.513469
0.455617	1.513165
0.457032	1.512864
0.458452	1.512566
0.459876	1.512271
0.461304	1.511979
0.462737	1.511689
0.464174	1.511403
0.465616	1.511119
0.467062	1.510839
0.468513	1.510561
0.469968	1.510285
0.471428	1.510012
0.472892	1.509742
0.474361	1.509475
0.475835	1.50921
0.477313	1.508947
0.478795	1.508687
0.480282	1.50843
0.481774	1.508175
0.483271	1.507922
0.484772	1.507672
0.486277	1.507424
0.487788	1.507178
0.489303	1.506935
0.490823	1.506694
0.492347	1.506455
0.493877	1.506218
0.495411	1.505983
0.496949	1.505751
0.498493	1.50552
0.500041	1.505292
0.501595	1.505066
0.503153	1.504842
0.504715	1.50462
0.506283	1.504399
0.507856	1.504181
0.509433	1.503965
0.511015	1.50375
0.512603	1.503538
0.514195	1.503327
0.515792	1.503118
0.517394	1.502911
0.519001	1.502706
0.520613	1.502502
0.52223	1.5023
0.523852	1.5021
0.52548	1.501902
0.527112	1.501705
0.528749	1.501511
0.530391	1.501317
0.532039	1.501126
0.533691	1.500935
0.535349	1.500747
0.537012	1.50056
0.53868	1.500375
0.540353	1.500191
0.542031	1.500009
0.543715	1.499828
0.545404	1.499649
0.547098	1.499471
0.548797	1.499294
0.550502	1.499119
0.552212	1.498946
0.553927	1.498774
0.555647	1.498603
0.557373	1.498434
0.559105	1.498266
0.560841	1.498099
0.562583	1.497934
0.564331	1.49777
0.566084	1.497607
0.567842	1.497445
0.569606	1.497285
0.571375	1.497126
0.57315	1.496969
0.57493	1.496812
0.576716	1.496657
0.578507	1.496503
0.580304	1.49635
0.582106	1.496199
0.583914	1.496048
0.585728	1.495899
0.587547	1.495751
0.589372	1.495604
0.591203	1.495458
0.593039	1.495313
0.594881	1.495169
0.596729	1.495027
0.598583	1.494885
0.600442	1.494745
0.602307	1.494606
0.604178	1.494467
0.606054	1.49433
0.607937	1.494194
0.609825	1.494058
0.611719	1.493924
0.613619	1.493791
0.615525	1.493658
0.617437	1.493527
0.619355	1.493397
0.621279	1.493267
0.623209	1.493139
0.625144	1.493012
0.627086	1.492885
0.629034	1.492759
0.630988	1.492635
0.632948	1.492511
0.634914	1.492388
0.636886	1.492266
0.638864	1.492145
0.640848	1.492024
0.642839	1.491905
0.644835	1.491786
0.646838	1.491669
0.648847	1.491552
0.650863	1.491436
0.652885	1.49132
0.654912	1.491206
0.656947	1.491092
0.658987	1.49098
0.661034	1.490868
0.663087	1.490756
0.665147	1.490646
0.667213	1.490536
0.669285	1.490427
0.671364	1.490319
0.673449	1.490212
0.675541	1.490105
0.67764	1.489999
0.679744	1.489894
0.681856	1.48979
0.683974	1.489686
0.686098	1.489583
0.688229	1.489481
0.690367	1.489379
0.692511	1.489278
0.694662	1.489178
0.69682	1.489079
0.698984	1.48898
0.701155	1.488882
0.703333	1.488784
0.705518	1.488688
0.707709	1.488592
0.709907	1.488496
0.712112	1.488401
0.714324	1.488307
0.716543	1.488214
0.718769	1.488121
0.721001	1.488028
0.723241	1.487937
0.725487	1.487846
0.727741	1.487755
0.730001	1.487666
0.732269	1.487576
0.734543	1.487488
0.736825	1.4874
0.739113	1.487312
0.741409	1.487225
0.743712	1.487139
0.746022	1.487054
0.748339	1.486968
0.750664	1.486884
0.752995	1.4868
0.755334	1.486716
0.75768	1.486634
0.760034	1.486551
0.762394	1.48647
0.764762	1.486388
0.767138	1.486308
0.769521	1.486228
0.771911	1.486148
0.774308	1.486069
0.776713	1.48599
0.779126	1.485912
0.781546	1.485835
0.783974	1.485758
0.786409	1.485681
0.788851	1.485605
0.791302	1.48553
0.793759	1.485455
0.796225	1.48538
0.798698	1.485306
0.801179	1.485232
0.803667	1.485159
0.806164	1.485087
0.808668	1.485015
0.811179	1.484943
0.813699	1.484872
0.816226	1.484801
0.818762	1.484731
0.821305	1.484661
0.823856	1.484592
0.826415	1.484523
0.828982	1.484454
0.831557	1.484386
0.83414	1.484319
0.83673	1.484252
0.839329	1.484185
0.841936	1.484119
0.844552	1.484053
0.847175	1.483988
0.849806	1.483923
0.852446	1.483858
0.855094	1.483794
0.85775	1.48373
0.860414	1.483667
0.863086	1.483604
0.865767	1.483542
0.868456	1.48348
0.871154	1.483418
0.87386	1.483357
0.876574	1.483296
0.879297	1.483236
0.882028	1.483176
0.884768	1.483116
0.887516	1.483057
0.890272	1.482998
0.893038	1.482939
0.895811	1.482881
0.898594	1.482823
0.901385	1.482766
0.904185	1.482709
0.906993	1.482652
0.909811	1.482596
