Optical constants

Refractive index of C₆H₆ (Benzene)

Chang et al. 2024: n 0.4–2.0 µm

Data: formula 1
Range: 0.4–2 µm
Temperature: 295 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.49963
Extinction coefficient k: 0

Permittivity ε₁: 2.24888
Permittivity ε₂: 0

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

Abbe number V_d: 30.755
Chromatic dispersion dn/dλ: -0.0827354 µm⁻¹

Group index n_g: 1.54824
Group velocity dispersion: 161.931 fs²/mm

Dispersion parameter D: -883.421 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): Chang et al. 2024: n 0.4–2.0 µm
c6h6 = ls.fetch_refractiveindex("organic", "benzene", "Chang", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(c6h6.range_nm)  # (400, 2000) 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_fdc14f1da4db/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/chang-2024).

# ... 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=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"]).

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_fdc14f1da4db/lightsmith?model=drude_lorentz"
c6h6_dl = ls.DrudeLorentz.model_validate(json.load(urllib.request.urlopen(url)))

A dispersive Drude–Lorentz model for time-domain solvers.

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

Sellmeier (formula 1), λ in µm

n^{2} - 1 = \frac{1.18 λ^{2}}{λ^{2} - {0.138}^{2}}

Valid from 0.4 to 2.0 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	1.18
C3	0.138

Comments and conditions

21.5–22.0 °C

Conditions

temperature: 295 K

References

H.-J. Chang, N. Munera, C. Lopez-Zelaya, D. Banerjee, G. Beadie, E. W. Van Stryland, D. J. Hagan. Refractive index measurements of liquids from 0.5 to 2 µm using Rayleigh interferometry. Opt. Mater. Express 14, 1253–1267 (2024)

doi:10.1364/ome.519907 Refractive index measurements of liquids from 0.5 to 2 µm using Rayleigh interferometry, Optical Materials Express (2024)

