Optical constants

Refractive index of C (Carbon, diamond, graphite, graphene, carbon nanotubes)

Larruquert et al. 2013: n,k 0.0197–10.1 µm

Data
tabulated nk
Range
0.01966–10.08 µm
Points
364
State
amorphous
Licence
CC0-1.0

Plot

Click the plot to set the calculator wavelength.

At one wavelength

Range 0.01966–10.08 µm
Refractive index n
2.54111
Extinction coefficient k
0.0203878
Permittivity ε1
6.45681
Permittivity ε2
0.103615
Absorption coefficient α
4360.12 cm⁻¹
Penetration depth δ = λ/(2πk)
4587.03 nm
Abbe number Vd
—
Chromatic dispersion dn/dλ
-0.26123 µm⁻¹
Group index ng
2.69461
Group velocity dispersion
— fs²/mm
Dispersion parameter D
— ps/(nm·km)
Photon energy
2.11001 eV

ε = (n + ik)², α = 4πk/λ, ng = 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

# C (Carbon, diamond, graphite, graphene, carbon nanotubes): Larruquert et al. 2013: n,k 0.0197–10.1 µm
c = ls.fetch_refractiveindex("main", "C", "Larruquert", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(c.range_nm)  # (19.6564, 10079.2) nm
eps = c.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

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

ta-C: tetrahedral amorphous carbon. Density: 3.25 g/cm3. Film deposited at room temperature.

References

J. I. Larruquert, L. V. Rodríguez-de Marcos, J. A. Méndez, P. J. Martin, A. Bendavid. High reflectance ta-C coatings in the extreme ultraviolet. Opt. Exp. 21, 27537-27549 (2013) (Numerical data kindly provided by Juan Larruquert)

Cite

J. I. Larruquert, L. V. Rodríguez-de Marcos, J. A. Méndez, P. J. Martin and A. Bendavid. High reflectance ta-C coatings in the extreme ultraviolet. Optics Express, 21, 27537 (2013), doi:10.1364/oe.21.027537; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