0.912636	1.48254
0.915471	1.482484
0.918315	1.482429
0.921167	1.482374
0.924028	1.48232
0.926898	1.482266
0.929777	1.482212
0.932665	1.482158
0.935562	1.482105
0.938468	1.482053
0.941383	1.482
0.944307	1.481948
0.94724	1.481896
0.950183	1.481845
0.953134	1.481794
0.956094	1.481743
0.959064	1.481693
0.962043	1.481643
0.965031	1.481593
0.968029	1.481543
0.971036	1.481494
0.974052	1.481446
0.977077	1.481397
0.980112	1.481349
0.983156	1.481301
0.98621	1.481254
0.989273	1.481206
0.992346	1.481159
0.995428	1.481113
0.99852	1.481066
1.00162	1.48102
1.00473	1.480975
1.00785	1.480929
1.01098	1.480884
1.01412	1.480839
1.01727	1.480795
1.02043	1.480751
1.0236	1.480707
1.02678	1.480663
1.02997	1.48062
1.03317	1.480576
1.03638	1.480534
1.0396	1.480491
1.04283	1.480449
1.04607	1.480407
1.04932	1.480365
1.05258	1.480324
1.05585	1.480283
1.05913	1.480242
1.06242	1.480201
1.06572	1.480161
1.06903	1.480121
1.07235	1.480081
1.07568	1.480041
1.07902	1.480002
1.08237	1.479963
1.08573	1.479924
1.0891	1.479885
1.09249	1.479847
1.09588	1.479809
1.09928	1.479771
1.1027	1.479734
1.10612	1.479697
1.10956	1.47966
1.11301	1.479623
1.11646	1.479586
1.11993	1.47955
1.12341	1.479514
1.1269	1.479478
1.1304	1.479443
1.13391	1.479407
1.13743	1.479372
1.14096	1.479337
1.14451	1.479303
1.14806	1.479268
1.15163	1.479234
1.15521	1.4792
1.15879	1.479166
1.16239	1.479133
1.166	1.4791
1.16963	1.479067
1.17326	1.479034
1.1769	1.479001
1.18056	1.478969
1.18423	1.478937
1.1879	1.478905
1.19159	1.478873
1.1953	1.478842
1.19901	1.47881
1.20273	1.478779
1.20647	1.478748
1.21022	1.478718
1.21397	1.478687
1.21774	1.478657
1.22153	1.478627
1.22532	1.478597
1.22913	1.478568
1.23295	1.478538
1.23677	1.478509
1.24062	1.47848
1.24447	1.478451
1.24834	1.478423
1.25221	1.478394
1.2561	1.478366
1.26	1.478338
1.26392	1.47831
1.26784	1.478283
1.27178	1.478255
1.27573	1.478228
1.27969	1.478201
1.28367	1.478174
1.28766	1.478147
1.29166	1.478121
1.29567	1.478095
1.29969	1.478068
1.30373	1.478043
1.30778	1.478017
1.31184	1.477991
1.31592	1.477966
1.32	1.477941
1.3241	1.477916
1.32822	1.477891
1.33234	1.477866
1.33648	1.477842
1.34063	1.477818
1.34479	1.477793
1.34897	1.477769
1.35316	1.477746
1.35736	1.477722
1.36158	1.477699
1.36581	1.477675
1.37005	1.477652
1.37431	1.477629
1.37858	1.477607
1.38286	1.477584
1.38715	1.477562
1.39146	1.47754
1.39578	1.477517
1.40012	1.477496
1.40447	1.477474
1.40883	1.477452
1.41321	1.477431
1.4176	1.47741
1.422	1.477388
1.42642	1.477368
1.43085	1.477347
1.43529	1.477326
1.43975	1.477306
1.44422	1.477285
1.44871	1.477265
1.45321	1.477245
1.45772	1.477225
1.46225	1.477206
1.46679	1.477186
1.47135	1.477167
1.47592	1.477148
1.4805	1.477129
1.4851	1.47711
1.48971	1.477091
1.49434	1.477072
1.49898	1.477054
1.50364	1.477035
1.50831	1.477017
1.51299	1.476999
1.51769	1.476981
1.52241	1.476963
1.52714	1.476946
1.53188	1.476928
1.53664	1.476911
1.54141	1.476894
1.5462	1.476877
1.551	1.47686

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: —

C₆H₆ (Benzene): all datasets

About C6H6 (Benzene)

Benzene (C₆H₆) is a colorless and highly flammable liquid with a sweet smell. It's an aromatic hydrocarbon, notable for its cyclic, planar structure which consists of a hexagonal ring of carbon atoms, with alternating double and single bonds, and with a hydrogen atom bonded to each carbon. Benzene is used as a starting material in the manufacture of a vast array of chemicals, including styrene (for making polystyrene), phenol, and aniline. Its ring structure serves as a basis for many other chemical compounds and is fundamental in organic chemistry. However, exposure to benzene has been linked to a number of health concerns, particularly leukemia, leading to restrictions on its industrial and commercial use in many countries.

More about C6H6 (Benzene) →

Listed in

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/organic/C6H6 - benzene/nk/Moutzouris.yml
ID: ds_44c7e8d3c065
API: /v1/datasets/ds_44c7e8d3c065

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