Cite

Hao-Jung Chang et al.. Refractive index measurements of liquids from 0.5 to 2 µm using Rayleigh interferometry. Optical Materials Express, 14, 1253 (2024), doi:10.1364/ome.519907; 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), Chang et al. 2024: n 0.4–2.0 µm: n and k versus wavelength
λ (µm)	n
0.4	1.529518
0.401617	1.529043
0.40324	1.528573
0.40487	1.528107
0.406506	1.527646
0.408149	1.52719
0.409799	1.526738
0.411455	1.52629
0.413118	1.525847
0.414788	1.525408
0.416465	1.524974
0.418148	1.524543
0.419838	1.524117
0.421535	1.523695
0.423239	1.523277
0.424949	1.522863
0.426667	1.522453
0.428391	1.522047
0.430123	1.521645
0.431861	1.521247
0.433607	1.520853
0.435359	1.520462
0.437119	1.520075
0.438886	1.519692
0.44066	1.519313
0.442441	1.518937
0.444229	1.518564
0.446024	1.518196
0.447827	1.51783
0.449637	1.517468
0.451455	1.51711
0.453279	1.516755
0.455111	1.516403
0.456951	1.516055
0.458798	1.51571
0.460652	1.515368
0.462514	1.515029
0.464383	1.514694
0.46626	1.514362
0.468145	1.514033
0.470037	1.513706
0.471937	1.513383
0.473844	1.513063
0.47576	1.512746
0.477683	1.512432
0.479613	1.512121
0.481552	1.511813
0.483498	1.511507
0.485452	1.511204
0.487414	1.510905
0.489385	1.510608
0.491363	1.510313
0.493349	1.510022
0.495343	1.509733
0.497345	1.509446
0.499355	1.509163
0.501373	1.508882
0.5034	1.508603
0.505434	1.508327
0.507477	1.508054
0.509528	1.507783
0.511588	1.507514
0.513655	1.507248
0.515732	1.506985
0.517816	1.506724
0.519909	1.506465
0.52201	1.506208
0.52412	1.505954
0.526239	1.505702
0.528366	1.505453
0.530501	1.505206
0.532645	1.504961
0.534798	1.504718
0.53696	1.504477
0.53913	1.504239
0.541309	1.504002
0.543497	1.503768
0.545694	1.503536
0.547899	1.503306
0.550114	1.503078
0.552337	1.502852
0.55457	1.502628
0.556811	1.502406
0.559062	1.502186
0.561321	1.501968
0.56359	1.501752
0.565868	1.501538
0.568155	1.501326
0.570452	1.501116
0.572757	1.500907
0.575072	1.500701
0.577397	1.500496
0.57973	1.500293
0.582073	1.500092
0.584426	1.499893
0.586788	1.499695
0.58916	1.499499
0.591541	1.499305
0.593932	1.499113
0.596333	1.498922
0.598743	1.498733
0.601163	1.498546
0.603593	1.49836
0.606032	1.498176
0.608482	1.497994
0.610941	1.497813
0.613411	1.497634
0.61589	1.497456
0.618379	1.49728
0.620879	1.497105
0.623388	1.496932
0.625908	1.496761
0.628438	1.496591
0.630978	1.496422
0.633528	1.496255
0.636088	1.496089
0.638659	1.495925
0.641241	1.495762
0.643833	1.495601
0.646435	1.495441
0.649048	1.495283
0.651671	1.495125
0.654305	1.49497
0.656949	1.494815
0.659605	1.494662
0.662271	1.49451
0.664948	1.49436
0.667635	1.494211
0.670334	1.494063
0.673043	1.493916
0.675763	1.493771
0.678495	1.493627
0.681237	1.493484
0.68399	1.493342
0.686755	1.493202
0.689531	1.493063
0.692318	1.492925
0.695116	1.492788
0.697925	1.492652
0.700746	1.492518
0.703579	1.492385
0.706422	1.492253
0.709278	1.492122
0.712144	1.491992
0.715023	1.491863
0.717913	1.491735
0.720814	1.491609
0.723728	1.491483
0.726653	1.491359
0.72959	1.491235
0.732539	1.491113
0.7355	1.490992
0.738472	1.490872
0.741457	1.490752
0.744454	1.490634
0.747463	1.490517
0.750484	1.490401
0.753517	1.490286
0.756563	1.490172
0.759621	1.490058
0.762691	1.489946
0.765774	1.489835
0.768869	1.489724
0.771977	1.489615
0.775097	1.489506
0.77823	1.489399
0.781375	1.489292
0.784533	1.489186
0.787704	1.489082
0.790888	1.488978
0.794085	1.488874
0.797294	1.488772
0.800517	1.488671
0.803752	1.48857
0.807001	1.488471
0.810263	1.488372
0.813538	1.488274
0.816826	1.488177
0.820127	1.488081
0.823442	1.487985
0.82677	1.48789
0.830112	1.487796
0.833467	1.487703
0.836836	1.487611
0.840218	1.487519
0.843614	1.487429
0.847024	1.487339
0.850447	1.487249
0.853885	1.487161
0.857336	1.487073
0.860801	1.486986
0.86428	1.4869