364 rows as published
C (Carbon, diamond, graphite, graphene, carbon nanotubes), Larruquert et al. 2013: n,k 0.0197–10.1 µm: n and k versus wavelength
λ (µm)nk
0.0196564260.8799011550.030901074
0.0199972330.8759398160.032472071
0.0203439480.8719420950.034032844
0.0206966760.8678251450.035537555
0.0210555190.8634602860.037031508
0.0214205830.8588772920.038550496
0.0217919770.8540818360.040097988
0.0221698110.8490641710.041669546
0.0225541950.8438052650.043256391
0.0229452440.83825570.044863068
0.0233430730.832324820.046576698
0.0237477990.8262105990.04836335
0.0241595430.8199117960.050108736
0.0245784260.8133569390.051691933
0.0250045710.8065050490.052801861
0.0254381050.7980104790.054009567
0.0258791560.7887808230.055509431
0.0263278540.7784281820.057423007
0.0267843310.7669728380.060011047
0.0272487230.7545041630.063501701
0.0277211660.7411660770.068088906
0.0282018010.727139670.073925514
0.0286907690.7126261810.08112057
0.0291882150.6978325390.08974155
0.0296942860.6829607240.099822078
0.0302091310.6682036130.111380104
0.0307329030.6538038240.124400559
0.0312657560.6401341460.138677523
0.0318078470.6272273060.15398667
0.0323593380.6150814570.170163993
0.032920390.6036838830.187074787
0.033491170.5930108230.204598544
0.0340718460.5830262670.222616249
0.034662590.5736721990.240979148
0.0352635770.5646916940.259649875
0.0358749830.5557767030.278853038
0.036496990.547068720.298732024
0.0371297820.5386675340.319335819
0.0377735450.5306440780.340682041
0.038428470.5230507860.362778105
0.039094750.5159279830.385631372
0.0397725820.5093088960.409255764
0.0404621670.5032243250.433677688
0.0411637080.4977079540.458943404
0.0418774120.4928039860.485131166
0.042603490.4885814260.512376407
0.0433421580.485171650.540942022
0.0440936320.482992230.571312729
0.0448581360.4840685110.60234859
0.0456358950.4884319750.632717234
0.0464271380.4954545940.661516449
0.0472321010.5045796040.687931459
0.048051020.515124610.710945843
0.0488841370.525913650.728815285
0.04973170.532594810.741795049
0.0505939570.5288357170.756880856
0.0514711650.5178701330.778595998
0.0523635820.5041029770.808498997
0.0532714710.4912205270.847533144
0.0541951020.4863325110.891369607
0.0551347470.4894280990.93617103
0.0560906840.498785090.97937764
0.0570631950.5113130211.02076124
0.0580525670.5255854761.061107734
0.0590590930.5417700181.100615982
0.0600830710.5598639911.139160203
0.0611248030.5797552781.176431055
0.0621845960.6011169221.211830532
0.0632627640.622505931.245837403
0.0643596260.6432176991.279565594
0.0654755050.663630391.313648153
0.0666107320.6840390991.348537727
0.0677656420.7047582661.384663891
0.0689405750.7262046451.422539714
0.070135880.7491746111.462811665
0.0713519090.7757193611.504164649
0.0725890220.8060527991.545389259
0.0738475840.8398368181.585734958
0.0751279670.8767626251.624516887
0.076430550.9163665621.660948353
0.0777557170.9576617991.694013409
0.0791038610.998201951.725493946
0.0804753781.0377986161.75720287
0.0818706761.0773329011.79005298
0.0832901651.1176973121.82482429
0.0847342651.1602735251.862149686
0.0862034041.2072104311.900086627
0.0876980151.2585757251.937524967
0.089218541.3142554221.973964497
0.0907654281.3744466522.008579349
0.0923391361.4390985392.04020779
0.0939401291.5076397352.068049838
0.0955688811.5793717822.091334289
0.0972258721.6532286752.10925619
0.0989115921.727423672.121625895
0.100626541.800456372.131738722
0.1023712221.8733522172.14070982
0.1041461541.9471719242.148919793
0.1059518592.0229449492.156568014
0.1077888732.1019252372.163723939
0.1096577372.185916532.170103639
0.1115590032.2763438752.172672441
0.1134932342.373469812.169775497
0.1154610012.4784289652.160304991
0.1174628862.5942644222.141012344
0.1194994792.7160730812.09444177
0.1215713842.8292689092.016216961
0.1236792122.9172939821.910487798
0.1258235852.9638054311.791395813
0.1280051382.9841435111.699590936
0.1302245153.001021221.637894126
0.1324823733.0306901461.597796956
0.1347793773.0780566321.561129376
0.1371162073.1263056681.506491589
0.1394935543.1643091891.442588609
0.1419121193.1999591941.385072423
0.1443726183.2407166211.332193565
0.1468757783.2882152081.277441379
0.1494223383.3435261021.21630804
0.1520130513.4087576921.142185148
0.1546486823.4677668111.041520481
0.157330013.506861590.917988672
0.1600578273.5191546080.781205587
0.162832943.501341370.640791791
0.1656561683.4531538910.506215539
0.1685283463.3768499910.386182883
0.1714503223.2764002410.288368325
0.174422963.1563772470.220374011
0.1774471383.0279554340.189578851
0.180523752.9211357910.191883258
0.1836537052.8374035440.212910208
0.1868379282.7745954590.244548104
0.1900773592.7309442980.282046528
0.1933729562.7053605420.322024285
0.1967256932.6975828610.361353902
0.200136562.7085764050.395661018
0.2036065652.7342162330.417940451
0.2071367342.7595868830.423664633
0.210728112.7807007550.417474309
0.2143817542.7955192460.403286715
0.2180987452.8037075370.384637327
0.2218801822.8056210310.364340987
0.2257271832.8026333920.34455616
0.2296408832.7959667320.326538501
0.233622442.7870708840.311044267
0.237673032.7771167980.298304128
0.241793852.7671929670.288264379
0.2459861172.7582253780.280585381
0.2502510712.7508170690.274727073
0.2545899712.7453880350.270074634
0.25900412.7422286820.265900316
0.2634947622.7410282810.261453575
0.2680632842.7415524850.256179421
0.2727110162.7432639760.249559902
0.2774393312.745308320.241344212
0.2822496262.7471187630.231617833
0.2871433242.7482076150.220575471
0.2921218692.7481307650.208554384
0.2971867332.7468283250.195959143
0.3023394122.7441200470.18315186
0.307581432.7401448950.170540755
0.3129143352.7352086270.158361691
0.3183397032.729344590.146750609
0.3238591372.7227908860.135868904
0.3294742672.715770690.125770838
0.3351867542.7084208570.11646883
0.3409982852.7010101390.107897291
0.3469105782.6933452390.100023526
0.3529253792.6857784630.092869941
0.3590444662.6783011190.086308513
0.3652696472.6708434370.080327072
0.3716027612.6636232850.074893329
0.3780456792.6565557820.069919653
0.3846003072.6496694770.065392185
0.3912685792.6430277780.061265061
0.3980524682.6366053610.057483915
0.4049539762.6304039860.054017269
0.4119751452.6244174410.050835386
0.4191180482.6186277080.047922572
0.4263847952.6130525240.045272211
0.4337775352.6077917630.042811946
0.4412984522.6026258660.040516095
0.4489497682.5976512770.038430183
0.4567337442.5929082420.036514775
0.4646526792.5883515940.034730947
0.4727089152.5839226850.033091067
0.4809048312.5796962180.031596844
0.489242852.5756553950.030214823
0.4977254352.5718040630.028910495
0.5063550922.568001730.027716128
0.5151343722.5644833150.02660951
0.5240658692.5610201340.02554027
0.5331522222.5576127980.024589594
0.5423961162.5544466270.023733096
0.5518002822.5513929810.02291274
0.56136752.5484440110.022142684
0.5711005952.5455976470.021425536
0.5810024452.5428312440.020773773
0.5910759752.5401997310.020184413
0.6013241622.5376945540.019624854
0.6117500332.535256580.019090767
0.6223566712.5328670020.018614915
0.6331472082.5306148420.018190143
0.6441248342.5284356220.017795212
0.6552927922.5263402130.017442547
0.6666543822.5243847470.017098178
0.6782129612.5224294070.016763282
0.6899719452.5205381240.016479676
0.7019348092.518766870.016217195
0.7141050872.5170207440.015964842
0.7264863762.5153117310.015758704
0.7390823342.513728010.015577489
0.7518966822.5121821080.015394987
0.7649332092.5106445190.015250668
0.7781957652.5092377630.015129567
0.791688272.5078550460.015002573
0.8054147112.506487490.014906144
0.8193791432.5052341180.01481777
0.8335856932.503937160.014744731
0.8480385592.5027173090.014725949
0.8627420112.5016417440.014689816
0.8777003952.5004812270.014653162
0.892918132.4994364880.014646155
0.9083997132.4984097410.014630625
0.9241497182.4974006510.014625017
0.9401728012.4964087250.014641633
0.9564736942.4954448230.014693544
0.9730572152.4945715710.014760247
0.9899282652.4937395420.014811794
1.0070918282.4929132450.014857776
1.0245529762.4921035980.014911119
1.0423168682.4913019130.014979265
1.0603887552.4905129230.015075517
1.0787739752.4897663940.015202922
1.0974779622.4891014040.015331316
1.1165062422.4884480630.015443046
1.1358644372.4878003460.015553728
1.1555582692.4871524280.015677512
1.1755935562.4865125960.01583304
1.1959762192.48597040.015987449
1.216712282.4853793360.016137547
1.2378078672.4848506590.016297204
1.2592692142.4842774530.016473119
1.2811026612.4837877250.016669144
1.303314662.4833071850.016855088
1.3259117762.4828347970.017042748