0.867774	1.486814
0.871281	1.486729
0.874803	1.486645
0.878338	1.486562
0.881888	1.486479
0.885453	1.486397
0.889032	1.486316
0.892625	1.486235
0.896233	1.486155
0.899855	1.486076
0.903492	1.485997
0.907144	1.485919
0.910811	1.485841
0.914492	1.485765
0.918188	1.485689
0.921899	1.485613
0.925626	1.485538
0.929367	1.485464
0.933123	1.485391
0.936895	1.485318
0.940681	1.485245
0.944483	1.485174
0.948301	1.485103
0.952134	1.485032
0.955982	1.484962
0.959846	1.484893
0.963726	1.484824
0.967621	1.484756
0.971532	1.484688
0.975458	1.484621
0.979401	1.484554
0.98336	1.484488
0.987334	1.484423
0.991325	1.484358
0.995332	1.484294
0.999355	1.48423
1.00339	1.484167
1.00745	1.484104
1.01152	1.484042
1.01561	1.48398
1.01971	1.483919
1.02384	1.483858
1.02797	1.483798
1.03213	1.483738
1.0363	1.483679
1.04049	1.48362
1.04469	1.483562
1.04892	1.483504
1.05316	1.483447
1.05741	1.48339
1.06169	1.483334
1.06598	1.483278
1.07029	1.483222
1.07461	1.483168
1.07896	1.483113
1.08332	1.483059
1.0877	1.483005
1.09209	1.482952
1.09651	1.4829
1.10094	1.482847
1.10539	1.482795
1.10986	1.482744
1.11434	1.482693
1.11885	1.482642
1.12337	1.482592
1.12791	1.482543
1.13247	1.482493
1.13704	1.482444
1.14164	1.482396
1.14625	1.482348
1.15089	1.4823
1.15554	1.482253
1.16021	1.482206
1.1649	1.482159
1.16961	1.482113
1.17433	1.482067
1.17908	1.482022
1.18385	1.481977
1.18863	1.481932
1.19344	1.481888
1.19826	1.481844
1.2031	1.4818
1.20797	1.481757
1.21285	1.481714
1.21775	1.481672
1.22267	1.48163
1.22761	1.481588
1.23258	1.481546
1.23756	1.481505
1.24256	1.481464
1.24758	1.481424
1.25262	1.481384
1.25769	1.481344
1.26277	1.481304
1.26787	1.481265
1.273	1.481227
1.27814	1.481188
1.28331	1.48115
1.2885	1.481112
1.2937	1.481074
1.29893	1.481037
1.30418	1.481
1.30945	1.480963
1.31475	1.480927
1.32006	1.480891
1.3254	1.480855
1.33075	1.48082
1.33613	1.480785
1.34153	1.48075
1.34696	1.480715
1.3524	1.480681
1.35787	1.480647
1.36335	1.480613
1.36886	1.48058
1.3744	1.480546
1.37995	1.480513
1.38553	1.480481
1.39113	1.480448
1.39675	1.480416
1.4024	1.480384
1.40807	1.480353
1.41376	1.480321
1.41947	1.48029
1.42521	1.480259
1.43097	1.480229
1.43675	1.480198
1.44256	1.480168
1.44839	1.480139
1.45424	1.480109
1.46012	1.48008
1.46602	1.48005
1.47195	1.480022
1.4779	1.479993
1.48387	1.479964
1.48987	1.479936
1.49589	1.479908
1.50194	1.479881
1.50801	1.479853
1.5141	1.479826
1.52022	1.479799
1.52637	1.479772
1.53254	1.479745
1.53873	1.479719
1.54495	1.479693
1.55119	1.479667
1.55746	1.479641
1.56376	1.479615
1.57008	1.47959
1.57643	1.479565
1.5828	1.47954
1.58919	1.479515
1.59562	1.479491
1.60207	1.479466
1.60854	1.479442
1.61504	1.479418
1.62157	1.479395
1.62813	1.479371
1.63471	1.479348
1.64131	1.479325
1.64795	1.479302
1.65461	1.479279
1.6613	1.479256
1.66801	1.479234
1.67475	1.479212
1.68152	1.479189
1.68832	1.479168
1.69514	1.479146
1.70199	1.479124
1.70887	1.479103
1.71578	1.479082
1.72271	1.479061
1.72968	1.47904
1.73667	1.479019
1.74369	1.478999
1.75074	1.478979
1.75781	1.478958
1.76492	1.478938
1.77205	1.478919
1.77921	1.478899
1.7864	1.478879
1.79362	1.47886
1.80087	1.478841
1.80815	1.478822
1.81546	1.478803
1.8228	1.478784
1.83017	1.478765
1.83756	1.478747
1.84499	1.478729
1.85245	1.478711
1.85993	1.478693
1.86745	1.478675
1.875	1.478657
1.88258	1.47864
1.89019	1.478622
1.89783	1.478605
1.9055	1.478588
1.9132	1.478571
1.92093	1.478554
1.9287	1.478537
1.93649	1.478521
1.94432	1.478504
1.95218	1.478488
1.96007	1.478472
1.96799	1.478456
1.97594	1.47844
1.98393	1.478424
1.99195	1.478408
2	1.478393

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) →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/organic/C6H6 - benzene/nk/Chang.yml
ID: ds_fdc14f1da4db
API: /v1/datasets/ds_fdc14f1da4db

Plot