1.3489006842.4823703360.01723762
1.3722881792.4819135710.017444935
1.396081172.4814656380.017674775
1.4202866882.4810938880.017900511
1.4449118872.4806880190.018112145
1.4699640422.4802621780.018355674
1.4954505552.4799373690.018598363
1.5213789592.4795285810.018843783
1.5477569152.4792184220.019098313
1.5745922162.4788170520.019366507
1.6018927932.4785330290.019654618
1.6296667122.4782194610.019924718
1.6579221812.4779183370.020198739
1.6866675482.4775811430.02049695
1.7159113082.4773259740.020808087
1.7456621022.4770545580.021105357
1.7759287212.4767733110.021412454
1.8067201082.4764760460.02175552
1.8380453622.4763085240.022086441
1.8699137392.4760412870.022391357
1.9023346562.4757524460.022748835
1.9353176932.475600130.023100448
1.9688725962.4753156410.023451522
2.0030092812.4751640440.023813878
2.0377378332.4748892650.024181152
2.0730685162.4747423810.024561755
2.1090117692.4744718590.024953389
2.1455782132.4743263160.025375301
2.1827786532.4741762520.025763193
2.220624082.4739543680.026164935
2.259125682.4737720220.026603399
2.2982948272.4736241840.027045827
2.3381430962.473479190.027483857
2.3786822622.4733358850.027922851
2.4199243032.4731942060.028364033
2.4618814072.4730631930.028795889
2.5045659722.4728452860.029252221
2.5479906092.4726796320.029755761
2.592168152.4725454030.030267251
2.6371116512.4724123980.030781982
2.682834392.472273360.031316515
2.7293498782.4721993180.031853602
2.7766718612.472126080.032362015
2.8248143222.4719926310.032872044
2.8737914852.4718676010.033406753
2.9236178242.4717427420.033956101
2.9743080612.4716190960.034520082
3.0258771752.4714961370.035099389
3.0783404042.471375540.035695349
3.1317132512.4712459070.036321989
3.1860114862.4712190450.036941261
3.2412511542.4711185240.037534861
3.2974485782.4709968420.038153586
3.3546203632.4708828120.038796796
3.4127834032.470755150.039469719
3.4719548862.470682930.040162638
3.5321522942.4706429940.040832824
3.5933934172.4705166250.041506787
3.655696352.4704018980.042230032
3.7190795022.4703739310.042952388
3.7835616042.4702867770.043654944
3.8491617092.4701583260.044391661
3.91589922.4700661590.045167721
3.9837937992.470037640.045932917
4.0528655672.469935870.046687335
4.1231349152.4698090020.047482967
4.1946226062.4697189450.048315591
4.2673497642.4696867380.049139163
4.3413378792.4695900460.049952404
4.4166088132.4694637590.050802882
4.493184812.46935580.051697069
4.5710884962.4693156620.052595909
4.650342892.4692353080.05348334
4.7309714122.4691146140.054405781
4.8129978872.469066590.055349522
4.8964465522.468992980.056282301
4.9813420652.4688659510.057246644
5.0677095142.4687983950.058243554
5.1555744172.4687396630.059231408
5.2449627382.4686141540.060237595
5.3359008922.4685149080.061287903
5.4284157482.4684632050.06234201
5.5225346442.4683632210.063394188
5.6182853912.4682302540.064486949
5.7156962822.4681483340.065613226
5.8147961022.4680808370.066735393
5.9156141342.4679594180.067869077
6.0181801672.4678258990.069048369
6.122524512.4677316630.070261813
6.2286779952.4676571990.071483056
6.3366719882.467581040.072705556
6.4465384022.4674866570.073933649
6.5583097012.4673525850.075185568
6.6720189122.4672035860.076483406
6.7876996342.4670896510.077817742
6.905386052.4669984190.07915807
7.0251129362.4668733970.080504018
7.1469156692.4667113580.08188576
7.270830242.4665591290.08331489
7.3968932662.4664318840.084774816
7.5251419972.4663171450.086250089
7.6556143282.4661990320.087737553
7.7883488132.4660748210.089238211
7.9233846732.4659259950.090756863
8.0607618112.4657485530.092309019
8.200520822.4655592370.09390764
8.3427029962.4653864460.095549134
8.4873503542.4652305040.097217687
8.6345056352.4650751870.098905317
8.7842123222.4649107290.100614878
8.9365146522.4647370190.102351855
9.0914576292.4645593070.104118302
9.2490870362.4643794170.10591219
9.4094494512.4641964920.10772942
9.572592262.4639955310.109569918
9.738563672.4637711110.111442103
9.9074127232.4635229840.113357189
10.079189312.4632703710.115321633

Optical transmission calculator

Free-standing sample in vacuum, normal incidence
Method
Transmittance T
—
Reflectance R
—

Fresnel reflection calculator

Direction
Rp
—
Rs
—
R = (Rp+Rs)/2
—
Phase φp
—
Phase φs
—
Brewster angle θB
—
Critical angle θC
—